construction of a test rig and scaled aircraft wing for validation final report
TRANSCRIPT
THE UNIVERSITY OF ADELAIDE
SCHOOL OF MECHANICAL ENGINEERING
MECH ENG 3110: MECHANICAL HONORS PROJECT
1180: CONSTRUCTION OF A TEST RIG AND SCALED AIRCRAFT WING FOR COMPARISON AND VALIDATION OF A BEAM THEORY BASED
WING MODEL.
FINAL REPORT
AUTHOR: SAMUEL POLGLASE
SUPERVISOR: DR MAZIAR ARJOMANDI
EXECUTIVE SUMMARY
This project seeks to design and construct a test rig and aircraft wing structure which can be used to validate a beam theory based wing model and also be used as an educational tool in aircraft structures. This report details the development of the structure and the methodology used for obtaining experimental data which has been used for the comparison and validation of the beam theory based wing model.
The design and construction of the test rig wing structure has been successfully completed with each satisfying their respective design requirements. The test rig design has been heavily influenced by its future use as an educational tool and the desire to produce a rig which is easy to use and flexible for future design changes which may be needed in order to accommodate the testing of different wing structures. The wing structure has been simplified in order to realise a successful manufacture within the time and cost constraints of the project without compromising the requirements needed for a successful comparison between the physical and modelled data. Structural and solid mechanics theory has been used to size the various components of the test rig and wing.
All the measurement equipment has been successful installed or set up on the test rig and wing and the virtual instrument needed to record experimental data has been successfully created. Recording of the experimental data has been successfully undertaken.
Comparisons between the physical model and the beam theory based wing model show good correlation for both spanwise deflection and the stress due to bending, however comparisons for the shear stress computation have not yet been finalised. The result is the validation of the deflection and bending stress computation steps of the beam theory based model but not the shear stress computations. This represent a successful outcome for the validation of the deflection and bending stress computation which form the majority of the beam theory based calculations contained in the model.
The final result of the project is the successful development of a test rig and wing experimental structure which has helped to validate a theoretical wing weight estimation model and can now be used as an educational tool in aircraft structures.
ACKNOWELDGMENT
The author would like to thank Dr Maziar Arjomandi for his guidance, advice and support in all aspects of the project. The outcomes of this project would not have been achieved were it not for his help, expertise and motivation when it was needed most.
The Mechanical Engineering Workshop staff, in particular Dr Michael Riese for his invaluable advice regarding design and manufacture. Richard Pateman, Steve and particularly Rob were instrumental in all practical aspects of manufacture and assembly.
Phil and Lydia of the Electrical Engineering Workshop for their invaluable help with load cell and strain gauges selection and instillation.
Felix Dorbath of the DLR in Harburg, Hamburg, Germany for his help in developing the beam sizing model and ongoing advice and expertise regarding this model.
Finally my family and in particular my wife, for her amazing support and love throughout the year.
DISCLAIMER
The content of this report is entirely the work of the student below and any additional material has been referenced accordingly.
Samuel POLGLASE
Date:
CONTENTS EXECUTIVE SUMMARY .......................................................................................................... ii
ACKNOWELDGMENT ............................................................................................................ iii
DISCLAIMER ......................................................................................................................... iv
CONTENTS............................................................................................................................. v
LIST OF FIGURES .................................................................................................................. viii
LIST OF TABLES ......................................................................................................................ix
LIST OF SYMBOLS .................................................................................................................. x
ACRONYMS .......................................................................................................................... xii
1. INTRODUCTION ............................................................................................................. 1
1.1. Motivation .............................................................................................................. 1
1.2. Background ............................................................................................................. 3
1.3. Scope ...................................................................................................................... 3
1.4. Project Objectives ................................................................................................... 4
2. LITERATURE REVIEW...................................................................................................... 5
2.1. Classical Weight Estimation Models ........................................................................ 5
2.2. Beam Model ........................................................................................................... 6
2.2.1. Euler/Bernoulli Beam Theory ........................................................................... 6
2.2.2. Shear Stress Computation ................................................................................ 8
2.3. Comparable Models ............................................................................................ 9
2.4. Shell Model ............................................................................................................. 9
2.5. Test Rig Benchmarking .......................................................................................... 10
3. METHOD OF INVESTIGATION ....................................................................................... 12
3.1. Experimental Data Required ................................................................................. 12
3.2. Suitable Test Rig and Wing .................................................................................... 13
3.3. Suitable Load Application ...................................................................................... 13
3.4. Suitable Measurement Devices ............................................................................. 13
4. EXPERIMENTAL TEST RIG ............................................................................................. 14
4.1. Test Rig Technical Task .......................................................................................... 14
4.1.1. Size ................................................................................................................ 14
4.1.2. Manoeuvrability ............................................................................................. 14
4.1.3. Material ......................................................................................................... 14
4.1.4. Destructible ................................................................................................... 15
4.1.5. Loading Frequency ......................................................................................... 15
4.1.6. Load Carrying Ability ...................................................................................... 16
4.1.7. Load Application Points .................................................................................. 16
4.1.8. Operational Procedure ................................................................................... 16
4.2. Test Rig Concept Designs ...................................................................................... 17
4.2.1. Concept 1....................................................................................................... 17
4.2.2. Concept 2....................................................................................................... 18
4.2.3. Concept 3....................................................................................................... 18
4.2.4. Final Design Choice ........................................................................................ 18
5. TEST RIG DETAILED DESIGN ......................................................................................... 20
5.1. Stress Analysis ....................................................................................................... 20
5.1.1. Design Loads .................................................................................................. 20
5.1.2. Static Analysis ................................................................................................ 21
5.1.3. Member Sizing ............................................................................................... 22
5.1.4. Connection Sizing ........................................................................................... 26
5.2. Load Application Components .............................................................................. 27
5.2.1. Winch ............................................................................................................ 27
5.2.2. Pulleys ........................................................................................................... 27
5.2.3. Cable .............................................................................................................. 28
5.3. Manufacture ......................................................................................................... 29
6. WING .......................................................................................................................... 30
6.1. Technical Task ....................................................................................................... 30
6.1.1. Size ................................................................................................................ 30
6.1.2. Geometry ....................................................................................................... 30
6.1.3. Material ......................................................................................................... 30
6.1.4. Joints ............................................................................................................. 30
6.2. Geometric Parameters .......................................................................................... 31
6.3. Wing Loads ........................................................................................................... 31
6.4. Spar Sizing ............................................................................................................. 32
6.5. Rib Sizing ............................................................................................................... 33
6.6. Wing Connection Joints ......................................................................................... 35
6.7. Linkage Mechanism............................................................................................... 37
7. EXPERIMENTAL MEASUREMENT EQUIPMENT ............................................................. 38
7.1. Load Cells .............................................................................................................. 38
7.2. Strain Gauges ........................................................................................................ 38
7.3. Deflection Measurement ...................................................................................... 40
7.4. Data Interface and Software ................................................................................. 40
8. COMPARISON RESULTS ............................................................................................... 41
8.1. Comparison Process .............................................................................................. 41
8.2. Load Values ........................................................................................................... 41
8.3. Vertical Deflection ................................................................................................ 42
8.4. Bending Stress ...................................................................................................... 43
8.5. Shear Stress .......................................................................................................... 45
8.6. Discussion ............................................................................................................. 46
9. BEAM MODEL MODIFICATION ..................................................................................... 48
10. MANAGEMENT ......................................................................................................... 48
10.1. Project Roles ..................................................................................................... 48
10.2. Risk Management .............................................................................................. 48
10.3. Project Cost ....................................................................................................... 49
10.4. Time Management ............................................................................................ 49
11. CONCLUSION ............................................................................................................ 50
REFERENCES ........................................................................................................................ 51
APPENDIX A ........................................................................................................................ 53
APPENDIX B ......................................................................................................................... 54
APPENDIX C ......................................................................................................................... 64
APPENDIX D ...................................................................................................................... 127
APPENDIX E ....................................................................................................................... 130
APPENDIX F ....................................................................................................................... 134
APPENDIX G ...................................................................................................................... 136
APPENDIX H ...................................................................................................................... 138
APPENDIX I ........................................................................................................................ 140
APPENDIX J ....................................................................................................................... 145
APPENDIX K ....................................................................................................................... 148
LIST OF FIGURES Figure 1: Beam deformation modes: (a) Due to normal forces. (b) Due to bending. (c) Due to shear forces. ......................................................................................................................... 7 Figure 2: Beam nodal displacements and rotations ............................................................... 7 Figure 3: Turbine Technologies TrueStructures structural laboratory (Image from www.turbinetechnologies.com). ......................................................................................... 11 Figure 4: Test rig concept designs. Concept 1 (left). Concept 2 (centre). Concept 3 (right) .. 17 Figure 5: Test Rig final design free-bodied diagram ............................................................. 21 Figure 6: Cross Section for beam member E-F-H-I-J ............................................................. 23 Figure 7: Cross Section for beam member M-Q-S ................................................................ 24 Figure 8: Cross Section for beam member A-B-C-D .............................................................. 25 Figure 9: Jarrett Dual Ratio Winch (Image from www.advansa.com.au) .............................. 27 Figure 10: Ronstan Upright pulley RF919 (left) and Wire Block pulley RF468 (right) (Image from www.ronstan.com) ..................................................................................................... 28 Figure 11: Dynex Cable (Image from: www.strongrope.com/dynex).................................... 28 Figure 12: Final Assembled Test Rig Structure ..................................................................... 29 Figure 13: Assumed wing lift distribution with magnitude and location of summed point loads. .................................................................................................................................. 32 Figure 14: Main (a) and Auxiliary (b) spar cross section dimensions .................................... 33 Figure 15: Flat pattern of the rib ......................................................................................... 34 Figure 16: Standard root connection joints for front and auxiliary (rear) spars (Nui,1988) ... 35 Figure 17: Front Spar and test rig connection interface ....................................................... 35 Figure 18: Main (right) and Auxiliary (left) test rig connection joints ................................... 36 Figure 19: Main spar connection joint (left) and Auxiliary spar connection joint (right) ....... 37 Figure 20: Three bar linkage mechanism for application of the load from the cable to wing. ........................................................................................................................................... 37 Figure 21: A&D Weighing Australia 'S' Type Tension and Compression Load Cells (Image from: www.aandd.com.au) ................................................................................................. 38 Figure 22: Vishay Precision Group EA-13-250BF-350 linear type strain gauge (Vishay Precision Group, 2010). ....................................................................................................... 39 Figure 23: Vishay Precision Group CEA-13-187UV-350 rosette type strain gauge (Vishay Precision Group, 2010) ........................................................................................................ 39 Figure 24: National Instruments SCXI-1314 Terminal Block (left) and SCXI-1000 Chassis (right) (Image from: www.ni.com) ................................................................................................. 40 Figure 25: Front spar vertical deflection for tip load of 630N ............................................... 42 Figure 26: Front spar vertical deflection for distributed load case 2 .................................... 42 Figure 27: Front spar change in deflection due to increasing tip load. ................................. 43 Figure 28: Front spar bending stress for tip load of 800N .................................................... 44 Figure 29: Front spar bending stress for distributed load case 1 .......................................... 44 Figure 30: Change in bending stress at strain gauge location for increasing tip load ............ 45
Figure 31: Front spar shear stress for tip load of 800N ........................................................ 45 Figure 32: Change in shear stress at strain gauge location for increasing tip load ................ 46 Figure 33: The final assembled rig and wing ........................................................................ 50
LIST OF TABLES Table 1: Test Rig design decision matrix .............................................................................. 19 Table 2: Experimental Loading Scenarios ............................................................................. 41
LIST OF SYMBOLS
A – Cross section area [m2]
C – Connection factor for column buckling computation.
E – Material Young’s modulus of elasticity [Pa]
Ec – Material Young’s modulus in compression [Pa]
Fs – Rib shear stress [Pa]
H – Wing box and cross section height.
I – Cross section moment of inertia about some arbitrary cross section [m4]
K – Beam element stiffness matrix.
Ks – Shape factor.
L – Length of the beam [m]
M – Moment about bending axis [N.m]
P – Beam element load vector.
Py – Normal force acting parallel to the wing [N] (x =1, 2, 3)
PW – Total wing load [N].
Q – Statical moment of area for the some arbitrary cross section [m3]
T – Torque [N.m]
V – Vertical shear force [N].
W – Wing box and cross section width.
WO – Aircraft empty weight.
WW – Wing weight.
dV – Distance from shear centre of the cross section to the surface of the cross section [m]
a – cross section height [m]
b – cross section width [m]
t – Component thickness [m]
tr – Rib thickness [mm]
ηs – Plastic correction factor
µ - Poisson’s ratio
d(y) – Beam deflection along the y-axis.
N’’ – Vector containing the double derivative of a beams shape function.
Z’’(y) – Curvature of a beam along the y-axis.
ε±(y) – Strain at the surface of a beam along the y-axis.
σ±(y) – Normal stress at the surface of a beam along the y-axis.
σY – Normal stress due to normal forces [Pa]
σN – Normal stress due to bending and normal forces [Pa]
τV – Shear stress due to vertical shear force [Pa]
τT - Shear stress due to Torque [Pa]
τXY – Shear stress due to shear and torsion forces [Pa]
σeqv – Equivalent or Von-Mises stress [Pa]
σb,max – Maximum bending stress [Pa]
σs,all – Fastener allowable shear stress [N]
σb,all – Fastener allowable bearing stress [N]
PS,all – Fastener shear-off load [N]
Pb.all – Allowable bearing load [N]
ACRONYMS
DLR: German Aerospace Institute (Deutschen Zentrums für Luft- und Raumfahrt).
BSM: Beam Sizing Model.
FAME-W: Fast and Advanced Mass Estimation – Wing
WDT: Wing Design Tool
SHS: Square Hollow Section.
RHS: Rectangular Hollow Section.
BOM: Bill of Materials.
UASME: University of Adelaide School of Mechanical Engineering.
LabVIEW: Laboratory Virtual Instrumentation Engineering Workbench.
SOP: Safe Operating Procedure
Samuel Polglase 1
1. INTRODUCTION
It has become increasingly clear over the last two decades that for aircraft conceptual design, effective weight prediction tools which are separate from the standard empirical and statistical methods are needed (Bindolino, et al, 2010). In particular an accurate estimation of the wings weight and the interaction between the aircraft and structural design of the wing is crucial for the successful completion of an aircraft conceptual design. Such an estimate of the weight of the wing can be accomplished in part by using a relatively simple model which incorporates the Euler/Bernoulli beam theory to compute the deflection and resulting stress in the wings primary structural members. Since these members form the majority of the wings weight (Bindolino, et all, 2010) such a model becomes a crucial component in the weight estimation of the wing.
There are several models in existence which use a similar weight estimation approach, namely one where the weight of the load bearing structure is calculated using load and stress based sizing loops. Such examples include the Airbus Fast and Accurate Mass Estimation tool (FAME), Dell Engineering Wing Design Tool (WDT) and the NeoCASS Aeroelastic Sizing Suite (Cavagna L, et al). However these models are all either the intellectual property of the creators or owned by the companies which employ them for weight estimation purposes. For this reason the German Aerospace Institution (DLR) has begun the development of their own model for the purpose of weight estimation in the conceptual design stage of new aircraft.
The result of development to date is the Beam Sizing Model (BSM). The BSM is at the point where it is undergoing comparisons and couplings with a much more complex and time expensive model which uses finite shell elements to model the wing (Dorbath, F. 2010). Due to the fact that the BSM has the potential to perform a vital role as part of a larger design tool it should be validated against a real, physical wing so that the results the model produces can be used with confidence knowing that they are an accurate representation of what is occurring in reality.
The added benefit of such a validation is that the wing and the structure which must be constructed to support and load the wing can be later used as an educational tool in the area of aircraft structures. Such a supporting structure should be designed using basic structural mechanics and statics, and the wing should be designed and constructed using methods and practices which reflect, as closely as possible, those used throughout the aircraft industry.
This project is being undertaken in collaboration with the DLR, and will continue earlier work undertaken by the student at the DLR in 2010.
1.1. Motivation
Before the detailed design of any new aircraft can take place there are a number of basic design parameters which must be set and evaluated during the conceptual design process (Dorbath F, 2008). Wing geometric parameters such as span length, chord length, taper ratio and sweep are set based on aircraft mission parameters and will be refined throughout the design process. It becomes necessary to use these parameters and the initial load estimates to calculate the weight of the wing. Conventionally this weight estimation has been performed using methods which employ statistical and empirical data as outlined by Stinton, 2001 and Corke, 2003. However these methods are inadequate for designs
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employing materials or layouts for which insufficient statistical data exists and must be replaced with methods which estimate the wing weight based on a structural model of the wing. It has been shown that a weight estimation tool which uses this approach requires only half the time per design cycle and only a fraction of the number of design cycles to converge the design when compared with the conventional design approach (Van der Velden, et al, 2000). The accurate estimation of the wing weight will also form a part of the weight estimation of the entire aircraft. Since this aircraft weight forms a crucial component of the entire aircrafts design it is vital that this estimation is as close to the final weight of the aircraft as calculated in the final detailed design stage. Accuracy in the conceptual stage will lead to less design iterations which has the potential to save the manufacturing company considerable cost and time.
The development of such an approach is therefore highly desirable for the conceptual design stage of all aircraft. Several weight estimation tools which are based on this structural modelling approach have been developed and are already used as part of the weight estimation of an aircraft concept design such as the Airbus FAME tool (Dorbath, F. 2008). These models can incorporate structural models which use a simple and fast one dimensional beam model of the wing and a more complex and time intensive three dimensional model incorporating finite shell elements. A coupling between the two methods is a sensible approach which will result in a model which incorporates both methods to achieve an accurate model within a relatively short time.
This coupling is achieved by taking the strength of each method, allowing the drawbacks of each method to be essentially nullified. The beam model will achieve very fast computation times, however its simplicity means it cannot accurately estimate the stress in regions where complex stresses occur. A method employing finite shell elements can accurately compute the stress in the complex regions; however it is a time intensive process. Thus, the coupling of these two methods involves employing the shell method for the small regions of complex stresses but saving considerable computation time by using the beam method on the regions of the wing where the stress is linear.
The project aims to validate the core structure of the model, which uses the beam theory, against a physical wing by undertaking a direct comparison between a real wing and the equivalent wing modelled within the beam model environment. This will also result in a more complete and detailed understanding of the beam model and what its strengths and limitations are. For the student this will result in an increased understanding of the structural interactions and complexities of an aircraft wing.
A large benefit of developing such a physical test structure is its ability to be used as an educational tool in the area of aircraft structures for undergraduate mechanical engineering students. This provides added motivation for developing such a physical model.
In order to continue collaboration with the DLR, improvements and further refinement of the beam model are set as extended goals of the project. These improvements will seek to increase the capacity of the beam model so that a greater variation of wing geometries can be modelled and sized.
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1.2. Background
In order to obtain the weight of the wing, which is needed to compute the overall weight of the aircraft, the size of the primary structures which comprise the wing need to be established based upon the aerodynamic loads experienced by the wing. The BSM computes the weight of the wing box structure by computing the weight of the wing spars and skin covers between the two spars. The BSM in its current state undertakes the following basic steps to obtain these weights.
The user inputs various geometrical, material, load and computation parameters. The model takes the geometrical inputs and the number of user defined beam elements to
generate a geometrical mesh of the wing. The aerodynamic forces on the wing are calculated with the geometric mesh of the wing and
load input data using the Vortex Lattice method. Using either the two dimensional lift distribution or the single tip loads on the wing the model
will use these forces and the Euler beam theory to calculate the deflection and normal stress due to the forces, or components of the force, which act normal to the surface of the wing.
The stress and deflection due to the induced torsion force (if the wing is swept) is calculated using the Saint-Vennat theory for thin walled structures.
The shear stress due to shearing forces is calculated using a simple shear stress formula. The combined Von-Mises stress of the front and rear spars and the top and bottom skin of the
wing is computed. Based on the difference between the actual stress level and the allowable stress level in the
material of the spars and skin, the thickness of the spars and skin is increased or decreased and the load calculation step is repeated until the stress levels are at or below the allowable level.
The mass of the entire wing is computed based on the thickness of the spars and skins and the density of the material.
The final weight of the wing box which is computed is an incomplete estimation as it does not include the weight of the ribs and stringers, the weight of the components outside the two spars and other mass such as fuel tanks and control lines, etc. This incomplete estimation shows the opportunity for advancements in and improvement of the beam model; however the focus of this project is the validation of the model in its current state and more specifically validation of the calculated stresses by which the structural components are sized and deflections which effect the aero-elastic deflections and thus the loads and stresses.
1.3. Scope
In order for the project to successfully validate the BSM there are several key aspects which must be met. The first of these is the design and construction of an experimental test rig and aircraft wing which can be used in conjunction to obtain the required experimental data. The test rig and wing must adhere to several design requirements which are based on its future use and the experimental data required.
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Once this has been achieved the experimental data must be recorded by the implementation of measurement instrumentation and the completion of an experimental program. The parameters that must be recorded in order to fulfil the project objectives are the applied load to the wing, the strain in the wings structural components and the deflection of the wing.
It is expected that an experimental test rig suitable for further use in the undergraduate mechanical engineering course will be produced and the required experimental data will be obtained leading to a successful validation of the core structure of the BSM.
1.4. Project Objectives
The major project goals which relate to the desire for a comparison and validation of the BSM have been set as follows.
Design and construct a suitable test rig which is capable of supporting and subjecting a wing to a load of less than or equal to 1000kg/m2 including a suitable safety factor. The test rig must also be mounted on four wheels and capable of relocation throughout the Mechanical Engineering laboratory area.
o This figure of 1000kg/m2 is based on the maximum designed wing loading for civilian transport aircraft.
Design and construct a suitable wing structure which can be fixed into the test rig and subjected to a load of less than or equal to 1000kg/m2 including a suitable safety factor.
Implementation of the required instruments to measure the applied load and the resulting strain and deflection of the wing while it is subjected to a total load of less than or equal to 1000kg/m2.
The successful comparison of the measured data from the scaled wing with the BSM.
The first three extended goals should be undertaken such that the final result is an experimental laboratory suitable for use in undergraduate course work.
As well as these above primary goals, several extended goals have been set which are to be completed once the primary goals have been successfully completed. These extended goals are as follows.
Extension of the ability of the BSM to allow the use of any user defined airfoil as part of the load calculation step and to test five different airfoil shapes to show the range of airfoil shapes that BSM is capable of using.
Extension of the ability of the BSM to undertake all steps using multiple unique wing sections with separate sweep angle and taper ratio.
The design and build of a second wing which contains a skin and stringers as part of the structure for comparison and validation of the DLR shell model.
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2. LITERATURE REVIEW
The classical statistical and empirical methods for computation of a wing’s weight are discussed briefly in order to recognise the difference between these methods and the method by which models such as BSM calculate the wing’s weight. Then the Euler/Bernoulli beam theory which forms the core of the stress and deflection calculation step of the BSM will be formalised and summarised in this literature review such that a solid understanding of the theory used by the BSM is reached. The formula used for the calculation of the shear stresses in the wing is also summarised. In order to understand the significance and usefulness of a model such as the BSM a short review of similar but much more advanced models is also summarised. This is followed by a short explanation of the theory behind the finite shell element model which is used by the DLR to calculate stresses in the wings more complex stress regions.
The final component of the review will be concerned with summarising a test rig structure which is similar to that which has been developed in order to validate the BSM. This test rig will essentially form a benchmark from which the design of the projects test rig can be developed.
2.1. Classical Weight Estimation Models
The classic and historical approach to estimating the weight an entire aircraft and sub-components during the preliminary design stage of a new aircraft is by using equations based on statistical data. This will result in a weight estimation which is an acceptable starting point from which the rest of the design steps can follow, but will require constant iterations once data which affects this weight becomes available or is changed. Two such equations are outlined below to demonstrate this classical approach to weight estimation.
Stinton, 2001 employs a method first demonstrated by Seehler and Dunn which estimates the weight of the wing as a ratio of the design gross weight Wo as shown in the equation 1.
푊푊 =
푎 퐹 푁(2.5푏 + 120)10 (1)
The weight factor aW and structural factor FW are both based on statistics as is the initial estimate of the design gross weight Wo.
Corke demonstrates a method for the estimation of the wings weight based upon equation 2.
푊 = 퐶 퐶 퐶 푊 푛 푆 퐴푡푐
(퐶 + 푇푅) (푐표푠푆푊퐸퐸푃) 푆 푞 푊 (2)
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The coefficients in equation 2 are different if the aircraft is classified as a Fighter, Transport or General Aviation aircraft. The coefficients are based upon statistical data which is derived from weight related data for aircraft which fall into these three general categories.
These two methods demonstrate the classical method which is used during the conceptual design stage of aircraft for the estimation of the wings weight. These equations can provide an excellent first estimate of the wing weight for conventional aircraft design as there is a large amount of statistical data for these designs employing conventional layouts. The limitations of this method of weight estimation are for designs where there is not sufficient statistical data such as a method employing a new layout or new, unconventional materials such as composites. For such a case a weight estimation method based on structural sizing due to loads and wing geometry, of which BSM aims to achieve, becomes a powerful and useful tool in the conceptual design stage.
2.2. Beam Model
2.2.1. Euler/Bernoulli Beam Theory
The Euler/Bernoulli beam theory or Classical beam theory provides a method for calculating the load carrying ability and deflection of a beam. The simplicity of the beam theory makes it a widely used and powerful tool in the fields of both structural and mechanical engineering. The Euler/Bernoulli beam theory has the following three main assumptions (Dorbath F. 2009).
The beam is slender meaning the length is much greater than all other dimensions. The beam cross section, which is rectangular to the beam axis before bending, remains
rectangular to the beam axis after bending. The cross section of the beam remains planar after bending.
These assumptions allow for two of three main deformation modes of a beam to be calculated. These modes of deformation are shown in figure 1 and are the deflection due to normal forces (a), bending moments (b) and shear forces (c).
The final mode of deformation which is not covered by the classical Euler/Bernoulli approach is the final deformation mode shown in figure 1(c) and is the shear deformation due to shear forces. This deformation mode is neglected due to the second major Euler/Bernoulli assumption. This deflection due to shear forces increases the bending of the beam, however for a beam with a high aspect ratio, which is usually the case for aircraft wings, the effect of this deflection due to shear is negligible and can therefore be ignored (Dorbath F. 2009). It is important to note however that for more unconventional wing shapes such as box wings this deformation mode cannot be ignored and a more thorough analysis using a beam theory such as the Timoshenko beam theory, which includes this deformation mode, is required. However it is important to note that the stress due to the vertical shearing force can be calculated simply using standard solid mechanics theory and is not ignored as part of the total stress calculation of the wing box.
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Figure 1: Beam deformation modes: (a) Due to normal forces. (b) Due to bending. (c) Due to shear forces.
The Euler/Bernoulli beam equation in its simplest form describes the relationship between a beams deflection and the applied load on the beam as shown in equation 3.
퐸퐼 = 푃 (3)
In equation 3 the curve d(y) describes the deflection along the length of the beam. If the Lagrange energy approach is used to solve for this curve then it can be described as a combination of the beams shape functions. The result of this is a stiffness matrix K which fully describes the deflections of the beam in up to six degrees of freedom for a beam with displacement and rotation about all axies as shown in figure 2. Equation 4 describes this relationship
퐾푑(푦) = 푃 (4)
For a beam with a node at both ends, as shown in figure 2 the stiffness matrix will be a twelve by twelve matrix if the displacement and rotation of the nodes in all three axies is desired for computation. The elements which make up this stiffness matrix are based on the shape functions for the beam and the final stiffness matrix and resulting Euler-Bernoulli beam matrix equation for such a beam is shown in appendix A. The inverse of the stiffness matrix K can be multiplied by the load vector P to obtain the deflection of the nodes in all three degrees of freedom.
Figure 2: Beam nodal displacements and rotations
Z X
Y
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Any single beam of length L can be divided up into any number of single beam elements resulting in a beam of length L comprising n number of elements of length L/n. This allows a global stiffness matrix to be constructed from the individual stiffness matrices of each element. With this global stiffness matrix the deflection at each nodal position along the beam can be found based on the inverse of the global stiffness matrix and the load vector which contains the loads applied in each degree of freedom at each nodal position along the beam.
The deflections of the beam can then be used to find the strain and hence the stress due to bending using the double derivative of the shape functions which define the curvature of the beam. Equation 5 below shows how the stress at the surface of the cross section is found using the double derivatives of the shape function and the deflections which have been found using the inverse of the global stiffness matrix.
휎±(푦) = 휀±(푦)퐸
푤ℎ푒푟푒:휀±(푦) = 푍 (푦)푡±
푎푛푑푍 (푦) = 푁 푑(푦) (5)
Using this above outlined theory it is therefore possible to calculate the deflection and rotation about all three axies as well as the normal stress due to bending at the surface of the beam using the Euler/Bernoulli beam theory.
2.2.2. Shear Stress Computation
As well as using the Euler/Bernoulli beam theory to calculate the normal stress due to bending the BSM also computes the shear forces which the wing is subjected to, due to the applied forces. These shearing stresses can be split into two separate components which are the shear stress due to the vertical and horizontal shear forces (lift and drag) and the shear stress due to the induced torsion of the wing.
SHEAR STRESS DUE TO LIFT AND DRAG:
The calculation of these stresses is carried out using equation 6 below (Timoshenko, 1996).
휏 = (6)
SHEAR STRESS DUE TO TORSION OF THE WING:
The calculation of this shear stress at each surface of the wing box is done using equation 7 below (Nui, 1999).
휏 = (7)
Samuel Polglase 9
2.3. Comparable Models
As previously mentioned there has been a shift in the last few decades away from weight estimations for aircraft which are based primarily on statistical and empirical data towards estimations which involves computations using the structural models of the aircraft. Three studies which employ such computational models are summarised below.
In the study ‘Multilevel Structural Optimization for Preliminary Wing-Box Weight Estimation’ by Bindolino G, et al. the wing box is summarized by a so called ‘stick model’ which is comprised of a series of beam elements. This ‘stick model’ is constructed based upon the geometric properties of the wing and the aerodynamic loads are applied to this model in order to obtain the stress on the elements. This stress level can form the basis for the constraint function during the optimization and sizing of the wing box structural components.
In a study which focused on the application of a design optimization for a large transport aircraft titled ‘Application of MDO to Large Subsonic Transport Aircraft’ by Van der Velden et al, a beam theory based weight estimation tool called FAME-W is used. The Airbus FAME is a very advanced tool which has been developed over several decades to arrive at a method to compute the entire mass of the aircraft in the conceptual stage (Dugas, M, Grabietz, M. 2004). FAME-W (Wing module of the tool) calculates displacements and stresses due to bending according to Bernoulli and torsion related displacements and stresses according to St. Venant (Dugas & Grabjetz, 2004).
In a similar study which was applied to a large business jet instead of larger transport aircraft titled ‘Preliminary Aerostructural Optimization of a Large Business Jet’ by Piperni, P. et al, a similar model called TWSAP is employed to calculate the wings structural properties. This model generates a beam finite element model representation of the wing (Piperni, P. et all 2007) for the calculation of the stress on the wings structural members due to the applied load.
Together, these studies show the growing interest in weight estimation models which include a computation based on structural layout, material properties and aerodynamic loads for the weight of the wing.
2.4. Shell Model
The shell model which has been developed by the DLR constructs the wing as a 3 dimensional shell using the ANSYS shell elements SHELL181. The shell is made up of four nodes I, J, K, L which all have six degrees of freedom meaning that the rotation and deflection in all three axies can be computed by ANSYS for all four nodes.
The shell model generates the model of the wing with the SHELL181 using an input file which describes the geometry of the wing. It then applies the load over the wing, with an input file describing the lift distribution of the wing, and also sets boundary conditions which simulate the clamping of the wing at the root by restricting rotation in all six degrees of freedom for all nodes at the root of the wing. ANSYS
Samuel Polglase 10
is then used to solve the model and the outputs in terms of element stress levels and deflections can be read using the post-processing functions of ANSYS. More specifically the quantities which can be obtained from ANSYS which are related directly to those computed using the beam model are as follows:
σVM = Element Von-Mises stress level. σN = Element Normal stress level. τXY = Element Shear stress level. δY = Nodal deflection in the global Y axis. δx = Nodal defection in the global X axis.
The element stress levels are then used to size the structural elements of the wing which make up the model and the load is applied and model solved until convergence of the stress levels to below the allowable is reached.
For comparison of results from the shell model with the beam model, the element stress levels are used as well as the deflection of the elements along the length of the wing in displacement and rotation. This allows for a direct comparison and allows the user to determine the areas along the wing where the results do not match due to the limitations of the beam model.
2.5. Test Rig Benchmarking
The TrueStructuresTM structural laboratory developed by Turbine Technologies and shown in figure 3 serves as an example of a similar test rig and wing structure to that which will be developed for the project. The main features of the TrueStructuresTM laboratory are as follows:
Compact structure employing an aircraft horizontal tail section. Infinitely variable point loading system to apply bending and torsional moments. Load cell providing an indication of the applied load. Preinstalled strain gauges to measure skin, web and beam stresses.
Samuel Polglase 11
Figure 3: Turbine Technologies TrueStructures structural laboratory (Image from www.turbinetechnologies.com).
This structural laboratory will serve as the benchmark for the test rig however the developed test rig will need to go further than the capabilities of the TrueStructuresTM in the following two ways:
The load should be applied at several stations along the length of the wing to simulate a spanwise load distribution.
The test rig should be constructed in such a way that it will be as simple as possible to test multiple different wing sections as they become available to the UASME. This requires a test rig which is flexible in terms of the structure, allowing different parts to be modified and/or changed to suit the wing sections which are required for investigation.
For these reasons the TrueStructuresTM structural laboratory is not appropriate for the purposes required by the UASME. This results in the motivation to develop a purpose built test rig and wing structure which fulfils the same features but provides more load application points and flexibility.
The cost of purchase and delivery of the TrueStructuresTM structural laboratory is approximately $20,000 (Turbine Technologies, Ltd, Product Guide). This cost will serve as cost benchmark against the produced test rig and wing structure and a goal of the project will be to produce all required equipment to below or at this price.
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3. METHOD OF INVESTIGATION
In order to adequately validate the stress and deflection computation steps of the BSM the steps which should be taken in order to obtain the required experimental data for comparison with the data obtained using BSM need to be clearly laid out. These steps include determining the experimental data required, designing and building an experimental test rig which will support the wing and subject it to a load, designing and building a suitable wing, determining suitable devices to measure the applied load, strain on the wing structure and deflection of the wing structure and implementing these devices onto the wing and test rig.
Once these steps have all been successfully completed the experiment which involves loading the wing and recording the strain and deflection can be undertaken and the comparison between the physical wing and the BSM can be realised.
3.1. Experimental Data Required
It is crucial for the successful comparison of the test data and the BSM that the correct experimental data is obtained from the test. This involves determining the main outputs from the BSM that are suitable for comparison and that should be used to validate the model, and then determining if these outputs can be obtained from the experiment.
The BSM models and sizes four main structural components. These are the main (front) and auxiliary (rear) spar and the upper and lower skin between the front and rear spar. The BSM structural model does not include stringers or ribs, although the ribs are assumed to lay on the span-wise element barriers meaning they do not resist the bending of the wing due to the lift force which is the dominant stress. Due to the complexities with constructing and loading aircraft skin panels, it was decided during the early stages of the project to simplify the experiment by only modelling the spars and ribs of the wing, in order to ultimately realise results within the time and cost constraints. However as a further project goal the design and construction of a wing comprising skin panels has been set so that the computed stress levels of the skin sections can be validated, as well as validating the DLR shell model.
With this in mind the main outputs from the BSM which were determined to be suitable for comparison, and those required to validate the model are as follows.
The bending stress and shear stress of the main (front) and auxiliary (rear) spar. o This data can be obtained from the physical wing by recording strain gauge data
attached to the main and auxiliary spars. The deflection of the wing at the tip in the z-axis direction, or the direction of the lift.
o This data can be obtained from the physical wing simply by measuring the deflection of the main and auxiliary spars.
The applied load on the physical wing should be identical to that which is applied in the BSM to ensure that the stress and displacements which are compared are for identical loads. The BSM allows for the user to input point loads along the wing at any nodal location. This will allow the applied load and the
Samuel Polglase 13
BSM input load to be identical because of the ability to measure the applied load during the experiment, the exact values of which can then be input into the BSM.
3.2. Suitable Test Rig and Wing
Once the parameters for comparison have been determined a suitable test apparatus or rig which is cable of supporting a wing structure and subjecting it to an applied load need to be designed and constructed. The specific design constraints which have been set for the test rig are discussed in section 4.1.
Once the test rig has been designed the wing size and shape can be determined. The wing must meet certain requirements in order for it to fit into the test rig structure and produce the needed experimental data. The shape of the wing should be set by consultation with the DLR and through a good understanding of what is feasible within the allowable time of the project. The cost of manufacturing the wing should also be kept as low as possible and will therefore become a driving factor in the final shape of the wing. The final shape of the wing will be the result of a balance between the geometric requirements and the time and cost constraints.
3.3. Suitable Load Application
It is not feasible to apply a load as an in service wing would normal experience, which is a pressure distribution over the entire surface of the wing. However it is possible to simulate this pressure distribution by applying loads at points along the span of the wing which correlate to the summation of this pressure distribution. Applying the load in this way is suitable for the comparison and validation, as the load input for BSM can be either an aerodynamic pressure distribution or point loads applied along the length of the wing.
3.4. Suitable Measurement Devices
Once the test rig and the wing have been successfully designed and built suitable measurement instrumentation should be implemented onto the test rig and the wing where needed so that the experimental data can be recorded for the comparison and validation with the BSM. This means purchasing and installing devices which can record the following information.
The applied load to the wing from the test rig. The induced strain of the front and rear spar from the applied load. The deflection of the main and auxiliary spars due to the applied load.
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4. EXPERIMENTAL TEST RIG
The test rig is the structure which will support the wing and subject the wing to the load. It has evolved from an initial technical task which describes the design limits for the test rig. From this technical task the initial concepts for the test rig have evolved and from these concept designs the final design has been chosen and developed into a detailed design ready for manufacture.
4.1. Test Rig Technical Task
The technical task for the test rig sets the limits for the designs and forms the basis from which the concept designs can evolve. The limits which have been set for the design have come from various constraints and are discussed below.
4.1.1. Size
The test rig should be reasonably compact and light enough for one person to manoeuvre it with relative ease. A limit should be placed on the width of the rig so that it is capable for being pushed through a double doorway.
The specific dimensional constraints of the test rig should be no greater than 1.5m wide, 2m long and 1.5m high.
4.1.2. Manoeuvrability
The test rig must be fully manoeuvrable so that one person can move the entire constructed rig without having to lift the rig in anyway. The rig will be too heavy and large for a single person to lift in any way and by making the rig manoeuvrable it eliminates the need for multiple people to move it and the potential injury that could arise from doing so.
To make the rig fully manoeuvrable it must have four heavy duty wheels attached to its base in each corner. The wheels should have brakes which allow no movement of the wheel in any direction when the rig is applying the load to the wing.
4.1.3. Material
The material from which the structure is constructed is important as it will affect the stress in the structure, the machinability, the cost and lifetime of the structure. The chosen material for the structural members must satisfy all of these considerations so that each consideration achieves the best outcome.
The chosen material is structural aluminium for the following reasons: o Lightweight material.
Samuel Polglase 15
o Several extrusions are available for off the shelf purchase. o Has good corrosion performance. o Cutting and drilling is simple.
Although most components should be constructed using aluminium some more crucial components may need to be made from a material with higher allowable stress levels such as steel.
4.1.4. Destructible
The method by which the rig is constructed is of vital importance. More specifically the way in which each structural member which makes up the rig is connected is important because this will affect the way in which the rig is assembled.
The structural components which make up the rig will be manufactured by the Engineering workshop on campus and it will be crucial to the timeline of the project that any component of the rig is only worked on once in the workshop. If the component has to go back into the workshop for tooling or re-working this will cause time delays and add pressure to the timetable. Thus is it desirable to make the components as simple as possible to reduce the risk of errors in the manufacture process and simplify the assembly of the rig.
One option is to have the workshop weld the entire rig structure together to assemble it. This has the benefit of making the rig quicker and cheaper to assemble. It also eliminates the need to have any holes drilled into the components which takes more time within the workshop and therefore at a greater cost. However it has the drawback of making the assembled structure heavy and cumbersome making it difficult to move out of the workshop and into the desired area in the laboratory. It would make attaching the wheels to the rig more challenging and could also present challenges when moving the rig for the final exhibition. The welding of structural aluminium is also not a recommended joining technique for this material due the reduction in strength of the parent material in the region surrounding the weld. Welding of steel is however a highly desirable method of joining for this type of material.
Due to the undesirable effect in terms of material strength when welding structural aluminium the majority of the joints in the rig structure should be bolted connections as this allows for ease of assembly and deconstruction if the rig needs to be moved a considerable distance or taken apart for modifications.
With these considerations in mind the following restrictions should be placed on the test rig design
All connections involving the structural aluminium should be made, where possible, using either bolted connections or rivets for more permanent connections.
Any connections involving steel can but do not necessarily have to be welded connections. No one single or permanently assembled component should be too heavy for a single person to
lift safely and without injury. The time needed to assemble and disassemble the test rig should be as low as possible.
4.1.5. Loading Frequency
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It is important to consider how much use the test rig will be subjected to as this will determine how robust the structure must be and will affect the stress considerations during the design phase.
The test rig will be used as a teaching tool for undergraduate engineering students and therefore is not likely to be loaded for more than 1-2 hours per week for any given week during a semester of study. There will also be periods when the rig will not be used at all, for example university holidays and non-teaching periods such as student exam periods. With this is mind the following requirements can be set.
Fatigue testing of the wing is not required and thus the test rig structure should not be designed to withstand high cyclic loading.
Re-enforcement of the structure should be kept to a minimum where possible. The design of the structure should be such that further re-enforcement can be added to the
structure if needed at a later time. The rig should be designed such that it can be capable of being set up quickly for the
experiment.
4.1.6. Load Carrying Ability
The test rig structure should be capable of carrying the specified maximum load without deformation in any of the structures members or joints. This load carrying ability must also be designed in the most efficient way possible.
The structure must carry the required total load of 1000kg/m2, with a suitable safety factor, in the most efficient way possible without any permanent deformation in any of the structural members or joints.
4.1.7. Load Application Points
The test rig should be capable of applying the total load as a combination of several smaller loads at points along the wing length. Obviously the more points chosen the more difficult it becomes to design the rig to be capable of this but also increases the time needed to apply the load to the wing. With this in mind the following requirements is placed on the design.
There should be three locations along the wing where the load is applied.
4.1.8. Operational Procedure
Since this test rig structure is to be used by undergraduate students in a teaching environment where time is often an issue the rig should be designed in a way that does not require much time for the experiment to be set up and undertaken. With this in mind the following requirements should be made:
The method for applying the load should be achieved using a method which is as simple as possible, and be able to be used by a single person without difficulty.
Samuel Polglase 17
Any permanently attached actuators should be easily reached.
4.2. Test Rig Concept Designs
The test rig concept designs are the next step in the development of the design once the parameters for the design have been set in the technical task. The three final concept designs are shown in figure 4 and represent the best of the several concepts for the test rig that were developed during the early design stage.
Several basic parameters such as the size and material used will remain the same in all concepts as it is clear that these should not change from concept to concept. These parameters are essentially non-negotiable and it would not make sense to develop a concept which is outside these parameters, because it would not fit the requirements established in the technical task.
4.2.1. Concept 1
The basic layout for the first concept design is shown in figure 4. The main features of this first concept are outlined below.
Load applied through the top of the rig using tensioned cable at three stations along the length of the wing to pull the wing upwards.
Cables are tensioned using turnbuckles and several cables at each span wise location will allow for a twist to be induced on the wing for different tension in the cables.
The upper central beams are re-enforced by a vertical member at the centre of the structure to prevent substantial deformation which would otherwise occur for the beams carrying the applied load.
Plate connected to the corner vertical beams on which the wing is connected to. Four wheels at each corner of the test rig. All components made from structural aluminium. All joints using bolted connections.
Figure 4: Test rig concept designs. Concept 1 (left). Concept 2 (centre). Concept 3 (right)
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4.2.2. Concept 2
The basic layout for the second concept design is shown in figure 4. The main features of this second concept are outlined below.
The wing is bolted on upside down and the load is applied using load slings and weights to pull the wing downwards.
Different amounts of weights on either side of the load sling can induce a torsional load on the wing.
Pulling the wing downwards reduces the need for a substantial amount of structural elements which make up the test rig.
An angled bracing member supports the vertical components which support the beam the wing is attached to.
Plate connected to the corner vertical beams is the connection member for the wing. Four wheels at each corner of the test rig. All components made from structural aluminium. All joints using bolted connections.
4.2.3. Concept 3
The basic layout for the third concept design is shown in figure 4. The main features of this third concept are outlined below.
Wing is bolted upside down and the load is applied downwards using tensioned cables and load slings.
The wires are tensioned using three separate winches. A beam runs down the centre of the rig and supports the winches, cable and pulleys for the
cable. Pulling the wing downwards reduces the need for a substantial amount of structural elements
which make up the test rig. An angled bracing member supports the vertical components which support the beam the wing
is attached to. A steel beam connected to the corner vertical members is the connection member for the wing. All other members other than the beam the wing is connected to are made from structural
aluminium. All joints using bolted connections.
4.2.4. Final Design Choice
From these three concept designs the final design was chosen based on a decision matrix which is shown below in table 1. The decision matrix address all of the design criteria from the test rig technical task and assigns a score out of ten for each concept based on how well is meets the specific design
Samuel Polglase 19
criteria. The result is a final total score for each of the concepts and the concept which has the highest score will be the one chosen as the final design.
Table 1: Test Rig design decision matrix
Size
Man
oeuv
rabl
e
Mat
eria
l
Des
truc
tible
Load
ing
Freq
uenc
y
Load
Car
ryin
g Ab
ility
Load
Ap
plic
atio
n Po
ints
Ope
ratio
nal
Proc
edur
e
Tota
l Sco
re
Concept 1 10 9 9 7 8 7 10 7 67
Concept 2 10 10 9 8 5 9 10 5 66
Concept 3 10 10 10 8 7 9 10 9 73
The final design choice, concept 3 has several main advantages over the first two concepts which make it the desirable choice for the final design. These main advantages are summarised below.
Application of the load using winches: This allows for a very simple and low effort application because a geared ratio winch can be used which will allow minimal applied effort on the winch handle even for the highest loads. It also means the load can be applied in a very short amount of time when compared with the time needed to tensions several wires using turnbuckles or load multiple weights into load slings.
The central beam can be designed to carry all of the applied loads of the test rig reducing the need for overhead structure which would increase cost, manufacturing time and assembly time.
The steel beam supporting the wing is considerably stronger than using an aluminium plate or beam and will thus be easier to design in terms of its cross sectional size than for an aluminium beam. There are also a much wider range of steel extrusions than is available for structural aluminium which increases the flexibility of choice.
Samuel Polglase 20
5. TEST RIG DETAILED DESIGN
Using the final chosen concept the detailed design for the test rig can be undertaken. This detailed design process involves a stress analysis of the entire rig and all the structural members and connections points of the rig. From this stress analysis the specific size of the members and fasteners can be selected. The remaining components such as the winches and wheels also need to be selected based on the requirements for such components.
During this process of establishing the size and shape of each of the structural components and the other remaining components the manufacturing drawings are developed and there will be a certain amount of design iterations because of limitations in the manufacturing and assembly process and based on advice from workshop staff. The detailed design will cycle through several iterations which will involve multiple changes to parts of the test rig resulting in a final design which is ready for manufacture and final assembly.
5.1. Stress Analysis
The first step for the detailed design of the test rig is to perform a stress analysis of the structure to determine the stress in all the members due to the design load so that the size of the members can be selected.
The benefit of the test rig being an internally loaded structure results in an inherent check for the structure which is a zero reaction force at the corners of the structure. This means that the static analysis of the structure will be correct if the reaction loads sum to zero at the four wheels.
5.1.1. Design Loads
The detailed design of the test rig will begin with defining the maximum design loads which should be applied to the wing. This maximum applied load to the wing is based upon a chosen load of 1000kg/m2 based on the area of the wing. This value represent the maximum design load for jet passenger aircraft and although there is no specific load required in order for the validation it is sensible to use a relatively high load to retain flexibility for the test rig if future design changes or new wing structures are required for testing.
Although the final area of the wing is not known at this stage of the design a suitable approximation is 1m2 based upon the area available for the wing and the geometric parameters which will likely be part of the final wings layout such as the following:
Length (semi-span): 1.8m Taper Ratio: 1 Sweep: 10⁰.
Samuel Polglase 21
Thus the total maximum design load for the test rig is 1000kg. This load is broken into three components of decreasing magnitude to be applied at distances along the length of the wing as shown in figure 10. The magnitude and location of these loads is not yet known so for the purpose of the rig stress analysis the magnitude is largest at the root and their locations are applied at increasing increments of 0.6m from the root beam or member A-B-C-D in figure 10. A safety factor of 2.5 is applied to these loads based on the standard used for structures of this type (Oberg, et al, 2000). This results in the following maximum design loads:
P1 = 500kg = 5000N*2.5 = 12500N P2 = 300kg = 3000N*2.5 = 7500N P3 = 200kg = 2000N*2.5 = 5000N
5.1.2. Static Analysis
A free body diagram of the entire structure can be seen in figure 5, this free body diagram is the beginning point for the static analysis of the structure.
Appendix C contains the entire static analysis of the entire rig including the free body diagrams and shear and bending moment diagrams for each of the members.
S
R
K
J
I
H
O
P
N
L
M
Q
E
C
B A
P3
P1+P2+P3
Z
Y
X
P2
P1
D
Figure 5: Test Rig final design free-bodied diagram
Samuel Polglase 22
The analysis is initially carried out using symbolic variables for the applied forces (P1, P2 and P3) and once the unknowns are found the values which correspond to the chosen design loads are inserted for the computation of the maximum shear force and bending moment in the beam.
From this analysis the members with the highest shear and bending moment are listed below as these are the values by which the cross section dimensions of the members will be sized.
MEMBER E-F-H-I-J
→ Vmax = 12750N → Mmax = 25500N.m
MEMBER M-Q-S
→ Vmax = 11858N → Mmax = 12763N.m
5.1.3. Member Sizing
Based on the maximum shear forces and bending moments which have been calculated in the previous section, the cross sectional dimensions for the members with the maximum forces and moments of all the beams which comprise the structure (members E-F-H-I-J and M-Q-S) where chosen.
The material chosen to be used for the beams was a standard aluminium structural section 6082 with the following mechanical stress limits.
Tensile Yield Stress: 240 MPa Maximum Shear Stress: 140 Mpa
The maximum shearing stress and maximum tensile stress due to bending for the members must be below these allowable limits.
The following equations are used to check the stress state of the beams (Gere & Timoshenko, 1997).
Bending Stress:
휎 , = (푃푎) (8)
Shear Stress:
휏 , = (푃푎) (9)
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MEMBER E-F-H-I-J
Due to the large maximum bending moment present for beam E-F-H-I-J the cross section for this beam should be one that performs extremely well under bending which is the classic ‘I’ beam shape as shown in figure 6.
The chosen ‘I’ beam cross section dimensions based on the maximum bending moment this member will undergo is as follows:
H = 140mm W = 80mm t = 8mm
Bending stress for the beam is:
σbmax = 236MPa < 240MPa – OK.
Shear stress for the beam is:
τVmax = 20MPa < 140MPa – OK.
MEMBER M-Q-S
The bending and shear stresses for this member are not as high as for member E-F-H-I-J meaning that a simple square hollow section (SHS) as shown in figure 7 would be suitable as the cross section for this member. Using an SHS will also allow for a relatively simple connection of all the members as they will all share this common SHS cross section.
W
t
t
X
Y
H
Figure 6: Cross Section for beam member E-F-H-I-J
Samuel Polglase 24
The chosen SHS cross section has the following dimensions:
H = 101.6mm t = 6.35mm
Bending stress for the beam is:
σbmax = 187MPa < 240MPa – OK.
Shear stress for the beam is:
τVmax = 41MPa < 140MPa – OK.
All other members of the beam except member A-B-C-D will use this same SHS section since their maximum shear and bending moments are below that of member M-Q-S.
MEMBER A-B-C-D
This member will utilize a steel Rectangular Cross Section (RHS) due to the additional strength required to resist the torsion this beam will undergo due to the attachment of the wing on this member and also because of the additional height of the cross section which is needed for the connection joints between the wing and this member.
The mechanical properties of the steel RHS are as follows:
Tensile Yield Stress: 260 MPa Maximum Shear Stress: 156 Mpa
The maximum torsion which the beam undergoes is 12.75 kN.m.
The layout of the RHS cross section is shown in figure 8.
H
t
Y
H
X
Figure 7: Cross Section for beam member M-Q-S
Samuel Polglase 25
The chosen RHS cross section has the following dimensions:
H = 150mm W = 100mm t = 8mm
The maximum shear stress due to torsion is calculated using equation 10 (AIAA Aerospace Design Engineers Guide, 1998).
휏 = 1 + 0.6 (Pa) (10)
Thus for the above RHS section the maximum shear stress due to torsion is:
τT = 35.7MPa < 156MPa.
VERTICAL MEMBERS
The members of the test rig which have a vertical compression force acting on them have also been checked to ensure no bucking will occur. The equation used for this buckling check is shown in equation 11 (Gere & Timoshenko, 1999).
푃 = (11)
W
t
X
Y
H
Figure 8: Cross Section for beam member A-B-C-D
Samuel Polglase 26
5.1.4. Connection Sizing
The size of the fasteners and connection plates for each of the connections on the test rig was calculated based on design equations outlined in ‘Airframe Stress Analysis and Sizing’ by Michael C. Y. Nui. A summary and explanation of the equations used is given below (Nui, 1999).
The fastener (bolt or rivet) shear-off load:
푃 , = 휎 ,휋퐷
4 (푁)(12)
The allowable bearing load for the connection plate:
푃 , = 휎 , 퐷푡(푁)(13)
The allowable bearing load for the connection member:
푃 , = 휎 , 퐷푡(푁)(14)
These equations allow the size and number of fasteners at each joint to be chosen based on the material properties of the fasteners and the layout and number of bolts which makes sense for each unique joint geometry and orientation.
All bolts chosen for the test rig were structural grade 8.8 hex head bolts due to their availability and excellent mechanical properties which are shown below.
Ultimate tensile strength = 800Mpa Allowable tensile strength = 640Mpa Allowable shear strength = 380Mpa
The allowable bearing strength of the aluminium plate material and the aluminium beam material approximates to the allowable tensile stress of the material (Northern Aluminium Company Limited, 1951). These ultimate bearing strengths are as shown below.
Plate – Aluminium 5083 H321: σb,ul = 317Mpa Beam – Aluminium 6082 T5: σb,ul = 340Mpa
Samuel Polglase 27
5.2. Load Application Components
To apply the load through the test rig to the wing a winch, pulley and cable system was chosen as this was deemed to be the safest, simplest, cheapest and most flexible method available. The interface between this system and the wing is a three bar linkage mechanism which is discussed in detail in section 6.7 as it forms part of the wing design.
The selected components which comprise this system are briefly summarized below.
5.2.1. Winch
The chosen winch to be used for the tensioning of the cable is the Jarrett F10217 shown in figure 9.
Figure 9: Jarrett Dual Ratio Winch (Image from www.advansa.com.au)
The features of this winch include (Advansa Jarrett Product Guide, 2011):
Gear Ratio: Dual 1:1 or 5:1 Handle: Quick removable and interchangeable handle making it suitable for the three winches
to be bolted close together without interference from three separate handles. Rated Capacity: 700kg breaking load which is higher than the maximum needed of 500kg. Spare parts are readily available
5.2.2. Pulleys
The chosen pulleys are Ronstan pulleys and can be seen in figure 10.
Samuel Polglase 28
Figure 10: Ronstan Upright pulley RF919 (left) and Wire Block pulley RF468 (right) (Image from www.ronstan.com)
The RF919 will be used for the travel of the cable as it moves from the winches, down through the structure and then up to the wing. Some of it features include (Ronstan, 2011):
Upright Design: This allows the cable to pass down and through the pulley while still being able to bolt the pulley to the central beam.
Breaking load of 1200kg.
The RF468 will be used on the three-bar linkage mechanism which forms the interface between the cable and the wing. Some of it features include (Ronstan, 2011):
Design allows the cable from the winch to be clipped to the pulley so that the pulley is free to run along the cable on the three-bar linkage mechanism. This allows the load to applied at any point along the cable dependant on where the pulley sits.
Breaking load of 900kg.
5.2.3. Cable
The chosen cable for the test rig is a fibre Dynex cable which is shown in figure 11.
Figure 11: Dynex Cable (Image from: www.strongrope.com/dynex)
This rope has several advantages over steel cable while still capable of being used on the winch and pulleys without fraying or abrasion of the rope (strongRope, 2011).
Breaking Strength: Higher than a steel cable of the same diameter. For a cable of 6mm diameter the breaking load is 40kN which is well above the maximum design load.
Recoil: The cable does not store energy like a conventional steel cable which results in a significant decrease of the chance of cable recoil should it break.
Abrasion: Excellent abrasion resistance.
Samuel Polglase 29
5.3. Manufacture
As previously mentioned the process of developing the detailed design of the rig involves the development of the manufacturing drawings. The drawings will be used by the School of Mechanical Engineering Workshop which will manufacture each structural component of the test rig. The process of developing these drawings is an iterative process involving many changes to both the design and the drawings based on advice from those involved in the manufacturing process and also changes to the design which occur during the sizing process of the structural members.
The finished product of this process is the final manufacturing drawings which are ready for submission to the workshop staff who will then manufacture the test rig using these drawings and the following manufacturing techniques.
Cutting: The beam members of the rig will be cut to size and all burrs will be removed. Drilling: The beam members will have holes drilled in the appropriate locations ready for
assembly. Laser Cutting; The plate members will be laser cut to the required shape. Bending: Those plate members requiring bending will be bent around the required radius. Welding: The wing connections will involve welding.
Figure 12 shows a rendered CAD image of the final assembled test rig structure. All the manufacture drawings of for the test rig can be seen in Appendix C along with the drawing Bill of Materials (BOM), which lists every component which is contained within the entire assembled structure including all fasteners and non-structural components.
Figure 12: Final Assembled Test Rig Structure
Samuel Polglase 30
6. WING
The wing is the other major design and construction component of the project. The wing does not contain as many structural components as the test rig but presents more challenges in terms of the material, shape of the components which comprise the wings structure and the manufacturing which is needed to produce the components. The possibility of obtaining an unused wing or components of a wing from some industry source was investigated with the hope of reducing or eliminating the need for the time expensive manufacturing associated with the wing and also to reduce the overall cost. Such a wing or wing components would require some machining work and possibly the addition of designed components in order to meet the requirements for a suitable comparison between the wing and the BSM.
However no such wing structure could be sourced which meant the wing had to be fully designed and built for the project. As with the test rig, the first step in the design of such a wing is to establish a technical task which summarises the design requirements for the wing. From this technical task the detailed design of the wing components can follow.
6.1. Technical Task
A small design technical task is established in order to define the design limitations and requirements for the wing.
6.1.1. Size
The wing should fit within the test rig and be a suitable size for connection between the end of the spars and the connection points on the test rig.
6.1.2. Geometry
The geometric parameters of the wing should result in a wing which is primarily not complex to build. This is the largest limitation for the wing and as such the geometry of the wing should be simple meaning, no taper ratio, no twist and a symmetric cross section. The wing should be swept to induce a torsional moment on the wing when the force is applied.
6.1.3. Material
The wing should be constructed with; if possible, standard aircraft grade aluminium 2024 T3 which has good properties particularly in structural rigidity. If this is not possible the wing should be constructed using structural grade aluminium which is available as off-shelf extrusions to reduce manufacture time.
6.1.4. Joints
Samuel Polglase 31
The various wing components should be joined using where possible aircraft standard techniques, however if these methods are too expensive or time consuming another method should be employed.
6.2. Geometric Parameters
The chosen geometric parameters based on the above technical task are listed below. Due to the fact that there is no need for components outside of the main and auxiliary spar such as the flaps, ailerons, etc. to be modelled, the wing will only consist of the spars and rib structure inside the two spars.
The geometric parameters of the wing which were chosen are as follows:
Span = 1.8m Root Chord = 0.71m Front Spar Location = 0.1*Root Chord Rear Spar Location = 0.8*Root Chord Taper Ratio = 1 Camber = 0 Sweep = 10°
As previously explained the skin structure of the wing is not modelled due to the complexity of manufacturing and assembling the skin to the other wing structural components. This changes the way that the wing carries the applied load in the following ways.
The skin (and accompanying stringers) will normally carry a large amount of the stress due to bending. If the skin is removed the spars will carry the entirety of the bending.
The skin will normally absorb the majority of the shear stress due to torsion which is caused by the aerodynamic twist of the wing. Without the skin the ribs and spars will work together to carry this torsion.
6.3. Wing Loads
The total load applied to the wing as established in the project objectives is 1000kg/m2. The total area of the wing which is to be constructed is just below 1m2 and so for continuity between the load designed for the rig, as in section 5.1.1.1, and the wing, a total load of 1000kg was chosen as the maximum design load for the wing. The safety factor which was chosen for the wing design was 1.2 which is often used within the aeronautical industry (Stinton D, 2001). This results in a total design load of.
PW = 1000*9.81*1.2 =11772N
The load is broken up into three separate loads applied along the length of the wing. The magnitude and location of application of these loads is based on the lift distribution of a wing which has a taper ratio of 1. This lift distribution can be assumed to be constant along the span of the wing with a quick reduction of the lift when the tip of the wing is reached (Corke, 2003). This assumed lift distribution is illustrated in figure 13.
Samuel Polglase 32
This lift distribution is broken up into 3 equivalent point loads of magnitude and applied distance from the wing root as shown in figure 13. A summary of these loads is given below.
P1 = (2/5)*PW = 4709N at 365mm from the wing root. P2 = (2/5)*PW = 4709N at 1097mm from the wing root. P3 = (1/5)*PW = 2355N at 1567mm from the wing root.
These loads are all below the loads used for the design of the test rig due to the larger safety factor used for the test rig. The final length of the wing has been reduced to correspond with this location of the final applied load P3, as above, as there is no need to construct the structure outside the influence of the applied load because it will not carry any load and is not required for the comparison.
6.4. Spar Sizing
The spars have been sized based upon the maximum bending moment and shear force that they will experience. The front spar must resist the entire bending moment of the wing and half of the vertical shear load and the rear spar must resist the other half of the vertical shear force.
The maximum bending moment that the front spar must resist is 10.57kN.m and half of the vertical shear load that each spar must resist is 5.88kN. Based on these maximums the cross section of each spar which can resist these loads has been calculated and can be seen in figure 14. All calculations for the spar sizing were done using the same equations outlined in sections 5.1.3 and 5.1.4.
(9/10)Span
(3/5)Span
(1/5)Span
L(y)
Y
(2/5)LT (2/5)LT
(1/5)LT
LT
Figure 13: Assumed wing lift distribution with magnitude and location of summed point loads.
Samuel Polglase 33
Figure 14: Main (a) and Auxiliary (b) spar cross section dimensions
The dimensions as explained in figure 14 are stated below:
Wfs = 80mm Hfs = 80mm tfs =6.0mm Wrs = 20mm Hrs = 50mm trs = 1.6mm
The spar material was chosen to be Aluminium 6082-T5 for the following reasons:
Lightweight material. Readily available in the required sections. Easily manufacturable. Suitable material properties:
o Ultimate yield strength: σy = 270MPa.
6.5. Rib Sizing
The sizing of the ribs is based upon shear stress due to the torsion which the ribs must resist. This shear stress can be calculated according to the shear stress for thin plates as shown below (Flabel, 2005)
퐹 =3푇푏푡 1 + 0.6
푡푏 (15)
In this case br is the largest dimension of the plate or rib and is equal to the required length which is 0.68m. The dimension t is the width of the airfoil at its largest point and is equal to 0.12m. The design torque T for this equation can be chosen arbitrarily as its required magnitude is not important, only
a)
b)
Wfs
Hfs
2tfs
tfs Hrs
Wrs
trs
Samuel Polglase 34
that some torque is applied to the wing so that the resultant twist can be measured. However, this torque would normally, in the case of aircraft design, be computed by using the distance between the wings aerodynamic centre, where the aerodynamic load acts from and the geometric centre of mass. This distance is the lever arm which results in a torque acting about the geometric centre of mass. This process was undertaken based on the geometric centre of a symmetric airfoil and the assumption that the aerodynamic centre of pressure is located at 25% of the chord length. This results in a design torque load of 1390N.m
If this torque and the geometric lengths, b and t, are used in equation 15 then the shear stress due to torsion is calculated as being:
퐹 = 471푘푃푎
In order to calculate the required thickness of the rib web based on this shear stress equation 16 (Flabel, 2005) is employed.
(퐹 )휂 =
휋 퐾 퐸12(1− 휇 )
푡푏 (16)
The parameters as outlined by Flabel, 2005 in equation 16 are as follows:
Ks = 6 ηs = 1.0 µ = 0.33 b = 0.12m – t as in equation 15. Ec = 73x109
With these parameters as the input and solving for the thickness, t, the solution for the thickness of the ribs tr is:
푡 = 0.1295푚푚 = 1.0푚푚
This thickness is rounded to 1mm due to the availability of material in this thickness.
In order for the rib to be manufactured a strip must be added to the outside of the rib to maintain its rigidity. This is because during the manufacture the flat pattern of the rib, as shown in figure 15 must have several groves cut into it so that it can be bent into the final desired shape. These cuts will act as barriers for the flow of shear through the rib and will be regions of stress concentrations. In order to maintain the shear flow and reduce the stress at these locations a strip is added to the rib to retain this rigidity and shear flow. This strip is riveted to the rib.
Figure 15: Flat pattern of the rib
Samuel Polglase 35
6.6. Wing Connection Joints
The connection joints between the wing and the test rig have been designed based on industry practice while considering the simplest manufacturing process for developing these connections.
The connection joint for the main spar should resist the moment of the wing and a component of the vertical shearing force while the rear spar resists only the remaining component of the vertical shear as shown in figure 16 (Nui, 1999)
Figure 16: Standard root connection joints for front and auxiliary (rear) spars (Nui,1988)
The connection joint between the wing and the test rig will comprise of the three components as shown from the CAD model in figure 17 and explained below.
Figure 17: Front Spar and test rig connection interface
Where: o A: The part of the joint which connects to the structure. o B: The part of the joint which connects to the wing.
A
B
Samuel Polglase 36
COMPONENT A:
The final design of component A for the main and auxiliary spars is shown in figure 18. The size and thickness of these components which comprise these two joints has been calculated using the connection equations outlined in section 5.1.4. The main features of this joint are as follows:
Steel extruded sections used for all components to allow for welding of the joint and ease of component procurement.
Welding used as the method for all joints. This method was chosen as it was the most obvious choice based on the type of joints needed.
The joints bolt to the test rig. This results in the movement of these joint along the root beam length being a relatively simple process if a change of the wings location is desirable. This gives flexibility to the design.
Figure 18: Main (right) and Auxiliary (left) test rig connection joints
COMPONENT B:
The final design for the main and auxiliary spars is shown in figure 19. The size and thickness of these components has been calculated using the connection equations outlined in section 5.3.1. The main features of the main spar connection joint as shown in figure 19 are as follows:
Steel plate sections to allow welding of the joint without reduction in the material yield strength. This also allows for easy component procurement.
The joint resists the entire bending moment experienced by the wing as per the standard method outlined in figure 16.
The main features of the auxiliary spar connection joint in figure 19 are as follows:
Aluminium bent plate to reduce weight and for the ease of product procurement. Joint only resists a portion of the shear load experienced by the wing.
Samuel Polglase 37
Figure 19: Main spar connection joint (left) and Auxiliary spar connection joint (right)
BOLTS:
The components are all joined using hex 8.8 bolts with the properties outlined in section 5.1.4. The size of theses bolts, which have been calculated using equations 12, 13 and 14 are as follows:
Bolts between connection A and B for the main spar: 2 x 26mm diameter. Bolts between connection A and B for the auxiliary spar: 1 x 16mm diameter. Bolts between connection B for the main spar and the main spar: 12 x 12mm diameter. Bolts between connection B for the auxiliary spar and the auxiliary spar: 5 x 4mm diameter.
6.7. Linkage Mechanism
The interface between the cable and wing is a three bar linkage type mechanism as shown from the CAD model in figure 20. This mechanism allows a cable to be strung between the two vertical links (shown as green in figure 20) on which a pulley will run. This allows for easy application of the load at any point along this cable such that the load can be applied at either the shear centre of the wings cross section or at some distance away from this shear centre so that a torque moment can be induced on the wing.
Figure 20: Three bar linkage mechanism for application of the load from the cable to wing.
The vertical linkages attach to the spars using brackets which apply the load through the shear centre of the spars which results in no torque being applied to the spars which would result in a twist of just the spar cross section, which is not desirable. The detailed design of this linkage mechanism was undertaken using the equations outlined in section 5.1.
The manufacture drawings for all of the wing components are included in Appendix C.
Samuel Polglase 38
7. EXPERIMENTAL MEASUREMENT EQUIPMENT
7.1. Load Cells
‘S’ Type load cells as shown in figure 21 have been chosen as the method to measure the applied load through the cable system to the linkage mechanism attaching to the wing. The type of load cells used for the measurement is the A&D Weighing Australia LC-1205-K500. These load cells have the following features:
5kN capacity. Compact, lightweight and easy to use. Pre-installed cable suitable for connection to the available data logger. Moisture proof and temperature compensated. 200% maximum safe overload.
Figure 21: A&D Weighing Australia 'S' Type Tension and Compression Load Cells (Image from: www.aandd.com.au)
Three of the LC-1205-K500 load cells are installed on the test rig to measure the applied load through the three cables.
7.2. Strain Gauges
Strain gauges allow the strain present at the surface of a material to be measured by measuring the voltage change across a circuit due to the expansion or contraction of the gauges material as they act as resistors in the circuit. Two types of strain gauges are required to measure the two types of strain present in the wing spars, the strain due to bending and strain due to shear. The two types of strain gauges used are outlined below.
Linear type strain gauges are used to measure the strain due to bending on the main and auxiliary spars. The linear type strain gauge chosen has the part number EA-13-250BF-350 and can be seen in figure 22. The data sheet for this gauge is included in appendix D along with a brief explanation of the relevance of each component of the part number.
Samuel Polglase 39
Figure 22: Vishay Precision Group EA-13-250BF-350 linear type strain gauge (Vishay Precision Group, 2010).
The strain due to bending is measured at four points along the length of the main spar. Four points are chosen as this will provide enough data for a suitable comparison between the two experimental data and BSM data. To measure the strain at each point four strain gauges are required such that two gauges form a half Wheatstone bridge at both the top and bottom surface of the spar. Thus for the front spar a total of 16 of these linear type gauges have been installed on the webs. In addition, 4 of these linear type gauges have been installed at the root of the auxiliary spar. This spar is not meant to undergo any strain due to bending meaning that the gauges installed here serve as a check to ensure this condition is met by the auxiliary spar.
Rosette type strain gauges are used to measure the strain due to shear forces on the main and auxiliary spars. The pattern of these gauges is aligned at 45⁰ to the bending axis of the components under investigation (horizontal axis of the spars in this case) such that the shear strain can be measured. The rosette type strain gauge chosen has the part number CAE-13-187UV-350. The components of this part number correspond to those described for the linear type gauge (refer to appendix D) with the main difference being the grid geometry UV which corresponds to a rosette type pattern and a different active gauge length of 187. The CAE-13-187UV-350 can be seen in figure 23.
Figure 23: Vishay Precision Group CEA-13-187UV-350 rosette type strain gauge (Vishay Precision Group, 2010)
On the main spar the strain due to shearing forces is measured at four points along its length. At each location two gauges are used on either side of the spar at the centre of the inner web and the average of these two gauges gives the result of the shear strain at this point. This results in eight of the rosette type gauges used on the main spar. The shear strain of the auxiliary spar is measured at the root of the
Samuel Polglase 40
spar to verify the maximum shear stress experienced by this spar. As with the main spar, the average result between the installed gauges is used as the final experimental result.
7.3. Deflection Measurement
At this stage of the project, measuring the deflection of the wing is achieved through the use of a tape measure. The distance of the wing from the ground is measured before the load is applied and then once the load has been applied the distance is again measured. The deflection can be obtained by a simple subtraction of the final distance from the initial distance. It was hoped that laser deflection recording instruments could be installed to more accurately measure the deflection of the wing, including not just vertical deflection, but twist of the wing as well. This was not achieved and is considered future work to improve the quality and accuracy of the experimental data which can be obtained from the experiment.
7.4. Data Interface and Software
The management and recording of the voltage signals from the load cells and strain gauges is achieved through the use of National Instruments terminal blocks and software. The cables from the load cells and gauges feed into these terminal blocks which are interfaced to a computer through the use of the LabVIEW (Laboratory Virtual Instrumentation Engineering Workbench) software.
The cables feed into the national instruments SCXI-1314 front-mounting terminal block as shown in figure 24. These terminal blocks are connected into the SCXI-1000 chassis, also shown in figure 24, which houses the terminal blocks, compiles the signal and forms the interface between the computer and the terminal blocks.
Figure 24: National Instruments SCXI-1314 Terminal Block (left) and SCXI-1000 Chassis (right) (Image from: www.ni.com)
The signal from the terminal block is accessed through the LabVIEW software which is also a product of National Instruments. LabVIEW is a visual programming language which allows the set-up of an automated virtual instrument for the purpose of processing and measuring equipment in a laboratory type environment. LabVIEW is able to detect the signal from the chassis and these signals can be separated into those corresponding to their position in the terminal blocks. Once these signals have been separated a virtual instrument can be built which allows the signals to be visualised on the screen and recorded to a designated folder. The block diagram and front panel environments of the virtual instrument as well as a flow chart describing the steps of the block diagram can be seen in appendix E.
Samuel Polglase 41
8. COMPARISON RESULTS
8.1. Comparison Process
Obtaining the required data needed for the comparison involves firstly recording the experimental data from the test rig and wing experiment. Then the theoretical data from the BSM can be generated and the two can be compared.
The experimental data is obtained by loading the wing using the winches and locking the winches to sustain the applied load. The LabVIEW virtual instrument described in appendix E has a feature which allows the user to record the experimental data to a text file in a location chosen by the user. This text file contains the load, through each of the load cells, and the stress at each strain gauge location, recorded ten times over a short time period. The text file allows the average of the load and stress data to be taken. These averages form the values which are used in the comparison. Each load sequence is repeated three times in order to obtain 3 average values which are used to graph the median value and standard deviation for each data point.
The generation of the theoretical data from the BSM is a quick and relatively simple procedure. Firstly the geometric inputs of the wing are put into model such that the wing generated by BSM has the same length and cross sectional properties. The wing in BSM is chosen to have 4 beam elements, giving it the same number of data points as the physical data will have (four points for strain gauge locations along the front span length). The element boundaries will be the points where the BSM data is calculated, and although these will not correspond exactly with the location of the recorded strain data on the physical wing, they will allow the trend of stress along the wing to be compared, which is the desire. However for deflection comparison, the deflection of the physical wing can be taken at any point along its length meaning that the data points will line up exactly. Once the geometric properties are input in the BSM the load cell data is used as the BSM load input data such that the loads are identical and applied at the same location along the length of the wing. The model is then run and the required deflection and stress data is read out from the model.
8.2. Load Values
For the comparison of the data five different load cases where chosen in order to give a good range of loading scenarios. These load cases are as summarised in table 2.
Table 2: Experimental Loading Scenarios
SCENARIO P1 P2 P3 Tip Load 1 0 0 400 Tip Load 2 0 0 630 Tip Load 3 0 0 800 Distributed Load 1 610 640 300 Distributed Load 2 950 900 420
Samuel Polglase 42
The distributed loads are chosen to simulate the spanwise load distribution a wing experiences during normal flight as illustrated in figure 13. Distributed load 1 is chosen as the nominal cruise flight condition of the aircraft and distributed load 2 as the case where the aircraft experiences an increased load factor of 0.5, such as when undergoing a pull up manoeuvre. Note that the for the distributed loads the P1 and P2 values should be the same (refer to figure 13), however it was difficult to do this in practice due to the way the applied loads interact as increasing the load at one station will decrease the load at the other two stations.
8.3. Vertical Deflection
Due to considerable movement in the lug joint between the front spar and test rig the deflection measurements were carried out after an initial tip pre-load of 300N was applied to the wing. This pre-load moves the deflection of the wing through an un-linear stage until the joint can be considered to be acting as a fixed joint, which is the assumption in the BSM.
In general the BSM shows good correlation for the deflection comparisons. In figure 25 the deflection due to tip load 2 is shown and in figure 26 the deflection due to distributed load case 2 is shown.
Figure 25: Front spar vertical deflection for tip load of 630N
Figure 26: Front spar vertical deflection for distributed load case 2
-10
-8
-6
-4
-2
00 0.5 1 1.5 2
Front Spar Vertical Deflection: Tip Load: 630N
Experimental
BSM
-20
-15
-10
-5
00 0.5 1 1.5 2
Front Spar Vertical Deflection: Distributed Load: Case 2
Experimental
BSM
Samuel Polglase 43
These figures show that the BSM has the same general trend with the experimental data but its values are consistently lower by an average of 21.8%, which is calculated in appendix F. Note that this is the average difference with the difference at the root ignored, because of the consistently large difference at this point, which is discussed further in section 8.5.
Figure 27 displays the increase in deflection at the four points along the wing due to an increasing tip load. This confirms that the increase in deflection is linear, as would be expected for the case of a tip load.
Figure 27: Front spar change in deflection due to increasing tip load.
The deflection of the rear spar was not taken into consideration as the BSM assumes the rear spar is clamped, along with the front spar. Further modification to the BSM could include a user choice to specify whether or not the rear spar is clamped or free to rotate about the joint, however for the purpose of validating the deflection computation of the BSM the accurate correlation for the front spar is sufficient as this deflection is calculated using the beam theory.
8.4. Bending Stress
As with the deflection comparisons the BSM generally shows good correlation for the bending stress comparisons in both the case of a single tip load and a distributed load. Figure 28 shows the comparison for the tip load case 3 and figure 29 for the distributed load case 1.
-12
-10
-8
-6
-4
-2
0400 450 500 550 600 650 700 750 800 850
Defle
ctio
n (m
m)
Tip Load (N)
Change in Deflection with Tip Load
0.4m
0.8m
1.2m
1.6m
Samuel Polglase 44
Figure 28: Front spar bending stress for tip load of 800N
Figure 29: Front spar bending stress for distributed load case 1
Percentage comparisons for the bending stress due to tip loads at the experimental points is possible by means of a linear curve fit using the four points. This allows the average percentage difference between the two sources to be calculated at 13% with an increasing difference as the tip load increases. These percentages can be viewed in appendix F. The trends in figures 28 and 29 show that values computed by BSM are generally higher than the experimental data and the table in appendix F puts this figure at approximately 13% higher. This low difference and similar trends along the length of the wing shows that there is good correlation between the physical data and BSM data for the case of bending stress.
Figure 30 displays the increase in bending stress at the four strain gauge points due to an increasing tip load. As was the case with the deflection in figure 27 the increase in bending stress is linear, which is the expected case for a tip load.
05
101520253035
0 200 400 600 800 1000 1200 1400 1600
Stre
ss (M
Pa)
Distance from Wing Root (mm)
Front Spar Bending Stress: Tip Load: 800N
Experimental
BSM
0
10
20
30
40
0 200 400 600 800 1000 1200 1400 1600
Stre
ss (M
Pa)
Distance from Wing Root (mm)
Front Spar Bending Stress: Distributed Load: Case 1
Experimental
BSM
Samuel Polglase 45
Figure 30: Change in bending stress at strain gauge location for increasing tip load
Figure 30 also displays the increase in the bending stress of the rear spar with increasing tip load. The bending load carried by the rear spar should be zero because the joint is pinned at this location, however the data clearly indicates the spar does carry a small portion of the load. However this portion is very close to zero as for the load of 800N the portion carried by the rear spar is only 1.3% or 0.68MPa of the total load of 51.46MPa. It is also important to note that this small amount of bending stress carried by the rear spar reduces the amount that the front spar is subjected to, which will contribute to the difference between the data for the front spar bending stress
8.5. Shear Stress
There is considerably less correlation for the case of shear stress as illustrated in figure 31 which is typical of the comparison for shear stress along the length of the front spar for all load scenarios. Figure 32 displays the increase in shear stress at the strain gauge location for an increasing tip load.
Figure 31: Front spar shear stress for tip load of 800N
0
5
10
15
20
25
300 400 500 600 700 800 900
Stre
ss (M
Pa)
Tip Load (N)
Change in Bending Stress with Tip Load
Front Spar Gauge 1
Front Spar Gauge 2
Front Spar Gauge 3
Front Spar Gauge 4
Rear Spar Gauge
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000 1200 1400 1600
Stre
ss (M
Pa)
Distance from Wing Root (mm)
Front Spar Bending Stress: Tip Load: 800N
Experimental
BSM
Samuel Polglase 46
Figure 32: Change in shear stress at strain gauge location for increasing tip load
The increase in shear stress is again linear, which would suggest that the strain gauges are operating properly, however the difference in shear values shown in figure 31 when the shear values should be constant for a single tip load indicates an issue with the gauges, particularly at the points closest to the root of the wing. This probable issue with the gauge signals was unable to be rectified before the end of the project meaning that the shear stress computation step of the BSM cannot be validated based on the current experimental data.
8.6. Discussion
Ignoring the case of shear stress, the experimental data and BSM displayed good correlation, with the experimental values being on average below the values computed by the BSM for the same load, geometry and material properties. For the deflection the average difference between the data was approximately 20%, if the large difference at the root is ignored. The main source of the difference between the experimental and BSM data, which is seen most profoundly at the measurement taken at 0.4m, is the looseness of the bolted connection between the front spar and test rig. Due to slightly different tolerances on the bolt holes there is movement of the joint which results in a joint which is not ideally fixed. This gives rise to the measured deflection, being on average greater than that which is predicted by the theory contained in BSM, which assumes a perfectly fixed joint.
Another source of error is the method which was employed in the deflection measurement. The method used was to employ a simple tape measure, which is quite mundane and has an error of ±1mm at best. This error will have a greater effect the smaller the deflection and hence a greater error near the root of the wing, where the deflection predicted by BSM is usually less than 1mm.
Considering these two errors, which appeared to have a considerable affect, an average correlation of approximately 20% down the length of the wing can be said to be acceptable for the purpose of validating the BSM deflection computation. Note that only the vertical deflection has been compared. The twist of the wing was not compared due to time constraints.
0
0.5
1
1.5
2
2.5
300 400 500 600 700 800 900
Stre
ss (M
Pa)
Tip Load (N)
Change in Shear Stress with Tip Load
Front Spar Gauge 1
Front Spar Gauge 2
Front Spar Gauge 3
Front Spar Gauge 4
Rear Spar Gauge
Samuel Polglase 47
The movement of the fixed joint also appears to affect the results of bending stress as the experimental data is also on average below the values computed for BSM. However the fact that the rear spar is carrying some of this bending load would also contribute to a lower portion being carried by the front spar, leading to an increase in the difference between the two data sources. However, as was the case with the deflection, on average the two data sources display good correlation with the experimental data being on average 13% less than the BSM values but increasing as the load increases. As with the deflection comparison, considering the effect of the errors this correlation is acceptable for the purpose of validating the BSM bending stress computation.
The result of the shear stress comparison is inconclusive and the BSM shear stress computation step cannot be validated using this data. The most likely source of the error in the experimental data is an issue with the installed strain gauges and this was unable to be rectified due to time constraints. An investigation into the accuracy of the shear strain signals is required by the installation of additional gauges at the four points to check their accuracy. Once this has been completed then a comparison should lead to a validation of the BSM shear computation step.
The result of the comparisons presented is the validation of both the vertical deflection and bending stress computation steps of the BSM. The experimental data compiled for the shear stress comparison could not be used for validation of the BSM shear stress computation and further investigation and data will be required before this can be rectified. However, since the deflection and bending stress computations form the large majority of the beam theory based computations which effect the sizing of the structural members and subsequent aerodynamic loads (due to the new deflection and structure cross section) the validation of these components results in the desired confidence in the beam theory based calculations of the BSM.
Further work to improve the accuracy of the deflection and bending stress data includes improvement of the fixed front spar connection, rear spar pinned connection and confirmation of strain gauge signals by instillation of more gauges to measure the bending stress results. For a complete validation of the BSM stress computation the shear stress computation still requires validation.
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9. BEAM MODEL MODIFICATION
As a further goal for the project a modification was made to the BSM with the aim of increasing its computational capability. This modification was set as a project goal to continue collaboration with the DLR and bring the BSM closer to the goal of it being used in the conceptual design stage of new aircraft concepts.
Before the commencement of this project the BSM used a standard symmetric airfoil scaled to size, based on the chord length and thickness ratio defined by the user, to compute the aerodynamic loads. This was suitable for the initial stages of the models construction and preliminary refinements however in order to improve the models flexibility it was deemed a necessary addition to allow the user to define any airfoil shape for this computation step.
This addition has been made to the Matlab code of the BSM and the user is now able to input any airfoil shape as defined by a text file. This flexibility is illustrated in appendix G.
10. MANAGEMENT
10.1. Project Roles
The project is undertaken by one student meaning all the roles which must be undertaken in order to realise a successful completion of the project objectives must be considered and performed by the student. As well as the roles which the student must perform there are several other stakeholders which are a part of the project as either partners of the project or users of the end product. These stakeholders are as follows.
University of Adelaide School of Mechanical Engineering (UASME): The owners of the final test rig and wing experiment and funders of the project.
DLR: The owners of the BSM and are interested in the findings of the comparison and the continued improvement of the BSM.
UASEM Workshop: Will oversee and complete all of the manufacturing components of the project.
A summary of the roles the student must perform and the stakeholder is shown in appendix H in the Responsibility Assignment Matrix (RAM).
10.2. Risk Management
An assessment of the risk associated with undertaking the entire project was undertaken. This assessment is summarised in appendix I which contains the project risk register for the project. This risk register categorises all the associated risks with undertaking the project, scores these risks to
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assess their occurrence, severity and detectability and then moves on the give information associated with risk prevention, contingency and action.
A risk assessment of the test rig and wing experimental apparatus was also undertaken and is summarised by the safe operating procedure (SOP) developed as a result of this risk assessment. The SOP can be found in appendix I.
10.3. Project Cost
The cost of the project should be kept to a minimum where possible, however the quality of the final experimental test rig is important and therefore there should be a balance between these two factors. The total cost of producing the test rig and wing structure including all structural and experimental data and all labour costs is $17,851.90. A detailed breakdown structure of the costs can be found in appendix J.
This final cost of $17,851.90 is compared to the $20,000 which would be the cost associated with purchasing the TrueStructuresTM structural laboratory and it can be seen that the cost of producing the project test rig and wing experiment is competitive. This is coupled with the added benefits of a more flexible structure and load application system resulting in a good investment by the university.
10.4. Time Management
Due to the project being undertaken by a single student the management of time throughout the life of the project was not a difficult process. The tasks which had to be completed in order to realise the project goals where broken down into packages of work and these packages where allocated a period of time when they had to be completed. This time summary is shown in the form of a Gantt Chart in appendix K.
The total time spent undertaking the project tasks by the student is 519 hours. A breakdown of this time spent by the student on a month by month basis is also shown in appendix K.
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11. CONCLUSION
The project has seen the successful design and construction of a test rig and wing structure suitable for validating the DLR BSM. Both the test rig and wing structure have been built to fulfil all of the design requirements set down in their respective technical tasks which results in the successful completion of the first two project goals. Load cells and strain gauges have been successfully installed and used to measure the applied load and resulting strain on the wing structure. The deflection of the wing has been successfully measured, but will need improvement in the future to improve accuracy and efficiency. The successful measurement of the load, deflection and strain results in the successful completion of the third project goal.
Comparisons between the experimental data and the equivalent BSM data has resulted in the successful validation of the vertical deflection and bending stress computation steps of the BSM. The shear stress comparisons have led to inconclusive results indicating possible issues with the installed strain gauges. This issue was unable to be rectified before the end of the project and thus the shear stress computation step of the BSM was unable to be validated, however a small amount of work should see the successful validation of this step. The result of the deflection and bending stress comparisons is a successful validation of the core beam theory contained in BSM and the confidence that this model accurately calculates these quantities meaning that the majority of the final primary goal is realised.
Of the extended goals, the first has been realised which has improved the flexibility of the BSM to include a user option to define the airfoil shape; however the other two were not completed.
The final result of the project is an increased confidence in the ability of the BSM to accurately compute the quantities required to give an accurate estimation of the wing box weight in the conceptual design stage. The test rig and wing structure experiment developed to achieve the validations, shown in figure 33, will now form a valuable education tool in the field of aircraft structures.
Figure 33: The final assembled rig and wing
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REFERENCES
Abbott, IH, von Doenhoff, AE 1959, Theory of Wing Sections Including a Summary of Airfoil Data, Dover Publishing
AIAA Aerospace Design Engineers Guide, Fourth Ed, AIAA, 1998
Bindolino. G, Ghiringhelli. G, Ricci. S, Terraneo. M, ‘Multilevel Structural Optimization for Preliminary Wing-Box Weight Estimation’, Journal of Aircraft, Vol. 47, No.2, 2010
Cavagna. L, Ricci. S, Riccobene. L, ‘A Fast Tool for Structural Sizing, Aeroelastic Analysis and Optimization in Aircraft Conceptual Design’, 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, California, 2009.
Corke, TC 2003, Design of Aircraft, Prentice Hall, United States of America
Dorbath, F, Differences Analysis between Beam and Shell Theory in Preliminary Aircraft Design, Technische Universität München, 2009
Dugas, M, Grabietz, M. 2004: Manual for FAME-W Release 4.00 F2, Issue 1.0, 2004
Flabel, JC 2005, Practical Stress Analysis for Design Engineers, Lake City Publishing Company, Idaho
Gere, JM & Timoshenko, SP 1997, Mechanics of Materials, PWS Publishing Company, Boston, MA
Nui, MC 1988, Airframe Structural Design, Hong Kong Conmilit Press Ltd, Hong Kong
Nui, MC 1999, Airframe Stress Analysis and Sizing, Hong Kong Conmilit Press Ltd, Hong Kong
Oberg. E, Jones. F. D, Horton. H. L, Ryffel. H. H, 2000, ‘Machinery’s Handbook Twenty-Sixth Edition’, Industrial Press Inc, New York.
Petermeier. J, Radtke. G, Stohr. M, Woodland. A, Takahashi. T, Donovan. S, Shubert. M, ‘Enhanced Conceptual Wing Weight Estimation Through Structural Optimization and Simulation’, 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Texas, 2010.
Stinton D 2001, The Design of the Aeroplane, Blackwell Science, Great Briton.
Van der Valen A, Kelm R, Kokan D, Mertens J, ‘Application of MDO to Large Subsonic Transport Aircraft, 38th AIAA Aerospace Sciences Meeting & Exhibit, Reno, 2000
A&D Weighing Australia, 'S' Type Tension and Compression Load Cells, 2011. Last viewed 25/05/2011
<http://www.aandd.com.au>
Advansa, Jarrett Boat and Trailer Winch Catalogue, 2011, South Australia
National Instruments, SCXI-1314 Terminal Block and SCXI-1000 Chassis, 2011. Last viewed 18/07/2011
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<http://www.ni.com>
Ronstan, Ronstan Product Guide, 2011. Last viewed 13/04/2011
<http://www.ronstan.com.au>
strongRope, Dynex and Dynex Dux Product Information, 2011. Last viewed 01/04/2011
<http://www.strongrope.com/dynex.htm>
Turbine Technologies, Laboratory Systems Catalog, 2010, USA
Vishay Precision Group, Precision Strain Gauges Interactive Data Book, 2010. Last iewed on 14/08/2011
<http://www.vishaypg.com>
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APPENDIX A
The Euler-Bernoulli beam equation for the deflection of a beam with two nodes and six degrees of freedom is as follow:
퐾푑 = 푃
2,
2,
2,
2,
2,
2,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
1,
1,
1,
1,
1,
1,
22
2
233
33
22
2
2323
2323
0000000000
040060020060
004006002006
0000000000
06001200600120
00600120060012
0000000000
020060040060
002006004006
0000000000
06001200600120
00600120060012
y
z
x
y
z
x
y
z
x
y
z
x
y
z
x
y
z
x
y
z
x
y
z
x
zzzz
xxxx
zzzz
xxx
zzzz
xxxx
zzzz
xxxx
RMMPPPRMMPPP
rrrdddrrrddd
LGJ
LGJ
EIL
EIL
EIL
EIL
EIL
EIL
EIL
EIL
LEA
LEA
EIL
EIL
EIL
EIL
EIL
EIL
EIL
EIL
LGJ
LGJ
EIL
EIL
EIL
EIL
EIL
EIL
EIL
EIL
LEA
LEA
EIL
EIL
EIL
EIL
EIL
EIL
EIL
EIL
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APPENDIX B
Static analysis of the test rig structural members follows.
The following applies:
F: Applied or Reaction force. M: Applied of Reaction moment. Subscripts:
o A: Applied o R: Reaction
Refer to the free bodied diagram in figure () for the letter assigned to each connection. The test rig is symmetric about the central Y axis meaning the stress in some members is identical.
Refer to the analysis below.
Begin with the wing to find the reactions at B and C.
Sum of the moment s to find the reaction moment at C (Note only reaction at C resists moment therefore total load at each point is used in the below equation:
→ ∑(MX)C = 0 = MRC(-0.6P1-1.2P2-1.8P3) → MRC = 0.6P1+1.2P2+1.8P3
Sum of vertical forces to find the reaction force at C:
→ ∑FZ = 0 = FRC – 0.5(P1+P2+P3) → FRC = 0.5(P1+P2+P3)
Vertical reaction force at B is equal to reaction force at C for symmetrical rig.
→ FRB = FRC = 0.5(P1+P2+P3)
MRC
C
FRF 0.5P1 0.5P2 0.5P3
0.6 0.6 0.6
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MEMBER A-B-C-D
Sum of moments to find the reaction force at D:
→ ∑(MX)A = 0 = -0.2FAB – FAC + 1.2FRD → 0 = -0.2(0.5(P1+P2+P3)) - 0.5(P1+P2+P3) + 1.2FRD → 0 = -0.6(P1+P2+P3) + 1.2FRD → FRD = 0.5(P1+P2+P3)
Sum of vertical forces to find reaction at A
→ ∑FZ = 0 = FRA – FAB – FAC + FRD → 0 = FRA – 0.5(P1+P2+P3) - 0.5(P1+P2+P3) + 0.5(P1+P2+P3) → FRA = 0.5(P1+P2+P3)
There is also torsion on the member as shown below
It follows that:
→ MRA = (0.35/0.85)MRD
Sum of Torsion
→ ∑T = 0 = MRA – MRC + MRD → 0 = MRD+MRA - 0.6P1+1.2P2+1.8P3 → MRD = 0.375P1+0.75P2+1.125P3 → MRA = 0.225P1+0.45P2+0.675P3
0.35 B 0.35 0.5 D C A
FRA FAB FAC FRD
MRD MRC MRA
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MEMBER D-O-M
Sum of moments to find the force in member O-Q:
→ ∑(MX)M = 0 = -MAD + XFOQcosϴ → FOQ = MAD/Xcosϴ → FOQ = = 0.375P1+0.75P2+1.125P3/Xcosϴ
Sum of vertical forces to find the first component of the reaction at M:
→ ∑FZ = 0 = -FAD + FOQsinϴ + FRM(1) → 0 = -0.5(P1+P2+P3) + (0.375P1+0.75P2+1.125P3/Xcosϴ)sinϴ + FRM(1) → FRM(1) = 0.5(P1+P2+P3) - (0.375P1+0.75P2+1.125P3/Xcosϴ)sinϴ
FAD
D
O
M
ϴ
FOQ
FRM(1)
MAD
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MEMBER A-N-L
Sum of moments to find the force in member N-P:
→ ∑(MX)M = 0 = -MAA + XFNPcosϴ → FNP = MAA/Xcosϴ → FNP = 0.225P1+0.45P2+0.675P3/Xcosϴ
Sum of vertical forces to find the first component of the reaction at L:
→ ∑FZ = 0 = -FAA + FNPsinϴ + FLM(1) → 0 = -0.5(P1+P2+P3) + (0.225P1+0.45P2+0.675P3/Xcosϴ)sinϴ + FLM(1) → FLM(1) = 0.5(P1+P2+P3) - (0.225P1+0.45P2+0.675P3/Xcosϴ)sinϴ
FAA
A
N
L
ϴ
FNP
FLM(1)
X
MAA
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MEMBER E-F-H-I-J
Sum of the moments to find the reaction force FRK:
→ ∑(Mx)F = 0 = 0.6P1 + 1.2P2 + 1.8P3 – 2FRK → FRK = 0.3P1+0.6P2+0.9P3
Sum of vertical forces to find the reaction force FRF:
→ ∑FZ = 0 = P1 + P2 + P3 – 0.3P1+0.6P2+0.9P3 → FRF = 0.7P1
+0.4P2+0.1P3
MEMBER L-F-M
Due to the symmetry of the section it is clear that:
→ FRM(2) = 0.5FAF = 0.5(0.7P1 +0.4P2+0.1P3)
→ FRL(2) = 0.5FAF = 0.5(0.7P1 +0.4P2+0.1P3)
E F
H I J
K
FRF FRK
P1 P2 P3 0.2 0.6 0.6 0.6
0.6 0.6 M
F
L
FRL
FAF
FRM(2)
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MEMBER L-F-M
Due to the symmetry of the section it is clear that:
→ FRS = 0.5FAK = 0.5(0.3P1+0.6P2+0.9P3) → FRR = 0.5FAK = 0.5(0.3P1+0.6P2+0.9P3)
MEMBER M-Q-S
→ FAs = 0.5(0.3P1+0.6P2+0.9P3)
Thus as a check for the system the sum of forces in the z-axis direction should be equal to zero
→ ∑FZ = FAM(2) - FAM(1) - FOQz + FAs → 0.5(0.7P1+0.4P2+0.1P3) + (sinϴ/xcosϴ)( = 0.375P1+0.75P2+1.125P3) - 0.5 (P1+P2+P3)] - (sinϴ/xcosϴ)(
= 0.375P1+0.75P2+1.125P3) + 0.5(0.3P1+0.6P2+0.9P3) = 0
Shear and Moment diagrams for the members follow.
With:
→ P1 = 5000N → P2 = 3000N → P1 = 2000N → X = 0.7 → ϴ = 45°
0.6 0.6 S
K
R
FRR
FAK
FRS
ϴ
x
FAM(2)
M Q
FAM(1)
FAS FOQ
S
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1700N.m T(N.m)
M(N.m)
V(N)
-8500N.m
1000N.m 5000N
5000N
0.2 0.8 B 0.2 D C A
M(N.m)
N(N)
7225N.m
-9596N
0.8 O M D
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V (N)
M(N.m)
25500 16500
7500
12750
12250
E F
H I J K 0.2 0.6 0.6 0.6
250
7750
-2450
V (N)
M(N.m)
0.6 0.6 M L
FAF
2450
2940
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Stress due to maximum Bending moment and Shear force for the critically stressed members follows:
-2550
V (N)
M(N.m)
0.6 0.6 S R
FAK
2550
3060
S
V (N)
M(N.m)
7771
ϴ
x
FAM(2)
M Q
FAM(1)
FAS FOQ
-2550
-7225
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MEMBER E-F-H-I-J
The chosen ‘I’ Beam member has the following cross section dimensions:
H = 140mm W = 80mm t = 8mm
The following cross sectional properties:
Ix = 7.55*10-6 Q = 9.504*10-5 d = 0.07m b = 0.008m
Bending stress for the beam is:
σbmax = (25500)*(0.07)/(7.55*10-6) = 236MPa < 240MPa – OK.
Shear stress for the beam is:
τVmax = [(12750)*(9.504*10-5)]/[(7.55*10-6)*(0.008) = 20MPa < 140MPa – OK.
MEMBER M-Q-S
The chosen SHS cross section has the following dimensions:
H = 101.6mm t = 6.35mm
Thus the beam will have the following cross sectional properties:
Ix = 3.675*10-6 Q = 7.605*10-5 d = 0.058m b = 0.00635m
Bending stress for the beam is:
σbmax = (11858)*(0.058)/(3.675*10-6) = 187MPa < 240MPa – OK.
Shear stress for the beam is:
τVmax = [(12763)*(7.605*10-5)]/[(3.675*10-6)*(0.00635) = 41MPa < 140MPa -- OK
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APPENDIX C
ALL MANUFACTURE DRAWINGS PRODUCED FOR THE PROJECT.
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APPENDIX D
Below is the data sheet for the linear strain gauge used with part number EA-13-250BF-350.
The components of the part number are explained below with a brief explanation of why they are applicable:
E – Open faced cast polyimide backing. Suitable for general purpose static testing. A – Constantan alloy material. Suitable for general purpose static testing and the most widely used
alloy material used (Vishay Precision Group, Precision Strain Gauges, Interactive Data Book, 2010). 13 – Self temperature compensation number which is 13 for aluminium. This number corresponds
to the thermal expansion coefficient of the material which the strain gauges attached to. 250 – Active gauge length in 0.001in. This length is not highly important but is chosen to be as large
as possible to assist in attachment to the test rig. BF – Grid and Tab geometry. Chosen for the simplicity and based on common selection for this type
of application (Vishay Precision Group, Precision Strain Gauges, Interactive Data Book, 2010). 350 – Resistance of the gauge in Ohms. This is a resistance commonly used in experimental stress
analysis testing (Vishay Precision Group, Precision Strain Gauges, Interactive Data Book, 2010).
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Below is the data sheet for the linear strain gauge used with part number CAE-13-187UV-350. The same part number explanation as described for the linear gauge are applicable for this rosette type gauge except for the grid geometry and active gauge length.
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APPENDIX E
The LabVIEW software was used to establish a virtual machine (VI) in the PC which was capable of detecting the load cell and strain gauge signals from the terminal blocks and chassis. This VI has two components, firstly the Block Diagram which forms the working part of the VI and secondly the Front Panel which forms the visual interface of the VI. Both are shown and explained in this appendix.
The VI block diagram is shown visually in the following figures 2 and 3 and is explained below by means of the flow chart.
DAQ Assistant
The signals from the terminal blocks are read and added into the block diagram. The load cells are added as a ‘Custom Voltage Excitation’ input and the strain gauges as a ‘Strain
Signal Select – Load Cells
The load cell signals are extracted from the DAQ Assistant by the ‘Signal Select’
Signal Select – Bending Strain
The signals from the strain gauges undergoing bending strain are extracted from the DAQ Assistant by the ‘Signal Select’ Function.
Signal Select – Shear Strain
The signals from the strain gauges undergoing shear strain are extracted from the DAQ Assistant by the ‘Signal Select’ Function.
Formula Convert from Voltage to kg to N
Successive formulas converting the Voltage signals from the 3 load cells into Kg and then N readings.
Formula calculate average strain
Two strain signals at the same location used to calculate the average bending strain at that location.
Formula calculate average strain
Two strain signals at the same location used to calculate the average shear strain at that location.
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The front panel is the means by which the user can interface with the VI. The panel allows the user to start the VI and record the data from the load cells and strain gauge signals. The front panel developed for this VI is shown in figure 4.
Load Cell Read-Out Signals.
Front Spar Bending Strain
Read-Out
Rear Spar Bending Strain
Read-Out Signals.
Front Spar Shear Strain Read-Out
Signals.
Rear Spar Shear Strain Read-Out
Signals.
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APPENDIX F The percentage difference tables for the front spar deflection and bending stress are contained below.
FRONT SPAR DEFLECTION % DIFFERENCES
Load Case 0.4 0.8 1.2 1.6 Average Average w/o 0.4 Experimental Tip Load 1 0.0 -1.0 -2.5 -4.0 BSM Tip Load 1 -0.4 -1.5 -3.0 -4.7 %Differnece Tip Load 1 100.0 33.3 16.7 14.9 41.2 21.6 Experimental Tip Load 2 -1.5 -3.0 -5.5 -8.0 BSM Tip Load 2 -0.6 -2.3 -4.7 -7.5
%Differnece Tip Load 2 -
150.0 -
30.4 -
17.0 -6.7 51.0 18.0
Experimental Tip Load 3 -2.5 -4.0 -7.8 -10.0
BSM Tip Load 3 -0.8 -3.0 -6.0 -9.5
%Differnece Tip Load 3 -
212.5 -
33.3 -
30.0 -5.3 70.3 22.9
Experimental Dist Load 1 -3.0 -4.5 -7.5 -11.0
BSM Dist Load 1 -0.9 -3.2 -6.1 -9.3
%Differnece Dist Load 1 -
233.3 -
40.6 -
23.0 -
18.3 78.8 27.3
Experimental Dist Load 2 -3.5 -5.5 -10.0
-15.5
BSM Dist Load 2 -1.3 -4.5 -8.6 -13.1
%Differnece Dist Load 2 -
169.2 -
22.2 -
16.3 -
18.3 56.5 18.9 TOTAL AVERAGE 59.6 21.8
FRONT SPAR BENDING STRESS % DIFFERENCES
Equation Load Case 0 400 800 1200 Average % Experimental y=-0.0097x+14.714 Tip Load 1 14.71 10.83 6.95 3.07 BSM Tip Load 1 15.40 11.50 7.70 3.80 %Difference Tip Load 1 4.45 5.79 9.69 19.11 9.76 Experimental y=-0.0139x+21.85 Tip Load 2 21.85 16.29 10.73 5.17 BSM Tip Load 2 24.20 18.14 12.10 6.00 %Difference Tip Load 2 9.71 10.20 11.32 13.83 11.27 Experimental y=-0.0159x+25.37 Tip Load 3 25.37 19.01 12.65 6.29 BSM Tip Load 3 30.87 23.15 15.40 7.70 %Difference Tip Load 3 17.82 17.88 17.86 18.31 17.97
TOTAL AVERAGE 13.00
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APPENDIX G
Five NACA airfoils have been tested in the BSM to display the ability of the model to generate different aerodynamic loads based on unique user input airfoil shapes. The airfoil shape is displayed with the corresponding lift distribution calculated by the BSM alongside it. The total lift force generated by the wing is also given.
NACA 0018
NACA 0024
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NACA 1408
NACA 4412
NACA 23018
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APPENDIX H
Table 1 below contains the Responsibility Assignment Matrix or RAM for the project as explained in section 10.1
PROJECT RAM Pr
ojec
t Man
ager
Engi
neer
ing
Man
ager
Desig
n Au
thor
ity
Draw
ing
Man
ager
Qua
lity
Man
ager
Man
ufac
turin
g M
anag
er
AUSM
E W
orks
hop
Man
ager
Asse
mbl
y M
anag
er
Elec
tron
ics M
anag
er
Elec
tron
ic A
ssist
ant
Soft
war
e M
anag
er
DLR
Cont
act
Ow
ner -
AU
SME
PROJECT LIFETIME TASKS
Project Coordination P S S
Project Communication P S
CONSTRUCTION OF TEST RIG
Develop concept designs for test rig P S
Final design for the test rig N S P N N M M M
Test rig design drawings S P M
Manage workshop work for test rig N N S P
Assemble test rig N N S P
CONSTRUCTION OF WING
Decide on wing geometry N P S M
Calculate wing load S P M
Wing design drawings S P M
Research wing connections S P Design wing connections and wing location S P N N M M M
Wing connection design drawings S P M
Manage workshop work for wing and wing connections N N S P ASSEMBLE RIG, WING AND CARRY OUT TESTING
Connect wing to rig N S S P
Connect load actuators N S S P
Install measurement devices N S P
Carry out Testing N M P S M PREPARE SOFTWARE AND COMPARE DATA
Prepare Matlab wing model code S P M
Prepare Matlab comparison code S P
Carry out comparison of data P S N N
PROCUREMENT
Samuel Polglase 139
Source rig components S M M P M
Source wing components P M M S M
Source load application components P M M S M
Source electronic equipment M M M S P M
DOCUMENT DELIVARABLES
Preliminary Report M S P N
Final Report P S N
Seminar Presentation P S N
Exhibition Poster and Presentation P S N
LEGEND:
P – Primary Responsibility.
S – Secondary Responsibility.
N – Must be notified.
M – Must give Approval.
Samuel Polglase 140
APPENDIX I
The risk register undertaken for the project is shown in below. This contains all the risks associated with undertaking the project and the items produced as a result of the project.
Risk Category Risk Name O
ccur
ance
Sco
re
Seve
rity
Scor
e D
etec
tabi
lity
Scor
e
RPN
Risk Prevention Contingency Action
By Action When
Equipment Test Rig
Equipment Failure
2 3 2 12
Understand and work within equiptment
specifications
High saftey factor for all
designed test rig
equiptment
Student When equiptment is chosen, installed and
used
Electrical
Equipment Failure
2 3 5 30
Understand and work within equiptment
specifications
Find professional to conduct
all work involving electrical
equiptment
Student When equiptment is chosen, installed and
used
Process Failure to meet work schedule 4 5 2 40 Good work ethic Reduce work
needed Student Througout project lifetime
Failure to meet time schedule 3 7 2 42 Good time
management
Adjust time schedule and apply
for extensions
where needed
Student Througout project lifetime
Failure to adhere to required
procedures
2 3 4 24
Make sure procedures to be
adhered to is well known. Seek
advice
Eliminate project work requiring set
procedure
Student Througout project lifetime
People Manufacture
Failure by Workshop Staff
1 5 1 5
Communicate where needed with Workshop Staff to prevent
error
Out source manufacture Student When manufacture is
underway
Strained Realtionship
with Stakeholders
1 4 2 8
Satisfy Stakeholers deesire and
balance needed where differing desires conflict
Use third party to help
with interactions
Student Througout project lifetime
Injury to End Users 2 9 1 18
Impliment required Risk
Assesment and Safe Operating
Procedure (SOP) for Test Rig
Reduce liabilty if incident occurs
Student, Experime
ntal Supervis
or
When establishing SOP and when
experiment is being undertaken
Samuel Polglase 141
Materials Off-Shelf
Component Failure
2 4 4 32
Ensure input load through cables is below smallest
maximum allowable of components
Visual inspection of components
during loading to observe failure
occuring
Test Rig users
Before, during and after
experimentation
Structural
Component Failure
2 5 3 30
Ensure input load through cables is below smallest
maximum allowable of components
Visual inspection of components
during loading to observe failure
occuring
Test Rig users
Before, during and after
experimentation
Incorrect or late delviery
from suppliers 3 5 2 30
Use preffered and trusted
suppliers
Establish secondary
supplier Student When ordering
supplier products
Environment Excessive material waste 4 3 2 24
Eliminate errors in drawings
which would result in error
and need for re-manufacture
Recycle any wasted
material
Student/Worksho
p Staff
During manufacturing
Impact due to
Purschased material
2 2 5 20
Minimise enviromental
effect by reducing
materials needed where possible
Use only materials
that have no negative
environmental impact
Student When deciding on materials
Management Excessive Cost 2 5 3 30
Consult with supervisor to ony
purchase afforadable
products
Find other funding Student When purchase
needs to be done
Communication Breakdown 3 4 2 24
Stay on top of emails and make necessary phone calls. Attend all meetings and appointments
Employ secretary Student Througout project
lifetime
Negative impact on
students ability as a
proffesional reputation
3 7 2 42
Conduct all practices
proffesionally. Complete work to Stakeholders
requested standard and on
time. Meet all deadlines
- Student Througout project lifetime
The SOP developed for the test rig and wing apparatus is shown below. This SOP is the result of an assessment of the risks associated with using the test rig and wing apparatus and implement instructions and warnings to prevent these risks becoming a reality.
Samuel Polglase 142
location DETAILS
School/Branch: School of Mechanical Engineering
TASK/ACTIVITY
Test Rig and Wing Experimental Apparatus Date: 26/05/2011
PREPARED BY Name, Position and Signature (insert names of the supervisor, HSR, HSO and operator involved)
Name
Samuel Polglase
Position
Undergraduate Engineer (Aerospace & Mechanical)
Signature
HAZARD IDENTIFICATION:
See Risk Assessment dated / /
RISK ASSESSMENT
SAFE OPERATING PROCEDURE DETAILS
STOP DO NOT OPERATE APPARATUS IF YOU HAVE NOT COMPLETED (1) THE COMPULSORY UNIVERSITY OF ADELAIDE OCCUPATIONAL HEALTH AND SAFETY INDUCTION COURSE, AND; (2) DO NOT POSSESS THE REQUISITE QUALIFICATIONS OR TRAINING FOR THIS PIECE OF PLANT.
Preparation – work area check:
Ready access to and egress from the apparatus (min of 600mm clearance required) Area is free from grease, oil, debris and objects, which can be tripped over.
(Use diatomaceous earth (“kitty litter”) or absorption pillow to soak up grease, coolant, oil and other fluids) Area is clear of unauthorised people before commencing work.
Personal Attire & Safety Equipment:
Approved closed toe type shoes must be worn at all times. Approved safety spectacles/goggles must be worn at all times, where required. Clothing must be tight fitting. Long hair must be confined close to the head by an appropriate restraint. Finger rings and exposed loose jewellery (eg bracelets and necklaces) must not be worn. Medic Alert bracelet must be
taped if exposed. Gloves must not be worn when operating apparatus, excepting where specifying otherwise.
Samuel Polglase 143
Apparatus Pre-operational Safety Checks – Safety Precautions that MUST be Observed: Visual inspection of apparatus to verify it is in good operational order, ensuring no damage to any stationary or moving
parts, electrical cords etc. Any unsafe equipment is to be reported to an authorised staff member and tagged out. Ensure the apparatus is positioned within sufficient light. Ensure all cable is running through pulleys correctly and entering the winches without knotting or twisting. Ensure all four wheels are fully locked. Be aware of other activities happening in the immediate area. Ensure that no slip and/or trip hazards are present.
Operation: Only one person can operate one winch at a time. DO NOT operate multiple winches at a time. All other persons in attendance should stand back approximately 1m from the apparatus while winches are being used. Ensure cable is running through pulleys correctly while operating the winch. Apply brake to the winch when cable is loaded to required tension. Observe load inputs to ensure input load does not exceed design maximum. Release brake once cable is no longer required to be tensioned and slowly wind back winch handle to return cables to
unloaded condition. NEVER LEAVE apparatus while cables are still in loaded condition.
Transportation: Only ONE person should move the apparatus at a time. Moving should be done at a slow walking speed. DO NOT move the apparatus when the cables are in the loaded condition. Dismantling of the apparatus should only be performed under supervision and after instruction to do so. Lifting and moving of dismantled parts should be performed following manual handling guidelines.
General Safety
Visual inspection of apparatus prior to use. Unsafe apparatus to be tagged out and reported to Workshop Manager. Keep all parts of your body and attire safely clear of the rotating and moving parts, at all times. Ensure scheduled maintenance for this machine has been carried out; including scheduled testing of Emergency Stop. Only authorised qualified staff to operate this machine, or students who have received full Competency Training from an
authorised qualified staff member (recorded in training register). NEVER LEAVE TEST APPARATUS LOADED WHILST UNATTENDED. Safety glasses must be worn at all times during the operation of this machine. Closed Toe Type Shoes must be worn during the operation of this machine. Loose hair to be securely tied back, loose clothing to be rolled up and/or secured, loose jewellery to be removed. Hearing protection to be worn, where appropriate to the task being performed. Leather Safety Gloves to be worn, where appropriate to the task being performed, and; Ensure fingers and leather safety gloves are kept clear from pinch-points under or around the winches and pulleys Release cable tension before leaving apparatus unattended.
Samuel Polglase 144
Note: This Safe Operating Procedure must be reviewed: a) after any accident, incident or near miss; b) when training new staff; c) if adopted by new work group; d) if equipment, substances or processes change; or e) within 1 year of date of issue.
Samuel Polglase 145
APPENDIX J
A summary of the costs associated with the project is given in this Appendix. The table below contains the Bill of Materials (BOM) list for the project which summarises all of the components contained within the test rig and wing experiment. At the end of the BOM the total cost for all the components is calculated to be $7,089.40.
BILL OF MATERIALS, COST AND SUPPLIER LIST ITEM QUANTITY COST($) SUPPLIER Notes
Test Rig Aluminium Beam 6082 Ref Drawings * Green Steel Ordered through workshop Aluminium Plate 5083 Ref Drawings * Green Steel Ordered through workshop Steel C350L0 Ref Drawings * Green Steel Ordered through workshop Steel AS3678 - 350 80X80X8 Angle
Ref Drawings * Green Steel Ordered through workshop
Steel AS3678 - 350 125X125X8 Angle
Ref Drawings * Green Steel Ordered through workshop
Bolt, Hex8.8 M12X160 72 ** United Fastners Ordered through workshop Bolt, Hex8.8 M12X40 4 ** United Fastners Ordered through workshop Washer, 8.8 M12 72 ** United Fastners Ordered through workshop Nut, Hex8.8 M12 72 ** United Fastners Ordered through workshop Bolt, Hex8.8 M20X230 8 ** United Fastners Ordered through workshop Bolt, Hex8.8 M20X180 4 ** United Fastners Ordered through workshop Washer, 8.8 M20 12 ** United Fastners Ordered through workshop Nut, Hex8.8 M20 12 ** United Fastners Ordered through workshop Bolt, Hex8.8 M10X30 15 ** United Fastners Ordered through workshop Washer, 8.8 M10 15 ** United Fastners Ordered through workshop Nut, Hex8.8 M10 15 ** United Fastners Ordered through workshop Bolt, Hex8.8 M5X35 16 ** United Fastners Ordered through workshop Bolt, Hex8.8 M5X15 12 ** United Fastners Ordered through workshop Washer, 8.8 M5 28 ** United Fastners Ordered through workshop Nut, Hex8.8 M5 28 ** United Fastners Ordered through workshop
Castor Wheels 4 0 From University
Stock Off Propulsion laboratory
Jarret F10218 2 Speed 5:1/1:1 Ratio Winch (700kg)
3 301.09 Advansa www.advansa.com.au
Ronstan RF919 Upright Pulley
6 79.5 Binks Marine www.binksonline.com.au
Ronstan RF468 Wire Block Pulley
3 65.46 Binks Marine www.binksonline.com.au
Dynex 3mm Cable 40m 86.4 Binks Marine www.binksonline.com.au
Samuel Polglase 146
Wing Structure Aluminium Beam 6082 Ref Drawings * Green Steel Ordered through workshop Aluminium Plate 5083 Ref Drawings * Green Steel Ordered through workshop Aluminium Plate 3004 Ref Drawings * Green Steel Ordered through workshop Bush - Steel Grade 350 4 0 Workshop Stock Bolt, Hex8.8 M12X40 12 ** United Fastners Ordered through workshop Washer, 8.8 M12 24 ** United Fastners Ordered through workshop Nut, Hex8.8 M12 12 ** United Fastners Ordered through workshop Dome Rivet, Al 3.2X4 78 ** United Fastners Ordered through workshop Bolt, Hex8.8 M30X80 2 ** United Fastners Ordered through workshop Washer, 8.8 M30 2 ** United Fastners Ordered through workshop Nut, Hex8.8 M30 2 ** United Fastners Ordered through workshop Bolt, Hex8.8 M20X80 1 ** United Fastners Ordered through workshop Washer, 8.8 M20 1 ** United Fastners Ordered through workshop Nut, Hex8.8 M20 1 ** United Fastners Ordered through workshop Bolt, Hex M4X13 5 0 Workshop Stock Bolt, Hex M4X11 20 0 Workshop Stock Bolt, Hex M4X6 9 0 Workshop Stock Washer, M4 34 0 Workshop Stock Nut, M4 34 0 Workshop Stock
Electrical Measurment
500kg Load Cell 3 1635 A&D Australia Ordered though Elec Eng
Workshop
Strain Gauges EA-13-250BF-350 (pk 5)
4 224 Thermo Fisher
Scientific Australia
Ordered though Elec Eng Workshop
Strain Gauges CEA-13-187UV-350 (pk 5)
2 388 Thermo Fisher
Scientific Australia
Ordered though Elec Eng Workshop
Strain Gauge Bond Kit 1 141 Thermo Fisher
Scientific Australia
Ordered though Elec Eng Workshop
528-2049 4 Core Cable 1.3 rolls 177.43 RS Components Ordered though Elec Eng
Workshop Other
NBR 12mm Rod Ends 6 133.8
CBC Bearing Power
Transmission Thread into ends of load cells
S Type Hooks 6 45.6 Bunnings For Load Cell ends Rope Ferrel Loop 9 76.5 Bunnings For rope ends 3mm Wire Rope Grips 12 23.4 Bunnings
All Metal COST: 2077.26 Note *: Cost froms part of total cost for all Metal.
All Fastner COST: 389.92 Laser Cutting
COST: 1245.04 Note **: Cost forms part of total cost for all Fastners.
TOTAL COST: 7089.4
Samuel Polglase 147
The table below contains a summary of the Labour hours and costs for the project which is shown to be a total of 215.25 hours at a cost of $50 per hour resulting in $10,762.5 total labour costs.
LABOUR SUMMARY DEPARTMENT HOURS COST($) TECHNICIAN Notes
Mechanical Engineering Workshop
158.25 7912.5 RD, SS, IB All construction of rig, wing and required re-
work
Electrical Engineering Workshop
57 2850 Lydia All preperation and instillation of strain
gauges
TOTAL 215.25 10762.5
Samuel Polglase 148
APPENDIX K
The table below contains a breakdown of the time spent by the student on the project by months.
MONTH HOURS March 20 April 98 May 92.5 June 58 July 34 August 73 September 82.5 October 61 TOTAL 519
The Gantt chart developed at the beginning of the project to break up the project work into discrete time tasks is shown in the following figure.
Samuel Polglase 149