A Parametric FEA System for A Parametric FEA System for Fixturing of Thin-walled Fixturing of Thin-walled Cylindrical ComponentsCylindrical Components

Presented By: Michael Cope

October 29, 2008

Authors: Yan Wang; Jianfan Xie, Zhijian Wang; Nabil Gindy

Accepted: 20 November 2007 by the Journal of Materials Processing Technology

FunctionFunction• “Propose a parametric FEA system that can automatically mesh components, assign material properties and boundary conditions, and create FEA files ready for calculation with limited human interference (Page 338)”

Why Does this Matter?Why Does this Matter?• Current cylinders can be modeled parametrically, but the FEA still needs to be inputted by hand (Pg. 340)

• Reducing Manufacturing costs while increasing component quality. (Pg. 338)

•Reduce the # of Spoiled Parts

ReferencesReferencesABAQUS, 2004. Analysis user’s manual, version 6.5, Hibbit,Karlsson & Sorensen, Inc., USA.Brave, U., Altuzarra, O., Lopez de Lacalle, L.N., Sanchez, J.A.,Campa, J.J., 2005. Stability limites of milling considering theflexibility of the workpiece and the machine. InternationalJournal of Machine Tool and Manufacture 45,1669–1680.Commercial product of Forkardt, Expanding mandrels for verylarge components, http://www.forkardt.com/products/specialchucks/page8.html.Commercial product of Forkardt, Clamping solution forthin-walled rings, http://www.forkardt.com/products/specialchucks/page7.html.Mehdi, K., Rigal, J.F., Play, D., 2002a. Dynamic behaviour of athin-walled cylindrical workpiece during the turning process.Part 1. Cutting process simulation, Transaction of ASME.Journal of Manufacturing Science and Engineering 124,562–568.Mehdi, K., Rigal, J.F., Play, D., 2002b. Dynamic behaviour of athin-walled cylindrical workpiece during the turning process.Part 2. Experimental approach and validation, Transaction ofASME. Journal of Manufacturing Science and Engineering 124,569–580.Ratchev, S., Govender, E., Nikov, S., 2002. Towards deflectionprediction and compensation in machining of low-rigidityparts. Proceedings of the Institution of Mechanical Engineers,Part 2 216, 129–134.

Ratchev, S., Liu, S., Huang, W., Becker, A.A., 2004a. A flexible forcemodel for end milling of low-rigidity parts. Journal ofMaterials Processing Technology 153–154, 134–138.Ratchev, S., Nikov, S., Moualek, I., 2004b. Material removalsimulation of peripheral milling of thin-wall low-rigiditystructure using FEA. Advanced in Engineering Software 35,481–491.Ratchev, S., Huang, W., Liu, S., Becker, A.A., 2004c. Modelling andsimulation environment for machining of low-rigiditycomponents. Journal of Material Processing Technology153–154, 67–73.Ratchev, S., Liu, S., Huang, W., Becker, A.A., 2004d. Milling errorprediction and compensation in machining of low-rigidityparts. International Journal of Machine tools & Manufacture44, 1329–1641.Thevenot, V., Arnaud, L., Dessein, G., Cazenave-Larroche, G., 2006.Integration of dynamic behaviour variations in the stabilitylobes method: 3D lobes construction and application tothin-walled structure milling. International Journal ofAdvanced Manufacturing Technology 27, 638–644.Tsai, J., Liao, C., 1999. Finite-element modelling of static surfaceerror in the peripheral milling of thin walled workpieces.Journal of Materials Processing Technology 94,235–246.Koelling, R., 1998. Apparatus and method for precision machiningof metal rings. US Patent, No. 5,711,195, issued 27th January.

How Does this Relate to ME How Does this Relate to ME 482?482?

For Turning

Total cost per part: Cc = Co Th + Co Tm + Co Tt /np + Ct /npSubstituting for Tm and np: Cc = Co Th + Co p DL/fv + (CoTt + Ct )pDLv(1/n -1)/( f C(1/n) )

Minimizing cost per part (dCc/dv = 0) gives cutting speed and tool life to minimize machining costs per part:

vmin = C{n Co/[(1 – n)(Ct + CoTt)]}nTmin = (1 – n) (Ct + CoTt)/(n Co)

What is Co?

Operator Cost!

Don’t forget Spoiled Products!

ParametersParametersNomenclaturea the oblique angle of conic thin-walled cyinderap the oblique angle of the pth section of anglevaryingthin-walled cylinderb The angle around the z axis of the referencebetween two nodes N(i, j, k) and N(i, j, k+1)BC(i, j, k) Boundary condition, which is the function ofvariables i, j and kCS the coordinate system on the centre of the topsurface of the thin-walled cylinderDL element size in the length direction of the componentDR element size in the radius direction of the componentDT element size in the thickness direction of componentE Young’s modulusE1(i, j, k) element vector of element C3D8 and is a functionof i, j and kE2(i, j, k) element vector of element C3D20 and is a functionof i, j and kF machining force specified by userFCi the force boundary condition on componentduring the ith stepFIX1 constraint on the bottom end surface of thecomponent

FIX2 constraint on the top end surface of the componentID(i, j, k) the identity number of a node and is a functionof i, j and kIDe the identity number of elementIDnm the identity number of the mth node of a elementL the total length of the straight or conic thinwalledcylinderLp the length of the pth section of the anglevaryingthin-walled cylinderLET the number of finite element across the cylinderthicknessNL the number of nodes in the length direction ofthe componentNR the number of nodes in the radius direction ofthe componentNT the number of nodes in the thickness directionof the componentN(i, j, k) node vector and is a function of variables i, j andkR/R0 Internal radius of the top surface of the thinwalledcylinderR(i, j, k) The distance from the node N(i, j, k) to the z axisof the reference coordinate system cylinder

Parameters ContinuedParameters Continued

S The number of section of the angle-varyingthin-walled cylinderT Thickness of the thin-walled cylinderTLi The tolerance constrains on the componentduring the ith stepTol Tolerance in the thickness direction on thethin-walled cylinderX(i, j, k) The X value regarding the CS of node N(i, j, k)XS boundary condition on X direction for XY symmetryY(i, j, k) The Y value regarding the CS of node N(i, j, k)YS1 boundary condition on Y direction for X symmetryYS2 Boundary condition on Y direction for of XYsymmetryZ(i, j, k) The Z value regarding the CS of node N(i, j, k)ˇ The angle of the component in the radiusdirection representing the symmetry boundarycondition Poisson ratio

Design PrinciplesDesign Principles3 Cylinder Types

1. Standard Thin Walled Cylinder

2. Conical Thin Walled Cylinder

3. Varying Angle Thin Walled Cylinder

Assumptions: Elastic Deformation, Point Force, Rigid Fixture/Support (Pg. 340

Design Principles cont…Design Principles cont…

Experimental EquipmentExperimental Equipment

• ABAQUS FEA software used to analyze systems

• Use of custom user interface to facilitate FEA

Design Principle ApplicationDesign Principle Application

• After the user inputs all the parameters, the system crunches the math.

• A fully usable file is then imported into ABAQUS

Correlation of Results and the Correlation of Results and the ModelModel

NONE!!!!

• No testing to validate model!

• “Much of the work to build a simulation is repeatable.” (Pg 346)

• Even a comparison with “Hand” calculations would have been better

Practical UsePractical Use

• Eliminate hours of work spent in FEA software

• Greater communication between design and manufacture

• Autonomy for the manufacturing engineer

• Reduce the cost of developing thin-walled cylinders

Technical AdvancementTechnical Advancement

• Accuracy Improved Manufacturing of parts

• Reduced vibration and deformation

• Opens the door for fully parametric FEA analysis software

Industries ImpactedIndustries Impacted• Aerospace

• Automotive

• Power

Questions?Questions?