Design Project Assignment: Phase 3

Computation Methods in Engineering

MME 213 A

Peter Siegfried, Trisha Sinay, Dakota Spallinger, Kevin Stewart

4/27/2012

Introduction and ContextAlong with the sport of Olympic diving, the development of the diving boards has also

progressed from tall cliff faces. Spring boards are flexible boards that allow the diver to vault into the air and perform difficult contortions before entering the water. These springboards started as long boards fixed on one end, with the material properties allowing for flexibility. As the sport progressed and new materials were introduced, springboards began to introduce actual springs. In the 1930’s a design was patented for an adjustable spring board, and in the 50’s this design was improved upon more to make it safer and more lightweight.

The current board, used in almost all high level diving competitions, is produced and patented by Duraflex. This board utilizes a aluminum extrusion to provide a rigid board with enough flex to vault the diver. It also contains holes cut out of the tip to reduce air resistance of the board and provide a safer diving experience. For this project, the goal is to improve upon this current design to create an adjustable springboard that meets the Olympic diving criteria, as well as being cheap, robust, and lightweight.

Rules and RegulationsThere are seven outlining specifications for an Olympic springboard. The first

specification are the dimensions of springboard. The springboard must be at least 4.8 meters long and 0.5 meters wide. The second specification is that the boards must be coated with a non-slip surface. The third specification is that the  springboard must have movable fulcrum that is easily adjustable by diver. The fourth specification is the vertical distance from the level of the platform, which supports the fulcrum assembly, should be 0.365 meters. The distance from the front of board to fulcrum assembly shall be a maximum of 0.68 meters. If the front surface projects past this point then the board must have a decreasing slope of 1/3. The fifth specification is that the manufacturer should recommend distance from rear to center of fulcrum. The sixth specification is that the springboard must be installed dead level at the leading edge when fulcrum is in all position. The last specification is that the springboards should be mounted on both sides of platform for synchronized diving and must be at least two boards.

Description and Key Features of a Diving BoardThe previous designs we found utilize combinations of springs and boards. The H. W.

Handley patent describes a diving board patented in 1936.  This particular diving board has an adjustable fulcrum support which will support different weights of persons and also different types of dives.  The resiliency must be adjusted and this is done by taking into account the

texture of the wood used.  The condition of the growth of the tree, the grains in the wood and also the amount of summer and winter wood are all taken into consideration.  Some material and finish of several parts may be specific to the likes of the manufacturers, also for certain uses of the springboards.

The design idea currently in use by olympic divers is the aluminum Duraflex diving board.  They started using this particular board in the 1960s and it is still being used in diving competitions everywhere.

    The Duraflex diving board addresses key features of a diving springboard.  It takes into consideration drainage effects of the board, drag resistance and also increased traction of the surface.  One major  improvement in the design is an increased the number of opening towards the tip of the board where motion use of the board is the greatest.  The openings are elongated and formed through the diving board platform.

Brainstorming Preliminary Design IdeasThese design ideas are compared to the aluminum Duraflex diving board. The scale used

was a 1 to 5 rating system with 5 meaning the criteria was met or design aspect is exceptional, and 1 meaning criteria not met or very poor. The weight for each criteria was determined by judging how necessary each outcome is to the customer.

5 Design Ideas Light weight

Cost Effective

Easily Adjustable

Meets FINA Regulation

Totals

Weight (%) 15 15 30 40 1.00

1: Width Gradient Board Adjustable at Mount

2 1 2 1 1.45

2: Screw/Spring Adjustable Board

4 4 4 5 4.40

3: Stiff Board Adjustable/Flexible Mounting Brackets

1 4 4 5 3.95

4: Fixed Back, Adjustable Front Support

4 4 5 5 4.70

5: Temperature Adjustable Flex Board

3 1 5 4 3.70

All diving boards will be sprayed with a cheap commercial slip-resistant coating.Design idea one entails a thicker depth of board in the back while the front is skinnier

increasing flexibility.  The advantage of this board is stability in the rear of the board for approach, and a flexible tip for vaulting the diver. Making the board adjustable was a problem however and it was decided that this board would be better suited for residential pools, not competitive diving competitions as required for this problem. The second idea has a spring running through the length of the board that is attached to a handle.  The handle can be cranked

to turn a screw and compress or depress the spring allowing for the flexibility to be adjusted according to the users preferences.  The third idea uses an adjustable mounting bracket with a spring system in the bracket.  It can be adjusted accordingly, and since the design is focused in the bracket design any commercial or current board could be used with this bracket implemented for adjustability.  The fourth idea is close to the third, but uses the front bracket to be adjustable. A movable slide can be adjusted to pull the front bracket closer to the back bracket, or push it farther away.  This either increases or decreases flexibility at the front of the board.  The fifth idea uses a copper wire running through the length of the board to set temperature.  A small current, set by the user, could be run through the wire, and much like heating coils in pavements, the temperature will determine flexibility of the board.

Selected Design After comparing all preliminary designs three of the five designs were ruled out because

they do not meet the FINA requirements. The remaining two designs were a uniform board with spring(s) down the length of the board to adjust the stiffness of the board and a board with a fixed back and the front support adjusts forward and back, up and down.

The chosen design was the fixed back and adjustable front support. This design was chosen because it met all of the initial requirements and was decided to be the most effective design based on the lay out of the structure.

In choosing a material for a diving board there are a few properties, which are necessary to know before calculations can be preformed. These properties include the Elastic Modulus (E), the density of the material (p), Ultimate Tensile Strength (UTS) and elongation at break. The Elastic Modulus describes the stress strain behavior of the material while still in the elastic region. It is important to have a large elastic region in the material so the board will not reach its elongation at break point. The material will be deformed in the diving process and as long as it deforms within the elastic region, it will be durable and robust. The density of the material is important for weight calculations, as the weight of the board will also contribute to deflections in the board end.  The UTS property describes the highest amount of stress the material can undergo. Knowing the stress at failure is important for safety, and knowing the UTS allows for the board to be engineered to only exist in safe stress/strain ranges. In this phase of the design process, multiple materials were tested for deflection and weight properties so that one material could be chosen for use in the board construction.

In choosing a material for a diving board there are a few properties, which are necessary to know before calculations can be preformed. These properties include the Elastic Modulus (E), the density of the material (p), Ultimate Tensile Strength (UTS) and elongation at break. The Elastic Modulus describes the stress strain behavior of the material while still in the elastic region. It is important to have a large elastic region in the material so the board will not reach its elongation at break point. The material will be deformed in the diving process and as long as it deforms within the elastic region, it will be durable and robust. The density of the material is important for weight calculations, as the weight of the board will also contribute to deflections in the board end.  The UTS property describes the highest amount of stress the material can undergo. Knowing the stress at failure is important for safety, and knowing the UTS allows for the board to be engineered to only exist in safe stress/strain ranges. In this phase of the design process, multiple materials were tested for deflection and weight properties so that one material could be chosen for use in the board construction.

After testing three aluminum super alloys, RSA-431 T6 alloy was chosen to be the material used in the design of the board. The board design will have a cross-sectional area similar to figure 1.

Figure 1: Cross section of diving board

Using this cross-sectional design, along with the material chosen, the board will weigh approximately 55 lbs. the board will deflect 2.5 inches under its own weight and it will deflect somewhere between 15-37 inches depending on weight and strength of the diver. A linkage angle between 0.7-1.2 degrees will be needed to keep the board tip at the same height as the fixed end.           The cross-sectional design was selected for two reasons, reduce weight and provide enough support. Since the design consists of three 3” by 1/3” supports with a thin sheet of material on top the weight is minimized. The three supports only allow minimal deformation and will be designed to easily adjust in the fulcrum.

The cross section design was chosen to reduce weight of the board while keeping strength and spring properties at appropriate levels. The materials were tested individually to model the deformation behavior each would display under the uniform load of their own weight as well as the fixed pressure from a diver. For all of the tests a cantilever model was used, as the design acts like a beam supported by one fixed end. The results of the testing showed the maximum deformation, response load in the fixed end, and weight characteristics of the diving board. The material selected was the RSP Technology RSA-431 T6 Aluminum Super Alloy. The results from the deformation testing are shown in figure 2.

Figure 2: Finite element analysis stress results

The maximum deformation is shows to be 37 inches for a diver jumping force of 450 lbs. The board modeled has a project weight of 55.5 lbs, with a maximum deformation from weight of the board of 1.7 inches. The response load in the base of the board for the weight is 55.5 lbs and from the diver 450 lbs. This material was chosen because it weighed less than the other two materials with no significant loss in deformation properties (under equal conditions the deformations ranged from 37 to 38 inches, while the weight ranged from 55 to 58 lbs.).

Abaqus and the 3-D model Before drawing anything began, a rough sketch with starting dimensions was created.

Once there was an outline of the total assembly, the Abaqus modelling was started. The model was created around the base and the rest of the parts were made to fit by adjusting the rough first dimensions. After all the parts were finished the final product was assembled. Many problems were encountered in the assembly process. Problems with interference between part constraints and some dimensions were slightly off and were persistent throughout the entire modeling process. Once the assembly was completed the board and fulcrum were meshed for loading, constraining and analysis.

Meshing the board was a formidable challenge, as it needed to be meshed using tetrahedral and was a free mesh structure. This input parameter may have been the reason for having the amount of errors encountered through the modeling process. After meshing, many overlap and interference errors were encountered so the seed size had to be increased from 5 to 10; this allowed the instance to be meshed correctly. The fulcrum and the board had to be tie constrained in order for the board to interact correctly with the fulcrum; this was a key step and much time was spent finding this out. Finally after all the constraints and adjustments to seed size and mesh were created, the final assembly was developed and is shown in figure 3.

Figure 3: Final assembly of the diving board

With this finished figure a finite element analysis could be run on the model to give stress, displacement, and weight characteristics.

Finite Element Analysis    The finite element analysis for this problem was done using the Abaqus CAE modeling software. The assembly shown in figure 3 was modeled with a concentrated load of 80 kg on the moving tip of the board. The fulcrum, was tied to the board and a boundary was placed to fix the

fulcrum in place. This resulted in the board deforming over the fulcrum as expected. The displacement output of the model, shown in figure 4, demonstrates the maximum displacement at the moving end of the board.

Figure 4: Finite element analysis displacement results

The maximum displacement was found to be 47 cm, or about 19 inches. The von Misses stress were also outputted and are shown in figure 5.

Figure 5: Finite element analysis von Misses stress results

These stresses were concentrated at the fulcrum and reached a maximum value of 13.04 GPa. One of the most important outcomes of this model however is the weight of the board was fairly low. The board used for the displacement and stress models had a mass of 79.2 kg, which is about 179 lbs, a good weight for an Olympic diving board.    Although this model performed extremely well there are two main issues with the board that could be improved upon. The first and easiest of the two improvements is the weight of the board. The board right now contains a solid top sheet of aluminum with the three main supports

running along the length of the board. Aluminum could be cut out of the runners to make hollow pipes or holes could be drilled out of the top sheet to reduce the weight of the board. This change would affect the performance of the board but would significantly reduce the weight and is something that needs to be further analyzed if this model was to be developed into a prototype. The second and more difficult improvement to make is in the response of the board at the fulcrum. The material used in the design of the board has an extremely high elastic modulus. This resulted in the stresses along the board to be fairly low with the highest stresses concentrated at the fulcrum contact point on the board. These concentrated forces could lead to fatigue over time in the board with excessive wear on the most common fulcrum locations. This could lead to lowered durability of the boar and reduce its working life span. This would be a safety problem that needs to be further analyzed for solutions if the board were to be selected for a physical model.

Summary and future workAfter modeling out assembly through Abaqus, we could accurately survey our results.

Our finished board was reduced in weight and we also made our base shorter.  Our final board weighed 79.2kg and we made it significantly lighter by extruding holes through the cross section of our board.  Our assembly met all of the FINA guidelines and our deflection analysis yielded accurate results that were expected of board with such a high Young’s Modulus.  Our deflection as 47 cm with the weight of an 80kg person standing on the end. The maximum von Misses stress in the board was found to be 13.04 GPa.    The future work necessary for this project is to determine actual physical characteristics of the developed models. The models give a fairly accurate representation of what should occur under the stresses of a diver, but more tests will need to be done to ensure the robustness and ease of adjustment for the diving board. These tests can only be done with a real physical prototype so the next logical step would be to develop the first board following our generated model.

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Appendix:

Selection matrix for preliminary design ideas.

5 Design Ideas Light weight

Cost Effective

Easily Adjustable

Meets FINA Regulation

Totals

Weight (%) 15 15 30 40 1.00

1: Width Gradient Board Adjustable at Mount

2 1 2 1 1.45

2: Screw/Spring Adjustable Board

4 4 4 5 4.40

3: Stiff Board Adjustable/Flexible Mounting Brackets

1 4 4 5 3.95

4: Fixed Back, Adjustable Front Support

4 4 5 5 4.70

5: Temperature Adjustable Flex Board

3 1 5 4 3.70

Cross section of final board design.

Preliminary stress and deflection testing.

Final board assembly.

Displacement results from finite element analysis testing.

Displacement results for finite element analysis testing.