Menachem M. Marcus1, Anand A. Mhatre1, Brady T. Cousins1, Daniel P. Henry1, Samuel E. Zilavy1, David Schmidt1
1University of Pittsburgh
INTRODUCTION
Wheelchairs fail frequently in a short period of time. Part failures with casters, brakes, seats and tires within few weeks to two years of wheelchair use are common. [1–7] Casters are the highest failure prone parts as per research evidence [2,8]. Studies documenting wheelchair incidents and repairs in the United States and Scotland found that nearly one-third of wheelchair part failures are caster failures. [8,9] Caster failures can be catastrophic. For example, caster stem bolt fractures can cause the wheelchair to tip and the user to fall out of the wheelchair, which is the most common wheelchair injury. [10] To improve the quality of wheelchair casters, the University of Pittsburgh’s Department of Rehabilitation Science and Technology (RST) and the International Society of Wheelchair Professionals are developing a caster durability testing standard. [11] They have developed a testing equipment to replicate community failures in a lab-based setting by benchmarking the test exposures to community’s shock and environmental exposures. The testing protocol predicts community failures for most of the caster models. In conjunction to such a physical testing approach, this study aims to develop a simulation-based approach using a finite element analysis (FEA) software to predict caster failures.
The goals of this study are:
1) Evaluate the mechanical properties of the caster including the stem bolt, axle bolt, and the steel caster fork. To perform an accurate fatigue analysis in FEA, the yield strength, fatigue/endurance strength, and ultimate tensile strength are required.
2) Using an FEA analysis and simulation software, develop a model to simulate the impacts and stresses that a caster will experience during testing.
3) Compare the failures found in the simulation analysis and laboratory-based testing.
METHODS
For the purpose of this study, the Whirlwind wheelchair casters, popularly known as the Zimbabwe caster was chosen.
Evaluation of caster’s mechanical properties
Due to the computational make-up and requirements of the FEA packages, the material properties of the parts being studied needed to be initially quantified. The yield strength, fatigue/endurance strength, and ultimate tensile strength of the stem bolt, axle bolt, and caster fork of the caster were obtained from information afforded by a Rockwell A hardness test.
FEA analysis
To simulate the caster fork, a FEA structural analysis was performed using ANSYS Mechanical. [12] Some modifications had to be made to the 3-D model to ensure a more accurate outcome. Mainly, the weld was assumed to be fully filled, and as weld failures have not been observed in either field or lab studies, the weld was made overly strong. The analysis included setting up boundary conditions for the axle bolt and stem bolt. Total load on the caster was taken as 30lbm and added in the simulation. Static and transient FEA analyses were conducted and the cycles to fork failure were determined for comparison with lab-based testing failures.
RESULTS
Evaluation of caster’s mechanical properties
Once the hardness values were found, tensile strength values were found from ASTM handbook. The ASTM standard A370 chart was used to translate the hardness value to a Brinell hardness value or straight to tensile strength [13]. For hardness values that do not have the tensile strength shown, the corresponding Brinell hardness value can be used with an equation from Machinery’s Handbook to find tensile strength [14]. This afforded a range of values for the tensile strength, averaging around 30 kpsi. The remaining properties were interpolated from this value.
FEA analysis – FEA boundary conditions
Firstly, for the axle bolt, APDL code was used to simulate the stiffness of the axle bolt and to distribute the load from the center point to the two end nodes in the same way the real axle would. Using the 188 elements to simulate the bolt, will supply an axial force that will prevent the fork ends from moving independent of one another. This setup, along with the applied coordinate system, can be seen in Figure 1.
To simulate the stem bolt, washers, and bearings, a complex APDL code was drawn up using further 188 nodes, as well as compression only elements. The compression only nodes were used to connect the stem to the fork, thus insuring that the two surfaces cannot pull on each other but compression between the two surfaces is allowed wherever the contact occurs. To simulate the stem-bearing, the bearing stiffness was obtained from the manufacturer, and was a complex spring matrix was created to simulated said stiffness. Next, the washer must stop the fork from moving in the Y direction, but because of the separation that occurs, compression only elements are again used to connect the top surface of the fork to a remote node that will be the wheelchair frame. This entire layout can be seen in Figure 3.
The last component required is the mass for resistance in the transient analysis. Using a 30lbm resistance as the baseline, 10 mass elements of 3lbm each were applied to the top surface of the bolt.
Beginning with the simpler of the two options, the static Y instance was approached first. After fixing the model in place using constraints on all the degrees of freedom as explained above, a life-cycle study was performed. As the fork and components are made from ductile material, the Von-Mises stress was used. Additionally, the Goodman criteria was used as the criteria for failure are more concerned with cracking than yielding. A Marin Factor of 0.7 was calculated, and using the 30lbm load, the simulation was run. The fork was seen to last to approximately 90,000 cycles.
The static X-Y application of load is very similar to the analysis of the static Y instance. All conditions were held the same except for the applied force. Assuming that the height of the bump was ½ inch, and calculating the approximate angle the force was applied in to be 40 degrees, the resulting 8.5g seen in the data was from a 6.5g in the Y direction, and a 5.5g in the X direction. This resulted in a larger moment in the fork and yielded a shorter life approximately 39,000 cycles.
When considering the X and Y transient analysis, many more assumptions must be made. This is because the mass resisting the motion in the x direction in unknown. Because of this, one must assume that the force in the X direction is the same as the force seen in the static analysis and the Y acceleration is only 6.5g. This also allows us to keep the springs fixed in the X direction. The results for this analysis was found to be around 20,000 cycles.
Failure comparison
The results of this study proved to be very promising. With lab-based failures appearing at around 40,000 cycles, the static X-Y simulation comes close to this number. A full table of the results can be seen in Figure 4. Additionally, the location of the failure as seen in the simulation, is one that has been repeatedly seen in the lab. This can be seen in Figure 5.
DISCUSSION
The team has plans of further improving this algorithm to include additional caster models, as well as including a wear model for the caster tire. This wear model will allow for significantly more accurate inputs for the loading conditions, and will better simulate the stresses and loads that the caster will be experiencing. Additionally, the team would like to compare simulation failures with community failures when reliable acceleration/strain measurements from the community become available.
CONCLUSION
A FEA simulation was performed on a caster model in an attempt to replicate reported field failures as found in a lab-based setting. Based on the results, the model is accurate enough to predict the cycles till failure, as well as the location of the failure.
REFERENCES
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ACKNOWLEDGMENTS
For this study, a University of Pittsburgh’s Mechanical Engineering Senior Design Group was sponsored by RST to investigate and develop the algorithms for the FEA analysis.