THE EFFECT OF SHAPE FACTORS ON WHEELCHAIR CROSS BRACE STRENGTH

Brad Lawrence, Rory Cooper, Jess Gonzalez, David VanSickle, Rick Robertson, and Mike Boninger Dept. of Rehab. Science and Technology, University of Pittsburgh, Pittsburgh, PA 15261 Human Engineering Research Laboratories, Highland Drive VA Medical Center, Pittsburgh, PA 15206

Abstract

Cross braces are one of the primary failure points on a wheelchair. Four round and four rectangular cross braces were tested using an ISO Double Drum Tester. The round cross braces have been found to break occasionally within five years of purchase. The rectangular cross braces were made with a larger cross-sectional area and designed to retrofit the wheelchair frame. The purpose of this study was to test the cross braces to failure and measure the differences in strength between the round and square cross braces. Student t-tests were used to analyze the data. Rectangular cross braces were found to last significantly longer with = 0.10.

Background

A few studies have examined fatigue life of cross braces, and the stresses associated with fatigue testing. Peizer, et al. (1) studied the effects of destructive testing on a lightweight wheelchair. The chair was weighted with 200 pounds of shot bags and rolled off a 6 inch wooden platform repeatedly. Deformations of the frame were measured at regular intervals. At 38 cycles, both cross braces buckled. Baldwin and Thacker (2,3) studied strain based fatigue of wheelchairs on a double drum machine. Two wheelchairs were mounted with strain gages near the cross pin of the cross brace tubes and on the side frame behind the front caster. Although the wheelchairs were not tested to failure, estimates of the number of fatigue cycles to failure were made using a strain based fatigue analysis. Neither of these test high cycle fatigue however.

Objective

The cross-sectional area of a constant section cross brace is limited by the diameter of the upper and lower braces where the members are welded together. Other shapes, such as a tube with a variable section would be cost prohibitive. In order to change the size of the cross-sectional area, the shape of the cross brace must be changed. A square or rectangular cross brace can maximize cross-sectional area within the constraints of the connecting members and also be readily retrofitted onto the wheelchair frame.

The objective of this study was to obtain the number of failures for each type of cross brace and observe if changing the shape resulted in an increase in fatigue life. With this information, recommendations for further cross brace design could be proposed. Future design could result in stronger cross braces that last longer without reducing function.

Methods

The ISO Double Drum Test (4) was modified to apply more stress on the cross brace. The drums were offset from the centerline to simulate a sinusoidal road surface. The offset on the rear drums was 8 cm, and the offset on the front drums was 4 cm. This increased the cyclic stress on the cross brace. The Double Drum machine was run at a surface speed of 0.6 meters per second for the rear drums. The speed of the front drums is 7% faster to simulate pseudo-random phase between the rear and front drums. Two twenty five pound plates were bolted to the chair on both sides of the back of the frame next to the seat. Two additional twenty five pound plates were bolted to clamps attached to the footrests. Elastic cord was used to stabilize the and prevent tipping. Minimal tension was placed on the cords when the chair was stationary. Two cords were attached from the front of the chair to the front frame of the two drum machine. Another two cords were attached from the rear of the chair to the back frame of the two drum machine. Finally, the caster spindles were tightened to reduce caster swivel.

The wheelchair used in the test had a 49 cm seat width, a 41 cm seat depth, and a 54 cm wheel base. The rear wheels were standard 24 inch diameter, 1-3/8 inch wide pneumatic tires. The front casters were 18 cm solid type casters. A 100 kilogram ISO Standard Dummy was loaded in the wheelchair (5), see Figure 1.

The rectangular cross braces measured 1.0 inches by 1.4 inches with a thickness of 0.11 inches by 0.14 inches. The round cross braces measured 1.1 inches in diameter and had a thickness of 0.13 inches. Ashby (6) lists shape factors for the stiffness and strength of various shaped members. Each shape factor is normalized to a solid circular section. The equation for a circular hollow tube for strength in bending is:

[(2 x radius)/thickness].

The equation for a rectangular tube for strength in bending is:

{(2/9)(h/t)[(1+3b/h)2/(1+b/h)3]},

where h = height, t = thickness, and b = base. Based on these equations, the rectangular cross braces are theoretically 44% stronger than the round cross braces.

INSERT FIGURE1.DOC

Results

Table 1 illustrates the random testing order, cross sectional area, and number of cycles to failure for the eight cross braces.

INSERT TABLE1.DOC

Two sample t-tests assuming unequal variances were run on the data. It was found the rectangular cross braces had a significantly larger number of cycles to failure ( < 0.10). A significance level of < 0.10 was use to avoid missing differences in fatigue cycle life due to the low number of test samples.

Discussion

Fatigue causes a crack to develop usually at the bolt hole where the two braces are connected as in Figure 2. Once the crack has reached a critical length, fast fracture occurs severing the cross brace causing the wheelchair to collapse. Some fast-fatigue failures may be inconvenient to the wheelchair user as well as costly (7).

INSERT FIGURE2.DOC

The data from the two drum test indicate the rectangular cross braces are stronger and more durable than the round cross braces. The mean fatigue life (number of cycles to failure) of the rectangular cross brace was nearly twice that of the round cross brace. One of the round cross braces had a fatigue life similar to that of the rectangular cross braces, and one of the rectangular cross braces had a fatigue life similar to that of the round cross braces. These results indicate that on average, wheelchairs will last longer with the rectangular cross brace design, but there will be variability in the fatigue life of an individual chair.

To provide further analysis strain gages will be mounted on the cross braces to obtain cyclic stress values. High-cycle fatigue analysis will be performed with the strain gage data to provide a tool for predicting cross brace fatigue life. The validity of this tool for predicting cross brace failure will be tested by correlating the theoretical fatigue data with the failure data obtained from the double drum test described in this study. Considerations will also be made as to the sensitivity of the test on speed and the size of the drum slats.

References

1) Peizer E., Wright D., and Freiberger H., "Bioengineering Methods of Wheelchair Evaluation," Bulletin of Prosthetics Research, pp. 77-100, Spring 1964.

2) Baldwin J.D. and Thacker J.G. , "Strain-based Fatigue Analysis of Wheelchairs on a Double Roller Fatigue Machine," Journal of Rehabilitation Research and Development, Vol. 32, No. 3, pp. 245-254, 1995.

3) Baldwin J.D. and Thacker J.G., "Characterization of Dynamic Stress Response of Manual and Power Wheelchair Frames", Journal of Rehabilitation Research and Development, Vol. 30, pp. 224-232, 1993.

4) ANSI/RESNA WC/08 1991: RESNA Standard: Wheelchairs - static, impact, and fatigue strength tests.

5) ANSI/RESNA WC/11 1990 RESNA Standard: Wheelchairs - test dummies.

6) Ashby M., Materials Selection in Mechanical Design, pp. 134-148, Elsevier Science, ISBN 0-08-041907-0.

7) Cooper R., Lawrence B., Robertson R., Heil T., Albright S., VanSickle D., and Gonzalez J., "Life Cycle Analysis of Depot Versus Rehabilitation Manual Wheelchairs", Journal of Rehabilitation Research and Development, Vol. 33, No. 1, 1996.

Acknowledgments

This project was supported through grants from the U.S. Department of Veterans Affairs, Rehabilitation Research and Development Service (B805-RA), the U.S. Department of Education, the National Institute on Disability and Rehabilitation Research, Rehabilitation Engineering Research Center on Technology to Improve Wheelchair Mobility (HE133005), and from the Paralyzed Veterans of America.

Brad Lawrence, B.S. Human Engineering Research Laboratories Veterans Affairs Medical Center 7180 Highland Drive, 151R-1 Pittsburgh, Pennsylvania 15206

CROSS BRACE STRENTGH