Preliminary results of wheel rolling resistance using a drum-based testing machine
Joseph E. Ott1,2, M. Mendel Marcus1,2, London C. Lee1,2, Jonathan L. Pearlman1,2
1Department of Rehabilitation Science and Technology, University of Pittsburgh, 2International Society of Wheelchair Professionals
In manual wheelchair propulsion, rolling resistance (RR) is the primary force resisting propulsion. Air resistance and bearing resistance are considered to be negligible in most cases [1-3]. Energy loss of the tire contacting the surface creates rolling resistance for manual wheelchair users (MWU). Accounting for almost all of the loss of kinetic energy in rubber, hysteresis (inelastic deformation), shows that material of the tire plays a critical role in the loss of energy . A free body diagram of the forces is shown in Figure 1. Rolling resistance can be reported as a drag force or as the coefficient of rolling resistance, µRR (mu). The formula to calculate µRR (mu) is the drag force (FRR) divided by the weight (W) on the wheel: µRR = FRR/W.
It is important to recognize the biomechanical impact of rolling resistance and the consequences for MWU. When RR increases the force required for a MWU to propel their wheelchair increases. This is linked to an escalation in the risk of upper extremity pain and injury, such as rotator cuff injuries [5-6]. MWU with injuries and pain have reduced activity and participation . Surface type can have a direct impact on RR with high pile carpet being harder to propel over as compared to tile . The positioning of the rear axle changes the load on the rear wheels and consequently changes RR . Setup parameters of the wheelchair, such as toe and camber, can affect rolling resistance by changing the orientation of the tire . Toe can be caused by manufacturing defects, malalignment of the wheels, or high manufacturing tolerances. Camber is chosen as a user preference to increase stability. However, if a setup involved camber and then the axle tube is rotated, toe would be induced. Furthermore, the tire pressure and tire type will also be influential in RR . More aggressive tires are expected to have a higher RR, as well as, underinflated or not properly maintained tire pressures.
Previous testing methods
To identify the gaps in previous research, a scoping literature review on rolling resistance test methods was performed. As a result, 40 articles were broken down into seven testing method groups including deceleration, motor draw, treadmill, physiological expenditures, drag tests, ergometer/dynamometer, and robotic test rig. Deceleration testing is when the distance traveled at the end of the ramp is measured after a whole wheelchair goes down a ramp . A drag test measures the force with a load cell while pulling the whole wheelchair . Motor draw measures the current draw on the motor as it performs a drag test. Treadmill testing measures the resistive force with a load cell as the whole wheelchair on a treadmill . Physiological expenditures testing is when instrumented push rims, heart rate, or oxygen are measured during propulsion . Ergometer and dynamometer testing measures a physiological expenditure or forces on the rollers with a wheelchair propelling on rollers . A recent invention is a robotic test rig, however, since only one exists, it is difficult to validate the results . Three criteria were used to evaluate each test method: the ability to test individual wheel µRR (mu), whether µRR (mu) was measured directly or through a proxy measurement, and the ability to test the multiple conditions that impact µRR (mu) (camber, toe, tire type, tire pressure, load distribution, and surfaces). Treadmill testing and drag testing are direct test methods. The remaining five testing methods are indirect and describe RR through proxy measurements. Proxy measurements make indirect tests are more difficult to interpret than direct testing and tend to only report comparative results. Not one of the test methods from the review has the ability to test at a component level. Some have the ability to test a few of the setup parameters, depending on the test design, but no one article tested every setup parameter. The reporting of results varied greatly with force measurements, comparative results, and coefficients of rolling resistance.
With the drawbacks of the previous testing methods, the University of Pittsburgh designed and built a new testing machine. The International Society of Wheelchair Professionals Standards Working Group (ISWP-SWG) guided the effort. Figure 2 shows the drum-based testing method. A four-foot diameter drum (1) rotates at a constant speed. The top section (2) of the frame holds the arm assembly. Two parallel one-and-a-half-inch precision ground rods that sit tangent to the top surface of the drum make up the arm assembly (3). A truck (4) slides on the rods courtesy of four air bushings, with two bushings on either rod. When compressed air is supplied into these bushings, they float on the rods. There is no friction induced into the system since there is no contact. At the front of the arm, a load cell (5) is mounted with linkage to connect it to the truck. Toe in and toe out adjustment is done with two plates (6) sitting on the truck. A camber block (7) on top of the truck can be switched out for different degrees of camber. The machine is capable of measuring RR under conditions of varied toe, camber, load, tire type, tire pressure, and surface type for individual wheelchair wheels including casters. To perform a test, the drum is rotated at a constant speed, and the air bearings are released with the truck floating on the rods. The pullback force on the truck (FRR) is measured by the load cell. As identified in the scoping review, tire pressure and toe were two parameters that can affect rolling resistance. A pilot test was conducted with the newly built system to measure the impact of RR based for a set of four tires under different conditions of tire pressure and toe. An increase in the toe and a decrease in tire pressure is predicted to increase RR based on prior evidence, which we hypothesized would be validated on our machine.
Four new tires were purchased based on the recommendation of frequently used wheels from our clinical faculty: Low polyurethane tire on a mag wheel (MG), Marathon Plus Evolution (MPE) on a lite spoke rim, Primo Orion (PO) on a lite spoke rim,and Primo Orion with an airless insert (PA)on a lite spoke rim. All wheels had the same aluminum anodized standard hand rims. The study design was to test three values for toe out (0º, 1º, 2º) and three values of tire pressure (40%, 70%, 100% of max inflation pressure). Three trials are run for each condition for every wheel. Tire pressure is only able to be tested on MPE and PO because the other two are airless. All testing was conducted with a drum surface speed of 1 m/s, a load of 75lbs on the wheel, no camber, and a bare metal drum surface, which is smooth. For the toe tests, 100% of max tire pressure was used. The protocol was designed to replicate conditions seen in the community.
For data collection, MATLAB R2018b sampled the load cell at 120 Hz during a two-minute trial . The data is filtered using an 800 unit moving average filter. The data was truncated to the center sixty seconds of each two-minute trial to ensure that only the steady-state date was being analyzed. The program writes all of the data to a worksheet to include the raw data, filtered data, voltage to force conversions, and the mean coefficient of rolling resistance with its standard deviation.
A mixed-model repeated measures ANOVA was chosen to analyze the impact of toe test and pressure on RR with the tire type as the between-subjects factor. The alpha level was set to .05 and assumptions were met.
A statistically significant impact of toe (F = 49572.007, df = 2, p < .001, Partial Eta Squared = 1.000) with toe at 2º being significantly higher than toe at 1º, which was higher than toe at 0º for all tires. Furthermore, there were significant results for tire type (F = 2440.866, df = 3, p < .001, Partial Eta Squared = .999) and an interaction effect between toe and tire type (F = 388.410, df = 6, p < .001, Partial Eta Squared = .993).
Tire pressure tests
A statistically significant impact of tire pressure (F = 155.548, df = 2, p < .001, Partial Eta Squared = .975) with tire pressure results at 40% being significantly higher than at 100%. Furthermore, there were significant results for tire type (F = 43.017, df = 1, p = .003, Partial Eta Squared = .915) and an interaction effect between toe and tire type (F = 13.205, df = 2, p = .003, Partial Eta Squared = .768).
The pneumatic tires had less rolling resistance than non-pneumatic tires in the toe tests. The MPE was the lowest rolling resistance per configuration and is followed by the PO. An interesting result is that PA had higher rolling resistance across all test when compared to MG. Figure 3 shows the details. To better show the effects of toe, Table 1 shows the percentage increases between tests. Overall, the increases were more drastic in pneumatic tires. At 2º of toe out, µRR (mu) quintuples for the pneumatic tires. Although this is just the forces acting on one rear wheel, it is equivalent to a MWU weight increasing by 300 percent. The non-pneumatic tires had less of an increase, but they started at a higher initial rolling resistance.
Tire pressure revealed an inverse relationship to RR. RR increased while tire pressure decreased for MPE. PO had an alternate result where RR at 70% was less than it at 100%, however, no significant difference was found between the 70% and 100% air pressure. Further testing will be conducted to identify at what percent reduction in air pressure RR is significantly impacted. Figure 4 shows the results. Overall, the 40% trial was the highest RR, which accounts for approximately a 50 percent increase in µRR (mu), over max inflation. Table 2 shows the percentage increases between trials.
The percent changes in tire pressure are not as high as the toe results. This means that toe is a more impactful factor in rolling resistance in this study. The tested intervals of toe-out are large amounts of toe but they were observed in wheelchairs in use . Further testing needs to be conducted at smaller intervals. These results show that it is possible to discern trends and measure data with the new drum-based testing machine. A limitation of this study is that it was a small-scale study with limited tire types and test parameters. Additionally, combinations of tire pressure and toe were not tested to investigate any compounding or canceling effects.
The long-term goal of this work is to evaluate the RR of a range of common wheelchair wheels under different conditions to help inform clinical provision. The data presented in this paper is aligned with previous research and provides insight into the impact of selecting pneumatic versus solid tires, the consequences of not having fully inflated tires, and the impact that toe-out can have on RR. Future work will explore a wider range of wheels and casters; additional conditions, such as camber and surface type.
The paper was supported by the following: Improving Health and Function Through Use of Performance Standards in wheelchair Selection Grant #: 90REGE0001-02-00, National Science Foundation Integrative Graduate Education and Research Traineeship award number IGERT 1144584, and U.S. Agency for International Development through Agreement Nos. APC-GM-0068, SPANS-037, APC-GM-0107, and FY19-A01-6024. A special thank you to the Human Engineering Research Laboratories for the use of their facility to build the testing machine and feedback along the way. Also, a thank you to the ISWP-SWG for their continued support of this research and helpful advice.
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