Determining the rolling resistance coefficient of wheelchairs

People moving on wheelchairs overcome the forces of resistance such as: air resistance, resistance of the ascent, inertia force and rolling resistance force. Under certain conditions of use of the wheelchair, the only resistance that must overcome the driving force during the movement is the rolling resistance force. This situation occurs during uniformly rectilinear movement, on a flat level surface at speeds of up to 20 km/h, because at this speed the air resistance is negligible. Rolling resistance is mainly influenced by the mass of the rolling object and the rolling resistance coefficient of the running gear. The value of the rolling resistance coefficient can be influenced, among others, by the surface, type and level of pressure in the tire, and the measurement method. There are test methods that in the resistance of rolling beyond the resistance resulting from the contact of the tire with the surface take into account the resistance to connection of the wheel with the driven object. One of them is the innovative method of measuring the rolling resistance coefficient of objects equipped only with the running gear according to the patent application P.424484 and the developed device for these tests in accordance with the patent application P.424483. The article presents the results of wheelchair rolling resistance test with a classic drive system and wheel attachment. These results show differences in the aspect of rolling resistance of classic wheelchairs with wheelchairs equipped with innovative propulsion solutions, such as a lever drive system or a hybrid drive The study was financed from the means of the National Centre for Research and Development under LIDER VII programme, research project no. LIDER/7/0025/L-7/15/NCBR/2016.


Introduction
Rolling resistance coefficient is one of the basics parameter that characterizes vehicles. It enables to determine the rolling resistance force that is counter-party to the propulsion force. The rolling resistance force depends mainly on the surface, wheels and vehicle's suspension. There are available publications on the research on the rolling resistance coefficient but the applied research method concern mainly car tires [1-2, 4, 6-10, 12-13, 15-16, 23] and road surfaces [1, 3-9, 11, 13, 23]. The article discusses the issue of research on the rolling resistance coefficient of non-road vehicles the example of which are wheelchairs. In case of wheelchairs the rolling resistance coefficient is influenced by: -elastic strain of pneumatic tire; -ground strain ( only on soft surface); -rolling resistance in wheel mounting; -wheel alignment.
Modern construction of wheelchairs are characterized by developer drive systems. The examples of such solutions are wheelchairs equipped with i.e. lever drive system [21], multishift transmission [22] or hybrid electro-manual drive [18]. Such solutions are characterized by a higher resistance of internal drive mechanisms. In literature there are available research results on rolling resistance of rear pneumatic wheels [14] and front non-pneumatic of wheelchairs with classic drive system. A lack of comprehensive research results on wheelchairs can be observed. Such results would allow to assess the influence of modernization resulting from the application of innovative drive systems in wheelchairs. The article presents research results of wheelchairs with classic drive system with variable pressure in pneumatic wheels.

Research object and methodology
The research objects were two wheelchairs with classic manual drive system. The first one had a steel frame, pneumatic rear wheels and non-pneumatic self adjustable front wheels ( fig.1). The second wheelchair had a different frame made of aluminum ( fig.2). Both wheels were loaded with a weight of 100 kg that reflects real working conditions. The weight of wheelchairs and the attached measurement system is presented in table 1. The tests were carried out on a hard surface.  The method and research equipment were in accordance with the description of way of measurement in patent application P.424484 [19] and the developed device for these tests in accordance with the patent application P.424483 [20]. The innovative method allowing to determine the rolling resistance coefficient of objects equipped with a drive system is also described in Warguła' s and team scientific article [17]. The measurement of force of a pulled vehicle under specified measurement conditions allows to determine the rolling resistance coefficient of research vehicles ( fig. 3).

Research results
The results of force measurement tests using the described research methodology are shown in Figure 4, indicating the characteristics of the force measurement from the start of the movement to the stopping of the tested object. The characteristics of the force values during the constant speed movement are shown in Figure 5. The research results of average value of the force necessary for the object to move at a constant speed with a constant load and variable pressure in pneumatic rear wheels are shown in table 2.

Results analysis
The developer method and research stand allowed to determine the rolling resistance coefficient for the tested wheelchairs on a hard surface of ceramic tiles at variable pressure of rear axle wheels.
The determined values are presented in table 3. Wheelchair with steel frame was characterized by lower values of the rolling resistance coefficient than the wheelchair with aluminum frame. The change of wheel pressure from nominal value of 6 bar to 1,5 bar did not influence significantly on the value of the rolling resistance coefficient (about 0,001). Tests were carried out in utmost pressure ranges of pneumatic tires, 6 bar is the maximum pressure declared by producer, whereas 1,5 bar is the minimal tire pressure assumed by the authors allowing the wheel to move without putting the rim at risk of damage

Conclusions
The values of the rolling resistance coefficients are in accordance with the data available in literature on pneumatic tires. It implicates that this method can be applied to continue research to determine the value of the rolling resistance coefficient of wheeled systems. Subsequent research will be carried out in order to determine the rolling resistance coefficient resulting from resistances of internal drive mechanisms of wheelchairs equipped with innovative drive systems i.e. 0,66 F -average force, SD* -standard deviation for the mean, SD** -standard deviation for a single measurement.

Tab. 3. The value of the rolling resistance coefficients of wheelchairs
The average value of the rolling resistance coefficient determined on the basis of rolling resistance force Wheelchair with aluminum frame Wheelchair with steel frame 6 bar 1,5 bar 6 bar 1,5 bar 0,022 0,021 0,017 0,016 zacji 2, p.