Research on plunging resistant force of drive shaft systems based on fractal methods

When drive shaft systems move axially, the friction between rollers and raceways inside tripod joints will generate a plunging resistant force (PRF). Excessive PRF causes significant noise in vehicles. To reveal the generation mechanism, an analytical model of the PRF is proposed by analyzing the axial motion mechanism of a drive shaft system. Based on the analytical model and fractal methods, a fractal model of the PRF is proposed to reveal influencing factors of the PRF more comprehensively. An effective method for correcting distribution of asperities between rollers and raceways is proposed to describe the contact state accurately. The fractal model shows that influencing factors of the PRF include the fractal dimension and the characteristic scale coefficient related to the roughness of contact surfaces, the material parameters, the working angle, and the correction coefficient for distribution of asperities. A measurement method for the PRF is subsequently proposed, as well as the fractal dimension and the characteristic scale coefficient are measured and determined. The effectiveness of the fractal model is verified based on the measurement of the PRF and the determined fractal dimension and characteristic scale coefficient. Numerical analysis results show that reducing the Poisson's ratio, the yield strength and the working angle, increasing the characteristic scale coefficient, the elastic modulus and the correction coefficient, and selecting a fractal dimension lower than 1.544 or higher than 1.782 can effectively reduce the PRF, thereby reducing the noise caused by the PRF.