The axles and wheels are assembled into a wheel set through interference fit, which bears the full weight of the vehicle, and is the most important part to ensure the safe operation of high-speed EMUs. The fatigue cyclic load cycles of high-speed train axles reach or even exceed 10⁹, which leads to the problems of complex process, long time period and high test costs for physical axle tests. Therefore, it is of great theoretical value and engineering significance to construct dimensionless variables expressing the essential laws of physics and obtain the corresponding laws of physics by taking the existing physical problems as the research object, and to further reflect and predict the test results of real axle through the scale model. Based on the similarity theorem and the dimensional analysis method, this paper analyzed and derived the similarity relationship between the fretting parameters of the wheel-axle interference fit with different scaling factors.

ABAQUS finite element software was used to verify the scaling relationship and carry out numerical simulation research on the distribution characteristics of fretting parameters. The results showed that the distribution of fretting parameters in different scaling coefficient models was consistent with the similarity relationship deduced theoretically; the maximum values of Mises equivalent stress, contact compressive stress, and axial frictional shear stress were located at the inner side of the axle wheel seat area near the gearbox seat, and the ratios to the outer side were 1.56, 1.81 and 1.58, respectively, but the axial slip amplitude of the outer side was slightly larger than that of the inner side, so the high-speed train axle contact edge of the wheel seat inside the most proned to fretting fatigue failure.

The maximum values of Mises equivalent stress, contact compressive stress and axial frictional shear stress in the interference fit area of the axle were 103.26 MPa, 148.21 MPa and 10.22 MPa, respectively. The Mises equivalent stress and contact compressive stress were distributed in a "W" shape along the axial direction of the axle. The stress values at the contact edge were larger than those in the contact middle area, however, the stress values on the outer side of the axle contact are negative and the inner side values were positive, indicating that the frictional shear stress on the inner and outer sides of the contact area was opposite in the axial direction. The magnitude distribution of the axial slip amplitude at the relative position of the axle shaft satisfied the scaling law and was proportional to the scaling factor. The maximum value of the axial slip amplitude under the prototype axle was −7.84 μm, which occured outside the contact. The section bending moments at the three contact positions of the axle wheel seat area also satisfied the scaling law, that was, it was proportional to the cube of the scaling coefficient, and the normalization coefficient defined in this paper was basically close to 1. In the wheel seat area of the axle, as the section moved from the outer edge of the wheel seat to the inner edge, the bending moment of the section increased continuously and reaches a maximum value at the inner edge of the wheel seat.