Modeling of the race roundness and roughness for ball bearing based on Fourier series and fractal theory

In the modeling and simulation of bearing dynamics, the roundness profile and surface roughness of the raceway is critical for ensuring the precision of the simulation results. This study proposes methods for modeling bearing raceway roundness profiles and surface roughness. The research begins with a quantitative measurement of 200 sets of new and worn bearing raceways using a roundness meter. The reliability of the roundness data is evaluated using relative entropy to assess measurement uncertainty. Following this, two approaches are introduced: roughness modeling based on fractal theory and roundness modeling based on the Fourier series. The high similarity of profiles and R-squared values demonstrate the effectiveness of these methods. Additionally, the effects of factors such as the outer and inner raceways and the condition of new versus worn bearings on roundness data are analyzed. Given the stability and reliability of the measurement data, the roundness model based on the Fourier series and the fractal dimension are adequate for evaluating the wear degree of the bearing raceway and the complexity of the roundness profile, respectively. • Profiles of 120 new and 80 worn bearings measured via roundness meter to build a comprehensive dataset (200 samples). • Measurement stability and uncertainty of roundness meter quantitatively assessed using relative entropy. • Roundness and roughness modeled via Fourier series and fractal dimension for bearing rings, respectively.