Accuracy prediction and roller number optimization of journal roller bearing based on averaging coefficient considering raceway roundness error

An accuracy prediction model of the journal roller bearing is built in this article to study the quantitative relationship among the bearing error motion, the raceway roundness error and the bearing structural parameter with the nonlinear roller force in consideration. Then, the influence of the inner or outer raceway roundness error on the averaging coefficient is studied separately for the bearing with the ideal/elliptical/trilobal outer or inner raceway. It finds that the roundness error of raceway with the wave number n = np*i ± 1 has main influence on the error motion where np is the roller number and i is a non-negative integer. For the bearing with an ideal outer or inner raceway, the roundness error of another raceway with the wave number n = m*i has no influence on accuracy where m is the prime number inside the roller number np. The matching relationship among the roller number, the roundness errors of inner and outer raceways determines whether the fluctuations of roller forces offset and whether an error motion occurs. A recommended way to improve the motion accuracy is to increase the roller number and select it as the optimized composite number np = 2*3*5*7*…, which equals the product of the first few prime numbers in prime sequence. The theory discussed in this article can be used to optimize the roller number, predict the error motion and calculate the raceway roundness error of journal roller bearing. It has significant importance for the design of precision rolling element bearings used in measuring instruments and machine tools.