Lapping system for ultra-precision bearing balls

The lapping mechanism for obtaining ultra-precision bearing balls is analyzed by simulation and experiments, and effective lapping system for mass production of balls is proposed. In the simulation, the configuration of a ball is represented by a Fourier series. Then the ball is assumed to be lapped between two lapping plates having V-shaped grooves with several V-angles, and the configuration of the lapped ball is represented by another Fourier series. The correction in profile is evaluated by the decrease of Fourier factors. In the experiments, lapping plate with R-groove (round groove) and S-groove (round groove having a pit) are used instead of V-shaped grooves for increasing the contact area between balls and the grooves. The experiments show that the combination of R and R (R + R) is effective to reduce the waviness of even order harmonics, and R + S decreases the 3rd-harmonic in waviness. The combination of S + S decreases the 3rd, however increases the 2nd and the 4th-order. To decrease every order harmonics, a lapping system with 3 steps (R + R &rarr R + S &rarr R + R) is proposed. The steel balls finished by this system show the following figures; roundness = 18 nm and Ra = 2 nm.