ON THE BIAS RATIO OF AUTOMOTIVE WORM-GEAR DIFFERENTIALS

An automotive worm-gear differential, which has the limited-slip action, is a planetary worm-gear train with two degrees of freedom. Bias ratio of an automotive gear differential is the output torque ratio of the low-speed shaft to the high-speed shaft. We derive mathematical expressions for bias ratios and mechanical efficiencies of automotive worm-gear differentials. The results shows that: (1) an automotive worm-gear differential will be locked up when making a turn of its sun gear is adjacent to the input shaft; (2) the desirable automotive worm-gear differential is the one with two worm-gear pairs and with its carrier adjacent to the input shaft; (3) the bias ratio of the desirable worm-gear differential is over 3; and (4) the bias ratio of a worm-gear differential is the smallest if the helical angle is 45 degrees.