Spirac machine-tool setting calculation method by predetermined contact pattern length factor

Based on the method that the length of the instantaneous contact ellipse at the reference point almost decides the length of the contact pattern, a machine-tool setting calculation method was obtained. According to the Spirac cutting theory, a mathematical model of the epicycloids hypoid gear was built and the parameters of the instantaneous contact ellipse at the reference point of the gear tooth surface were obtained. By adding the cutter tilt angles to the machine setting iteration variables and taking the contact pattern length factors equaling to the predetermined values as the iteration conditions based on the required position of the reference point, the required pressure angle and the required spiral angle of the tooth surfaces at the point, the machine-tool setting parameters were solved. Finally, with a pair of epicycloids hypoid gear as an example, the result obtained from this method was compared with that from the Spirac to verify its accuracy, and the tooth contact analysis under different predetermined contact pattern length factors was accomplished. The results show that with this method, the problem of repeated adjustment of the cutter tilt is solved, and through precise control of different predetermined contact pattern length factors of the gear tooth surfaces equal to the design values, the pre-control of the contact pattern lengths of the gear tooth surfaces is achieved.