Error Analysis On Non-circular Gear Hobbing Machining

In recent decades, along with the development of the locomotive, aerospace, machinery equipment and other industrial areas, the precision processing technology develops rapidly,gears design and manufacturing technology is towards the direction of high precision, smooth transmission, high bearing strength, long working life, low manufacturing cost and little operation noise. In this background, how to meet the increasing precision requirements of gears manufacturing, making gears machining high quality, high efficiency, high integration and high reliability has become a hotspot in gear manufacturing industry. A gear pair made up of a non-circular gear also known as special-shaped gear and another gear can be achieved non-uniform transmission ratio motion of the two axes. So some special functions can be realized by its own unique geometrical features. The mutative transmission ratio equipment or organizations can be considered to use non-circular gears to make the complex structure greatly simplified and improve the performance of organizations. So an error analysis on non-circular gear hobbing process to improve the non-circular gear machining accuracy has very important construction value. So the following studies were carried out in this paper:(1)In view of the situation that the transmission elements of traditional CNC gear hobbing machine are too many and complicated, leading to transmission errors which cannot guarantee the machining precision, Based on SOV theory, with a YS3118 CNC gear hobbing machine as example, the method of using state-space model to describe the transmission error flow delivery was proposed in this paper. First the coordinate system to describe transmission parts gear geometric characteristics was constructed, mathematical modeling of the revolute pair deviations caused by machining errors or assembly errors was fulfilled, the coordinate system transformation containing error parameters in gear drive combined with kinematics theory was described and the expressions of errors flow in transmission process using state-space model have been set up. Ultimately through a calculation example, the effectiveness of this method was verified. According to each level of the transmission gear deviation vector, the terminal errors of the tool can be calculated and this model can be extended to other machine tools with gears transmission systems. Actually with the measurement results of the transmission parts gear states, based on gear design tolerances and distortion estimation and computation, the possible final hob states can be predicted by the recursive calculations results for subsequent transmission state. Also the conclusion that as the spindle speed increases, the spindle radial error mean decreases is obtained.(2)Aiming at the problem of non-circular gear hobbing process is difficult to preciselycontrol,a time-driven mathematical model for non-circular gear hobbing machining has been proposed; On the basis of higher-order non-circular gear pitch curves the radius of curvature greater than zero, the judgement function for gear hobbing machining was put forward, the linear relationship between the order n and eccentricity e was obtained and three mathematical models related to polar angle were deducted according to the kinematic principle. The exact corresponding polar angles in the model based on the algorithm of equal arc length were solved.The image curves of velocities and angular velocities on time obtained were analyzed about the dynamic property of five synchronal axes, including both their velocities and angular velocities.then the optimal processing model was obtained by contrastive analysis.The cubic spline interpolation functions of velocities and angular velocities on time were solved by spline interpolation on the image curves, finally through a calculation example, the effectiveness of the proposed method is verified. The example showed that the aliquot polar angles obtained directly by CAD software were more accurate than that obtained by numerical integration, the polar angles can be imported into CAM simulation machining process. By contrasting the)(twv- graphs, the equal arc length processing scheme was more conducive to speed control than the equal polar angle and the hob working with a constant speed was helpful to prolong its life. The time-driven mathematical model provided a more effective way to get high-order, non-circular gears, it solved the problem that it was hard and not accurate to measure polar angles, also a reliable theoretical basis was established for an online real-time monitoring of velocities and angular velocities in non-circular gear hobbing machining.