Study On Measuring Involute Profile Gear In A Polar Coordinate Method

The gear is a key component which can not be replaced in the gear transmission mechanism. It is widely used in machinery, transportation, aerospace, instruments and meters, and other fields. It has a direct effect on the transmission performances for the geometric accuracy of the gear. The measurement and evaluation of the gear is very important. Compared with the gear measurement instrument based on electronic generating method, the instrument based on polar coordinate method has a more simplified structure and wider applications, especially for the gearwheel and internal gear measurement. Based on polar coordinate measuring principle, the paper focuses on the mathematical model of measuring involute profile in a polar coordinate method and compensation on the measuring error. In order to eliminate the influence of the installation eccentricity on the gear measuring error, the model of compensation on the installation eccentricity is developed. It is designed for the measurement and control system based on DSP and FPGA. It is available to measure and evaluate involute profile in a polar coordinate method.The main content of the paper is the items as follow.1 According to the polar-coordinate measuring principle, the mathematical model of measuring involute profile in a polar coordinate method based on the ball probe and variable offset distance is established. The paper analyzes and solves the compensation on the radius of the ball probe, determination of measurement range and selection of samples.2 The paper analyzes emphatically the measuring error, which is caused by the change of the offset distance in the measurement and control system in a polar coordinate method based on variable offset distance. The mathematical model of the measuring error is presented. According to the mathematical model of measuring involute profile based on the ball probe and variable offset distance, the model of compensation on the profile deviation is established. The measurement and control system in a polar coordinate method based on unchanged offset distance is developed in order to eliminate the measuring error. The compensation model is established. The factors generating measuring error are analyzed in aspects such as length, angle and position error of the start measuring point, and so on. 3 According to the kinetic theory of the gear error, the mathematical model of the meshing line increment generated by the installation eccentricity is developed. It is based on the relationship between the installation and the meshing line increment. The models of compensation on profile deviation, pitch deviation and cumulative pitch deviation are presented.4 The measurement and control system based on DSP and FPGA is designed in order to control the motors and detect the signals from grating and inductive probe. The system includes the circuit of motor control, the data acquisition circuit of the grating signal, the AD conversion circuit, the communication circuit and the protection circuit.