Forecast of the quality of manufactured transmission parts based on a probabilistic model of the functioning of technological systems

The method of probabilistic estimation of the kinematic error of transmissions with excessive connections depending on the quality of manufacturing of their parts is considered. The method is based on the results of the analysis of the technological accuracy of the equipment involved in the production of gear parts, followed by the synthesis of a model of gear accuracy. The geometric accuracy of the technological system is the expected errors of the finished product. Its connection with technological accuracy is probabilistic in nature. To open this connection, a separation of systematic and random errors characterizing the technological process was made. On the basis of well-known works on the accuracy of technological processes, a technique for separating systematic and random errors has been developed. The basic formulas of this technique are given. As an example, a method for synthesizing a probabilistic model of the output accuracy of ball screw gears is considered. This method, with minor modifications, can also be used to calculate the kinematic accuracy of roller screw, worm, and spiral-pinion gears. The effectiveness of the developed algorithm for calculating accuracy has been proven in practice. Increasing the efficiency of the method of synthesis of a probabilistic model of the output accuracy of ball screw gears is possible if the influence of elastic properties of transmission parts on its output accuracy is taken into account in the mathematical model: 1) clarified the features of the technological environment in which the production of the main transmission elements with excessive connections is carried out; 2) a method for the synthesis of a probabilistic model of the output accuracy of gears with redundant connections has been developed, which allows taking into account the basic errors of technological systems; 3) the developed probabilistic model is verified based on the hypothesis of normal distribution of manufacturing errors.