Mechanical-mathematical model of unbalanced non-rigid gimbal gear

Introduction. The paper is devoted to the development of an ingenious mechanical-mathematical model of the unbalanced non-rigid gimbal gear with account for its axis flexibility. The work objective is to create a new highly adequate model of the imbalance of the basic non-rigid high-speed gimbal drive as an efficient means to solve the problems of balancing under car designing, manufacturing and servicing. Materials and Methods. The descriptive content of the model of the unbalanced transmission is presented as a set of allowances. Formalized schemes of the model of the non-rigid gimbal gear imbalance before and after driving it into rotation are built on their basis. These schemes represent a double-beat model and a model- fragment of the multiple-bearing gimbal gear. Using the relations available in the literature, the following is determined: additional elastic deflection of the axis of the rotating transmission from the initial technological deflection of its axis according to the first eigenform; the coefficient of the elastic deflection modification; and the imbalance of the elastic deflection of non-rigid cardan shaft axles. Research Results. New mathematical models of the cardan transmission imbalance are developed. They help to determine the initial and compensating imbalances in the transmission correction planes perfectly balanced at low speed and driven into rotation at an operating speed. The effect of the compensating imbalances established in the correction planes is considered when balancing the transmission at the operating rotation speed. In this connection, a method for determining the coefficient of change in the elastic deflection of the gear rotation axis is developed. The value of the deflection of the rotation axis of the non-rigid gimbal gear is determined. Discussion and Conclusions. With the help of the obtained results and relations, the following can be performed with high reliability: the substantiation of the standards of accuracy of the transmission balancing; the analysis of its operational imbalance; the classification of the basic car cardan gears by the “flexibility” criterion; the formalization of the solution to the design tasks of the gimbal gear balancing and to other problems of ensuring the balance of this transmission in operation.