Influence of geometric parameters of crankshaft-planetary reducer on cyclograph of work of contact pairs

Background. Crank-planetary reducers (CPR) have a number of advantages: compactness, high load capacity, high structural rigidity, to name a few. At the same time, there is no regulated methodology for their kinematic and force calculation, which limits their development and mass production. The creation of effective methods for calculating these reducers to improve their performance at the design stage is of great practical importance. Objective. The aim of this work is to develop an analytical method for calculating the angle of pressure and the contact force in contact pairs “satellite hole – pin of output link” of the CPR depending on the angle between the cranks of its crankshaft (V-shaped), number of satellites and number of pins. Based on the developed method, check the possibility of designing a CPR with arbitrary values of these parameters and investigate their impact on the cyclogram of contact pairs and the associated maximum value of contact force, taking into account the nonlinearity of materials’ deformation. Methods. At the first stage, based on the formulas of analytical geometry, the possibility of theoretical implementation of CPR with an arbitrary value of the angle between the crankshaft cranks, the number of satellites and the number of pins of the output link is shown. The values of pressure angles in the contact pairs “satellite hole – pin of output link” are analysed and on the basis of the received results the cyclogram of work of leading pairs is calculated. In the second stage, using the principle of possible displacements, the formula for calculating the contact force in the leading contact pairs is written as a function of the input shaft rotation angle. When calculating the contact force, a nonlinear model of material deformation was used. Results. An analytical method for constructing a cyclogram of the contact pairs of a CPR and the contact forces calculation was developed depending on the geometric parameters of the reducer. The possibility of theoretical implementation of reducers with arbitrary value of the angle between the crankshaft cranks, the number of satellites and the number of output link’s pins is shown Conclusions. The dependence of the contact force is obtained as a rotation angle function, the number of satellites and the number of source pins. With a constant number of simultaneously active leading contact pairs and, accordingly, a uniform load transfer between them, the law of change in the contact force per cycle is similar to parabolic. Otherwise, the change in the contact force per cycle is quite complex. The obtained results can be used in the refined calculation of the efficiency of the CPR and in making various design decisions at the design stage