The tooth profile modification of cycloidal gears is important in the design and manufacture of precision reducers or rotary vector (RV) reducers for robots. The traditional modification design of cycloidal gears is mainly realized by setting various machining parameters, such as the size and center position of the grinding wheel. The traditional modification design has some disadvantages such as complex modification calculation, uncontrollable tooth profile curve shape and unstable meshing performance. Therefore, a new tooth profile modification method is proposed based on the consideration of the comprehensive influences of pressure angle distribution, meshing backlash, tooth tip and root clearance. Taking the pressure angle and modifications of tooth profile as the parameters of the modification function and the meshing backlash of gear teeth as constraints, the mathematical model for tooth profile modifications is built. The modifications are superimposed on the normal direction of the theoretical profile—the force transmission direction. The mathematical relationship between the modifications and the pressure angle distribution, which determines the force transmission performance, is established. Taking the straight line method, cycloid method and catenary method as examples, by means of the tooth contact analysis technology, the transmission error and minimum meshing backlash, which reflects the lost motion, of the newly modified profile are analyzed and verified. This proposed method can flexibly control the shape change of the modification profile and accurately pre-control the transmission accuracy of the cycloid-pin gear. It avoids the disadvantages of traditional modification methods, such as uncontrollable tooth profile shape and unstable meshing accuracy. The method allows good meshing characteristics, high force transmission performance and more precise tooth profile curve. The study provides a new design method of the modified profile of cycloidal gears.

A real-time optimal control of parallel hybrid electric vehicles (PHEVs) with the equivalent consumption minimization strategy (ECMS) is presented in this paper, whose purpose is to achieve the total equivalent fuel consumption minimization and to maintain the battery state of charge () within its operation range at all times simultaneously. Vehicle and assembly models of PHEVs are established, which provide the foundation for the following calculations. The ECMS is described in detail, in which an instantaneous cost function including the fuel energy and the electrical energy is proposed, whose emphasis is the computation of the equivalent factor. The real-time optimal control strategy is designed through regarding the minimum of the total equivalent fuel consumption as the control objective and the torque split factor as the control variable. The validation of the control strategy proposed is demonstrated both in the MATLAB/Simulink/Advisor environment and under actual transportation conditions by comparing the fuel economy, the charge sustainability, and parts performance with other three control strategies under different driving cycles including standard, actual, and real-time road conditions. Through numerical simulations and real vehicle tests, the accuracy of the approach used for the evaluation of the equivalent factor is confirmed, and the potential of the proposed control strategy in terms of fuel economy and keeping the deviations of at a low level is illustrated.

In order to obtain locally conjugated tooth surface contact, a tooth surface mismatch modification method is proposed based on the fully conjugated characteristics of cycloidal bevel gear. Firstly, according to the principle of fully conjugated, the mathematical model for calculating the cutting parameters of cycloidal bevel gear is established, and the calculating method of the cutting parameters of the fully conjugated tooth surface is deduced. Secondly, the double crowned tooth surface modification method is studied, and the tooth length direction modification is realized by modifying the radius of the cutter blade edge, and the tooth profile direction modification is realized by modifying the shape of cutter blade edge, so that the fully conjugated tooth surfaces meshing with each other are mismatched in the directions of tooth length and tooth profile. On this basis, the mismatch coefficients of tooth surface are calculated by means of polynomial expression of second order. Five coefficients in the mismatch relationship of tooth surface are corrected to modify the tooth surface of pinion again, and the original cutting parameters of pinion are corrected. And then, the required mismatch relationship of tooth surface is obtained. Finally, a pair of cycloidal bevel gear is analyzed in the process of tooth surface mismatch modification. The results of gear cutting experiments are consistent with the simulation results, which verify the effectiveness and feasibility of the proposed tooth surface mismatch modification method.