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 manufacturing error of a cycloidal gear is the key factor affecting the transmission accuracy of a robot rotary vector (RV) reducer. A methodology is proposed to realize the digitized measurement and data processing of the cycloidal gear manufacturing error based on the gear measuring center, which can quickly and accurately measure and evaluate the manufacturing error of the cycloidal gear by using both the whole tooth profile measurement and a single tooth profile measurement. By analyzing the particularity of the cycloidal profile and its effect on the actual meshing characteristics of the RV transmission, the cycloid profile measurement strategy is planned, and the theoretical profile model and error measurement model of cycloid-pin gear transmission are established. Through the digital processing technology, the theoretical trajectory of the probe and the normal vector of the measured point are calculated. By means of precision measurement principle and error compensation theory, a mathematical model for the accurate calculation and data processing of manufacturing error is constructed, and the actual manufacturing error of the cycloidal gear is obtained by the optimization iterative solution. Finally, the measurement experiment of the cycloidal gear tooth profile is carried out on the gear measuring center and the HEXAGON coordinate measuring machine, respectively. The measurement results verify the correctness and validity of the measurement theory and method. This methodology will provide the basis for the accurate evaluation and the effective control of manufacturing precision of the cycloidal gear in a robot RV reducer.

In order to improve the tooth surface geometric accuracy and transmission quality of hypoid gears, a new digitized reverse correction method is proposed based on the measurement data from a one-dimensional probe. The minimization of tooth surface geometrical deviations is realized from the perspective of mathematical analysis and reverse engineering. Combining the analysis of complex tooth surface generation principles and the measurement mechanism of one-dimensional probes, the mathematical relationship between the theoretical designed tooth surface, the actual machined tooth surface and the deviation tooth surface is established, the mapping relation between machine-tool settings and tooth surface deviations is derived, and the essential connection between the accurate calculation of tooth surface deviations and the reverse correction method of machine-tool settings is revealed. Furthermore, a reverse correction model of machine-tool settings is built, a reverse correction strategy is planned, and the minimization of tooth surface deviations is achieved by means of the method of numerical iterative reverse solution. On this basis, a digitized reverse correction system for hypoid gears is developed by the organic combination of numerical control generation, accurate measurement, computer numerical processing, and digitized correction. Finally, the correctness and practicability of the digitized reverse correction method are proved through a reverse correction experiment. The experimental results show that the tooth surface geometric deviations meet the engineering requirements after two trial cuts and one correction.

The accurate measurement of tooth surface deviation is an important prerequisite for the quality monitoring of high-precision spiral bevel gears. A measurement method for tooth surface deviation of spiral bevel gears is proposed based on a one-dimensional probe, which can accurately measure and evaluate tooth flank. According to the forming principle of the spiral bevel gear tooth surface, the theoretical surface is constructed as the measurement reference flank. A series of measures and methods are adopted to ensure the accuracy and correctness of one-dimensional probe measurement. These effective methods include the construction of a precise positioning model of the gear blank and its surface, the measurement planning of reduction dimension which the gear needs to rotate once the normal angle after each point is measured, and the compensation for the increasing dimension of the one-dimensional probe. In addition, minimization of the normal deviation of the tooth flank is achieved by using the optimum matching technique of the theoretical and the actual surfaces. The deviation degree of the actual surface relative to the theoretical surface can be accurately calculated and evaluated by establishing a deviation model, which ensures the correctness of the evaluation result of the deviation. Finally, the test of tooth surface deviation is carried out on a JD45+ gear measuring center (GMC) using a one-dimensional probe and a Gleason 650GMS GMC using a three-dimensional probe. The measurement results show that the evaluation results of the one-dimensional probe are in good agreement with those of the three-dimensional probe. The proposed theory and method not only expand the measurement range of the GMC using a one-dimensional probe, but also have certain reference significance for the precision measurement of other complex surfaces.

Due to the inconsistency between a theoretically designed tooth surface and the actual measured reference surface, the tooth surface error data obtained by the traditional measurement method is unreliable, and incorrectly reflects the machining accuracy of straight bevel gears. This has become a key problem in the current measurement process, and needs to be resolved. In this paper, a new measurement method is proposed to achieve accurate measurement and evaluation of the machining error of straight bevel gears. The 3-dimensional (3D) model surface designed by the manufacturer is directly extracted as a theoretical reference to complete the measurement, which ensures the correctness of the error results. A measurement strategy of normal rotation of the measured point is adopted to make up for the disadvantages of the one-dimensional (1D) probe and improve the measurement accuracy. The problem of the sensitive direction of the probe deviating from the normal direction is compensated for by increasing the dimension of the 1D probe and reducing the dimension of the 3D normal. According to the constructed error calculation model, the minimum tooth surface error is obtained through reconstruction and optimal matching techniques. Finally, the accuracy and effectiveness of the measurement method are verified through measurement comparison experiments. This method solves the technical problem of the inconsistency of the measured reference surface, and uses a low-cost 1D probe to achieve precise measurement of the 3D surface. It not only improves the disadvantages of current measurement methods, but also provides effective technical support for other gear measurements.