RV reducers contain multi-tooth contact characteristics, with high-impact resistance and a small backlash, and are widely used in precision transmissions, such as robot joints. The main parameters affecting the transmission performance include torsional stiffness and transmission errors (TEs). However, a cycloid tooth profile modification has a significant influence on the transmission accuracy and torsional stiffness of an RV reducer. It is important to study the multi-tooth contact characteristics caused by modifying the cycloid profile. The contact force is calculated using a single contact stiffness, inevitably affecting the accuracy of the result. Thus, a new multi-tooth contact model and a TE model of an RV reducer are proposed by dividing the contact area into several differential elements. A comparison of the contact force obtained using the finite element method and the test results of an RV reducer prototype validates the proposed models. On this basis, the influence of load on the different modification methods is studied, including a TE, the mechanical performance, and the transmission efficiency. In addition, the proposed reverse profile is particularly suitable for situations with a large clearance and torque. This study provides a reliable theoretical basis for a multi-tooth contact analysis of a cycloid profile modification.

Transmission error is the key index for characterizing the transmission precision of precision reducers, and its accurate measurement is significant for the precision evaluation of precision reducers. Transmission error is generally measured under the conditions of zero-load and low speed. However, low speed is a general concept and there is no general standard of measurement speed or solid scientific basis. Therefore, it is difficult to obtain consistent transmission precision evaluation results for the same precision reducer. The concept of optimal measurement speed in the transmission precision evaluation of precision reducers was put forward in order to reduce the influence of measurement speed. The determination method of optimal measurement speed was proposed and the calculation model of the optimal measurement speed was established, according to the Stribeck friction model of precision reducers. Taking a certain type of RV reducer as an example, the transmission error measurement experiments were carried out under different speeds. The friction torque of the RV reducer and the peak-to-peak value of the measured transmission error were the least under the optimal measurement speed. The influence of speed on the measurement results can be effectively reduced. The determination of optimal measurement speed of transmission errors could improve the measurement precision of the transmission errors for the objective evaluation of transmission precision of precision reducers.

A sensorless vector active disturbance rejection control (ADRC) method for permanent magnet synchronous motors (PMSM) utilizing a Luenberger observer is presented. This method aims to address the challenges associated with weak active disturbances, substantial steady-state speed amplitude fluctuations, and difficulty in achieving a balance between overshoot and speed control in the sensorless PMSM control system. Mathematical models of the Luenberger observer and the ADRC were analyzed, leading to the proposal of a second-order ADRC control method based on the Luenberger observer. A mathematical model of the permanent PMSM has been introduced. Additionally, the necessary conditions for the convergence of the Luenberger observer were derived and examined. The allowable range of error feedback gain values was determined, and rotor position data were acquired using a phase-locked loop. The principle of the ADRC was analyzed, and the ADRC simulation results, along with the PI simulation results, were detailed. When the target speed is 1000 r/min, the steady-state error and load disturbance resistance of the ADRC control method outperform those of the PI control method. Finally, the control method was experimentally tested on an STM32F4 chip, demonstrating the advantages of small steady-state error and strong active disturbance ability.

Intelligent production of small modulus powder metallurgy gearing requires rapid and accurate measurement to ensure product quality. Currently, the contact measurement method exemplified by gear measuring centers lack efficiency and require gear mounting reference, which prevent them from meeting the requirements for on-line inspection of small modulus gears. Therefore, an optical method of gears was intensively researched. It combined the advantages of laser and vision inspection, which meet the requirements for accuracy and efficiency in on-line inspection. Based on the measurement principle of the line laser sensor and vision camera, a model of the measurement system was established; a standard block was designed to calibrate the system. The surface data of tooth flank were acquired by laser scanning and evaluated to analysis the accuracy. The result of method was validated by comparison with the gear measurement center. Both are of good agreement. Sufficient experiments verify the feasibility of proposed method for on-line inspection.

As the most widely used gear measuring instrument, the gear measuring center can measure the individual deviations of a gear tooth flank other than the comprehensive deviations of the gear. However, gear transmission error is an important transmission performance indicator in the gear meshing process. It is an important trend of gear measuring to obtain the transmission error from individual deviations. In this study, a calculation method of gear transmission error is proposed based on the point clouds of the gear obtained by optical sensors. According to the gear meshing principle, a method is introduced to determine the contact status between the tooth flanks formed by the point clouds. According to this introduced method, the single tooth pair meshing process and the meshing process of multiple tooth pairs are analyzed to determine the gear transmission error curve. The comparison results of tooth contact analysis and gear measurement experiments verify the proposed virtual measurement method.