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.

This paper presents a method to improve the alignment accuracy of mask in linear scale projection lithography, in which the adjacent pixel gray square variance method of CCD image is used to find the best position of the focal length of the motherboard and then realize the alignment of the focal plane. Two image positions in the focal plane from the CCD are compared the traits overlap through the image splicing principle, and to establish the correction of four typical errors on the basis of the whole grating errors. At the same time, using the rotation error of the mask to summarize Grayscale Variation Function of CCD Image, and threshold functions are used to express the factors including wave crests of the amplitude, period error and phase error, which govern the rotation accuracy and weight alignment accuracy expression of the four error factors is established. In the experiment, it is finally corrected the slope of the mask and be adjusted the same direction of the slide plate with the help of dual-frequency laser interferometer, the influence of alignment error on lithography accuracy was discussed and verified in the static case and the CCD maximum resolution pixel corresponds to 0.1 μm, the accuracy of scale is 0.79 μm in only 200 mm measurement range.

Transmission efficiency is the key index when concerning characterizing the performance of precision reducers, and it is usually required to be measured and evaluated. Apart from that, the efficiency value at the rated torque in the efficiency curve is taken as the evaluation value of the efficiency characteristics of precision reducers. However, at present, the research on the efficiency characteristics of precision reducers mainly focuses on theoretical analysis, the development of measurement devices and the measurement methods, while the analysis model of the efficiency curve has not yet been established. In this context, from the perspective of transmission efficiency measurement and evaluation of precision reducers, the efficiency calculation model of precision reducers is established in this paper. Besides, based on the essential change law of the efficiency curve, the efficiency curve analysis model is also set up. To be specific, taking a certain type of RV (rotate vector) reducer as an example, the actual measurement experiments are carried out, and the efficiency curves at different speeds are obtained. The results show that the efficiency of the precision reducer is affected by the measured speed and load torque, and has a positive correlation with the load torque and a negative correlation with the speed. Then, it is proved that the efficiency curve model proposed in this paper can accurately describe the change law followed by the efficiency curve of precision reducers, thus laying a theoretical foundation for the efficiency measurement and evaluation of precision reducers.

In light of the alteration pattern of transmission error following wear of a cycloid gear and needle tooth, this study employs the precision planetary cycloidal 80E reducer as an example. Theoretical deduction and simulation analysis of the change in transmission error were conducted, relying on the Archard wear model and an error model. Utilizing the principles of Archard wear theory and error theory, a functional relationship between wear duration and transmission error is deduced. Subsequently, a dynamic simulation of the 3D model is executed using ADAMS software, and the simulation results are processed with MATLAB software. A comparative and analytical examination is conducted between the theoretical curve and the simulation curve of transmission error to explore the influence of the cycloid gear and needle tooth wear on transmission error. Finally, the precision of the simulation results is further confirmed through experimental validation. The findings revealed that the transmission error curve gradually increased during the initial wear of the cycloid gear and the needle tooth, with the rate of increase increasing proportionally with wear duration. By comparing the theoretical calculations, simulation outcomes, and experimental results, the validity and accuracy of the transmission error calculations grounded in Archard wear theory and error theory are confirmed. This research provides a theoretical basis for accurately predicting the survival of precision planetary cycloidal reducers throughout the lifespan.

With the development of intelligent manufacturing systems, data-driven fault diagnosis has become a hot research topic. Traditional data-driven fault diagnosis methods often rely on expert-extracted features, wherein feature extraction process requires considerable effort and affects the final results to a great extent. However, end-to-end fault diagnosis methods based on deep learning can automatically learn feature representations from raw data. In this study, first, the raw vibration signals of various fault states of a planetary gearbox were segmented and preprocessed into input table data types. Second, a convolutional neural network with wide kernels in the first layer was used to extract gear fault features from the raw vibration data of the gearbox. Then, the multi-head attention mechanism was incorporated to focus on different feature spaces and obtain diverse feature information. Finally, using the Softmax layer, the fault features were classified and fault diagnosis of the gearbox was achieved. Validation experiments and comparative analysis indicated that the proposed fault diagnosis model exhibits stronger learning ability as well as a simpler and convenient diagnostic process compared with the traditional methods. The proposed model has broad application prospects in data-driven fault diagnosis.