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The remaining useful life prediction of Industrial robot RV reducer is challenging due to the strong redundancy, unstable degradation initiation point, and environmental interference that may obscure the key state information during long-term operation. To address this problem, this paper proposes a novel remaining useful life prediction method for robot RV reducer with multi-depth network and multi-kernel support vector data description. Firstly, the degradation features are constructed by the hidden layer node of deep belief network to reduce the interference and redundancy. Secondly, the first predicting time node is determined by multi-kernel support vector data description to locate the stable degradation initiation node. Then, the temporal convolutional network is applied to predict the remaining useful life in the degradation stage, which improves the prediction accuracy. Finally, the effectiveness of the proposed method is verified by the accelerated fatigue experiment of a self-made robot. [ABSTRACT FROM AUTHOR]

The cycloid gear wear of RV reducers leads to the degradation of the industrial robots' transmission accuracy, but the degradation law with respect to the wear volume is still unclear. In this paper, a method for determining transmission error (TE) through a combination of numerical and simulation analysis is proposed. The wear model of cycloid gear was ascertained based on the theory of Archard. Then, the full rigid body and rigid–flexible coupling model of RV reducers were established using the multibody dynamics theory. Finally, the static transmission error (STE) and dynamic transmission error (DTE) were investigated. The results show that as working hours increase, the cycloid gear wear volume increases, and transmission accuracy deteriorates, but the rate tends to slow down. [ABSTRACT FROM AUTHOR]

Due to the noise interference and the weak characterization ability of the fault vibration signal of rotation vector (RV) reducer crankshaft bearing, it is difficult to obtain satisfactory results for the available fault diagnosis methods. For that, this paper proposes a variable‐speed‐condition fault diagnosis method with WSO‐VMD and ResNet‐SWIN. A signal reconstruction method with WSO‐VMD was carried out, Firstly, the performance of VMD algorithm is improved by using war strategy optimization algorithm to select parameters adaptively. Then the signal is reconstructed considering the fault characteristic frequency, so as to realize the noise reduction of the signal. By using the residual network module and attention mechanism to replace the first stage of the original SWIN model, a novel ResNet‐SWIN fault diagnosis model is established to enhance the feature extraction ability for the weak signal. The experiments with the constant‐operating‐condition and the variable‐operating‐condition are carried out to verify the effectiveness of the proposed method. The results show that, whether at variable‐speed or constant‐speed conditions, WSO algorithm has been proven to be the fastest convergence speed compared with WOA, SSA, and NGO optimization algorithms, and by the signal reconstruction with WSO‐VMD, the variance evaluation indicator of the reconstructed signal has 36%, 21%, 46%, and 40%, respectively. ResNet‐SWIN model has achieved the optimal diagnosis accuracy compared with SWIN, VIT, and CNN‐SVM models in both variable‐speed and constant‐speed conditions. [ABSTRACT FROM AUTHOR]

The thin-walled rings of the RV reducer main bearings are prone to structural elastic deformation, which can significantly change the bearing mechanical characteristics. According to the actual assembly state of the RV reducer, the simulation model of the planetary frame–main bearings–pin gear housing is established considering the ring deformation. The model was used to calculate and comparatively analyze the ring deformation and contact characteristics of thin-walled bearings under rigid and flexible conditions, on the basis of which the mechanism of ring deformation was described, and the effects of load conditions, ring thickness and radial clearance on ring deformation, flexible contact characteristics, and ultimate carrying capacity were analyzed. The results show that the distribution of contact loads is the main factor affecting the ring deformation. The ring deformation can optimize the bearing contact characteristics, and the greater the deformation, the more pronounced the optimization effect. However, excessive ring deformation makes the contact ellipse more susceptible to truncation, which, in turn, reduces the ultimate carrying capacity. This study indicates a 38.2% decrease in the carrying capacity of the flexible ring model compared to that of the rigid ring model. In this paper, the effect of ring deformation on bearing mechanical characteristics is deeply discussed. The research results have important guiding significance for the structural optimization design of thin-walled bearings. [ABSTRACT FROM AUTHOR]

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters' variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system. [ABSTRACT FROM AUTHOR]

In order to study the influence of various factors on the transmission error of an RV (rotate vector), the working principle and structure of reducer are analyzed, and the ratio is calculated. The mass-spring equivalent model is used to calculate the force, and the mathematical model of transmission error is established and combined with the translation-torsion coupling model. The transmission performance of the RV reducer was characterized using ADAMS and compared with the mathematical model. The effects of three different modification methods and load analysis techniques at different output terminals on the transmission error and frequency ratio are compared. Increasing the meshing clearance between cycloid gear and pin tooth will increase the error. An RV reducer test bench is established to compare the influence of different speeds and torques on transmission error. The analysis shows that the gap between the secondary cycloidal pin gear transmission and the crankshaft installation error is the main cause of the tooth gap. The simulation and experimental results verify the accuracy of the mathematical model. [ABSTRACT FROM AUTHOR]

Grease in the normal operation of the rotate vector (RV) reducer has a role that cannot be ignored, for the variable working conditions of the RV reducer, the performance of the lubricant changes directly affect its reliable operation. Therefore, the study of the rheological properties of the grease has become the focus of the study of RV reducer performance. Here, SK‐1A grease is taken as the research object, and its rheological characteristics under wide temperature range working conditions (−20–40°C) are investigated through rheological experiments to analyze the potential influence of the performance of RV reducer. However, the ordinary way of research is too complicated to better research the rheological properties of grease for a variety of working conditions. The Elman neural network (ENN) model was used to predict the rheological properties, and the results were compared with those of back propagation (BP) and radial basis function (RBF) neural networks. The results demonstrate that the ENN model demonstrates high prediction accuracy for grease rheological property prediction by comparing three types of predictions. This method can provide a theoretical reference for the accurate prediction of the rheological properties of lubricating grease affected by complex multifactors. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Light Industry Machinery is the property of Light Industry Machinery Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The rotary vector (RV) reducer is one of the most important transmission components inside the joints of robots. The high precision motion control of the robot can be realized in the normal operation and service life of agricultural robots. However, the complex structure of the RV reducer cannot fully meet the variable conditions in actual work and the harsh working environment. Mechanical, cracks, and pitting faults can often occur at the same time or successively in actual operation, due to lubrication, manufacturing errors, and unreasonable forces. The signals collected by the sensor are also the mutual coupling of multiple fault sources. Therefore, it is necessary to explore the composite fault diagnosis of the RV reducer. In this study, a blind fault separation was proposed from the compound signals of the RV reducer using time-frequency image ridge extraction and improved sparse component analysis. The fault feature of the RV reducer was then extracted from the core transmission component of agricultural robots. The composite fault diagnosis of the RV reducer was finally realized with the unknown number of fault sources under the reciprocating motion of the joint arm and the time-varying speed of the agricultural robot. Firstly, the ridge extraction from time-frequency images (RETF) was used to synchronously intercept the vibration signals of the manipulator in the constant speed period. Then, the blind source separation (SMF-DPC-OMP) was combined with the sinC function to improve morphological filtering (SMF), density peak clustering (DPC), and orthogonal matching pursuit (OMP), in order to separate and extract the composite faults of stationary signals. The sinC function was taken as a new structural element to construct the average combined morphological filter. The vibration signal in the constant speed period was subjected to morphological filtering for better impact characteristics and sparsity of the signal. The DPC was used to estimate the mixing matrix of sparse signals, and then the sensing matrix was constructed. The separation source signal was reconstructed to combine with the OMP algorithm in the frequency domain. Finally, the reconstructed time-domain signal was subjected to the fast Fourier transform for fault identification. The test bench was utilized to collect the composite fault signals of the sun gear and planetary gear wear of the RV reducer. The results show that the blind separation was effectively realized on the composite faults of the RV reducer. The RETE was used to identify the motion state of the RV reducer, when the timefrequency diagram was blurred, due to the variable speed condition. The SMF-DPC-OMP effectively completed the blind separation of composite faults when the number of fault sources was unknown. The SMF-DPC-OMP saved about 75% of the running time cost than before. A more concise spectrum was achieved to better suppress the fine side frequency and interference components. It is suitable for the composite fault diagnosis of the RV reducer in the articulated industrial robot. The finding can provide a strong reference for the fault feature extraction in the actual production. [ABSTRACT FROM AUTHOR]

Abstract Grease in the normal operation of the rotate vector (RV) reducer has a role that cannot be ignored, for the variable working conditions of the RV reducer, the performance of the lubricant changes directly affect its reliable operation. Therefore, the study of the rheological properties of the grease has become the focus of the study of RV reducer performance. Here, SK‐1A grease is taken as the research object, and its rheological characteristics under wide temperature range working conditions (−20–40°C) are investigated through rheological experiments to analyze the potential influence of the performance of RV reducer. However, the ordinary way of research is too complicated to better research the rheological properties of grease for a variety of working conditions. The Elman neural network (ENN) model was used to predict the rheological properties, and the results were compared with those of back propagation (BP) and radial basis function (RBF) neural networks. The results demonstrate that the ENN model demonstrates high prediction accuracy for grease rheological property prediction by comparing three types of predictions. This method can provide a theoretical reference for the accurate prediction of the rheological properties of lubricating grease affected by complex multifactors.

The cycloid gear wear of RV reducers leads to the degradation of the industrial robots’ transmission accuracy, but the degradation law with respect to the wear volume is still unclear. In this paper, a method for determining transmission error (TE) through a combination of numerical and simulation analysis is proposed. The wear model of cycloid gear was ascertained based on the theory of Archard. Then, the full rigid body and rigid–flexible coupling model of RV reducers were established using the multibody dynamics theory. Finally, the static transmission error (STE) and dynamic transmission error (DTE) were investigated. The results show that as working hours increase, the cycloid gear wear volume increases, and transmission accuracy deteriorates, but the rate tends to slow down.

In view of the noise generated during the operation of the RV reducers, the tooth surface of the involute gear and the cycloid gear are modified, the modification amount is obtained based on the empirical modification formula, and the orthogonal test table is established. With the RV110E type reducer as the research object, the noise value of the reducer under different modifications is obtained based on the RecurDyn software. The results show that the noise reduction effect of the RV reducer is significant for the involute gear modification, and the maximum noise value is reduced by 7.78 dB(A). The virtual prototype of the RV110E type reducer is built with Romax software, and the parameters of involute gear modification are imported. Comparing the simulation results before and after the modification, it can be seen that the transmission error of the combined modified involute gear is reduced, the peak load per unit length of the tooth surface is reduced, the problem of tooth surface off-load and noise are improved, and the transmission stability of the reducer is effectively improved. The research results have certain reference significance for gear modification of different types of RV reducers.

Aiming at the demand for reliability evaluation of RV reducers, the Gamma models, which can represent the performance degenerate process of reducers, are established respectively combining with transmission error data and backlash data of reducer performance degenerate test. A maximum likelihood estimation method is applied to estimate the parameters of degenerate models. Taking the models above as marginal distribution functions, a binary degenerate model of RV reducers is established through Copula function. The reliability and expected failure life of RV reducers are evaluated. The results show that the reliability evaluated by degenerate models based on transmission error and backlash is essentially in agree with the test results. The models can represent the degenerate process of RV reducers accurately. Gaussian Copula function is more suitable for representing the correlation between transmission error degenerate data and backlash degenerate data. Through the binary degenerate model, the expected failure life of RV reducers can be evaluated at different reliability under this working condition.

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Rotate vector (RV) reducers have advantages of high torque ratio, and extremely reliable functioning under dynamic load conditions, and so forth, and they are extensively used in precision transmissions, such as industrial robots. The torsional stiffness of RV reducers is a main parameter affecting the meshing vibration and transmission performance. In addition, the variable loads and tooth modifications have significant influence on the torsional stiffness of RV reducers. In this paper, a new method of calculating torsional stiffness for RV reducers considering variable loads and tooth modifications is presented. The dynamic stress and deformation of meshing teeth are calculated based on Hertz formulation, and the number of meshing teeth is determined by analyzing the dynamic stress of meshing teeth. Then, the torsional stiffness of RV reducers is obtained. Finite element method is applied to calculate the deformation of cycloidal‐pin gear in the maximum force position δmax. The influence of variable applied loads and different tooth modifications of cycloidal‐pin gear transmission on torsional stiffness are also studied. The results show that variable applied loads and different tooth modifications influence the torsional stiffness of RV reducers by changing teeth deformation and clearance, respectively. [ABSTRACT FROM AUTHOR]

The rotating arm bearing is a key component of RV reducers, and its dynamic parameters directly affect the overall performance of RV reducers. Thus, taking the rotating arm bearing of RV reducers as the research object and considering the geometric parameters of the rotating arm bearing and the change of physical parameters under the working condition, a dynamic calculation model of the rotating arm bearing is established. The relationship between the bearing clearance, oil film thickness, temperature rise and the synthetic clearance of the rotating arm bearing is analyzed. The influence of the bearing clearance on the time-varying support stiffness of the rotating arm bearing under different working conditions is obtained by numerical calculation. With the decrease of the synthetic clearance, the radial support stiffness of the bearing tends to be stable. The results show that when considering the synthetic clearance of the rotating arm bearing, the radial support stiffness decreases by 9.7%, so the influence of the synthetic clearance of the rotating arm bearing on the dynamic performance of the system cannot be ignored.

The thin-walled rings of the RV reducer main bearings are prone to structural elastic deformation, which can significantly change the bearing mechanical characteristics. According to the actual assembly state of the RV reducer, the simulation model of the planetary frame–main bearings–pin gear housing is established considering the ring deformation. The model was used to calculate and comparatively analyze the ring deformation and contact characteristics of thin-walled bearings under rigid and flexible conditions, on the basis of which the mechanism of ring deformation was described, and the effects of load conditions, ring thickness and radial clearance on ring deformation, flexible contact characteristics, and ultimate carrying capacity were analyzed. The results show that the distribution of contact loads is the main factor affecting the ring deformation. The ring deformation can optimize the bearing contact characteristics, and the greater the deformation, the more pronounced the optimization effect. However, excessive ring deformation makes the contact ellipse more susceptible to truncation, which, in turn, reduces the ultimate carrying capacity. This study indicates a 38.2% decrease in the carrying capacity of the flexible ring model compared to that of the rigid ring model. In this paper, the effect of ring deformation on bearing mechanical characteristics is deeply discussed. The research results have important guiding significance for the structural optimization design of thin-walled bearings.

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.

This paper proposed method that combined transmission path analysis (TPA) and empirical mode decomposition (EMD) envelope analysis to solve the vibration problem of an industrial robot. Firstly, the deconvolution filter timedomain TPA method is proposed to trace the source along with the time variation. Secondly, the TPA method positioned the main source of robotic vibration under typically different working conditions. Thirdly, independent vibration testing of the Rotate Vector (RV) reducer is conducted under different loads and speeds, which are key components of an industrial robot. The method of EMD and Hilbert envelope was used to extract the fault feature of the RV reducer. Finally, the structural problems of the RV reducer were summarized. The vibration performance of industrial robots was improved through the RV reducer optimization. From the whole industrial robot to the local RV Reducer and then to the internal microstructure of the reducer, the source of defect information is traced accurately. Experimental results showed that the TPA and EMD hybrid methods were more accurate and efficient than traditional time-frequency analysis methods to solve industrial robot vibration problems. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to reveal the influence law of RV reducer modal on transmission error, the RV-40E is used as the research object, the equivalent model method is used to construct its mass stiffness dynamic model and then the mathematical model of the RV reducer transmission error and natural frequency is established. For the intermediate stiffness, it is found that the transmission error is negatively correlated with the natural frequency. In order to verify the model, the RV-40E products of Nabtesco and domestic companies are selected to conduct a comparative test of natural frequency, stiffness and transmission error. It is found that the greater the first-order natural frequency of the RV reducer is, the greater the stiffness was and the smaller the transmission error is. The above research provides a method for the modal and performance testing of the RV reducer, and provides an important reference basis for the transformation of the RV reducer from structure design to performance design.

The rotation error is the most important quality characteristic index of a rotate vector (RV) reducer, and it is difficult to accurately optimize the design of a RV reducer, such as the Taguchi type, due to the many factors affecting the rotation error and the serious coupling effect among the factors. This paper analyzes the RV reducer rotation error and each factor based on the deep Gaussian processes (DeepGP) model and Sobol sensitivity analysis(SA) method. Firstly, using the optimal Latin hypercube sampling (OLHS) approach and the DeepGP model, a high-precision regression prediction model of the rotation error and each affecting factor was created. On the basis of the prediction model, the Sobol method was used to conduct a global SA of the factors influencing the rotation error and to compare the coupling relationship between the factors. The results show that the OLHS method and the DeepGP model are suitable for predicting the rotation error in this paper, and the accuracy of the prediction model constructed based on both of them is as high as 95%. The rotation error mainly depends on the influencing factors in the second stage cycloidal pinwheel drive part. The primary involute planetary part and planetary output carrier's rotation error factors have little effect. The coupling effects between the matching clearance between the pin gear and needle gear hole ( δ J ) and the circular position error of the needle gear hole ( δ t ) is noticeably stronger. [ABSTRACT FROM AUTHOR]

With the increase of service time, the rotation period of rotating machinery may become irregular, and the Ensemble Empirical Mode Decomposition (EEMD)can effectively reflect its periodic state. In order to accurately evaluate the working state of the Rotate Vector (RV) reducer, the torque transfer formula of the RV reducer is first derived to theoretically prove periodicity of torque transfer in normal operation. Then, EEMD is able to effectively reflect the characteristics of data periodicity. A fault diagnosis model based on EEMD-MPA-KELM was proposed, and a bearing experimental dataset from Xi'an Jiaotong University was used to verify the performance of the model. In view of the characteristics of the industrial robot RV reducer fault was not obvious and the sample data is few, spectrum diagram was used to diagnose the fault from the RV reducer measured data. The EEMD decomposition was performed on the data measured by the RV reducer test platform to obtain several Intrinsic Mode Functions (IMF). After the overall average checking and optimization of each IMF, several groups of eigenvalues were obtained. The eigenvalues were input into the Kernel Extreme Learning Machine (KELM) optimized by the Marine Predators Algorithm (MPA), and the fault diagnosis model was established. Finally, compared with other models, the prediction results showed that the proposed model can judge the working state of RV reducer more effectively. [ABSTRACT FROM AUTHOR]

The robot joint is an important component of the construction robot, and its fault diagnosis can ensure the exact execution of building jobs, stable operation, and timely prevention of probable safety mishaps. However, deep learning‐based fault diagnosis needs a multitude of measured fault data, which is difficult to obtain for various reasons. To solve the problem of insufficient data, a digital twin‐assisted fault diagnosis system for robot joints is proposed. First, a simplified dynamics model of the robot joint is developed to generate the virtual entity data which can be used as the X‐domain data for the digital twin model. Second, a CycleGAN‐based digital twin model is proposed to map the virtual entity (X‐domain) data to the physical entity (Y‐domain) utilizing only a small amount of measured data. In the end, a test‐rig for the robot joint is built to simulate the robot's working conditions, and the CNN‐ResNet classifier is utilized to verify the effectiveness of the simulated data generated by the digital twin model. The results show that the fault diagnosis accuracy can be increased from 32.5% to 98.86% utilizing only 400 sets of measured data. [ABSTRACT FROM AUTHOR]

There are many factors affecting the assembly quality of RV （Rotate Vector） reducer， and the assembly quality is unstable. In response to this situation， an optimized BP neural network quality prediction model based on the Sparrow Search Algorithm （SSA） is established. The transmission error of the key performance index of the reducer is used as the output index， and the key size parameters of the assembly parts are selected as the input influencing factors. After data preprocessing， use the quality prediction model to make predictions. The results show that the BP neural network prediction model improved by the Sparrow algorithm has good prediction accuracy， can effectively predict the selected index parameters， and provides help for the selection of parts in the assembly link of the RV reducer.

This paper proposes a new method for predicting rotation error based on improved grey wolf–optimized support vector regression (IGWO-SVR), because the existing rotation error research methods cannot meet the production beat and product quality requirements of enterprises, because of the disadvantages of its being time-consuming and having poor calculation accuracy. First, the grey wolf algorithm is improved based on the optimal Latin hypercube sampling initialization, nonlinear convergence factor, and dynamic weights to improve its accuracy in optimizing the parameters of the support vector regression (SVR) model. Then, the IGWO-SVR prediction model between the manufacturing error of critical parts and the rotation error is established with the RV-40E reducer as a case. The results show that the improved grey wolf algorithm shows better parameter optimization performance, and the IGWO-SVR method shows better prediction performance than the existing back propagation (BP) neural network and BP neural network optimized by the sparrow search algorithm rotation error prediction methods, as well as the SVR models optimized by particle swarm algorithm and grey wolf algorithm. The mean squared error of IGWO-SVR model is 0.026, the running time is 7.843 s, and the maximum relative error is 13.5%, which can meet the requirements of production beat and product quality. Therefore, the IGWO-SVR method can be well applied to the rotate vector (RV) reducer parts-matching model to improve product quality and reduce rework rate and cost. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Cycloid gear tooth profile modification is very important to the performance of RV reducer，in order to select the shape modification method and parameter size reasonably and improve the stress state of the cycloid tooth surface，an equidistant & radical-moving modification method based on particle swarm optimization algorithm to optimize bearing capacity is proposed. Based on the RV-60E reducer as an optimization example，the mechanical analysis of the cycloid needle wheel transmission part is carried out first，and the mathematical model of the cycloid wheel shape is established with the goal of reducing the maximum bearing capacity of the needle teeth. The required shape modification parameter values and tooth profile curve are obtained by using the proposed optimization design method. Compared with equidistant trimming，radical-moving and angle fitting modification methods，it is found that the maximum contact force of cycloidal gear profile modification method based on particle swarm optimization algorithm is reduced by 15.9%，16.0% and 11.8%，respectively，thus improving the bearing capacity and life of RV reducer.

Taking RV-40E reducer as the object，the dynamic characteristics of RV reducer under free mode are studied by combining modal simulation and modal analysis experiment. Firstly，the RV reducer is modeled and simulated based on Ansys，and the simulation results of natural frequency and mode shape are obtained. After comparing the experimental modalities of the domestic and Nabtesco RV-40E reducer，the test results show that the first-order modal of domestic RV-40E reducer is generally lower than that of Nabtesco，with a maximum difference of 11.1%. At the same time，the simulation and experimental results are compared. The largest domestic difference in the first-order mode is -5.8%，and that of Nabtesco is +5.9%. The above research provides effective data and methods for the structural optimization design and modal performance analysis of the RV reducer.

There are many factors affecting the assembly quality of rotate vector reducer, and the assembly quality is unstable. Matching is an assembly method that can obtain high-precision products or avoid a large number of secondary rejects. Selecting suitable parts to assemble together can improve the transmission accuracy of the reducer. In the actual assembly of the reducer, the success rate of one-time selection of parts is low, and "trial and error assembly" will lead to a waste of labor, time cost, and errors accumulation. In view of this situation, a dendritic neural network prediction model based on mass production and practical engineering applications has been established. The size parameters of the parts that affected transmission error of the reducer were selected as influencing factors for input. The key performance index of reducer was transmission error as output index. After data standardization preprocessing, a quality prediction model was established to predict the transmission error. The experimental results show that the dendritic neural network model can realize the regression prediction of reducer mass and has good prediction accuracy and generalization capability. The proposed method can provide help for the selection of parts in the assembly process of the RV reducer. [ABSTRACT FROM AUTHOR]

In fault diagnosis research, compound faults are often regarded as an isolated fault mode, while the association between compound faults and single faults is ignored, resulting in the inability to make accurate and effective diagnoses of compound faults in the absence of compound fault training data. In an examination of the rotate vector (RV) reducer, a core component of industrial robots, this paper proposes a compound fault identification method that is based on an improved convolutional capsule network for compound fault diagnosis of RV reducers. First, one-dimensional convolutional neural networks are used as feature learners to deeply mine the feature information of a single fault from a one-dimensional time-domain signal. Then, a capsule network with a two-layer stack structure is designed and a dynamic routing algorithm is used to decouple and identify the single fault characteristics for compound faults to undertake the diagnosis of compound faults of RV reducers. The proposed method is verified on the RV reducer fault simulation experimental bench, the experimental results show that the method can not only diagnose a single fault, but it is also possible to diagnose the compound fault that is composed of two types of single faults through the learning of two types of single faults of the RV reducer when the training data of the compound faults of the RV reducer are missing. At the same time, the proposed method is used for compound fault diagnosis of bearings, and the experimental results confirm its applicability. [ABSTRACT FROM AUTHOR]

In order to discuss the influence of wear dynamic evolution on the degradation of core transmission performance, transmission error and meshing torsional stiffness of RV reducer, taking BX-40E reducer as the research object, based on Langkali-Nikraves contact force model and Archard wear theory, the wear coefficients with different position conditions were obtained through equivalent wear experiments. The RV transmission dynamic model considering wear, meshing stiffness, meshing force, meshing tooth pairs and transmission error linkage was established by using centralized parameter method and dynamic subsystem method. Compared with the traditional tooth profile wear simulation, which distribution and size of the wear depth curves were more and more different with wear dynamic evolution, theoretically concluded that the dynamic update of wear coefficient is necessary and correct for the accurate simulation of tooth surface wear. The transmission error shows a "double hump" distribution mapped to the wear depth of the tooth profile, and deteriorates with the wear accumulation. The equivalent torsional stiffness of cycloid pin teeth decreases piecewise approximately linearly due to wear. In the previous stage, the reduction rate is small because the tooth detachment first occurs at the tooth top and root, and the single tooth torsional stiffness near the tooth top and root is smaller. The research results provide a new idea and theoretical basis for improving the transmission accuracy, stability holding ability, wear reduction and life extension of RV reducer. [ABSTRACT FROM AUTHOR]

In order to analyze the resonance response of RV gear reducer system，the natural frequency of RV gear reducer system should be determined first. Taking RV-320E gear reducer as the research object and considering tangential degrees of freedom of crank shaft and cycloid wheel rotation motion，the 16 degrees of freedom dynamic model of RV gear reducer is established by centralized mass method. The dynamics differential equation of the system is established by Newton's second law and the differential equation of fixed axis rotation，and the natural frequency of the system is calculated. The influence of the material properties of the parts on the first-order natural frequency is analyzed and the influence graph is drawn.

The CAD parametric modeling of RV reducer parts is carried out， and the parametric assembling model of cycloidal gear modification amount and dimension error of parts is established. Based on multi-body dynamics simulation technology， with bearing clearance， dynamics simulation model that includes gear contact and pin-slot contact is established. Considering the small period factors that affect the angular transmission error of RV reducer， the diameter of the needle tooth center circle and the diameter of the needle tooth groove in the same assembly dimension chain are selected to combine the errors， and the dynamics simulation is carried out under rated working conditions，the variation rule of the angular transmission error is analyzed.

The transmission characteristics of the precision RV reducer is mainly determined by the mesh state of planetary gears and input gear shaft，and vibration modal characteristics of the crank shaft have important effects on the dynamic behavior of the RV reducer. Taking the RV-80E as an example，based on the 3D model of the first-stage reducer，the vibration modal characteristics of the crank shaft considering three states，namely the free，bearing support and mesh state，are obtained using the finite element analysis method. Through the simulation analysis， induced by the meshing gear series，the two eccentric shaft edges and the head deformation of the crank shaft considering the mesh state is the biggest，better with the working mode of the RV reducer than the other states，and the natural frequencies of the crank shaft increase remarkably. The research results provide a theoretical basis for optimization design of dynamic characteristics and meshing characteristics of crank shaft in first-stage reducer part.

Due to their advantages of compact size, high reduction ratio, large stiffness and high load capacity, RV reducers have been widely used in industrial robots. The dynamic characteristics of RV reducers in terms of vibratory response and dynamic transmission error have a significant influence on positioning accuracy and service life. However, the current dynamic studies on RV reducers are not extensive and require deeper study. To bridge this gap, a more effective and realistic lumped parameter dynamic model for RV reducers is developed, considering the tooth profile modification of cycloid gears and system errors. Firstly, for an efficient solution, the equivalent pressure angle and equivalent mesh stiffness of the cycloid–pin gear pair are introduced in the dynamic model based on the loaded tooth contact analysis. Secondly, the differential equations of the system are derived by analyzing the relative displacement relationships between each component, which are solved using the Runge–Kutta method. With this, the effects of errors such as machining errors, assembly errors and bearing clearances on the dynamic behaviors and transmission precision are investigated by comparison to quantify or qualify their influence. This research is helpful in characterizing the multi-tooth mesh and dynamic behavior, and revealing the underlying physics of the RV reducer.

In order to get the optimal profile of cycloid gear after sectional modification, a multi-objective optimization design method is proposed that considers both the modification parameters and macro-parameters of the cycloid gear. An algorithm of meshing force, meshing efficiency and anti-gluing ability between the cycloid gear and the pin gear was derived, and the related independent parameters were extracted as optimization variables. Taking high efficiency, high strength and light weight as the objective, the mathematical models of double-objective and three-objective optimization were established, and the influence of key design variable on the objective function was analyzed, and NSGA-II multi-objective genetic algorithm was used to solve the Pareto optimal solution of the optimization mathematical model. Results show that the optimized parameters can significantly improve the meshing efficiency, reduce the volume and meet the design requirements of high strength, high efficiency and lightweight on the premise of ensuring the strength of cycloid gear surface. [ABSTRACT FROM AUTHOR]

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