# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 1 Introduction  
The tolerance, characterized by two parameters, bandwidth and position, is defined as a range of allowable changes in work piece size, geometric shape, or relative position. It is the physical quantity that limits the processing error of work pieces, reflects the requirements for manufacturing accuracy, and reflects the machining difficulty. The RV reducer is the critical component of industrial robots. The transmission error, defined as the difference between the actual output angle and the theoretical angle at the same input angle [1], directly affects the performance and work efficiency of industrial robots. As a standard medium-sized reducer in the basic series, the RV-40E covers the most prevalent load range for industrial robot applications, with its dimensional and performance characteristics being representative of this reducer class. Currently, the accuracy requirements or tolerance design of various components of the RV-40E reducer mainly rely on the experience of engineers, so some tolerance values are suboptimal. Therefore, in order to reduce the transmission error of the RV-40E reducer and lower its production cost, it is necessary to conduct research on the accuracy selection or tolerance values of various components of the RV-40E reducer. The transmission error of RV reducers has garnered significant research attention in recent years. [PERSON] et al. explored the impact of tooth profile modification and clearance on the transmission error using a contact analysis model for cycloid pin teeth [2]. [PERSON] developed an equivalent model for the transmission error by considering the over-constraint effects in the multi-crankshaft mechanism and verified its accuracy through experiments [3]. Through mathematical modeling and experimental verification, [PERSON] et al. identified the primary error sources in key parts and their impact mechanisms on transmission accuracy [4]. [PERSON] et al. incorporated manufacturing and assembly errors alongside elasticity factors to propose an analytical method for the dynamic transmission error [5]. [PERSON] et al. investigated the error characteristics under loaded conditions using a multi-body dynamics approach [6]. [PERSON] et al., on the other hand, conducted a comprehensive analysis of the transmission error by formulating a mathematical model of the RV reducer and integrating it with a translation-torsion coupling model [7]. Meanwhile, virtual prototype technology has found widespread applications in transmission error analysis. [PERSON] et al. utilized ADAMS software to construct a virtual prototype of the RV reducer and analyzed the system's natural frequency and dynamic characteristics through finite element analysis [8]. [PERSON] et al. developed a virtual prototype of the RV reducer based on multi-body dynamics theory with ADAMS software, incorporating the planetary gear system and the backlash model between the eccentric shaft and the bearing [9]. Additionally, they investigated the variation in transmission error as a function of clearance. [PERSON] et al. integrated virtual prototype simulation, physical testing, and theoretical modeling to conduct a systematic analysis of the dynamic transmission performance of the RV reducer [10]. They employed a multi-fidelity model and Bayesian updating techniques to assess system reliability and quantify the impact of manufacturing and assembly errors on a transmission accuracy sensitivity analysis of transmission error-related parameters using a virtual prototype simulation [11]. [PERSON] employed virtual prototype technology in conjunction with the orthogonal experiment method to investigate the combined error effects of the cycloid wheel and pin wheel on the transmission error [12]. [PERSON] et al. applied virtual prototype technology in conjunction with rigid-flexible coupling modeling to investigate the dynamic performance and error sources of the RV reducer [13; 14]. [PERSON] et al.