# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 2 Materials and Methods
### Accuracy of Components and Tolerance of Parts  
The RV-40E reducer mentioned above includes four tapered roller bearings, four cylindrical needle roller bearings, two angular contact ball bearings, and some distance sleeves, gaskets, seals, etc. These externally purchased components, including distance sleeves, gaskets, collars, and sealing rings, have a minor impact on the transmission error and are therefore neglected in this study. Only four tapered roller bearings supporting the crankshaft, four cylindrical needle roller bearings supporting the cycloidal gear, and two angular contact ball bearings supporting the planetary carrier are related to the transmission error of the RV-40E reducer. Therefore, the selection of bearing accuracy levels depends on the existing bearing manufacturing technology level and the manufacturing cost requirements of the RV-40E reducer. However, if multi-objective optimization needs to be carried out by comprehensively considering transmission errors and manufacturing costs, factors affecting bearing accuracy levels can be added to the virtual prototype, and optimization results can be obtained by combining experimental design methods. The RV-40E reducer is a representative RV reducer. The transmission accuracy and manufacturing cost of industrial robot RV-40E reducers are related to the selection of accuracy levels for components, such as bearings, and the design of tolerance values for parts such as cycloid gears. Bearings and other components can balance the transmission accuracy and manufacturing cost of the RV-40E reducer by selecting a grade that meets the requirements of accuracy or cost-effectiveness. According to the GB307 national standard, bearings have five accuracy grades: B, C, D, E, and G. Grade B is the highest accuracy bearing, while grade G is the lowest accuracy ordinary bearing. Except for a few RV reducers with particularly high accuracy requirements, such as the popular RV-40E reducer, due to cost limitations, its bearing accuracy levels are higher accuracy grades C and D, and ordinary accuracy grades E and G. The selection of accuracy levels for components, such as bearings, is relatively simple, while the design of tolerance values for parts such as cycloidal gears is difficult to meet the comprehensive requirements of transmission accuracy and manufacturing costs. Since the RV-40E reducer is designed based on the experience of engineers, currently, it is unknown whether the selection of accuracy levels for components, such as bearings, and the design of tolerance values for gears meet the requirements of transmission accuracy or cost-effectiveness. Transmission accuracy and manufacturing cost are two interrelated important indicators of the RV-40E reducer. Due to the fact that researching manufacturing costs will also involve a large amount of data on enterprise manufacturing processes and processing equipment, this article mainly studies the optimization problem of tolerance value design closely related to transmission accuracy. In the design of the RV-40E reducer, the key characteristic tolerances are critical parameters for ensuring transmission accuracy, operational stability, and service life. Due to the extensive workload involved, this study focuses on investigating key characteristics closely related to transmission errors, including the hole center distance between the planet carrier and the cycloid wheel, the eccentric distance, the central circle of pin-wheel distribution, the pin-wheel diameter, and the cycloid wheel modification amount, among others. The determination of these tolerance parameters is primarily based on the production experience accumulated by the enterprise over many years, industry standards, and the recommended values provided in mechanical design manuals. Based on the RV-40E reducer drawings and technical requirements, medium and high accuracy bearings were selected according to the current domestic technical level, while the errors of individual bearings were not considered at this stage.