# Research on Part Tolerances for RV-40E Reducer Based on Virtual Prototype Technology
## 1 Introduction
[15] analyzed the effects of multifactor error interactions on the transmission accuracy of the RV reducer by employing virtual prototype technology and the response surface methodology (RSM). [PERSON] et al. [16] revealed the significant influences of angular acceleration and load inertia on the transmission errors under variable-speed conditions by constructing a multi-body dynamics model of the RV reducer that considers typical part geometrical errors. [PERSON] et al. [17] proposed a piecewise modification method for cycloidal gears based on the spline interpolation theory and verified its advantages over combined modifications in terms of contact stress and load distribution through a virtual prototype. [PERSON] et al. [18] used ADAMS to establish a coaxiality-efficiency model of the RV reducer, which revealed the influence of coaxiality errors on efficiency. [PERSON] et al. [19] used an Abaqus-ADAMS rigid-flexible coupling model to investigate the contact stress characteristics of the key components of the RV reducer. [PERSON] et al. [20] verified the dynamic characteristics of the novel ZHPRER reducer through multi-body dynamics simulations and experimental validations. Based on the multi-tooth contact and transmission error model, [PERSON] et al. [21] verified the influence of tooth profile modification and load and proposed a reverse modification method applicable under large clearance and large torque conditions. [PERSON] et al. [22] revealed the degradation relationship between cycloidal gear wear and the transmission error by employing a rigid-flexible coupling model and the Archard wear theory. Compared with traditional modeling methods, virtual prototype technology enables a more intuitive simulation of dynamic behavior under complex work ing conditions, reducing the reliance on complex assumptions and computational efforts associated with conventional mathematical modeling. Parallel to these developments, tolerance design and optimization have received growing attention. [PERSON] et al. analyzed the transmission error of the RV reducer considering the effects of manufacturing and assembly tolerances, employing gear theory, tooth contact analysis, and the Monte Carlo method [23]. [PERSON] examined the influence of critical part tolerances on transmission accuracy and proposed an optimization design method [24]. [PERSON], [PERSON] et al. conducted an in-depth study based on the finite element method to investigate the mechanism by which tolerance and friction affect the contact force and transmission performance in the RV reducer [25]. [PERSON] et al. incorporated the design constraints of gear pair clearance and allowable backlash to construct a multi-objective optimization model that balances processing cost, quality loss, and tolerance cost for the cycloid pinion gear pair in the RV reducer [26]. [PERSON] et al. analyzed the geometric distribution characteristics of assembly errors using 3 DCS software [27]. Subsequently, the team further introduced a genetic algorithm to optimize the tolerances of the key components of the RV reducer, thereby minimizing the manufacturing costs while ensuring assembly accuracy [28]. [PERSON] et al. evaluated the effects of varying tolerances on transmission accuracy using the Monte Carlo simulation [29]. [PERSON] [30] revealed that the momentum loss of the cycloidal reducer is jointly influenced by torsional stiffness and tolerances through combined finite element and kinematic analyses, thereby clarifying the key role of tolerances in determining accuracy. [PERSON] et al. [31] optimized the tolerance and modification parameters of the RV reducer based on a gear contact analysis model that considers tooth profile modifications and manufacturing errors, aiming to minimize costs while ensuring reliability. [PERSON] et al. [32] quantified the effects of pin errors on momentum loss based on the BDTCA model, optimized the tolerance allocation using a discrete particle swarm optimization algorithm, and verified the validity of the bi-directional test. [PERSON] et al.