# Transmission Performance Analysis of RV Reducers Influenced by Profile Modification and Load
## 1 Introduction  
RV reducers are planocentric reduction mechanisms used for precise transmission applications. Such mechanisms incorporate numerous cycloid-pin teeth that are engaged concurrently. Therefore, RV reducers have a compact and highly rigid construction that is robust against shock-load and overloading. Furthermore, a minimal backlash and inertia assure a rapid acceleration and extremely accurate positioning. An RV reducer is ideally suited for precision mechanical control in industrial robots, machine tools, and assembly equipment, where precise positioning and a torsional stiffness capability are required [1]. Transmission errors (TEs) are key parameters used to represent the transmission performance of an RV reducer. The TE measurement method of a precision planetary cycloid reducer is defined in GB/T 37718-2019 [2]. The optimal measurement speed can be determined according to the Stribeck friction model [3,4]. The determination of optimal measurement speed of transmission errors could improve the measurement precision. A cycloid profile modification is one of the factors causing the TEs of an RV reducer [5, 6, 7]. However, to avoid the influence of machining errors on an RV reducer assemble, a cycloidtooth profile modification is commonly used in engineering practice. The modification methods often include a modification of the moved distance, equidistance, rotation angle, and their combination [8]. An angular modification needs to be used with other methods concurrently. In [9], based on a tooth contact analysis, the TE caused by different combinations of modifications is quantitatively analyzed. To reduce the impact of a modification on the RV reducer transmission accuracy, the optimal cycloidal tooth profile modification method has been studied by numerous researchers. In [10], a modification method for designing the modification gap curves by adjusting the positions of five key points on the cycloid profile was proposed. This method can improve the carrying capacity of cycloidal drive, eliminate noise and vibration and develop the transmission accuracy. Compared with the designed modified tooth profile, the actual tooth profile with machining errors can be accurately measured to compensate such errors between the actual and designed tooth profiles [11; 12]. In addition, judging the optimal modified tooth profile according to the amplitude frequency vibration response of the transmission system caused by different modified tooth profiles is an effective method [13]. The torsional stiffness of an RV reducer achieves a relatively large benefit from its multi-tooth contact characteristics, and thus can ensure a high transmission accuracy. Therefore, the contact force calculation of a cycloid-pin is particularly important when multiple teeth mesh together to transmit a power load [14; 15]. Among the many studies conducted in this area, [PERSON] proposed a numerical method to determine the number of teeth that are loaded simultaneously [16; 17]. The model can be used to investigate the effect of changing the geometrical design parameters of the tooth profile of the cycloid gear. However, the contact area of each mesh tooth is treated as a whole, and the contact force is calculated using a single contact stiffness. Such a treatment method results in some errors in the actual contact status [18]. To reduce this deficiency, [PERSON] established a hybrid contact force model. The contact cylinder surface is divided into many differential elements using the discrete element theory. Each differential element calculates the contact force separately according to the compression depth. Therefore, the contact model is more accurate for a complex profile contact [19]. Studies on cycloid tooth profile modification have mostly focused on the design method of optimizing the tooth profile, and the evaluation index is often limited to the transmission accuracy. The influences of the modification of the mechanical properties, contact area, and transmission efficiency have rarely been reported.