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基于烏鴉搜索算法的行星滾柱絲杠參數優化

Optimization research of planetary roller screw mechanism parameters based on crow search algorithm

  • 摘要: 針對行星滾柱絲杠結構參數匹配問題,提出一種基于烏鴉搜索算法的參數優化模型。考慮行星滾柱絲杠螺紋嚙合點位置的影響,建立絲杠、滾柱以及螺母空間螺旋曲面方程,得到螺紋嚙合點處位置與螺紋牙厚之間的關系。根據螺紋副和齒輪副嚙合關系,確定內齒圈和滾柱端部輪齒設計參數。利用空間螺旋曲面方程,獲得螺紋嚙合點處的法向量,并推導行星滾柱絲杠各零件間的受力關系。以行星滾柱絲杠結構參數作為設計變量,以螺母外徑、絲杠中徑、滾柱長度等參數最小為優化目標,考慮行星滾柱絲杠結構約束和主要承力部件強度約束,利用烏鴉搜索算法作為優化算法,建立行星滾柱絲杠參數優化模型,從而實現優化變量最佳匹配。最后,針對三種負載,利用該優化模型得到三組行星滾柱絲杠結構參數,并將其優化結果與國外產品手冊進行對比,從而驗證了本文優化模型有效性。

     

    Abstract: Because structural parameter matching has a strong influence on the service behavior of planetary roller screw mechanisms (PRSM), understanding how to effectively design the structural parameters of PRSM is highly important in practical industrial applications. This study proposes a parameter optimization model based on a crow search algorithm (CSA) to solve the structural parameter matching problem of PRSM. The relationship between the main structural parameters of PRSM can be deduced according to the working principle and geometric conditions. The screw, roller, and nut space spiral surface equation are established by considering the influence of the meshing point position of PRSM on thread meshing clearance. The relationship between the meshing point position and PRSM tooth thickness is obtained using the tangent contact condition of the spiral surface. To achieve no backlash meshing and improve PRSM transmission accuracy, the thread tooth thickness of the screw, roller, and nut can be adjusted. According to the meshing relationship between the thread pair and the gear pair of PRSM, the structural parameters of the annular gear and the gear at the end of the roller are determined. The normal vectors at the meshing point of the screw, roller, and nut are calculated using space spiral surface equations. To test the strength of the PRSM, static analysis of the roller is used to deduce the force relations between the main parts of the PRSM. PRSM structural parameters serve as design variables. An optimization goal is to reduce the outer diameter of the nut, the nominal diameter of the screw, and the length of the roller. The spatial structure constraints and component strength constraints of PRSM are considered. The CSA was introduced to be the optimization algorithm. The parameter optimization model of PRSM is established for achieving optimum matching of the optimization variables. Finally, using the proposed optimization model, three groups of PRSM structural parameters are obtained for three different types of load. In this study, the optimization results are compared with a foreign PRSM product manual to validate the effectiveness of the optimization model. The results show that the PRSM structural parameters obtained from the proposed model are essentially consistent with those from the foreign PRSM product manual. Furthermore, the proposed model provides the structural parameters of thread teeth, which are not included in the foreign product manual. The proposed PRSM optimization model is promising for its application in actual production.

     

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