基于乌鸦搜索算法的行星滚柱丝杠参数优化

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

  • 摘要: 针对行星滚柱丝杠结构参数匹配问题,提出一种基于乌鸦搜索算法的参数优化模型。考虑行星滚柱丝杠螺纹啮合点位置的影响,建立丝杠、滚柱以及螺母空间螺旋曲面方程,得到螺纹啮合点处位置与螺纹牙厚之间的关系。根据螺纹副和齿轮副啮合关系,确定内齿圈和滚柱端部轮齿设计参数。利用空间螺旋曲面方程,获得螺纹啮合点处的法向量,并推导行星滚柱丝杠各零件间的受力关系。以行星滚柱丝杠结构参数作为设计变量,以螺母外径、丝杠中径、滚柱长度等参数最小为优化目标,考虑行星滚柱丝杠结构约束和主要承力部件强度约束,利用乌鸦搜索算法作为优化算法,建立行星滚柱丝杠参数优化模型,从而实现优化变量最佳匹配。最后,针对三种负载,利用该优化模型得到三组行星滚柱丝杠结构参数,并将其优化结果与国外产品手册进行对比,从而验证了本文优化模型有效性。

     

    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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