基于等效缩比建模方法的行星滚柱丝杠接触应力分析与验证

Equivalent reduced-scale modeling-based contact stress analysis and verification for planetary roller screws

  • 摘要: 行星滚柱丝杠副凭借高承载、长寿命的优势,广泛应用于航空航天、数控装备和工程机械等重点领域。然而,开展其全尺寸原型的承载特性与疲劳寿命试验,存在成本高、试验设备要求严苛等难题。为此,提出了一种基于等效缩比建模的行星滚柱丝杠副缩比方法,并通过仿真对比原型与缩比模型的接触应力完成验证。主要研究内容如下。首先基于Hertz弹塑性接触理论与Buckingham定理(相似第二定理),推导了包含几何、材料与动力学特征的9个独立相似准则,确立了原型与缩比模型间的载荷等效映射关系。同时构建简化的滚柱丝杠啮合模型,在20%~100%额定载荷下开展接触应力仿真分析,根据丝杠与滚柱螺纹的接触应力分布,验证缩比模型的有效性。

     

    Abstract: Planetary roller screw mechanisms are widely used in key fields such as aerospace, CNC equipment, and engineering machinery due to their high load-carrying capacity and long service life. However, the testing of full-scale prototypes for load-carrying characteristics and fatigue life is challenged by high costs and stringent requirements for test equipment. To address this issue, a scaling method based on equivalent reduced-scale modeling is proposed for planetary roller screw mechanisms. The validity of the method is verified by comparing the contact stresses of the prototype and the scaled model through simulation. The main research contents are as follows. Firstly, based on Hertzian elastoplastic contact theory and Buckingham's π theorem (the second similarity theorem), nine independent similarity criteria covering geometric, material, and dynamic characteristics are derived, and an equivalent load mapping relationship between the prototype and the scaled model is established. Meanwhile, a simplified meshing model of the roller and screw is constructed, and contact stress simulations are carried out under loads ranging from 20% to 100% of the rated load. The effectiveness of the scaled model is validated by analyzing the contact stress distribution on the screw and roller threads.

     

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