考虑廓形特征的机器人异型盘磨削接触力建模

目的 为表征具有尖端小、比压大廓形特征的机器人异型盘磨削接触力，针对异型盘薄板与橡胶板双层结构形式，提出一种考虑廓形特征影响的包含薄板挠曲形变和橡胶板弹性形变的机器人异型盘磨削接触力建模方法。方法 首先，基于弹性薄板弯曲理论，分析薄板挠曲形变与接触力关系。其次，依据静态弹性理论，建立橡胶板在弹性形变区域内弹性形变与接触力模型。再次，开展有限元数值模拟实验求解橡胶板弹性形变参数和薄板挠曲形变参数，并通过变量替换建立接触力与异型盘法向进给位移数值形式反函数模型。最后，搭建机器人异型盘磨削实验平台，分别开展1种平面与3种曲率曲面工件的机器人异型盘接触力模型验证实验和1种侧曲面圆台铸铁工件的机器人异型盘磨削一致性验证实验。结果 机器人异型盘接触力模型验证实验结果表明，当盘倾角较大时，能够较为准确地预测接触力。机器人异型盘磨削一致性验证实验结果表明，在相同的磨削参数条件下，3条磨削路径(路径1、2、3)的磨削深度平均值分别为0.066 3、0.063 2、0.064 5 mm，最大偏差分别为0.013 9、0.009 0、0.010 8 mm，变异系数分别为11.2%、6.4%和9.6%。实验验证了所提方法的有效性。结论 所提方法考虑了异型盘廓形特征，将工件表面曲率、盘倾角、廓形参数和异型盘尺寸等参数包含在磨削接触力模型中，并描述了磨削接触力与异型盘法向进给位移的数值形式反函数关系，能够度量异型盘磨削作业接触区域和解释磨削接触力影响因素，可为机器人异型盘的高效率、高质量恒定接触力磨削提供理论依据。

Contact Force Modeling for Robotic Grinding with Special-shaped Disc Considering Profile Features

In order to characterize the contact force of robotic grinding with special-shaped discs with small pointed tips and significant base pressure difference, the work aims to propose a modeling method to calculate the grinding contact force of the robotic special-shaped disc considering the flexural deformation of the thin plate and the elastic deformation of the rubber disc within a two-layer structure. Firstly, the relationship between contact force and the flexural deformation of the thin plate was analyzed based on the theory of thin plates. Furthermore, according to the static elastic theory, the elastic deformation and contact force model of rubber plate in the elastic deformation region was established. Then, the finite element numerical simulation was conducted to explore the elastic deformation parameters of the rubber disc and the flexural deformation parameters of the thin plate. By employing the variable substitution, a numerical inverse function model of the contact force in relation to the normal feed displacement of the special-shaped disc was derived. Finally, a robotic experimental platform dedicated to special-shaped disc grinding was constructed. Validation experiments were performed on a flat workpiece and a workpiece with three different curved surfaces to verify the effectiveness of the contact force model across various workpiece shapes and surface curvatures. The results of these validation experiments confirmed that the contact force model accurately predicted the contact force, particularly when the disc inclination angle was significant. In the consistency verification experiments for robotic special-shaped disc grinding, it was observed that under identical grinding parameter conditions, the average grinding depth for the three different grinding paths was 0.066 3, 0.063 2, and 0.064 5 mm, respectively. The maximum deviations were 0.013 9, 0.009 0, and 0.010 8 mm, respectively. The coefficients of variation for each path were determined as 11.2%, 6.4%, and 9.6%, respectively. The experimental validation confirmed the effectiveness of the proposed method. The proposed method considers the morphological features of the special-shaped disc and incorporates parameters such as workpiece surface curvature, disc inclination angle, profile parameters, and disc dimensions into the grinding contact force model. It also describes the numerical inverse function relationship between the grinding contact force and the normal feed displacement of the special-shaped disc. This method enables the measurement of the contact region in special-shaped disc grinding operations and provides insights into the factors affects the grinding contact force. It serves as a theoretical basis for efficient and high-quality grinding with the constant contact force in robotic special-shaped disc grinding operations.