基于半圆型波纹周期梁的柔顺恒力机构优化设计

为了解决柔顺恒力机构中正刚度模块的几何非线性问题，基于半圆型波纹周期梁设计了正刚度模块，负刚度模块采用双稳态梁，利用正负刚度叠加原理设计了柔顺恒力机构。采用莫尔积分法和柔度矩阵法建立了正刚度模块的理论模型，采用椭圆积分法建立了负刚度模块的理论模型，并通过ANSYS有限元仿真软件分析了柔顺恒力机构的力-位移曲线以验证理论模型，两者相对误差在10%以内。为了扩大恒力区间范围，采用响应面法对柔顺恒力机构的几何参数进行优化，并对影响恒力范围的几何参数进行了灵敏度分析。利用3D打印技术加工柔顺恒力机构样机进行实验验证，实验结果表明，机构能在输入位移1.1～6.2 mm的范围内保持约18.8 N的恒力，验证了所设计的柔顺恒力机构的可行性、优化方法的有效性和理论模型的准确性。

Optimal Design of Compliant Constant-force Mechanism Based on Semicircular Corrugated Periodic Beam

In order to solve the geometric nonlinear problem of the positive stiffness module in the compliant constant-force mechanism, the positive stiffness module was designed based on the semicircular corrugated periodic beam, the negative stiffness module adopted a bistable beam, and the compliant constant force mechanism was designed by using the principle of positive and negative stiffness superposition. The theoretical model of the positive stiffness module was established by using the Mohr integral method and the compliance matrix method, and the theoretical model of the negative stiffness module was established by the elliptic integral method. The force-displacement curve of the compliant constant force mechanism was analyzed by ANSYS finite element simulation software to verify the theoretical model, and the relative error between the two was within 10%. In order to expand the range of constant-force, the response surface method was used to optimize the geometric parameters of the compliant constant-force mechanism, and the sensitivity analysis of the geometric parameters affecting the constant-force range was carried out. The prototype of the compliant constant-force mechanism was processed by 3D printing technology for experimental verification. The experimental results showed that the mechanism can maintain a constant-force of about 18.8N within the input displacement range of 1.1~6.2mm. The feasibility of the designed compliant constant-force mechanism, the validity of the optimization method and the accuracy of the theoretical model were verified.