Abstract
This paper presents a general framework to design a cam profile using the finite element method from given displacements of the follower. The arbitrarily complex cam profile is described by Lagrangian finite elements, which are formed by the connectivity of nodes. In order to obtain the desired profile, a penalty-type functional that enforces the prescribed displacement of the follower is proposed. Additionally, in order to ensure convexity of the functional, a numerical stabilization scheme is used. The nodal positions are then obtained by solving a nonlinear system of equations resulting from minimizing the total functional. The geometrical accuracy of the cam profile can be controlled by the number of finite elements. A case study is considered to illustrate the flexibility, accuracy, and robustness of the proposed approach.
Highlights
Cam mechanisms are widely used in various mechanical machines, such as machine tools, sewing machines, and engines due to their unlimited motions, operation speed, motion accuracy, and structural rigidity
A penalty type functional to enforce the prescribed displacement of the follower is proposed; A stabilization scheme is added to guarantee convexity of the functional; For the Newton–Raphson solution method, the consistent linearization of the weak form is presented; The arbitrary desired accuracy of the cam profile can be achieved by increasing the number of finite elements; The resulting profile represented by finite elements can be used for cam manufacturing
The formulation is based on a the other hand, for the fine meshes, parameter affects the coordinates
Summary
Cam mechanisms are widely used in various mechanical machines, such as machine tools, sewing machines, and engines due to their unlimited motions, operation speed, motion accuracy, and structural rigidity. The follower motion affects the kinematic and dynamic characteristics of cam systems. Biswas et al [26] presented two approximate analytical methods for determining disk cam profiles of roller followers. We propose a finite element method to design a cam profile from a given displacement of the follower. A stabilization scheme is added to guarantee convexity of the functional; For the Newton–Raphson solution method, the consistent linearization of the weak form is presented; The arbitrary desired accuracy of the cam profile can be achieved by increasing the number of finite elements; The resulting profile represented by finite elements can be used for cam manufacturing.
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