Abstract
The stresses and deformations of an eccentric cylindrical cam during the process of hydro-joining have been calculated in orthogonal curvilinear coordinates according to the mechanical model of the cam and governing equations in terms of appropriate complex potentials with suitable boundary conditions. The radial and shearing stress coefficients determined for an example cam are far less than that of the tangential stress during hydro-joining. The tangential stress coefficient of the outer surface of the cam is greater than that of the internal surface when the polar angle exceeds a particular value. The position of the maximum value of the radial stress coefficient is located on the internal surface of the cam, and the maximum shear stress coefficient is located between the inside and outside surfaces of the cam. The cam deformations on the internal and external surfaces under internal pressure respectively attain maximum values at particular angles. The maximum values of the radial and y-directional deformations are located at the position of the minimum wall thickness. The radial deformations determined for an example cam are far larger that the tangential deformations during hydro-joining. The errors between the theoretical and numerical solutions for the tangential stress and the y-directional deformation are both very small.
Highlights
When the stresses exceed the strength of cam material under the action of the contact pressure, the failure of the cam will occur[1,2]
We develop the finite element model of the cam and determine the numerical solutions for the stress and deformation of the cam
Substituting 0 in Equation (1), we obtain x2 y acth 0 2 a2 csc h2 0 .The following equations are for the stresses and deformations of an eccentric cylindrical cam (ECC) in terms of complex functions in orthogonal curvilinear coordinates
Summary
When the stresses exceed the strength of cam material under the action of the contact pressure, the failure of the cam will occur[1,2]. An eccentric cylindrical cam (ECC) has a cylindrical structure of variable cross-section, and the basic equations governing stresses and deformations are variable coefficient differential equations, which are very difficult to solve[3,4]. To obtain the stresses and deformations of an ECC, many researchers have adopted numerical methods based on the finite element model of the cam[5,6,7,8]. We determine the positions and values of the maximum stress and deformation of an example ECC. We develop the finite element model of the cam and determine the numerical solutions for the stress and deformation of the cam. Where a is a real constant, i , and z x iy
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