Research on ultrasonic testing method for tangential contact stress based on equivalent medium theory

As a weak link, the joint surface of machine tools directly affects the stiffness and machining accuracy of the entire machine tool. However, obtaining the distribution of contact stress is a key problem that urgently needs to be solved in exploring the mechanical properties of joint surface connections. In this paper, a tangential contact stress ultrasonic testing method based on the equivalent medium theory is proposed, providing data support for accurately characterizing the contact state of the joint surface. A virtual material model of rough contact interface based on fractal theory is established to explore the coupling relationship between the propagation speed of ultrasonic critical refracted longitudinal waves, the tested object’s material parameters, and stress. Moreover, the expression of the equivalent material parameters of the ultrasonic critical refracted longitudinal wave propagation layer with stress variation is derived. An ultrasonic acoustic time difference model considering changes in contact surface material parameters is constructed based on the principle of acoustic elasticity of ultrasound. Furthermore, a critical refractive detection model for longitudinal wave’s tangential contact stress is established based on equivalent medium theory. Experimental specimens and stress detection plans are designed, and the tangential contact stress of the specimens is measured based on the division of surface grids. The equivalent stress value of each node is calculated based on the von Mises stress by measuring the stress in the X/Y direction. In addition, a shear stress distribution cloud map of the contact surface is drawn. Finally, the accuracy of the detection results is confirmed by combining theory, simulation, and experimental methods. The proposed tangential contact stress detection method based on critical refractive longitudinal waves is significant for low-stress assemblies.