Based on fractal theory,continuous smooth exponential model of elastic-plastic contact,and considering the influence of friction factors and applying an improved W-M function that simulating three-dimensional fractal profile surface,the fractal model of energy dissipation for tangential contact in joint interfaces and its equivalent viscous damping model are proposed.It is shown from the models that the tangential contact damping dissipating energy of joint interfaces decreases with the increase of normal load on joint interfaces,the friction coefficient,but increases with the increase of plastic index of contact materials,the ratio of the tangential dynamic load amplitude to normal contact load,the fractal dimension,the fractal roughness of joint interfaces. The variation rule of the tangential contact damping dissipating energy of joint interfaces with the fractal dimension is very complex. The tangential equivalent viscous damping of joint interfaces decreases with the increase of friction coefficient,the fractal roughness of joint interfaces,but increases with the increase of normal load on joint interfaces,the ratio of the tangential dynamic load amplitude to normal contact load,the plastic index of contact materials. The tangential contact equivalent viscous damping of the joint surface increases at first and then decreases with the increase of the fractal dimension,and the maximum value is taken when the fractal dimension is equal to 2. 7. There is an obvious nonlinear relationship between the tangential contact equivalent viscous damping of joint interfaces,when fractal dimension D value is between 2. 1 and 2. 5. There is an obvious linear relationship between the tangential contact equivalent viscous damping of joint interfaces and the normal contact load,when fractal dimension D value is between 2. 5 and 2. 9.