Dynamic Characteristic Analysis Of High-Speed Rotating Circular Saw Blade Based On Absolute Nodal

For the circular saw blades with high speed rotation,because of the advantages of absolute nodal coordinate Formulation(ANCF)in the precise modeling of large rotation and large deformation,this method is first introduced into the study of the dynamic characteristics of circular saw blades.In addition,the dynamic characteristics of circular saw blades under thermal load are further analyzed by combining the heat conduction equation with the absolute nodal coordinate method.Through the above analysis,not only provides theoretical basis for the dynamic stability design of circular saw blades,but also has important reference value to solve the similar fixed axis rotating disk type members.The main works of this paper are as follows:(1)Based on the Kirchhoff plate theory and the continuum mechanics,the generalized elastic force of triangular plate element under the absolute nodal coordinate formulation is deduced in detail.On this basis,the mass matrix and generalized external force matrix of the system are deduced,and the dynamic equation of the system is established by the principle of virtual work.(2)In order to solve the problem of low computational efficiency of the absolute nodal coordinate formulation,a set of methods for improving the computational efficiency of the dynamic equation of ANCF triangular plate element is proposed by separating the generalized coordinates from the nonlinear generalized elastic force matrix and deriving the explicit equations of the generalized elastic force Jacobian matrices.On this basis,the model is compared with the large deformation model of Ansys to verify the correctness of the above theory.(3)The dynamic characteristics of high speed rotating circular saw blades without thermal load are studied.First,the dynamic equation of circular saw blade at rest is solved,and the result is verified by energy conservation.Further,the circular saw blades in rotation are studied,two methods are put forward to establish the dynamic model of circular saw blades,and the boundary conditions under the latter model are simpler,the dynamic equations are more regular and the calculation is more advantageous.On the basis of this,the modal analysis of circular saw blades the results show that the rotational effect will reduce the natural frequency of the N ? 2 to zero and the critical speed of circular saw blade appeared,and the critical velocity of the circular saw increases with the increase of the thickness of the saw blade and the radius of the inner edge,and decreases with the increase of the outer radius.In addition,the natural frequencies of circular saw blades are fitted and analyzed,the approximate functions of each order natural frequencies relative to the rotational speed are obtained,which can provide the design basis for designers conveniently and quickly.Finally,the correctness of the modal analysis results are ensured by the comparison with the Mote experiment and the theoretical results.(4)The dynamic characteristics of circular saw blades under the action of thermal load are studied.Firstly,the generalized elastic force of flexible plate under thermal load is deduced by the heat conduction equation,and the dynamic model of the system is obtained,and the correctness of the thermal load model is verified from the point of view of energy conservation.On this basis,the influence of the temperature rise of the inner and outer edges on the natural frequencies of each order is studied,and the results show that the temperature rise of the outer edge will reduce the natural frequencies of each order,and the temperature rise of the inner edge will increase the natural frequency of the N?2,thus the critical rotational speed of Further,through the analysis of the stress state on circular saw blades,it is found that the temperature rise of the inner edge increases the critical rotational speed,because the compressive stress produced by it can offset the centrifugal tensile stress produced by the rotation to some extent,thus reducing the effect of rotational effect on the wave.It is shown that the dynamic stability of circular saw blades can be improved by the reasonable compressive stress in the inner edge part.