Research On Stiffness Characteristics And Forced Response Of Cracked Shaft

As the most widely used construction machinery,it is very important to ensure the safe and reliable operation of rotating machinery.The crack of rotating shaft is one of the outstanding faults of rotating machinery,which seriously affects the stability of its operation.If the crack can’t be found in time,the crack will expand rapidly and lead to shaft fracture,which will cause serious production accidents.The ship’s propulsion shaft system runs under complex cyclic loading for a long time,and it is easy to produce surface cracks,which is extremely harmful to the ship’s power plant system.Researching the dynamic behavior of crack shaft can provide some theoretical support for crack identification and diagnosis.In this paper,based on the fracture mechanics energy balance fracture theory,the additional strain energy of the crack is obtained from the relationship between the stress intensity factor and the crack propagation energy rate.According to the energy method,the stiffness matrix of the crack element is obtained.Based on the crack opening and closing line theory,the stress intensity factor is zero method is used to simulate the crack periodically opening or closing,and the time-varying stiffness model of the crack element is obtained.Then,the crack stiffness model is substituted into the finite element model of the propulsion shaft system,and the stiffness characteristics and forced response characteristics of the crack shaft system are analyzed.The effects of crack depth,inclination angle and the front shape of the crack on the breathing characteristics of crack and time-varying characteristics of each component of the complete stiffness matrix are investigated.The results show that the crack depth has the greatest influence on the two aspects.As the crack depth deepens,the stronger the breathing characteristics it exhibits,the more severe the stiffness reduction;Slant cracks will produce more coupling stiffness components;The front shape of the crack has a stronger effect on the breathing characteristics of crack than on the stiffness characteristics.The effects of crack parameters,eccentric excitation and torsional excitation on the dynamic response of the shaft system are analyzed.The results show that the crack parameters and eccentric excitation have a significant effect on the fundamental frequency and the 2x frequency amplitude,and have little effect on the 3x frequency amplitude;Torsional excitation will cause the bending-torsional coupling vibration of the slant crack shaft,and the combined frequency component of 2x excitation frequency plus the rotation frequency is the most obvious.The response characteristics of various positions of the cracked shaft system were studied,and it is found that the influence of the super harmonic frequency component and the coupling vibration are limited to the shaft between the two bearings where the crack is located.The case of double cracks is considered,and it is found that the difference between the two crack phase angles has a greater effect on the system response than the difference between the two crack inclination angles.Based on the ABAQUS finite element analysis software,a three-dimensional solid model of the cracked propulsion shaft system with elastic support is established.The response of the shaft system with different crack depths and the response of different positions of the shaft system are analyzed,which show same characteristics as the theoretical model.