Research On Tire Vibration Characteristics Based On Three-dimensional Thin Shell Model

Tire is a typical vibration system,which can absorb the impact of road roughness and directly affect the comfort,handling stability and noise of vehicle system.Due to the complexity of tire structure and the variability of vehicle driving conditions,so far,there are not any theoretical models for tire vibration modeling that can fully reflect the vibration characteristics of tires in various frequency bands.In this paper,a three-dimensional tire model based on cylindrical shell for tire high-order bending vibrations is established to investigate the vibration characteristics of tires at low(0-300 Hz)and high(300-500 Hz)frequencies.Firstly,a three-dimensional tire physical model was established based on the Lovesimplification.The tire belt was simplified to a three-dimensional elastic shell with width and thickness.The prestress induced by the belt element and the inflation pressure in tangential and transverse directions,the elasticity of the tire sidewall in three directions were fully considered.The proposed model can not only calculate the tire in-plane and out-plane bending and torsion behavior in low frequency range,but also present the high frequency bending deformation of tire belt in lateral direction.The wheel is simplified into a rigid body with six degrees of freedom.The differential equation of tire motion is established by Lagrange equation.Secondly,two sets of displacement function for belt vibration were proposed based on solution method.One set was built using the binary Fourier series for modal expansion method.The differential equation of motion is matrixed by means of orthogonality of trigonometric function.The natural frequencies in 0-500 Hz were solved by modal expansion method,and the corresponding natural modes were drawn.Another set of displacement functions based on Rayleigh-Ritz method are also proposed.The low frequency vibration modes of tires below 250 Hz are solved using this method efficiently and simply,which simplifies the calculation process.Thirdly,the modal experiments for free/fixed tire were both carried out by hammering test.The tire with size of tire 205/55 R16 was excited by the force hammer.The excitation point is located at the center line of tread and shoulder,respectively.The response signals of 60 points along circumference and lateral were collected by a three-direction acceleration sensor and were recorded and analyzed by the frequency analyzer.The computation results are in good agreement with the experimental results,and the maximum error is less than 10 %.Finally,the influence of tire physical parameters on natural frequencies were investigated.It is found that the belt density and sidewall stiffness mainly affect the low-order vibration frequencies of tires,while the belt density,elastic modulus and Poisson's ratio mainly affect the high-frequency transverse vibration frequencies of belt.In this paper,a 3D tire-wheel vibration model with full consideration of the width and thickness of the belt as well as the lateral normal and shear strain were established.New displacement function in the tangential,radial and lateral directions for tire vibration is proposed.It can not only calculate the natural frequencies of the low-order in-plane and out-plane vibration,but also predict bending vibration of the belt in the mid-or high-order frequency range efficiently and accurately.The model provides a useful method for studying the vibration behavior in a wider frequency range.