Nonlinear Vibrations Of An Engine Front End Accessory Drive System And Its Parameters Optimization

Because of its advantages of a simple structure,high reliability,long service life,easy assembly and replacement,compact accessories layout,etc.,a serpentine belt drive is extensively employed in engine front end accessory drive systems(EFEADS)to power engine accessories including an air conditioner,an alternator,a power steering pump,a water pump,an oil pump,etc.With improvement of science and technology of the automobile industry,higher requirements such as a stronger accessory transmission ability,higher power,lower price,lower noise level,higher operational reliability,and longer working life are imposed.Design quality directly and greatly influences operational performances and reliabilities of accessory components,which further affects the overall performance of the vehicle.The present design of an EFEADS is mainly based on experience of designers,several initial design schemes have to be provided and a good one is selected from these schemes according to experimental results and some calculations.This design method has high requirements on design engineers and the experimental validation test is time consuming and costly,these disadvantages are not conducive to the rapid development of new EFEADSs and that the newly developed EFEADS has the best working behavior cannot be ensured.Therefore,it is necessary to establish an accurate dynamic model to effectively predict dynamic performances of the EFEADS under various working conditions,and the best way to quickly get the optimal design is to optimize the structure parameters and layout of the EFEADS based on this model.In terms of key problems on modeling and calculation of the nonlinear vibrations of the EFEADS as well as its design optimization,four major respects are investigated in this work,regarding modeling and experimental tests of the static and dynamic characteristics of the key components including the serpentine belt and the auto-tensioner,the influence of the tensioner dry-friction on torsional vibrations of the EFEADS,modeling and calculation of nonlinearly coupled belt-pulley vibrations of the EFEADS,and global design optimization of the EFEADS.The specific research contents are listed as follows:(1)The transverse hysteretic damping characteristics are investigated based on a transverse vibration test.Results show that the excitation force-displacement response curve is a hysteresis curve,and the orientation of the hysteresis curve swings left and right around each natural frequency as if it is a symmetrical point.It is validated that the mutations of loss angle occur at the location near each natural frequency mainly results in this phenomenon.Neglecting the stick-slip of the tensioner arm caused by its inner dry-friction,the tensioner can be simplified as a linear torsional spring-viscous damping system.(2)A dynamic model of torsional vibrations of an EFEADS with a dry-friction auto-tensioner is established,and an improved multiple harmonic balance(IMHB)method is used to calculate periodic torsional vibrations of the system.The IMHB method is validated by comparing with the results calculated by Runge-Kutta method and the IMHB method.Influences of the dry-friction torque on dynamic responses of the EFEADS,especially on the stick-slip phenomenon of the torsional vibratins of the tensioner arm,are investigated.Energy consumptions by different dry-friction torques in one oscillation cycle are calculated.It is shown that the energy consumption first increases with thensioner dry-friction torque and then decrease and thus suggestions on designs of the dry-friction damping are given according to it.(3)A generic dynamic model of nonlinearly coupled belt-pulley vibrations of the FEADS with arbitrary numbers of accessory pulleys and an au-totensioner is established.This model is a hybrid continuous and discrete model that consists of multiple partial differential equations and ordinary differential equations.Factors including the manufaction error of pulleys and their jumps in the radius direction during operation,bearing wear,etc.,are considered in this model and they and equivalent to pulley eccentricity.A generalized accurate spatial discretization(GSD)method is proposed;this method transforms the governing partial differential equations of the EFEADS into ordinary differential equations and thus the difficulty of solving partial differential equations is overcomed.The generic dynamic model and the GSD method are validated via a modal test and an EFEADS test-bed experiment.The GSD method has similar calculation accuracy and efficiency with Galerkin method,but the GSD method is easier to implement and has more universality as its trial functions only need to meet homogeneous boundary conditions.(4)Global optimal design of the EFEADS based on the generic dynamic model of nonlinearly coupled belt-pulley vibrations of the FEADS.Those parameters that have great influence on dynamics of the EFESDS are found through frequency sensitivity analysis.It is shown that system vibrations including transverse vibrations of belt spans and rotational vibrations of pulleys and the tensioner arm are sensitive to structural parameters including the tensioner initial torque,tensioner torsional stiffness,tensioner arm length,tensioner intial installation angle,etc.(5)The weighted sum method and penalty factor method are used to transform the constrained multi-objective optimization problem to a single-objective optimization problem,and the final objective function is then built.A global optimization method called dynamic adaptive PSO-GA(DAPSO-GA)is proposed to optimize the tensioner parameters.Superiority of the DAPSO-GA than its similar algorithms,in terms of searcing ability of optimal solution,convergence ability and stability of solutions,is validated via several benchmark function tests.(6)The globally optimal design parameters of the EFEADS are found using the DAPSO-GA.The optimaztion results of the EFEADS with and without pulley eccentricities considered in the generic dynamic model are compared with each other,and the reasonableness of the optimization results is discussed according to the modal analysis.It is shown that the system vibration problem is greatly improved after optimization,the large transverse vibration problem of belt spans due to pulley eccentricity is effectively solved and the vibration amplitudes of belt spans are more evenly distributed.