Investigation On Transverse Vibration Of Chain Drives Based On Multi-DOF System Model

PURPOSE AND MEANING OF THE RESEARCH Chain drives have been widely used since they are one of the most efficientpower transmission mechanisms. But the transverse vibration of chain drives canresults in considerable load, which increase the wear of gemel, decrease theefficiency of the drive. Especially chain drives resonate when the outside excitationfrequency equal to natural frequency. So it is significative that investigate thetransverse vibration of chain drives to solve chain drives stability, resonance,invalidation, and so on. In many chain drive systems, a damper is used to improve performance byeliminating flop and sway on the slack side and reducing noise and vibration on thetight side. In spite of using dampers to eliminate flop, sway and dither on the slackside, the effects of dampers on the transverse vibration of chain drives has not beenscarcely researched. Dampers will change the natural frequency and response ofchain drive systems. It is necessary to study how to solve the transverse vibrationof chain drives with dampers, and study the effects of dampers on the naturalfrequency and response of chain drive systems. Few domestic academician investigate the transverse vibration of chain drivesvia computer simulation. Some study the effects of dampers on the chain drives,these studies limited the effects of dampers on the polygonal action, transmissionratio, meshing impact, and so on. Or regarded chain drive systems as continualsystem, then study the effects of dampers on the chain drives. In so far as regardingchain drive systems as discrete system, and study the effects of dampers on thetransverse vibration of chain drives have not been reported.MAIN CONTENT AND ACHIEVEMENTS OF THERESEARCH1. Transverse Vibration of Chain DrivesThis thesis employ a innovative calculation/ simulation method in investigatingthe transverse vibration of chain drives based on finite centralized mass distributedmodeling, basing on the researches of former scholar. Using effective calculationlanguage Matlab calculated/ simulated the transverse vibration of chain drives.Presented the programming approach of calculation of the differential equation/eigenfunction of vibration, and produced the related program. Take an example ofthe roller chain 06B-1-39 GB/T 1243-1997 and calculated the natural frequencyand mode shapes of the transverse vibration, simulated motion of the chain links.Investigated the effects of chain span tension / chain link pitch/ chain link mass onthe natural frequency of the chain drive system.(1) Presented the programming approach of calculation of the differentialequation of vibration, and produced the related program. Take an example of theroller chain 06B-1-39 GB/T 1243-1997 and calculated from the first to fifthnatural frequency and mode shapes. Compared this solution with the solution inliterature [24] . The values of natural frequency of the two solutions are very close.But the process of ratiocination and calculation in literature [24] are comprehensive.The solution in this thesis are simple, furthermore, the calculated mode shapes werepresent by mode shape figures, which are intuitionistic and visual.(2) Regard meshing impact load as the excitation of the transverse vibration ofchain drives, solved the respond of each chain links and present solutions byfigures. Studied representative chain links 1,2,10,20,30,39, discovered theamplitude attenuate of vibration get smaller, as the distance between chain linksand driving sprocket becomes farer.(3) Investigated the effects of chain span tension / chain link pitch/ chain linkmass on the natural frequency of chain drive system. As a result, the naturalfrequency increase as the chain spans tension largen;the natural frequencydecrease as the chain span tension become larger;the natural frequency decrease asthe chain links mass increase.(4) As soon as the excitation frequency equal to the natural frequency of chaindrive system, the system will be resonate.2. Transverse Vibration of Chain Drives with dampersThe damper is modeled as a single degree of freedom system which consists ofa mass and a spring. A model of transverse vibration of chain drives with damperhas been derived. The model based on finite centralized mass distributed modeling,which derived from Multi-DOF System Theory. Both the stiffness matrix anddifferential equation of system have been derived. Calculated the differentialequation, simulated the motion of the chain links of chain drive with damper.Investigated the effects of mass and stiffness of damper on the natural frequency ofchain drive system.(1) The damper is modeled as a single degree of freedom system which consistsof a mass and a spring. A transverse vibration model of chain drives with damperhas been derived. Both the stiffness matrix and differential equation of system havebeen derived.(2) Calculated the differential equation using Matlab program. Take an exampleof the roller chain 06B-1-39 GB/T 1243-1997 and calculated from the first tofifth natural frequency and mode shapes. Compared this natural frequency with thenatural frequency of the chain drive without damper. The values of naturalfrequency decreased after installed the damper.(3) Regard meshing impact load as the excitation, solved the respond of eachchain links of the chain drive with damper installed at the chain link 10/20/30.Studied representative chain links 1,2,10,20,30,39, and compared these chainlinks motion with the corresponding links of the system without damper. It is foundthat damper can reduce the vibration amplitude of the chain links between thedamper and driven sprocket evidently. But the effects of dampers on chain linksbetween the damper and driven sprocket can be neglected. As the distance betweenthe damper and chain links shorter, affect of reducing vibration of the system better.(4) Investigated the effects of mass and stiffness of damper on the naturalfrequency of chain drive system. It is found that the vibration frequency reduces asmass of damper becomes larger. On the contrary, the first natural frequencyincrease as the stiffness of damper becomes larger. The effects of dampers on theother natural frequency can be neglected.