Analysis Of The Fast-slow Dynamics Of Harmonic Gear Drives System Under Different Gap Clearance Conditions

Harmonic gear reducer is one of the commonly used and vital transmission mechanical devices at present.There are many complex nonlinear factors in this device,which restrict the accuracy of harmonic gear reducer to be further improved.The research on harmonic gearing system has been focused on the design of experiments,the establishment of accurate mathematical models or the description of the dynamics of the phenomenon.In this paper,we analyze the major nonlinear factors involved in the harmonic gear transmission system,and establish a dynamics model of the harmonic gear transmission system,which contains different types of nonlinear factors such as time-varying torsional stiffness,gear clearance,kinematic error,and so on.Based on the bifurcation knowledge of nonlinear disciplines,fast-slow dynamics knowledge and numerical simulation,the fast-slow dynamics behavior and its dynamics mechanism that appear in the system are investigated.Moreover,there are many non-smooth factors in the transmission system.Considering the non-smooth factor gear clearance,we establish the dynamics model of the non-smooth harmonic gear transmission system and analyze the dynamics behavior of the system under this non-smooth factors.The specific research contents of this paper are as follows:(1)The evolution of the fast-slow oscillations in a harmonic gear train with different torsional stiffness coefficients is analyzed under the gear clearance conditionf(θ)=θ-φ.The further analysis reveals that this type of fast-slow oscillations is caused by a novel dynamical mechanism that has not been investigated before.The equilibrium curve of the fast subsystem changes sharply in the vicinity of the slow variable a =0,leading to a rapid transition of the system trajectory between the spiking and quiescent states,which induces the fast-slow oscillations.Changing the dimensionless coefficients of the system under the gear clearance condition of f(θ)=θ+φ leads to a different type of fast-slow oscillations of the system.The mechanism of this fast-slow oscillations is different from the previous one.In this case,the system trajectory is transited between different attractors via the fold bifurcation point,thus leading to the fast-slow oscillations.(2)The gear clearance,as one of the common non-smooth factors in the harmonic gear transmission system,has made it difficult to control the relationship between the output angular displacement and the input angular displacement of the system,which reduces the stability and transmission accuracy.The research shows that when the value of the gear clearance is in a definite zone,the change of the value of the gear clearance will only quantitatively change the dynamic characteristics of the system,but not fundamentally change the motion characteristics of the system.When a smaller torsional stiffness coefficient is adopted,the vibration frequency of the dynamic error response of the system increases obviously,but the corresponding vibration amplitude does not change to a significant extent,which shows that the appropriate torsional stiffness can improve the dynamic response of the system and enhance the ability of the system to absorb external disturbances and resist shocks.In order to make the harmonic reducer satisfy more application situations,the evolution of the dynamical behavior of the system under different external excitations is investigated.When the system is in the bilateral shock state under light load.And when it is in the heavy load state,the system switches to the unilateral shock state,and the larger load moment leads to multiple vibration responses in the dynamic error trajectory of the system,which may lead to the phenomenon of speed fluctuation at the output of the system.