Research On Gear Reverse-order Meshing

As a mechanical part that transmits motion and power,gears are widely used in mechanical transmission systems,and the design and manufacturing level has direct effect on the performance and reliability of the equipment.The gear transmission process could be divided into two stages,meshing transmission that occurs on the tooth flanks of one pair of gear teeth,and alternating meshing transmission used to ensure transmission continuity from the previous pair of gear teeth to the next pair of gear teeth.The classic gear meshing principle only studies the meshing of one pair of tooth flanks and does not involve the alternating meshing between tooth pairs,while modern gear meshing theory has the means to study the alternating meshing of tooth pairs,but the work so far is still focused on the meshing of one pair of tooth flanks and the research of alternating meshing of tooth pairs is ignored.The contact ratio must be greater than 1 to ensure the continuity of the transmission during the alternating transmission of gear teeth;In order to ensure the stability of the transmission,theoretically,the base pitch of the driving and driven gears should be equal.Affected by machining errors and loads,the actual base pitches of the driving and driven gears are not equal,resulting in the meshing-in impact and meshing-out impact.There have been extensive and in-depth researches in this area at home and abroad.Thanks to the contact ratio must be greater than 1,it is found that the gear tooth alternating transmission process occurs in the meshing area of multiple pairs of gear teeth with alternating impact besides meshing-in and meshing-out impact.Not only alternating impact included in the gear tooth alternating transmission process,but also a general physical phenomenon with richer connotations,which is called "reverse order meshing".Several key issues related to the reverse order meshing phenomenon have been studied in depth.The main research contents are as follows:(1)It reveals the reverse order meshing phenomenon.The change of the meshing sequence during the meshing process is studied from a completely new angle,the meshing sequence is opposite to normal under certain conditions,and a new concept—reverse order gear meshing is proposed.The reasons for the reverse order meshing are discussed,and it is concluded that this phenomenon may be related to many factors such as machining errors,assembly errors,thermal deformation and load deformation,but the base pitch error,that is,the normal base pitch of meshing teeth are no longer equal,which is the root cause of the reverse order meshing.According to whether the reverse order meshing phenomenon occurs on the same tooth flank,it is classified into microscopic reverse order meshing process and macroscopic reverse order meshing process,and the motion laws of the two reverse order meshing phenomena are analyzed.Starting from the base pitch error,the micro-reverse order meshing phenomenon is emphasized,and the mathematical model of it is established.The kinematic models of the angular velocity error and angular acceleration error of the driven gear during the meshing process are obtained.(2)The meshing stiffness model of gears with specific profile is established.Aiming at the time-varying meshing stiffness,transmission error and load distribution of parallel shaft gear pairs with tooth profile error,dynamic gear pair integrated error(DGPIE)is introduced based on the unified principle of gear error and loaded elastic deformation,and further considering the integrated error of gears to establish meshing stiffness,load distribution coefficient and load dynamic integrated error model of parallel shaft gear system.The time-varying meshing stiffness,load distribution coefficient and load dynamic integrated error of the gear pair with specific profile modification such as tooth tip relief,pressure angle error and middle drum modification are calculated.(3)The reverse order meshing process of the loaded gear pair and its effect on meshing impact are studied.Combining the analysis conclusions of meshing stiffness,load distribution and integrated error of dynamic gear pair under different modification parameters and different acting torque(load),considering the combined effects of system error and gear tooth deformation,based on the analysis result of reverse order meshing,the phenomenon of meshing impact under different working conditions was analyzed.Taking the meshing impact phenomenon with no load as an example,the analytical model of the reverse order meshing is used to draw the curves,and thereby revealing the causes of meshing impact.When considering the loaded elastic deformation,the dynamic characteristics of the gear pair with speed-increased alternating will become worse and the noise will be louder;and the dynamic characteristics of the gear pair with speed-decreased alternating,the transmission noise will increase;when gear pair with multiple alternating is loaded,the transmission performance becomes worse and the noise will increase.Two ways to improve meshing impact are summarized: gear modification and gear pairing.(4)The transmission performance of gears with specific profile is studied from the dynamic point of view.Since the root mean square of the gear vibration acceleration is proportional to the gear noise,the vibration acceleration can be used to study the transmission noise.On the basis of establishing the dynamic performance analysis model of spur gears,the meshing stiffnesses corresponding to five gear pairs with specific profile are substituted into the model,and the root mean square of vibration acceleration in the bending-torsional direction of the driving and driven gears is obtained under the corresponding conditions.By comparing and analyzing the root mean square of accelerations in all directions,the dynamic response trends corresponding to different modifications are obtained.The conclusion is basically consistent with the gear assignment criterion,which verifies the correctness of the influence of reverse meshing theory on transmission performance after load.(5)The applications of reverse order meshing in measurement and machining are described.In addition to designing gear modification for specific working conditions to reduce or avoid the impact of meshing to provide a basis for improving meshing performance and transmission stability,it can also be used in measurement and machining fields.According to the characteristics of the reverse order meshing in the integrated error measurement,the reliability of the data of the meshing segment is analyzed,and a method of determining the tooth profile evaluation area based on the meshing segment data is proposed.In the inter-tooth honing process,the motion law of the gears in the reverse order meshing process is used to realize the tooth root finishing,tooth root modification and tip chamfering,and even tip relief can be achieved by the motion control of the reverse order process.