Stability Evaluation And Forward-reverse Rotation Meshing Analysis Of Line Gear With Intersection Axis Of The Same Plane

Line gear(LG)is a kind of precision gear transmission systems based on space curve meshing.So far,the research and the development of the design philosophy,manufacturing technology foundation,application prospects and strength analysis of LG have greatly developed.However,if the meshing stability of LG is not guaranteed,LG mechanism can't achieve accurate transmission.At present,there are no researches on the meshing stability of LG to consider the difference between the basic vector direction of the line tooth meshing and the difference between the forward and reverse meshing of LG,which may cause the phenomenon of meshing failure and shedding.In this paper,the intersecting axis LG with any angle in the same plane is taken as the research object,then the meshing stability of LG is deeply analyzed and studied during the actual transmission of LG.At the same time,in order to improve the applicability and stability of LG under different working conditions,the meshing characteristics of LG between forward-reserve rotation are compared,the main contents of this paper are as follows:1.The mathematical model is established which is suitable for the intersecting axis LG with any angle in the same plane.First of all,based on the design philosophy of LG,the contact line equation of the driving wheel with that of driven wheel is deduced by establishing the coordinate system.After that,by using spatial geometric modeling theory,the three basic vectors for the contact line of driving wheel with that of driven wheel at the meshing point are deduced and calculated,then transforming them into the same coordinate system by means of coordinate transformation.Finally,through selecting the appropriate design parameters of LG,an example simulation of the derived analytic formula is substituted.2.The mechanical model is established which is suitable for the intersecting axis LG with any angle in the same plane.Through the mathematical model of LG,based on the theory of mechanics and the method of establishing local coordinate system of the linear tine section,the linear tine of driving wheel with that of driven wheel are modeled and calculated by mechanical analysis,and the results show that LG has different forces between the forward and reverse rotation.Further,the mechanical model of LG in forward and reverse rotation is established by the difference of the direction of the basic vector of LG,and the mechanical comparison analysis of the positive and negative rotation is carried out,then a parameter—the angle of the secondary normal vector is defined,in addition,the mechanical model of linear tine is analyzed and calculated by this parameter during the forward and reverse rotation.By selecting the transmission parameters of LG,the mechanical analysis results of the forward-reverse rotation for LG are calculated,which can prove the difference between them.3.Combined with the results of LG mechanical analysis,the meshing characteristics of LG during the reverse rotation are analyzed,and the evaluation index of meshing stability is proposed and explained.The contact line equation,the basic vector and the meshing equation of space curve are derived when the LG reverses.The parameters for evaluating the meshing stability of LG are proposed: the angle of the secondary normal vector,the angle of the main normal vector and the angle of the forward and reverse rotation,and the analytical formula is derived.Through calculating an example of LG,the relationship between the selection of the axial angle and the angle of the secondary normal vector is analyzed,and the value of the angle of the main normal vector under different transmission ratios are calculated,and the existence of the angle of the main normal vector and the angle of the forward and reverse rotation is verified,which provides a new idea and theoretical method for improving the meshing stability of LG.4.The parameter design system of LG is established based on software.Through selecting a set of dimensional parameters of LG with intersect axis in the same plane,and simulating the parameters model of LG based on three-dimensional software.And a parameter design system for evaluating the meshing stability of LG is introduced,which can optimize the model parameters of LG and help improve the meshing stability.The scatter diagram between the axial angle and the angle of the secondary normal vector is drawn by software,which can be more intuitively to express the relationship between the two parameters.