Theory And Application Of Moving-axis Gearing

Gear geometry,also regarded as gear meshing theory,is an interdisciplinary of mechanical engineering and geometry,which investigates the gearing principle,tooth surface generation and the conjugate surfaces relations.Current literatures of gear theory are based on the fixed-axis gearing,which is assumed that the relative position of the contact gear axes does not change in the transmission processing.If the relative orientation and position of contact gears are change in the driving processing,the moving-axis gearing can be proposed.The theory of moving-axis gearing is the generalized case of the tradition theory,which can explain the problems in gear design and manufacture better.On this basis,the theory of moving-axis gearing covering driving principle,gear geometric design,gear manufacturing and gear mechanism is established.The work of the paper can be summarized as follows:(1)Driving principle:The basic concept of moving-axis gear is proposed: In the driving process of a gear pair,the relative position and orientation of the axes is assumed as changing;The relative angle and offset are defined as the function of the angle of drive gear;The traditional fixed-axis gearing is a special case of the moving-axis gearing theory with constant axes angle and offset.The basic ellipsoidal coordinate system for moving-axis gearing is established: Based on the gearing concept and the screw theory,the instantaneous axis is deduced;The ellipsoidal coordinate system is established by assuming the angle of drive gear,the gear ratio and instant axis are the basic parameters;Three main coordinate surfaces,including the axode,axial surface and transverse surface are investigated;The pitch surface is also discussed by extending the line contact to point contact.(2)Tooth geometry design:The principle and method for the generation of gear pair with line contact are investigated: According to the meshing principle,the existence of the generator is discussed,and two types of the generators,namely fixed-axis generator and moving-axis generator(the generating by a fixed-axis generator can be regarded as fixed-axis gearing while that by a moving-axis generator can be regarded as moving-axis gearing)are discussed;Based on the moving-axis generator and the basic rack with free-form tooth surface,a free-form tooth surface construction method for generator is established;Combined with the generating kinematics,the equations of conjugate tooth surface with line contact are deduced.The principle and method for the generation of gear pair with point contact are investigated: Based on the pitch surface of the spatial gear,the motion frame of the generator is built;Based on the general screw generator,the position and orientation of the generator is calculated;Based on the velocity of the contact pointed in pitch surface,the generating kinematics is established,and the equation of the conjugate tooth surface with point contact are deducedThe principle and method for the gear modification are investigated: Based on the tooth geometry of the basic rack,the mifictication basic tooth surface is shaped through the addition of modified function in the profile and lengwise direction,the final modified tooth geometry is obtained through the moving-axis generation theory;In order to reduce the error sensitivity for bevel gear,tooth profile and tooth lengthwise for forging bevel gear are modified.(3)Gear manufacturing:A mathematical model of gear generating method which can be applied to various types of process and machine tool is established: The coordinate relationship between the cutter and the work gear is obtained;A general linkage mathematical model for gear manufacture is established;Based on this,the shaping and milling generating method are investigated.(4)Gear mechanism designThe concept of moving-axis gearing mechanism is put forward,the mechanical characteristics of single level transmission and the corresponding gear train are synthesized: The feasibility and application advantages of the moving-axis gearing is discussed;Three types of single-stage gearing are investigated;Three types of moving-axis gear train is also discussed.