# Cutting bevel gear theorem of digital twisting wheel grinding machine

The profile of the rack and the geometrical projection of the rack profile formed by the movement of the grinding wheel when the CNC gear grinding machine grinds the right-handed bevel gear. It can be seen that in order to form the helix angle and the taper angle of the bevel gear, the grinding wheel rotates the B0 angle in the (y, z) plane according to the spiral direction of the gear (the magnitude of the grinding wheel is not equal to the shape of the bevel gear design). At the same time as the helix angle, the NC interpolation motion of the gear axis in the D0 angle direction is made in the (x, z) plane. It can be seen that the D0 angle is the angle between the v_x and v_z motion synthesis speed v_0=v_x v_z direction of the grinding wheel in the (x,z) plane and the working axis, and it is also the rack cone angle formed by the grinding wheel movement ( Hereinafter referred to as the grinding rack taper angle). The plane perpendicular to the axis of the grinding wheel and passing through its geometrically symmetrical center is now referred to as the 0 plane. It can be seen that the H angle is the taper angle of the rack formed by the movement of the grinding wheel on the 0 plane.
The three-dimensional diagram of the rack tooth profile can obtain the geometric relationship between the grinding wheel mounting angle B0, the grinding rack taper angle D0 and the H angle: tanH=ABoB=ABoCoCoB=accb=tanD0cosB0(1) with the grinding wheel as the component 0, the workpiece ( The bevel gear is the member 1; the middle distance is the horizontal distance from the geometric center of the grinding wheel to the apex of the upper end of the bevel gear; h is the distance between the two end sections of the bevel gear; An0 is the bottom cone angle of the grinding wheel. WW is a vertical section through the contact point of the gear root cone with the grinding wheel, and is also the projection of the plane of the rack section formed by the movement of the grinding wheel. The NN is a horizontal section projection through the geometric center of the grinding wheel, ie the end section of the grinding rack.
The geometrical profile of the rack formed by the grinding motion is in the developing motion, and the plane of the grinding rack section is tangent to the cylinder of the tapered gear section. Therefore, the left and right helix angles and the end face tooth angles on the rack section plane will be equal to the helix angles Bcl1, Bcr1 and the section cylinder end face pressure angles Actl1, Actr1 on the conical gear joint cylinder, respectively. If mn is the bevel gear manufacturing profile, and Z1 is the number of teeth, the bevel gears with machine adjustment parameters B0, D0 and An0 can be obtained. The parameters are the pitch diameter dcl(r). )=mnZ1PcosB0l(r)(6) base circle diameter dbl(r)=mnZ1cosA0l(r)PcosB0l(r)(7) can be seen from equations (6) and (7), and the left and right sides of the gear tooth profile are processed. The pitch circle diameters will not be equal. Therefore, in order to obtain the required bevel gears, different grinding parameters must be used on both sides of the tooth profile of the gear teeth during the grinding process.
The adjustment parameters for grinding the bevel gear are calculated based on the plane or space meshing bevel gear pair 1472 studied by the tooth surface contact theory. There is already a relatively complete design method. Through this design method, the conical gear can be obtained. The following parameters: the production profile rack die mn, the number of teeth Z1, the gear processing cone angle D1, the left and right side base circle diameter dbl and dbr, and the left and right side base circle spiral angles Bbl and Bbr. The adjustment parameters of the CNC cone grinding wheel grinding machine include: grinding wheel installation angle B0, grinding rack cone angle D0, cone gear pitch diameter dc1 and grinding wheel bottom cone angle An0. Let's discuss how to determine the individual grinding parameters to ensure that the bevel gear meets the meshing requirements.
Conclusion The CNC cone grinding wheel grinding machine can realize the grinding of the bevel gear. However, when grinding the left and right sides of the helical bevel gear profile, different machine adjustment parameters must be used for two grindings. This is a disadvantage of using a CNC tapered wheel grinding machine to grind a helical bevel gear. When grinding a straight-tooth bevel gear, the machine adjustment parameters on both sides of the tooth profile are the same.

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