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The basic method of tool design In the tool design process, the method of designing small teeth, large teeth and R39 arc teeth is generally adopted [1]. When designing the pinion small teeth, it is assumed that all the teeth of the cut gear are small teeth, and the small tooth shape is the base tooth shape of the workpiece, and the conjugate tooth shape is the tool base tooth shape, according to the tooth thickness and the tooth. The groove width is designed to be the imaginary shape cutter required for machining small teeth. The parameter of the imaginary shape cutter is the parameter of the small tooth of the shaper knife to be designed. The design method of the large tooth of the shaper knife is similar to that of the small tooth, and the arc tooth can be designed according to the non-involute tooth shape.
In the design of the involute tooth shape, since the number of teeth of the cut gear is less than the minimum number of teeth, if the conventional method is adopted, the undercut phenomenon cannot be eliminated, so the method of increasing the radius of the tooth tip circle of the tool is adopted. The basic principle of the method [2] is: under the limit condition that the cut gear does not produce the top cut, first calculate the minimum center distance a10min and the minimum tooth thickness displacement coefficient X0min; secondly, calculate the cut gear just at a10min The tool tip circle radius ra0 value does not produce the transition curve interference, and the maximum value and the maximum center distance a10max and the maximum tooth thickness displacement coefficient X0max are converted. Finally, the ra0 value is increased by the arc smooth connection. To ensure the required radial clearance of the gear being cut. Since the value of ra0 is always smaller than the radius of the tooth tip circle of the gear cutter that does not produce the undercut, the arc smooth connection is used to increase the radius of the tool tip circle without causing root cutting; It is also rare in the processing of the teeth with very few teeth, so it is only used as an accounting item in the design.
The regrind thickness of the tool and the back angle of the tooth tip can be selected as the re-grinding thickness b020mm of the gear shaping cutter. Increasing the b0 can increase the number of re-grinding and the tooth strength of the gear shaping cutter and prolong the service life. Taking the tooth tip back angle e7.5 of the pin cutter, increasing e is beneficial to improve the cutting conditions and improve the life of the pinion cutter.
Calculation formula of geometric parameters of the shaper cutter (1) No backlash meshing equation: When the gear is inserted, the gear cutter and the gear are meshed without backlash, so the following equation is established: 10m(Z1 Z0)2cos10(1)inv102(X0 X1 ) (Z0 Z1) tg inv (2), X10.
(2) The minimum tooth thickness displacement coefficient without topping: under the limit condition, the minimum meshing center distance that does not produce the top cut after conversion is a10min[12m(Z1 Z0)cos]2 ra12-rb12(3) will be a10min Substituting equations (1) and (2), the minimum tooth thickness displacement coefficient X0min can be calculated.
(3) Under the limit condition, the radius of the tooth tip of the gear cutter that does not produce the transition curve interference after the conversion is: ra0a102-[12m(Z1 Z0)cos]2-min2 (mZ0cos2)2(4) The effective involute minimum radius of curvature when working with the cut gear (4) The maximum radius of the addendum top circle without interference: ra0maxra0min b0tge (5) where ra0min does not produce a transition curve when the meshing center distance is a10min Interfering pinion cutter tip circle radius (5) Pinion cutter tip circle radius increase value: (a10min-ra0min)-rf1(6)(6) The pitch of the pinion cutter after the arc smooth connection: ra0yra0 (7) (7) The relationship between the flank angle of the flank and the back angle e of the dentition: When the radius of the tip of the spigot is no longer directly determined by the displacement coefficient (calculated according to the tooth thickness), the tooth should be re-established. The relationship between the side helix angle 0 and the back angle e of the tooth tip to coordinate the relationship between the radius of the tool tip circle and the tooth thickness.
It can be seen from the ra0ymX0 curve that the relationship between the radius of the tool tip circle and the tooth thickness can be approximated as a straight line, and the straight line equation is tg0Ktgtge(8) where Km(X0max X0min)(ra0y)max-(ra0y)min125 Therefore, the relationship can be converted to tg01.25tgtgera0ymX0 curve (8) spigot tooth thickness S0 and cogging width e0: S0e1 2mX0tg (9) e0S1-2mX0tg (10) 3 design process of the spigot knife The design of the small tooth is taken as an example to illustrate the design steps of the shaper. The design of the large tooth of the shaper cutter can be carried out by changing the pitch tooth thickness and the pitch groove width parameter of the shaper cutter.
Parameters of locking gear small teeth: modulus m7mm, number of teeth Z10, pressure angle 15, split tooth thickness S14.778mm, split pitch width e9.046mm, min0.172mm. Substituting the above parameters into equation (3), Equation (1) and formula (2), can be obtained: a10min105.81mm, X0min0.1216. Using a10min instead of a10 in equation (4), calculate the shaper cutter that does not produce transition curve interference when the mesh center distance is a10min. The radius of the tip of the tooth is ra0min73.96mm.
Substituting ra0min into equation (5): ra0maxra0min b0tge76.59mm due to (a10min-ra0min) 31.85mm, larger than the radius of the root of the gear to be cut rf130.25mm, therefore, in order to reduce the root circle error of the cut gear, according to the formula (6 Calculate the increase of the radius of the top circle of the gear shaping cutter 1.6mm.
Substituting ra0max, ra0min and substituting into equation (7), the maximum and minimum values ​​of the top circle radius ra0y of the gear shaping cutter after the arc is smoothly connected are (ra0y)max78.19mm; (ra0y)min75.56mm. Substituting ra0max Equation (4), formula (3), and formula (2) can be obtained: a10max107.68mm, X0max0.4423. The limit center distance of the tip of the toothed cutter tip is 113.52mm, so at the center of 105.81107.68mm Within the range of the distance, there is no phenomenon that the tip of the tool becomes sharp.
The main parameters of the pinion cutter small teeth (mm) main parameters X0min0.1216X0max0.4423 minute round tooth thickness 9.51010.22 tooth top height 5.568.19 tooth root height 11.208.95 pinion knife small teeth main parameters see, among them gear teeth The top fillet radius rc 2.93 mm (calculated according to the relevant formula in Reference [3]). In addition, during the use of the tool, the maximum error of the radius of the root of the cut gear is 0.76mm, which will not affect its normal meshing.
The design of other structural parameters of the pinion small teeth is the same as that of the ordinary special shaper cutter, and will not be described here.