The tooth profile of the large diameter involute spline broach is usually ground on a spline grinder with a forming wheel. When an experienced operator grinds the teeth, the shank of the broach is often raised a few times higher, and the knives of the broach are improved by increasing the rake angle of the broach. After the tooth angle correction, the broaching precision of the broach can be significantly improved.
The rake angle of the involute spline broach is g=10°-20°, and the back angle a=2°～4° (usually take g=15°, a=3°). When the involute profile of the broach is projected onto the base surface, its tooth profile angle is reduced. In order to compensate for this change, the tooth profile angle error of the broach is corrected. Since the influence of the tooth angle error on the tooth profile error increases with the increase of the broach diameter, the tooth profile correction of the large diameter broach is especially important. Since the tooth profile of the involute spline knives is projected onto the base surface exactly the same as the spur gear shaping cutter, the corrected tooth profile angle a0' can be calculated by the tooth profile correction formula of the spur gear shaping cutter. , that is, tana0'=tana0/(1-tangtana)(1) where a0
To correct the theoretical tooth angle before. Correction calculation example: The parameters of an internal spline broach are: tooth number Z0=28, tooth angle a0=20°, tooth tip diameter Da0=116.065mm, root circle diameter Df0=109.6mm, base circle diameter Db0=102.9903112 Mm, the index circle diameter D0 = mZ0 = 1212 mm. The maximum overlap coefficient of the broach correction tooth == effective mesh length L / base circumference t = 4.007923117 / 11.55548589 = 0.3468415915. According to the formula (1), the corrected broach tooth angle a0'=20.26183269°=20°16', cosa0'=0.9381198361, and the corrected base circle diameter Db0'=D0cosa0'=105.0694216. Since the base circle diameter Db0=D0cosa0=105.2455734mm before correction, the difference between the radius of the base circle before and after correction is ∆r0=(105.0694216-105.2455734)/2=-0.08807635mm. According to the calculation formula of the tooth profile error ∆J=∆r02p/Z0e(2), the maximum error of the tooth profile before and after correction is ∆J=-0.007mm.
It can be seen from the calculation results that the tooth profile error value is small and negligible because the broach overlap coefficient e is small. Due to the performance of the broaching machine and the heat treatment of the broach and the limitation of the sharpening equipment, the broach length cannot be too long, which determines that the broaching allowance A0 of the broach cannot be too large (if the broaching margin required by the process is large, It can be considered to use a set of broaching, but the concentricity of the broaching workpiece is not as good as that of the single broach), that is, the effective meshing length of the yoke involute tooth shape is not too long (generally much smaller than the base circumference), so the involute The overlap factor e of the wire spline broach is usually much smaller than one. When designing a large diameter involute spline broach with a large involute tooth shape effective engagement length, it is preferable to verify ∆J as described above for the sake of reliability. If the ∆J is small, or the accuracy of the workpiece is not high, the tooth angle may not be corrected; if the ∆J is large, or the workpiece precision is very high, the razor should be designed with the corrected tooth angle. For involute gears or pinion cutters, the meshing overlap factor e≥1 is usually used, so the tooth profile error is also large (∆J≥0.02mm), which cannot be ignored.
From the derivation of the tooth profile correction formula, the root cause of the tooth profile error is that the presence of the rake angle causes the tooth profile angle to change when the involute tooth profile of the tool is projected onto the base surface (the front angle tends to The tooth profile angle projected on the base surface is small). Based on this, the tooth angles of the broach and the shaper should be corrected. However, since the overlap coefficient of the broach is small, the influence of the tooth angle error on the tooth profile error ∆J is reduced, so that it cannot be corrected. However, the gear shaping is a developed cutting, and the effective meshing length is always greater than the base circumference. Otherwise, it cannot be guaranteed that the first tooth immediately participates in the meshing (cutting) when the preceding tooth exits the meshing (cutting), so the overlap coefficient e≥ must be guaranteed. 1, the pinion knife must correct the tooth angle although it has only 5° front angle. The broaching process is a forming cut, and the broach overlap coefficient e can be much less than 1, so that the front angle of the involute spline broach reaches 15° without correcting the tooth angle.
The rake angle of the involute spline broach is g=10°-20°, and the back angle a=2°～4° (usually take g=15°, a=3°). When the involute profile of the broach is projected onto the base surface, its tooth profile angle is reduced. In order to compensate for this change, the tooth profile angle error of the broach is corrected. Since the influence of the tooth angle error on the tooth profile error increases with the increase of the broach diameter, the tooth profile correction of the large diameter broach is especially important. Since the tooth profile of the involute spline knives is projected onto the base surface exactly the same as the spur gear shaping cutter, the corrected tooth profile angle a0' can be calculated by the tooth profile correction formula of the spur gear shaping cutter. , that is, tana0'=tana0/(1-tangtana)(1) where a0
To correct the theoretical tooth angle before. Correction calculation example: The parameters of an internal spline broach are: tooth number Z0=28, tooth angle a0=20°, tooth tip diameter Da0=116.065mm, root circle diameter Df0=109.6mm, base circle diameter Db0=102.9903112 Mm, the index circle diameter D0 = mZ0 = 1212 mm. The maximum overlap coefficient of the broach correction tooth == effective mesh length L / base circumference t = 4.007923117 / 11.55548589 = 0.3468415915. According to the formula (1), the corrected broach tooth angle a0'=20.26183269°=20°16', cosa0'=0.9381198361, and the corrected base circle diameter Db0'=D0cosa0'=105.0694216. Since the base circle diameter Db0=D0cosa0=105.2455734mm before correction, the difference between the radius of the base circle before and after correction is ∆r0=(105.0694216-105.2455734)/2=-0.08807635mm. According to the calculation formula of the tooth profile error ∆J=∆r02p/Z0e(2), the maximum error of the tooth profile before and after correction is ∆J=-0.007mm.
It can be seen from the calculation results that the tooth profile error value is small and negligible because the broach overlap coefficient e is small. Due to the performance of the broaching machine and the heat treatment of the broach and the limitation of the sharpening equipment, the broach length cannot be too long, which determines that the broaching allowance A0 of the broach cannot be too large (if the broaching margin required by the process is large, It can be considered to use a set of broaching, but the concentricity of the broaching workpiece is not as good as that of the single broach), that is, the effective meshing length of the yoke involute tooth shape is not too long (generally much smaller than the base circumference), so the involute The overlap factor e of the wire spline broach is usually much smaller than one. When designing a large diameter involute spline broach with a large involute tooth shape effective engagement length, it is preferable to verify ∆J as described above for the sake of reliability. If the ∆J is small, or the accuracy of the workpiece is not high, the tooth angle may not be corrected; if the ∆J is large, or the workpiece precision is very high, the razor should be designed with the corrected tooth angle. For involute gears or pinion cutters, the meshing overlap factor e≥1 is usually used, so the tooth profile error is also large (∆J≥0.02mm), which cannot be ignored.
From the derivation of the tooth profile correction formula, the root cause of the tooth profile error is that the presence of the rake angle causes the tooth profile angle to change when the involute tooth profile of the tool is projected onto the base surface (the front angle tends to The tooth profile angle projected on the base surface is small). Based on this, the tooth angles of the broach and the shaper should be corrected. However, since the overlap coefficient of the broach is small, the influence of the tooth angle error on the tooth profile error ∆J is reduced, so that it cannot be corrected. However, the gear shaping is a developed cutting, and the effective meshing length is always greater than the base circumference. Otherwise, it cannot be guaranteed that the first tooth immediately participates in the meshing (cutting) when the preceding tooth exits the meshing (cutting), so the overlap coefficient e≥ must be guaranteed. 1, the pinion knife must correct the tooth angle although it has only 5° front angle. The broaching process is a forming cut, and the broach overlap coefficient e can be much less than 1, so that the front angle of the involute spline broach reaches 15° without correcting the tooth angle.
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