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1 Theoretical basis for the smoothing of the involute gear transmission 2 The calculation and analysis of the sliding friction between the involute profiles shows that when the B2P meshing segment is engaged, the driven gear profile is oriented along the surface of the drive gear tooth toward the root of the drive gear. Sliding; when the PB1 meshing segment is engaged, the driven gear tooth profile slides relative to the driving gear tooth tip surface along the driving wheel tooth profile surface; at the node P, the two tooth profiles are pure sliding without sliding. To this end, the distribution law of the sliding friction force of the tooth profile surface can be summarized.
3 Assume that the normal load is evenly distributed. The overlap coefficient of the involute gear transmission is such that pb is the base of the gear. According to the definition of the overlap coefficient in the involute gear transmission, the length of the meshing segment B1B2 is pb. Wherein the length of 2(-1)pb belongs to two pairs of teeth, and the length of (2-)pb belongs to a pair of teeth.
4 output torque T of the driven wheel when the two pairs of teeth mesh
Let the distance between the N1N2 and N1N2 lines be e, the sliding friction coefficient be f, the friction angle, the gear modulus be m, and the pressure angle on the index circle be: e=pb2tg=fpb2=fmcos2(2) The same reason can be proved: the transfer of one tooth from the B2 point to the H point and the other tooth from the V point to the B1 point simultaneously, the (synthetic) load they bear is Fn2, their action line Always on the N1N2 line, the direction always points to N2, ((. Control can be listed: Fn2=T1rb1 e(3)TD2=Fn2(rb2-e)(4) Substituting (2) and (3) into (4) After finishing, TD2=T1Z2-fZ1 f(5)5 The method of the output torque TE2 of the driven wheel when the pair of teeth is engaged at any point E in the HP area is compared with the method of making the driven gear tooth at any point E of the HP area. The directional load is FnE2 and the tangential load is fFnE2.
The output torque TQ2 of the driven wheel makes the normal load of the driven gear tooth at the arbitrary point Q in the PV region FnQ2, and the tangential load is fFnQ2. The output torque fluctuation law of the driven wheel is known from (5), and the tooth is counted. If the input torque of the driving wheel is constant after the influence of friction, TD2 will remain unchanged. Calculate the first-order partial derivatives of TE2 and TQ2 for the variables E1 and Q1 respectively (due to the limited space, the specific derivation process is omitted). The relationship between the incremental coefficient of the center distance and the meshing angle makes the involute spur gear drive correctly installed and incorrect. The center distances under the installation conditions are A and A(1), respectively, which are the center distance increment coefficients. According to the theory of involute gear transmission, it is not difficult to list the relationship between the incremental coefficient of the center distance and the meshing angle: =cos-1cos1 (33) The output torque of the driven wheel is calculated by the equations to represent the fluctuation rate of the output torque of the driven wheel. The definition is: =T2max-T2minT2min (34) The above equations clearly reveal the close mathematical relationship between the output torque volatility of the driven wheel and the sliding friction coefficient between the teeth and the number of gear teeth.
Conclusion A series of analysis, research and calculations on the output torque volatility equations of the driven wheel show that the friction between the involute gear tooth profile will cause a certain fluctuation of the output torque of the driven wheel; the output torque volatility of the driven wheel will follow the tooth profile. The inter-sliding friction coefficient increases and increases, and decreases as the number of gear teeth increases. Therefore, in the involute gear mechanism where the surface quality of the gear teeth is low or the lubrication condition between the teeth is poor and the number of teeth is small, the output torque of the driven wheel is likely to be more fluctuating, resulting in the gear mechanism and the work it drags. The mechanism is not running smoothly and vibrating. Finally, it should be emphasized that effectively reducing the surface roughness of the profile, maintaining a good interdental lubrication environment so as to greatly reduce the sliding friction coefficient f between the profiles and appropriately increasing the number of gear teeth within the allowable range is to prevent or reduce The only way for the output torque of the moving wheel to fluctuate.
3 Assume that the normal load is evenly distributed. The overlap coefficient of the involute gear transmission is such that pb is the base of the gear. According to the definition of the overlap coefficient in the involute gear transmission, the length of the meshing segment B1B2 is pb. Wherein the length of 2(-1)pb belongs to two pairs of teeth, and the length of (2-)pb belongs to a pair of teeth.
4 output torque T of the driven wheel when the two pairs of teeth mesh
Let the distance between the N1N2 and N1N2 lines be e, the sliding friction coefficient be f, the friction angle, the gear modulus be m, and the pressure angle on the index circle be: e=pb2tg=fpb2=fmcos2(2) The same reason can be proved: the transfer of one tooth from the B2 point to the H point and the other tooth from the V point to the B1 point simultaneously, the (synthetic) load they bear is Fn2, their action line Always on the N1N2 line, the direction always points to N2, ((. Control can be listed: Fn2=T1rb1 e(3)TD2=Fn2(rb2-e)(4) Substituting (2) and (3) into (4) After finishing, TD2=T1Z2-fZ1 f(5)5 The method of the output torque TE2 of the driven wheel when the pair of teeth is engaged at any point E in the HP area is compared with the method of making the driven gear tooth at any point E of the HP area. The directional load is FnE2 and the tangential load is fFnE2.
The output torque TQ2 of the driven wheel makes the normal load of the driven gear tooth at the arbitrary point Q in the PV region FnQ2, and the tangential load is fFnQ2. The output torque fluctuation law of the driven wheel is known from (5), and the tooth is counted. If the input torque of the driving wheel is constant after the influence of friction, TD2 will remain unchanged. Calculate the first-order partial derivatives of TE2 and TQ2 for the variables E1 and Q1 respectively (due to the limited space, the specific derivation process is omitted). The relationship between the incremental coefficient of the center distance and the meshing angle makes the involute spur gear drive correctly installed and incorrect. The center distances under the installation conditions are A and A(1), respectively, which are the center distance increment coefficients. According to the theory of involute gear transmission, it is not difficult to list the relationship between the incremental coefficient of the center distance and the meshing angle: =cos-1cos1 (33) The output torque of the driven wheel is calculated by the equations to represent the fluctuation rate of the output torque of the driven wheel. The definition is: =T2max-T2minT2min (34) The above equations clearly reveal the close mathematical relationship between the output torque volatility of the driven wheel and the sliding friction coefficient between the teeth and the number of gear teeth.
Conclusion A series of analysis, research and calculations on the output torque volatility equations of the driven wheel show that the friction between the involute gear tooth profile will cause a certain fluctuation of the output torque of the driven wheel; the output torque volatility of the driven wheel will follow the tooth profile. The inter-sliding friction coefficient increases and increases, and decreases as the number of gear teeth increases. Therefore, in the involute gear mechanism where the surface quality of the gear teeth is low or the lubrication condition between the teeth is poor and the number of teeth is small, the output torque of the driven wheel is likely to be more fluctuating, resulting in the gear mechanism and the work it drags. The mechanism is not running smoothly and vibrating. Finally, it should be emphasized that effectively reducing the surface roughness of the profile, maintaining a good interdental lubrication environment so as to greatly reduce the sliding friction coefficient f between the profiles and appropriately increasing the number of gear teeth within the allowable range is to prevent or reduce The only way for the output torque of the moving wheel to fluctuate.
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