Multi-displacement linear gear construction flow smoothing discussion
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1 Elastohydrodynamic Lubrication Formula The key to the calculation of elastohydrodynamic lubrication is the calculation of film thickness. After comprehensive research and comparison, it is found that Yang Peiran. The film thickness calculation of Wenshi cast is more reasonable, and the minimum film thickness returned is hmin=6.760.530.750u0.75E-0.06r0.41w-0.16(1) center film thickness hc=11.90.400.740u0.74E-0.14r0.46w -0.20(2) viscosity coefficient; 0 dynamic viscosity at atmospheric pressure; u entrainment speed; E equivalent elastic modulus, 1E = (1-21) / E1 (2-2) / E22; r equivalent curvature Radius, r = RR;, R cycloidal gear tooth profile and arc gear tooth profile radius of curvature; w unit length of load.
It is known from the formulas (1) and (2) that the calculation of the film thickness requires calculation of the equivalent curvature radius, the entrainment speed, and the load per unit contact length.
(1) Calculation of equivalent curvature radius According to the equation of the cycloidal gear profile curve, the radius of curvature of the cycloidal gear can be derived = S3AC-DF(3)S=C2 F2C=-Lzi12z2sin(zi122z2) ai12sin(i122) R(G-zi12z2) Sin(-zi122z2)F=-Lzi12z2cos(zi122z2) ai12sin(i122)-R(G-zi12z2)cos(-zi122z2)D=-Lz2i212z2cos(zi122z2) ai212cos(i122) R(G-zi12z2)cos(-ai122r2) RJsin(-zi122Z2)A=Lz2i212z2sin(zi122z2)-ai212sin(i122) R(G-zi12z2)2sin(-ai122r2)-RJcos(-zi122z2)G=kcos2-1k2-2kcos2 1,J=ksin2-k3sin2(k2- 2kcos2 1)2,=atan(sin2k-cos2) type i12 gear ratio, i12=Z2/Z1=Z2Z1; z2, z1 arc gear tooth number and cycloid gear tooth number; z arc gear and cycloid gear tooth difference ;L arc gear arc tooth center circle radius; k generative coefficient; r2 arc gear pitch circle radius; R arc gear arc tooth arc radius; h circle diameter coefficient; corresponding phase angle when the gear meshes.
When calculating the equivalent radius of curvature, the positive contact is taken when the cycloid gear is in contact near the tooth tip, and the negative sign is taken when the cycloid gear is in contact with the arc gear.
(2) Calculation of the entrainment speed According to the theoretical model of hydrodynamic lubrication, the entrainment speed of the two sliding surfaces is half of the sum of the tangential speeds of the two moving surfaces, ie u=(u1 u2)/2, and the meshing point is obtained by The vector rM2=L-Rei(4) in the moving coordinate system S2 is the vector rM1=Lei(z2i122)-Rei(-z2i122) in the moving coordinate system S1 (the hypocycloid gear center fixed and cycloidal gear) -ae-i(i122)(5) is launched by u2=drM2dt, u1=drM1dt 62
U2=R2(kcos2-1k2-2kcos2 1)(6)u1=2c2 d2 f2 2cdcos-2cfcos2 2dfcos( 2)(7) where c=Lz1, d=R(G-z1), f=ai12, 2 is a circle The angular velocity of the arc gear is rotated, and the formula (6) and formula (7) are substituted into the calculation formula of the entrainment speed to determine the entrainment speed u.
(3) Calculation of load on unit contact length Since the coincidence degree of the multi-tooth difference cycloidal gear is approximately equal to 1, it can be considered that the load is borne by a pair of teeth. The multi-tooth difference cycloidal gear is usually made up of a large gear as the driving wheel. According to the geometric relationship of the gear at the meshing point, the unit contact length is loaded. w=M1 k2-2kcos2Br2sin2 (8) where the torque M can be based on the motor input power P and The gear shaft speed n is calculated.
2 Elastohydrodynamic lubrication calculation and analysis of gear and lubricant related parameters: modulus m=20, number of teeth z1=8, z2=11, tooth width B=20mm, n=900r/min, 0=006Pas,=2.110-8P- 1a, P=10kW, E1=E2=2.11011Pa, 1=2=0.3, k=1.7724, h=1.3034, ka=0.6845, kf=1.0063. The program is programmed by MATLAB to calculate hmin and hc and meshing phase angle at the meshing point. The relationship between them is as shown in the figure. It can be seen that either hmin or hc has a minimum value when the top of the cycloidal gear is in contact with the root of the circular gear, that is, the gear is more likely to wear when meshing here, so select here. For the analysis point, the relationship between the design parameters k and h and hmin of the multi-toothed cycloidal gear is as shown.
Hmin, hc meshing phase angle 2 relationship hmin and k, h relationship curve from which we can see that k is smaller, h is larger, the minimum film thickness is smaller, the main reason is that the entrainment speed u decreases with the decrease of k Large and reduced.
3 Conclusion Through calculation and analysis, it is found that the gear is well lubricated during the whole meshing process, and the lubricating film formed by the meshing of the cycloid gear tooth tip and the arc gear tooth root is thinner. Therefore, it is preferable to use a larger k and a smaller h when the gear is designed to meet other conditions.
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