1 contact state of the involute gear transmission meshing process analysis of the meshing condition of a pair of external gear pairs with a degree of coincidence greater than 1, the two points of N1N2 are the two tangent points on the common tangent line of the two gear base circles, and the line segment N1N2 is the pair of gears The theoretical meshing line; point A is the meshing point of the tooth root of gear 1 and the tooth top circle of gear 2, point B is the lower boundary point of the single tooth meshing zone of gear 1; C is the node; point D is the single tooth meshing of gear 1 The upper boundary point of the zone; the point E is the meshing point of the tooth root of the gear 2 and the tooth top circle of the gear 1; therefore, BD is a single tooth meshing zone; AB, DE double tooth meshing zone; the actual meshing line of the AE gear transmission.
Therefore, when the capstan gear 1 rotates counterclockwise, the point A on the gear 1 of the pair of teeth meshes with the point A on the crown circle of the gear 2 while the point D on the gear 1 of the other pair of teeth Engaged with point D on the tooth top circle of the gear 2; when the driving wheel continues to rotate, the gear 1 of the first pair of teeth meshes with the point i of the gear 2 between point A and point B, while the second pair of wheels The gear 1 of the tooth meshes with the j point of the gear 2 between point D and point E; when the gear 1 of the first pair of teeth meshes with the gear 2 at point B, the gear 1 of the second pair of teeth simultaneously With the gear 2 teeth will mesh at point E. When the driving wheel continues to rotate, the gear 1 and the gear 2 of the first pair of teeth will mesh at the point k between point B and point D, and the second pair of teeth disengage; the gear drive enters the single tooth meshing zone; The node C is located in the single-tooth engagement zone; when the gear 1 and the gear 2 are engaged at point D, the gear transmission will enter the double-tooth engagement zone from the single-tooth engagement zone and the other pair of gear teeth on the left will simultaneously engage at point A. The above-described meshing process will be repeated while the driving wheel continues to rotate. During the gearing meshing process, the load on the gear teeth is distributed at different meshing points. For example, AB and DE are double tooth meshing zones, BD is a single tooth meshing zone, and the load distribution is ALMNOPQ.
2 Contact mechanics of contact stress in gear meshing process The contact stress of external gear pair meshing process can be calculated by using the two axes of parallelism. The Hertz formula: Cp1PR2 R1R1R2p1-L21E1 1-L2E20.5642R2 R1R1R2p1-L21E1 1-L2E2 ( 1) When E1E2E, L1L20.3, E1 and E2 in the formula Cp0.418pER2 R1R1R2 are the elastic moduli of the elastic bodies 1, 2; L1 and L2 are the Poisson ratios of the elastic bodies 1, 2; R1 and R2 are elastic The radius of curvature of the bodies 1, 2; the maximum contact stress on the Cp contact surface.
According to the geometrical parameters of the gear, the radius of curvature of the two teeth of any one of the meshing points can be obtained by using the involute property. QijiNj(i A, B, C,; j 1, 2) 1 radius of curvature QA1AN1 at the meshing point A, radius of curvature QA2AN2 of the gear 2 at the meshing point A; radius of curvature QB1BN1 of the gear 1 at the meshing point B, radius of curvature QB2BN2 of the gear 2 at the meshing point B; actual meshing line of the gearing The maximum contact stress of each meshing point on the actual meshing line can be obtained by substituting the radius of curvature Qij of the two teeth of each of the meshing points and the corresponding load into the equation (1).
Taking an involute standard spur gear transmission as an example, the parameters are: modulus 2mm, number of teeth z121, z242; large gear width is 8mm, pinion width is 10mm, torque on the drive wheel is T 6400N#mm. In order to make the change trend of the contact stress more clear, points F and J are inserted between points A and B of the double-toothed meshing region, and points G and H are inserted at points D and E.
The maximum contact stress at which the representative meshing points on the actual meshing line are meshed is as shown in Table 1. The first column indicates the meshing point and the meshing state, such as: where BB indicates that the meshing point B is in the double-toothed engagement, and B indicates that the meshing point B is in the single-tooth engagement, and the other meshing points are expressed in a similar manner. The second column indicates the distance of the meshing point from the point A; the third column indicates the radius of curvature of the gear 1 at the meshing point; the fourth column indicates the radius of curvature of the gear 2 at the meshing point; and the fifth column indicates the maximum contact at the point of the meshing state. Stress Cp.
The position on the mesh line, the ordinate indicates the maximum contact stress at the corresponding point. Figure 3 graphically shows that the maximum contact stress during the meshing process does not occur at the lower boundary point B of the single tooth meshing region of the pinion, but at the starting point A of the pinion gear pre-engagement. Table 1 and Figure 3 show the maximum contact force of node C at 553 MPa, the maximum contact force at point B of the single-teeth meshing zone is 585 MPa, and the maximum contact force at point A of the pinion meshing is 622 MPa.
The maximum contact stress variation curve of the gear transmission curve 3 The finite element solution of the contact stress of the gear meshing process For the sake of comparison, the finite element analysis of the meshing process contact problem of the same gear transmission. The finite element analysis model is established by combining the gear meshing principle, contact mechanics and finite element method. In this paper, a finite element analysis is performed on the representative meshing points on the actual meshing line described in the previous section. In order to save space, only the grid diagram and equivalent stress cloud diagram of partial finite element analysis are given here. The pair of gears are in a finite element mesh diagram at the simultaneous engagement of point A and point D. Figure 5 is an equivalent stress cloud diagram of the pair of gears at the simultaneous engagement of point A and point D.
The equivalent stress cloud of the gear drive at the moment of engagement at point C.
The maximum contact stress of a representative meshing point and the maximum equivalent stress of the contact point area. Fig. 7 is a graph showing the relationship between the maximum contact stress and the equivalent stress of the gear transmission when meshing along the actual meshing line, which is obtained by finite element analysis.
It can be seen from Table 2 and Figure 7 that the contact stress and the equivalent stress are similar in the course of the meshing process, but the maximum value of the entire meshing line appears at the point B single tooth engagement. Comparing the calculation results of the finite element with the Hertz formula, we can see that the calculation result of the finite element and the maximum contact stress of the Hertz formula are basically the same. The maximum contact stress is at point A, but the finite element analysis is only at the point E. The result is much larger than the Hertz solution.
The results of the finite element analysis of the large contact stress and the equivalent stress variation curve at the E point mesh are much larger than the Hertz solution. This is because the contact stress in the gearing meshing process by the Hertz formula is originally an approximate solution, especially at the top of the tooth. When the pre-meshing occurs, the stress concentration is actually generated in the tooth height direction/edge effect 0, and this stress concentration cannot be considered by the Hertz formula, just as the roller bearing/edge effect 0 cannot be solved by the Hertz formula. The finite element method can be solved similarly [425], and the finite element method analysis can reflect the stress concentration when the spur gear is engaged.
4 Conclusion In the involute spur gear transmission studied in this paper, the maximum contact stress during the meshing process is not at the lower boundary point of the single-tooth meshing region of the pinion (point B), but at the root and the large of the pinion. The point at which the tooth tip of the gear meshes (point A of the double-tooth meshing area), which is different from the gear national standard and the domestic mechanical design textbook, and the calculation of the contact stress of the gear transmission of the national standard and the domestic mechanical design textbook is used. The Hertz formula is used as the basis. Therefore, the calculation formula of the contact stress of the gear transmission of the national standard and the domestic mechanical design textbook is only applicable to the gear transmission of a certain parameter.
The finite element method calculates the contact stress in the gear transmission process, and can analyze the stress concentration phenomenon when the tooth top meshes. Compared with the Hertz solution, the Hertz formula can not reflect the edge stress concentration problem when the tooth top meshes. In this paper, the contact stress of the involute spur gear transmission process of a specific parameter is studied comprehensively. It is more instructive to study the contact stress of the involute spur gear transmission process with different parameters. The author will introduce another article.
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