CN105718651A - Involute straight tooth bevel gear tooth end profile modification and parameterized modeling method - Google Patents

Abstract

The present invention relates to an involute straight tooth bevel gear tooth end correction and parameterized modeling method. The method comprises the following steps: S1, performing finite element analysis on an involute straight tooth bevel gear whole profile is not modified, so as to obtain a gear circumferential displacement difference of each key engaging position and a tooth surface equivalent touch stress distribution graph; S2, on the basis of the gear circumferential displacement difference, determining a profile modification amount of tooth end profile modification, and on the basis of the tooth surface equivalent touch stress distribution graph, determining a profile modification length; S3, by using the profile modification length and the profile modification amount as variables, establishing an equation of a tooth end profile modification curve and a profile modification tooth surface; and S4, according to the equation of the tooth profile modification curve and the profile modification tooth surface, establishing a three-dimensional model of a profile-modified gear. The method provided by the present invention effectively improves the conditions of uneven gear load distribution and stress concentration, which are caused by tooth surface plastic deformation, improves transmission precision, reduces the vibration noise level of gear engagement and prolongs the service life of gears.

Description

A kind of involute bevel gears tooth end relief and parametric modeling method

Technical field

The present invention relates to the correction of the flank shape of gear and modeling method, more particularly, it relates to a kind of involute bevel gears tooth end relief and parametric modeling method.

Background technology

Owing to involute bevel gears is in actual use procedure, it is subject to the impact of the factors such as the accuracy of manufacture, mismachining tolerance and loading conditions, the mesh tooth face causing reality deviate from the spherical involute of its Design Theory, therefore gear vibrates in running, noise strengthens, and seriously reduces the NVH quality of gear.Obtain gear tooth surface elasticity amount after stand under load by the means of finite element analysis, further determine that the parameter such as profiling quantity and correction of the flank shape length of gear face, finally improve the stand under load situation of gear teeth face, reduce the vibrating noise level that gear engagement produces.

The correction method of traditional involute bevel gears mainly includes profile modification, axial modification, tooth end relief etc..Publication number CN1936749A have employed increment, flank profil and teeth directional comprehensive correction of the flank shape method and involute bevel gears carry out correction of the flank shape, but the determination process of its profile modifying parameters is not made reasonable dismissal, only gives the experience recommended range of profile modifying parameters.Publication number CN101937211A have employed flank profil, involute bevel gears is carried out correction of the flank shape by axial modification method, have employed Finite Dynamic Element simulation method and determine the big end tooth exterior feature profiling quantity of bevel gear, correction of the flank shape profile is made at gear teeth central cross-section first by 3D sculpting software, and correction of the flank shape profile is equidistantly stretched to the flank of tooth modeling process realizing teeth directional modification of equidistance gear, profile modifying gear processing is realized finally by Digit Control Machine Tool, it it is a kind of relatively reasonable profile modifying gear processing method, but its shortcoming is in that to realize teeth directional modification of equidistance only, parametrization correction of the flank shape can not be carried out according to actual needs, change profile modifying parameters.Publication number CN85102760B is by carrying out electrochemical corrosion to harmonic gear, thus reaching the purpose of correction of the flank shape.

Summary of the invention

The technical problem to be solved in the present invention is in that, it is provided that a kind of involute bevel gears tooth end relief and parametric modeling method.

The technical solution adopted for the present invention to solve the technical problems is: a kind of involute bevel gears tooth end relief of structure and parametric modeling method, comprises the following steps:

S1, involute bevel gears to non-correction of the flank shape carry out finite element analysis, obtain the circumferentially displaced difference of gear and the flank of tooth equivalence distribution of contact figure of each crucial position of engagement；

S2, based on the circumferentially displaced difference of described gear, it is determined that the profiling quantity of tooth end relief, based on flank of tooth equivalence distribution of contact figure, determine correction of the flank shape length；

S3, with correction of the flank shape length and profiling quantity for variable, set up tooth end relief curve and the equation of the correction of the flank shape flank of tooth；

S4, threedimensional model according to the establishing equation profile modifying gear of tooth end relief curve and the correction of the flank shape flank of tooth.

In such scheme, the equation of described tooth end relief curve is as follows:

$\left\{\begin{array}{c}{y}_1(r,R_{c1})=R_{c1}-\sqrt{{R_{c1}}^2-{\[r-(R-b+{\mathrm{\ΔL}}_1)\]}^2}\\ x_1(r,R_{c1})=r\\ R-b\≤r\≤R-b+\mathrm{\Δ}{L}_1\end{array}\right.$

$\left\{\begin{array}{c}{y}_2(r,R_{c2})=R_{c2}-\sqrt{{R_{c2}}^2-{\[r-(R-{\mathrm{\ΔL}}_2)\]}^2}\\ x_2(r,R_{c2})=r\\ R-\mathrm{\Δ}{L}_2\≤r\≤R\end{array}\right.$

In formula: r is gear start radius；R_ci(i=1,2) for the arc radius of modification curve；R be outer cone from；B is the facewidth；Δ L_i(i=1,2) for correction of the flank shape length；

In such scheme, it is characterised in that described correction of the flank shape tooth surface equation is as follows:

$x=rcos\left(\mathrm{\β}\sin \mathrm{\α}\right)sin\mathrm{\α}cos\mathrm{\β}+rsin\left(\mathrm{\β}sin\mathrm{\α}\right)sin\mathrm{\β}+y_i(r,R_{ci})x_{\stackrel{\→}{n_p}}$

$y=rcos\left(\mathrm{\β}\sin \mathrm{\α}\right)sin\mathrm{\α}cos\mathrm{\β}+rsin\left(\mathrm{\β}sin\mathrm{\α}\right)sin\mathrm{\β}+y_i(r,R_{ci})y_{\stackrel{\→}{n_p}}$

Z=rcos (β sin α) cos α

In formula: r is gear start radius；α is cone generating angle；β is the angle on the field of conjugate action between initial segment and instantaneous gyroaxis, and wherein on base cone, involute start angle is 0；R_ci(i=1,2) for the arc radius of modification curve；For being parallel to the unit vector of base cone axis；AndRespectively unit vectorX, y to projection coordinate.

In such scheme, the described crucial position of engagement includes four single bi-tooth gearing transfer points.

Implement involute bevel gears tooth end relief and the parametric modeling method of the present invention, have the advantages that

1, the present invention proposes a kind of involute bevel gears correction method based on the circumferentially displaced difference of gear and teeth directional equivalence distribution of contact figure, achieves the three-dimensional modeling process of profile modifying gear by means of mathematical analysis software and 3D sculpting software.

2, the present invention effectively improves the gear load skewness owing to tooth surface elasticity causes and stress concentration status, improves transmission accuracy, reduces the vibrating noise level of gear engagement so that the service life of gear improves.

3, the present invention is directed to the feature of gear mesh elastic deformation, driving gear is adopted increment unsymmetric shape modification, driven gear does not do correction of the flank shape.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:

Fig. 1 is the schematic diagram of theoretical spherical involute；

Fig. 2 is the three-dimensional model diagram of the non-correction of the flank shape straight bevel gear of standard；

Fig. 3 is standard straight bevel gear limited element calculation model schematic diagram；

Fig. 4 is gear mesh schematic diagram mesh cycle；

Fig. 5 is the circumferentially displaced difference schematic diagram of key position gear；

Fig. 6 is the non-correction of the flank shape straight bevel gear facewidth to equivalence distribution of contact figure；

Fig. 7 is straight bevel gear tooth end relief parameter schematic diagram；

Fig. 8 sets up the correction of the flank shape flank of tooth model obtained in Matlab；

Fig. 9 be into the three-dimensional model diagram of straight bevel gear of correction of the flank shape；

Figure 10 be after correction of the flank shape the straight bevel gear facewidth to equivalence distribution of contact figure.

Detailed description of the invention

In order to the technical characteristic of the present invention, purpose and effect are more clearly understood from, now comparison accompanying drawing describes the specific embodiment of the present invention in detail.

In the involute bevel gears tooth end relief and parametric modeling method specific embodiment of the present invention as follows:

On the basic circle conical surface a bit, a bit on the basic circle conical surface, rotary becomes spherical involute or on basic circle reference cone face.As it is shown in figure 1,1 P on incisal plane₀Spherical involute PP is formed behind rotation β angle, base cone face₀.To hold greatly spherical involute for start line, small end spherical involute is terminated line, uses variable cross-section sweeping order can obtain the non-correction of the flank shape straight bevel gear flank of tooth of standard, and uses array commands to set up non-profile modifying gear threedimensional model as shown in Figure 2.

Select and there is for a pair the involute bevel gears of basic parameter in table 1:

Table 1

Finite-element preprocessing software Hypermesh uses Solid185 unit non-profile modifying gear model carries out stress and strain model, and import and ANSYS arranges corresponding material properties (wherein material properties is 40Cr, elastic modulus E=2.1 × 10⁵Mpa, Poisson's ratio ν=0.3) and boundary condition (gear pair contact to coefficientoffrictionμ=0.2, drivewheel torque T=50N.m, the all degree of freedom staff cultivation of driven pulley axis hole node, the radial and axial degree of freedom of drivewheel axis hole node is all fixed, only release circumference degree of freedom), finally give FEM (finite element) model as shown in Figure 3.

According to gear schematic diagram mesh cycle, as shown in Figure 4, it is determined that four key position: P in Meshing Process of Spur Gear₁、P₂、P₃、P₄, i.e. single bi-tooth gearing transfer point.

For 4 key positions listed above, with reference to finite element stimulation result, obtain the circumferentially displaced difference schematic diagram of its gear, as shown in Figure 5.

The circumferentially displaced difference schematic diagram of gear according to Fig. 5, it is known that P₃Position occurs in that the maximum of teeth directional displacement difference, respectively 10.2 μm (corresponding gear small ends) and 14.12 μm (the big end of corresponding gear), it is thus determined that gear small end profiling quantity △ T₁=11 μm, gear big end profiling quantity △ T₂=15 μm.The facewidth obtained is emulated to equivalence distribution of contact figure, as shown in Figure 6, it is determined that correction of the flank shape length △ L according to FEM calculation₁=△ L₂=0.975mm.

Tooth end relief parameter schematic diagram is as shown in Figure 7.Wherein the arc radius computing formula of modification curve is as follows:

R_ci=Δ L_i ²/2ΔT_i

The equation of modification curve G'N' is as follows:

$\left\{\begin{array}{c}{y}_1(r,R_{c1})=R_{c1}-\sqrt{{R_{c1}}^2-{\[r-(R-b+{\mathrm{\ΔL}}_1)\]}^2}\\ x_1(r,R_{c1})=r\\ R-b\≤r\≤R-b+{\mathrm{\ΔL}}_1\end{array}\right.$

Modification curve GN equation is as follows:

$\left\{\begin{array}{c}{y}_2(r,R_{c2})=R_{c2}-\sqrt{{R_{c2}}^2-{\[r-(R-{\mathrm{\ΔL}}_2)\]}^2}\\ x_2(r,R_{c2})=r\\ R-\mathrm{\Δ}{L}_2\≤r\≤R\end{array}\right.$

Wherein variable i=1 represents circular curve G'N'；I=2 represents circular curve GN；R_ciFor arc radius；B is the facewidth；△ T_iFor profiling quantity；△ L_iFor correction of the flank shape length；R be outer cone from.

Here a unit vector being parallel to straight line PG is introducedCan be tried to achieve by following formula:

$\stackrel{\→}{n_p}=\left[\begin{array}{c}\frac{\left(sin\right(\mathrm{\β}sin\mathrm{\α})cos\mathrm{\β}-cos(\mathrm{\β}sin\mathrm{\α}\left)sin\mathrm{\α}cos\mathrm{\β}\right)}{\sqrt{{\cos }^2\left(\mathrm{\β}sin\mathrm{\α}\right){\sin }^2\mathrm{\α}+{\sin }^2\left(\mathrm{\β}sin\mathrm{\α}\right)}}\\ \frac{\left(cos\right(\mathrm{\β}\sin \mathrm{\α})sin\mathrm{\α}\cos \mathrm{\β}+sin(\mathrm{\β}sin\mathrm{\α}\left)sin\mathrm{\β}\right)}{\sqrt[.]{{\cos }^2\left(\mathrm{\β}sin\mathrm{\α}\right){\sin }^2\mathrm{\α}+{\sin }^2\left(\mathrm{\β}\sin \mathrm{\α}\right)}}\\ 0\end{array}\right]$

Therefore correction of the flank shape flank of tooth Σ 1 and Σ 2 equation are as follows:

$x=rcos\left(\mathrm{\β}\sin \mathrm{\α}\right)sin\mathrm{\α}cos\mathrm{\β}+rsin\left(\mathrm{\β}sin\mathrm{\α}\right)sin\mathrm{\β}+y_i(r,R_{ci})x_{\stackrel{\→}{n_p}}$

$y=rcos\left(\mathrm{\β}\sin \mathrm{\α}\right)sin\mathrm{\α}cos\mathrm{\β}+rsin\left(\mathrm{\β}sin\mathrm{\α}\right)sin\mathrm{\β}+y_i(r,R_{ci})y_{\stackrel{\→}{n_p}}$

Z=rcos (β sin α) cos α

Wherein i=1,2.

Matlab inputs following procedure code be used for building the correction of the flank shape flank of tooth:

clearall

closeall

[l, k]=meshgrid (21:0.5:34,0:0.05:pi/3)；Space networks ruling

A=0.18044026*pi；Cone generating angle

B=k*sin (a)；Angle between initial segment and instantaneous gyroaxis on the field of conjugate action

C=1188.28125-sqrt (1188.28125*1188.28125-(l-27.634908) .* (l-27.634908))；Profiling quantity

X＝ ( l.*cos ( b ) .*cos ( k ) .*sin ( a ) +l.*sin ( k ) .*sin ( b ) +c.* ( cos ( k ) .*sin ( b )-cos ( b ) .*sin ( k ) .*sin ( a ) ) ./sqrt ( cos ( b ) .^2.*sin ( a ) .^2+sin ( b ) .^2 ) )-sin ( U1 ) .* ( l.*cos ( b ) .*sin ( k ) .*sin ( a )-l.*cos ( k ) .*sin ( b ) +c.* ( cos ( b ) .*cos ( k ) .*sin ( a ) +sin ( k ) .*sin ( b ) ) ./sqrt ( cos ( b ) .^2.*sin ( a ) .^2+sin ( b ) .^2 ) )；X-coordinate

Y＝ ( l.*cos ( b ) .*sin ( k ) .*sin ( a )-l.*cos ( k ) .*sin ( b ) +c.* ( cos ( b ) .*cos ( k ) .*sin ( a ) +sin ( k ) .*sin ( b ) ) ./sqrt ( cos ( b ) .^2.*sin ( a ) .^2+sin ( b ) .^2 ) ) +sin ( U1 ) .* ( l.*cos ( b ) .*cos ( k ) .*sin ( a ) +l.*sin ( k ) .*sin ( b ) +c.* ( cos ( k ) .*sin ( b )-cos ( b ) .*sin ( k ) .*sin ( a ) ) ./sqrt ( cos ( b ) .^2.*sin ( a ) .^2+sin ( b ) .^2 ) )；Y coordinate

Z=l.*cos (b) .*cos (a)；Z coordinate

Surf (x, y, z)；Build correction of the flank shape curved surface

The cloud data of the MATLAB correction of the flank shape curved surface set up is derived, and use 3D sculpting software Proe on the basis of straight bevel gear surface equation, straight bevel gear axial modification curved surface is built by border mixing, and build teeth groove entity and gear entity further, obtain the correction of the flank shape flank of tooth as shown in Figure 9.

Correction of the flank shape backgear is carried out Finite Element Simulation Analysis, obtain after correction of the flank shape the straight bevel gear facewidth to equivalence distribution of contact figure, as shown in Figure 10, it is seen that declining occurs in correction of the flank shape back-geared equivalence contact stress maximum, and increment and tooth root place stress concentrate situation to improve.

Above in conjunction with accompanying drawing, embodiments of the invention are described; but the invention is not limited in above-mentioned detailed description of the invention; above-mentioned detailed description of the invention is merely schematic; rather than it is restrictive; those of ordinary skill in the art is under the enlightenment of the present invention; without departing under present inventive concept and scope of the claimed protection situation, it may also be made that a lot of form, these belong within the protection of the present invention.

Claims (4)

1. an involute bevel gears tooth end relief and parametric modeling method, it is characterised in that comprise the following steps:

S1, involute bevel gears to non-correction of the flank shape carry out finite element analysis, obtain the circumferentially displaced difference of gear and the flank of tooth equivalence distribution of contact figure of each crucial position of engagement；

S2, based on the circumferentially displaced difference of described gear, it is determined that the profiling quantity of tooth end relief, based on flank of tooth equivalence distribution of contact figure, determine correction of the flank shape length；

S3, with correction of the flank shape length and profiling quantity for variable, set up tooth end relief curve and the equation of the correction of the flank shape flank of tooth；

S4, threedimensional model according to the establishing equation profile modifying gear of tooth end relief curve and the correction of the flank shape flank of tooth.

2. involute bevel gears tooth end relief according to claim 1 and parametric modeling method, it is characterised in that the equation of described tooth end relief curve is as follows:

In formula: r is gear start radius；R_ci(i=1,2) for the arc radius of modification curve；R be outer cone from；B is the facewidth；△ L_i(i=1,2) for correction of the flank shape length.

3. involute bevel gears tooth end relief according to claim 1 and 2 and parametric modeling method, it is characterised in that described correction of the flank shape tooth surface equation is as follows:

Z=rcos (β sin α) cos α

In formula: r is gear start radius；α is cone generating angle；β is the angle on the field of conjugate action between initial segment and instantaneous gyroaxis, and wherein on base cone, involute start angle is 0；R_ci(i=1,2) for the arc radius of modification curve；For being parallel to the unit vector of base cone axis；AndRespectively unit vectorX, y to projection coordinate.

4. involute bevel gears tooth end relief according to claim 1 and parametric modeling method, it is characterised in that the described crucial position of engagement includes four single bi-tooth gearing transfer points.