CN104330065A - Spiral bevel gear tooth surface curvature interference detection method - Google Patents

Abstract

The invention discloses a spiral bevel gear tooth surface curvature interference detection method. Only by providing coordinate values of a plurality of discrete points of two tooth surfaces, tooth surface interference position can be accurately judged and actually-measured engagement position can be prejudged, and efficient and convenient and fast tooth surface curvature interference detection is provided for a gear pair, so that the technical problem that the gear pair can only carry out pairing rolling inspection on a rolling inspection machine to detect the tooth surface curvature interference is solved; not only the position of tooth surface interference can be accurately judged, but also the actually-measured engagement position can be prejudged. The detection method helps to expand the detection function of a gear measurement center without carrying out rolling inspection on the gear rolling inspection machine; whether the two tooth surfaces have tooth surface curvature interference can be judged directly according to the position vector and normal vector of the tooth surface points measured by the gear measurement center; and if interference occurs, the position of the interference can be judged.

Description

A kind of spiral bevel gear flank of tooth curvature interference method of inspection

Technical field

The invention belongs to gears meshing analysis and testing technology field, be specifically related to a kind of spiral bevel gear flank of tooth curvature interference method of inspection.

Background technology

The necessary condition realizing correct engagement without curvature interference at contact point place during two flank engagement.When Gear Processing because the factors such as machine tool error, alignment error, heat treatment deformation cause larger tooth surface error, during two mating gears engagements, there is flank of tooth curvature interference and cannot correct engagement.

The inspection of flank of tooth curvature interference only calculates in tooth surface design phase analysis at present, and judged with relative Geodesic torsion by the Relative normal curvature calculating two tooth face meshing point, the method is the determination methods based on local topology.As Shen Yunbo, in the paper " method of face gear drive engagement process Relative normal curvature interference detection " of the people such as Fang Zongde, propose the method for the Relative normal curvature extremal curvature interference inspection of a kind of the whole engagement process of gear drive, namely the method is a kind of determination methods based on local topology, finished gear pair needs inspection machine carries out pairing to roll inspection rolling, by particular location and the degree of rolling tested stamp trace and rule of thumb judge flank of tooth curvature interference.

In addition, carry out at gear measuring center the important means that the detection of flank of tooth three-dimensional has become flank of tooth detection, but this flank of tooth detects just for measurement and the analysis of the tooth accuracy of single gear, cannot analyze two flank engagement performances.

Summary of the invention

The object of this invention is to provide a kind of spiral bevel gear flank of tooth curvature interference method of inspection, only need the coordinate figure of some discrete points that two flank of tooth are provided, the position of flank interference can be judged accurately and the position of engagement can be surveyed to it and carry out anticipation.

In order to realize above object, the technical solution adopted in the present invention is: a kind of spiral bevel gear flank of tooth curvature interference method of inspection, comprises the steps:

(1) theoretical tooth surface equation and the steamboat benchmark flank of tooth of spiral bevel gear bull wheel is set up;

(2) three-dimensional detection is carried out to the large and small actual measurement processing flank of tooth of taking turns, obtain large and small position vector and method arrow of taking turns actual measurement processing flank of tooth check point;

(3) based on mesh equation, to vow according to the position vector of bull wheel actual measurement processing flank of tooth check point, method and large steamboat ratio of gear is set up and surveyed with bull wheel the steamboat subsidiary face processing flank of tooth total conjugated;

(4) digital tooth that steamboat subsidiary face is set up in the matching of bicubic nurbs surface is carried out to the discrete point on steamboat subsidiary face;

(5) net point calculated respectively by position equation in the digital tooth in the steamboat benchmark flank of tooth and steamboat subsidiary face is vowed according to the position vector of steamboat actual measurement processing flank of tooth check point and method;

(6) flank of tooth topological variation value of the steamboat actual measurement processing flank of tooth, steamboat subsidiary face and steamboat reference field is calculated respectively with thus calculate steamboat subsidiary face and the flank of tooth topological variation value δ processing the flank of tooth surveyed by steamboat ^ij, according to δ ^ijjudge whether the large and small flank of tooth of taking turns of surveying processing flank of tooth curvature interference occurs.

The steamboat benchmark flank of tooth in described step (1) is that theoretical tooth surface equation, mesh equation and the large steamboat ratio of gear relation according to bull wheel is set up, this steamboat benchmark flank of tooth and the theoretical flank of tooth total conjugated of bull wheel.

The flank of tooth topological variation value of the steamboat actual measurement processing flank of tooth and steamboat reference field computation process as follows:

${\mathrm{\δ}}_1^{\mathrm{ij}}=\sqrt{{(x_1^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_1^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_1^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_1$

Wherein, γ ₁it is steamboat actual measurement processing flank of tooth check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

The computing formula of the flank of tooth topological variation value of steamboat subsidiary face and steamboat reference field is as follows:

${\mathrm{\δ}}_3^{\mathrm{ij}}=\sqrt{{(x_3^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_3^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_3^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_3$

Wherein, γ ₃for steamboat subsidiary face check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

The flank of tooth topological variation value δ of the flank of tooth surveyed by steamboat subsidiary face and steamboat ^ijcomputing formula:

${\mathrm{\δ}}^{\mathrm{ij}}={\mathrm{\δ}}_1^{\mathrm{ij}}-{\mathrm{\δ}}_3^{\mathrm{ij}}.$

According to δ ^ijwhat judge to survey processing large and smallly takes turns the flank of tooth that whether the principle of flank of tooth curvature interference occurs is as follows: if δ ^ijbe less than 0, illustrate this steamboat actual measurement the flank of tooth and steamboat subsidiary face have gap, this point is without curvature interference; If δ ^ijbe greater than 0, illustrate that in this point two flank of tooth gap be negative, then this some generation curvature interference, can not correct engagement; δ ^ijlarger, interfere more serious, the actual measurement position of engagement appears in the maximum position of interference degrees.

The spiral bevel gear flank of tooth curvature interference method of inspection of the present invention only needs the coordinate figure of the some discrete points providing two flank of tooth, the position of flank interference can be judged accurately and the position of engagement can be surveyed to it and carry out anticipation, for gear pair provide efficiently, the flank of tooth curvature interference method of inspection easily, solve gear pair and can only roll technical barrier inspection machine carrying out matching and rolls inspection inspection flank of tooth curvature interference, not only can judge the position of flank interference accurately but also the position of engagement can be surveyed to it and carry out anticipation.This method of inspection has expanded the measuring ability of gear measuring center, inspection is rolled without the need to rolling at gear on inspection machine, the position vector of the flank of tooth point that can directly detect according to gear measuring center and method are vowed and are judged whether two flank of tooth flank of tooth curvature interference occurs, if interfered, can judge the position of interfering.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the spiral bevel gear flank of tooth curvature interference method of inspection of the present invention;

Fig. 2 is the perspective view of net point in rotating and projection plane;

Fig. 3 is without curvature interference surface deviation topological diagram;

Fig. 4 curvature interference surface deviation topological diagram.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, the present invention is described further.

Be illustrated in figure 1 the process flow diagram of the spiral bevel gear flank of tooth curvature interference method of inspection of the present invention, as seen from the figure, this method of inspection comprises the steps:

(1) theoretical tooth surface equation and the steamboat benchmark flank of tooth of spiral bevel gear bull wheel is set up: set up the theoretical tooth surface equation of bull wheel according to the basic parameter of spiral bevel gear and machined parameters, wheel blank parameter and machined parameters, as shown in table one and table two, are set up by coordinate transform and mesh equation and are set up bull wheel tooth surface equation respectively:

r ₂＝r ₂(θ _g,φ _g)

In formula, θ _g, φ _git is bull wheel tooth surface parameters.

Steamboat benchmark flank of tooth Σ ₀be defined as the steamboat flank of tooth with bull wheel flank of tooth total conjugated---be linear contact lay during bull wheel flank engagement, and ratio of gear is gear ratio, and known bull wheel tooth surface equation is r ₂(θ _g, φ _g), according to mesh equation

And bull wheel engagement corner with steamboat engagement corner relation:

Steamboat reference field Σ can be obtained ₀tooth surface equation r ₀(θ _g, φ _g).

Table 1 wheel blank parameter

Table 2 machined parameters

Parameter	Bull wheel machined parameters	Steamboat machined parameters
			Cutter diameter D C2/mm	228.6	152.4
Point width p w2/mm	2.5511	2.5511
			Cutter number	12	7.5
Radial S r/mm	97.82527	80.099557
			Angle cutter spacing q/mm	73.157580	51.194019
Roll and compare m p	1.268996	1.624315
			Workhead offset E m/mm	-0.1	0.1
Axial position of wheel X G/mm	-0.8	-0.8
			Berth X B/mm	0.378493	-0.554708
Wheel blank established angle r/ (°)	48.2833	35.8675

(2) respectively three-dimensional detection is carried out to the large and small actual measurement processing flank of tooth of taking turns at gear measuring center, obtain large and small position vector and method arrow (position vector and the method that obtain flank of tooth discrete point are vowed) of taking turns actual measurement processing flank of tooth check point: bull wheel actual measurement processing flank of tooth check point position vector and method are vowed and are expressed as steamboat actual measurement processing flank of tooth check point position vector and method are vowed and are expressed as subscript ij represents the numbering of check point, as shown in Figure 2.

(3) structure steamboat subsidiary face: based on mesh equation, surveys position vector, the method arrow of processing flank of tooth check point according to bull wheel and the steamboat subsidiary face processing flank of tooth total conjugated surveyed by the foundation of steamboat ratio of gear and bull wheel greatly.

Bull wheel is surveyed flank of tooth check point be transformed in steamboat coordinate system through coordinate transform, corresponding position vector and method are vowed and are solve mesh equation

Bull wheel actual measurement flank of tooth check point can be obtained be transformed into engagement corner during steamboat coordinate system thus obtain the corresponding check point detected with bull wheel on the steamboat subsidiary face of flank of tooth total conjugated the position vector of this point can be expressed as r' _ij.

(4) the digital tooth Σ that steamboat subsidiary face is set up in the matching of bicubic nurbs surface is carried out to the discrete point on steamboat subsidiary face ₃.

The digital tooth Σ in steamboat subsidiary face ₃equation is: r ₃=r ₃(u, v).

(5) according to the check point on the steamboat actual measurement flank of tooth position vector and method vow and find corresponding point on steamboat reference field the net point calculated respectively by position equation in the digital tooth in the steamboat benchmark flank of tooth and steamboat subsidiary face is vowed according to the position vector of steamboat actual measurement processing flank of tooth check point and method:

1. coordinate figure (the L of check point on steamboat rotating and projection face on the steamboat actual measurement flank of tooth is calculated _ij, R _ij), as shown in Figure 2,

$L_{\mathrm{ij}}=x_1^{\mathrm{ij}}$

$R_{\mathrm{ij}}=\sqrt{{\left(y_1^{\mathrm{ij}}\right)}^2+{\left(z_1^{\mathrm{ij}}\right)}^2}$

2. according to the check point on the steamboat actual measurement flank of tooth coordinate (L on rotating and projection face _ij, R _ij) set up corresponding point on steamboat reference field position equation

$x_0({\mathrm{\θ}}_g^{\mathrm{ij}},{\mathrm{\φ}}_g^{\mathrm{ij}})=L_{\mathrm{ij}}$

$\sqrt{y_0{({\mathrm{\θ}}_g^{\mathrm{ij}},{\mathrm{\φ}}_g^{\mathrm{ij}})}^2{+z}_0{({\mathrm{\θ}}_g^{\mathrm{ij}},{\mathrm{\φ}}_g^{\mathrm{ij}})}^2}=R_{\mathrm{ij}}$

Solving equation group, can obtain on steamboat reference field with check point corresponding point position vector and method is vowed

3. in like manner, according to the check point on the steamboat flank of tooth position vector and method vow, calculate steamboat digitizing subsidiary face Σ by position equation ₃on corresponding point position vector can be expressed as method is vowed

(6) flank of tooth topological variation value of the steamboat actual measurement processing flank of tooth, steamboat subsidiary face and steamboat reference field is calculated respectively with thus calculate steamboat subsidiary face and the flank of tooth topological variation value δ processing the flank of tooth surveyed by steamboat ^ij, according to δ ^ijjudge whether the large and small flank of tooth of taking turns of surveying processing flank of tooth curvature interference occurs.

1. steamboat actual measurement flank of tooth Σ is calculated ₁with steamboat reference field Σ ₀flank of tooth topological variation value, the surface deviation of each measuring point is:

${\mathrm{\δ}}_1^{\mathrm{ij}}=\sqrt{{(x_1^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_1^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_1^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_1$

γ ₁for steamboat actual measurement flank of tooth check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

2. steamboat subsidiary face Σ is calculated ₃with steamboat reference field Σ ₀flank of tooth topological variation, according to surface deviation definition, determine that the surface deviation of measuring point is:

${\mathrm{\δ}}_3^{\mathrm{ij}}=\sqrt{{(x_3^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_3^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_3^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_3$

γ ₃for steamboat subsidiary face check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

The measuring point obtained on all steamboat subsidiary faces can obtain the flank of tooth topological variation of steamboat subsidiary face and steamboat reference field to the steamboat reference field upper deviation.

3. the flank of tooth topological variation value in the COMPREHENSIVE CALCULATING steamboat actual measurement flank of tooth and steamboat subsidiary face:

${\mathrm{\δ}}^{\mathrm{ij}}={\mathrm{\δ}}_1^{\mathrm{ij}}-{\mathrm{\δ}}_3^{\mathrm{ij}}.$

According to the topological variation δ of the flank of tooth ^ijjudge whether the size wheel flank of tooth of surveying processing flank of tooth curvature interference occurs: if δ ^ijbe less than 0, illustrate this steamboat actual measurement the flank of tooth and steamboat subsidiary face have gap, this point without curvature interference, as shown in Figure 3; If δ ^ijbe greater than 0, illustrate that in this point two flank of tooth gap be negative, then this some generation curvature interference, can not correct engagement, as shown in Figure 4; δ ^ijlarger, interfere more serious, the actual measurement position of engagement appears in the maximum position of interference degrees.

Above embodiment only understands core concept of the present invention for helping; the present invention can not be limited with this; for those skilled in the art; every according to thought of the present invention; the present invention is modified or equivalent replacement; any change done in specific embodiments and applications, all should be included within protection scope of the present invention.

Claims (6)

1. a spiral bevel gear flank of tooth curvature interference method of inspection, is characterized in that, comprise the steps:

(1) theoretical tooth surface equation and the steamboat benchmark flank of tooth of spiral bevel gear bull wheel is set up;

(2) three-dimensional detection is carried out to the large and small actual measurement processing flank of tooth of taking turns, obtain large and small position vector and method arrow of taking turns actual measurement processing flank of tooth check point;

(3) based on mesh equation, to vow according to the position vector of bull wheel actual measurement processing flank of tooth check point, method and large steamboat ratio of gear is set up and surveyed with bull wheel the steamboat subsidiary face processing flank of tooth total conjugated;

(4) digital tooth that steamboat subsidiary face is set up in the matching of bicubic nurbs surface is carried out to the discrete point on steamboat subsidiary face;

(5) net point calculated respectively by position equation in the digital tooth in the steamboat benchmark flank of tooth and steamboat subsidiary face is vowed according to the position vector of steamboat actual measurement processing flank of tooth check point and method;

(6) flank of tooth topological variation value of the steamboat actual measurement processing flank of tooth, steamboat subsidiary face and steamboat reference field is calculated respectively with thus calculate steamboat subsidiary face and the flank of tooth topological variation value δ processing the flank of tooth surveyed by steamboat ^ij, according to δ ^ijjudge whether the large and small flank of tooth of taking turns of surveying processing flank of tooth curvature interference occurs.

2. the spiral bevel gear flank of tooth curvature interference method of inspection according to claim 1, it is characterized in that: the steamboat benchmark flank of tooth in described step (1) is that theoretical tooth surface equation, mesh equation and the large steamboat ratio of gear relation according to bull wheel is set up, this steamboat benchmark flank of tooth and the theoretical flank of tooth total conjugated of bull wheel.

3. the spiral bevel gear flank of tooth curvature interference method of inspection according to claim 1, is characterized in that: the flank of tooth topological variation value of the steamboat actual measurement processing flank of tooth and steamboat reference field computation process as follows:

${\mathrm{\δ}}_1^{\mathrm{ij}}=\sqrt{{(x_1^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_1^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_1^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_1$

Wherein, γ ₁it is steamboat actual measurement processing flank of tooth check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

4. the spiral bevel gear flank of tooth curvature interference method of inspection according to claim 1, is characterized in that: the computing formula of the flank of tooth topological variation value of steamboat subsidiary face and steamboat reference field is as follows:

${\mathrm{\δ}}_3^{\mathrm{ij}}=\sqrt{{(x_3^{\mathrm{ij}}-x_0^{\mathrm{ij}})}^2+{(y_3^{\mathrm{ij}}-y_0^{\mathrm{ij}})}^2+{(z_3^{\mathrm{ij}}-z_0^{\mathrm{ij}})}^2}\cos {\mathrm{\γ}}_3$

Wherein, γ ₃for steamboat subsidiary face check point measuring point to steamboat reference field line and steamboat reference field on the angle of measuring point normal.

5. the spiral bevel gear flank of tooth curvature interference method of inspection according to claim 1, is characterized in that, the flank of tooth topological variation value δ of the flank of tooth surveyed by steamboat subsidiary face and steamboat ^ijcomputing formula:

${\mathrm{\δ}}^{\mathrm{ij}}={\mathrm{\δ}}_1^{\mathrm{ij}}-{\mathrm{\δ}}_3^{\mathrm{ij}}.$

6. the spiral bevel gear flank of tooth curvature interference method of inspection according to claim 1, is characterized in that, according to δ ^ijwhat judge to survey processing large and smallly takes turns the flank of tooth that whether the principle of flank of tooth curvature interference occurs is as follows: if δ ^ijbe less than 0, illustrate this steamboat actual measurement the flank of tooth and steamboat subsidiary face have gap, this point is without curvature interference; If δ ^ijbe greater than 0, illustrate that in this point two flank of tooth gap be negative, then this some generation curvature interference, can not correct engagement; δ ^ijlarger, interfere more serious, the actual measurement position of engagement appears in the maximum position of interference degrees.