CN103791870B - Planar double-enveloping worm measuring method - Google Patents

Abstract

A kind of planar double-enveloping worm measuring method, belongs to precision measurement technique and apparatus, technical field of mechanical transmission. The method engages principle based on gear space, establishes the tooth surface equation of worm screw, and this kind of modeling method is consistent with the working method of planar double-enveloping worm. Then according to the definition of worm screw error term, set up the mathematical model of worm screw error term, it is carried out coordinate transform, convert it into the coordinate of worm measuring machine three motion axles, utilize method of value solving, obtain three-dimensional numerical solution. Computer carries out sample path planning according to coordinate figure, coordinate figure is inputted the motion of digital control system control survey machine, data collection system synchronizing gathers three axle raster values and surveys head data, the data gathered are carried out data processing, thus the high precision realizing the helical line error to planar double-enveloping worm, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation is measured.

Description

Planar double-enveloping worm measuring method

Technical field

The present invention relates to a kind of planar double-enveloping worm measuring method, belong to precision measurement technique and apparatus, technical field of mechanical transmission.

Background technology

Enveloping worm is a kind of grinding type worm screw become based on wheel face envelope. Compared with cylindrical worm gearing transmission, enveloping worm drive has an engagement, and the number of teeth is many, the worm gear flank of tooth be doublet contact, supporting capacity by force, transmission efficiency height, long service life and can carrying out meet the advantages such as the grinding of repairing type principle, apply increasingly extensive.

Along with the development of science and technology, the precision of enveloping worm drive system is proposed more and more higher requirement, and its precision measurement is the bottleneck problem of its development of restriction always.

At present, the detect delay of planar double-enveloping worm is mainly launched from two aspects: one is adopt general three-dimensional coordinates measurement machine or gear measuring center to carry out worm screw single error surveying quantifier elimination; Two is research and development Special measuring instruments, comprehensively measures. As, planar double enveloping worm profile of tooth and helical line error are carried out by gear measuring center survey quantifier elimination and have been reported. Certain institute domestic is that Shoudu Iron and Steel Co machine works have developed first planar double-enveloping worm error-detecting instrument in the world, this instrument uses plane to survey head, comprehensive helical line error, comprehensive circular pitch error and the comprehensive error of division can be measured, utilize straight line sword to survey head measurement and can obtain overall graph of errors. In essence, this instrument belongs to comprehensive measurement.

So far, to the research of enveloping worm detection, all really do not solve the actual problems of measurement in the production of such worm screw. The backwardness of detection technique hinders applying of enveloping worm drive.

Summary of the invention

In order to realize the measurement of planar double-enveloping worm, the present invention provides the planar double-enveloping worm measuring method on a kind of special worm measuring machine, it is possible to the helical line error of planar double-enveloping worm, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation are carried out high precision measurement. The method both can be applied on horizontal measuring engine, it is also possible to is applied on vertical measuring engine.

The method applied in the present invention comprises the steps:

S1: the mathematical model setting up worm screw error term

I) flank of tooth mathematical model is set up according to space meshing principle:

Wherein S₁(O₁-x₁,y₁,z₁) and S₂(O₂-x₂,y₂,z₂) it is the moving coordinate system being connected with worm and worm wheel respectively, z₁With z₂Overlap with the revolution axis of worm gear respectively at worm screw,It is worm screw corner,Being worm gear corner, set up the circular cone that an axis overlaps with worm gear axis, and female plane and this circular cone are tangent, u is that in female plane, point is to the distance of female plane and circular cone tangent line, and t is the coordinate figure on the axle that in female plane, this some place is vertical with u, i₁₂Being transmitting ratio, a is worm screw and the width between centers of worm gear axis, r_bBeing main base radius, �� is female plane camber angle, and formula (1) is simplified shown as f (x₁,y₁,z₁)=0, sets up lathe coordinate system S (O-X, Y, Z), and Z is worm axis direction, is machine tool rotary main shaft axis direction, and X is worm screw radial direction, and Y is the direction vertical with X, Z, so f (x₁,y₁,z₁)=0 can represent

f(X,Y,Z)=0(2)

Ii) on flank of tooth mathematical model basis, definition according to helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation, sets up the mathematical model of helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation.

A) helical line error mathematical model

Worm indexing annulus face equation is

${(a-\sqrt{X^2+Y^2})}^2+Z^2={R_2}^2---\left(3\right)$

Wherein R₂Being worm gear reference radius, formula (2) obtains helical line error mathematical model with (3) connection is vertical:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ {(a-\sqrt{X^2+Y^2})}^2+Z^2={R_2}^2\end{array}\right.---\left(4\right)$

B) axial profile of tooth error mathematic model

The profile of tooth measured is the axial profile of tooth of larynx planimetric position on symmetrical plane, it is necessary to determine the axial cross section of symmetrical plane position, the angle that the axial cross section of symmetrical plane position is correspondingFor

Wherein �� is pressure angle, ��=0.45 �� ��/Z₂, Z₂For the worm gear number of teeth. Axial profile of tooth error mathematic model is obtained by formula (2) and (5) connection are vertical:

C) normal direction profile of tooth error mathematic model

The method vector of the larynx plane place left and right flank of tooth is oppositely parallel, at larynx plane place, got true origin and is normal direction profile of tooth with the plane of this method vector normal and the friendship line of the flank of tooth, and plane equation is

AX+BY+CZ=0(7)

Wherein (A, B, C) is method vectorDirection vector. Stand by formula (2) and (7) connection and obtain normal direction profile of tooth error mathematic model:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ \mathrm{AX}+\mathrm{BY}+\mathrm{CZ}=0\end{array}\right.---\left(8\right)$

D) error of division mathematical model

Angle intervals �� '=360 ��/Z between each head of worm screw₁, wherein Z₁For worm screw head number, theoretical �� ' is the error of division with the difference of actual �� '.

E) axial tooth thickness deviation mathematical model

The transverse tooth thickness measured is the axial tooth thickness of larynx planimetric position on symmetrical plane, so transverse tooth thickness measurement point be worm shaft in profile of tooth with the intersection point in worm indexing annulus face, by formula (3) with (6) connection is vertical obtains intersecting point coordinate.

Iii) by ii) in mathematical model carry out coordinate transform, represent with (X, Z, ��), X-axis is along worm screw radial direction, and Z axle is along worm screw axial direction due, and �� axle is the rotation axis around worm screw rotating shaft Z axle, is C axle.

Iv) utilize the method for iteration to obtain the numerical solution of (X, Z, ��) three coordinates, compile array stand-by;

S2: utilize worm measuring machine to determine worm screw larynx planimetric position

I) tested worm screw is arranged on worm measuring machine, then utilizes survey head to determine transverse plane position, draft worm screw larynx plane starting position as benchmark, based on initial larynx planimetric position, worm screw is carried out helical line error measurement;

Ii) move axially 5��10 ��m or-5��-10 ��m, and position after movement is decided to be worm screw larynx planimetric position, again worm screw is carried out helical line error measurement;

Iii) repeating step ii) 10 times so that about the worm screw larynx planimetric position that 10 times are measured is evenly distributed on initial larynx planimetric position, position time minimum using helical line error is as by measurement worm screw larynx planimetric position;

S3: helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation are measured by control worm measuring machine.

1. the method measuring helical line error is as follows:

I) step S1 is input to digital control system according to the array that spiral-line mathematical model is tried to achieve, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), helical line error is carried out sweep measurement, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the scanning coordinate of process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves helical line error, and rendering error curve, finally complete helical line error and measure.

2. the method measuring tooth error is as follows:

I) array that step S1 tries to achieve according to axial profile of tooth or normal tooth shape mathematical model is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), tooth error is carried out sweep measurement, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the scanning coordinate of process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves tooth error, and rendering error curve, finally complete tooth error and measure.

3. the method measuring worm indexing error is as follows:

I) flank of tooth mathematical model set up according to step S1, solve the point coordinate of each head of worm screw on larynx plane punishment degree annulus, these points are carried out coordinate transform, with (X, Z, ��) represent, and solve (X, Z, ��) the numerical solution of coordinate, it is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), the error of division is measured, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the coordinate of measuring process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves the error of division, and rendering error curve, finally complete the error of division and measure.

4. worm shaft is measured as follows to the method for tooth pitch error:

I) the transverse tooth thickness measurement point coordinate figure obtained in step S1 is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), axial tooth thickness deviation is measured, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the coordinate of measuring process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves axial tooth thickness deviation, and rendering error curve, finally complete axial tooth thickness deviation and measure.

S4: measuring error correction

In measuring process, the method vector at each point place projection �� Y along the Y direction is change, and worm measuring machine survey head does not move along the Y direction in measuring process, and the change that survey head radius projects in the Y direction causes Z-direction to introduce measuring error �� Z. Formula (2) is utilized to obtain the method vector of each point on the flank of tooth

Thus derive each point lead angle ��,

$\mathrm{\γ}=\arccos =\frac{\sqrt{A^{\′2}+B^{\′2}}}{\sqrt{A^{\′2}+B^{\′2}+C^{\′2}}}---\left(10\right)$

Wherein

(A ', B ', C ') for spiral-line is at (x₁,y₁,z₁) the direction vector of tangent line put, calculate the magnitude of error �� Z=�� Ytan �� that Z-direction is introduced, it is achieved to the correction of measuring error surveyed head radius and project change in the Y direction and cause.

The planar double-enveloping worm measuring method of the present invention has following advantage:

1, production scene can be realized to be detected by planar double-enveloping worm;

2, there is efficient measuring speed;

3, use scanning feeler, obtain mass data, it is to increase measuring accuracy;

4, larynx planimetric position is accurately obtained.

Accompanying drawing explanation

Fig. 1 tooth surface equation system of coordinates

The female plane of Fig. 2

Fig. 3 worm spiral line schematic diagram

Fig. 4 worm indexing annulus face sketch

The symmetrical axial cross section of Fig. 5

Fig. 6 error of division measures schematic diagram

Fig. 7 axial tooth thickness deviation measures schematic diagram

Fig. 8 worm measuring machine structure diagram

Fig. 9 measurement procedure figure

Embodiment

Below in conjunction with accompanying drawing, planar double-enveloping worm measuring method is illustrated further. Such as Fig. 8, the method both can be applied on horizontal measuring engine, it is also possible to is applied on vertical measuring engine, is described for horizontal measuring engine here.

Horizontal measuring engine comprises lathe bed, main axle unit and measuring unit, and main axle unit and survey seat cellular installation are on lathe bed. Main axle unit comprises main shaft and tailstock, and �� axle Circular gratings is connected with main shaft, and Z axle grating is arranged on lathe bed to measure the movement surveying seat unit along Z-direction; Surveying seat unit comprise base, Y-direction planker, X-direction planker and survey head, Y-axis grating is arranged on base to measure Y-direction planker move, and X-axis grating is arranged on Y-direction planker to measure X-direction planker move, and surveys head and is arranged on X-direction planker. In measuring process, computer can control the motion of three axles by the motor that control card controls to be connected with X-axis with main shaft, Z axle, and Y-axis is then by its motion of ball screw mandrel Non-follow control. X-axis grating in data collecting system, Y-axis grating, Z axle grating, �� axle Circular gratings and survey head and be input in control card by acquisition data, be uploaded to computer by control card, carry out data processing. Tested worm screw be arranged on main shaft and tailstock top between. Tested worm screw parameter: a=140mm, i₁₂=33, Z₁=1, Z₂=33, ��=10 ��, r_b=45mm, R₂=112.5mm, ��=23.578178 ��.

S1: the mathematical model setting up worm spiral line error

I) flank of tooth mathematical model is set up according to space meshing principle:

As shown in Figure 1, wherein S₁(O₁-x₁,y₁,z₁) and S₂(O₂-x₂,y₂,z₂) it is the moving coordinate system being connected with worm and worm wheel respectively, z₁With z₂Overlap with the revolution axis of worm gear respectively at worm screw,It is worm screw corner,It it is worm gear corner, set up the circular cone that an axis overlaps with worm gear axis, and female plane and this circular cone are tangent, u is the distance that in female plane, point arrives female plane and circular cone tangent line, t is the coordinate figure on the axle that in female plane, this some place is vertical with u, as shown in Figure 2, formula (1) is simplified shown as f (x₁,y₁,z₁)=0, sets up lathe coordinate system S (O-X, Y, Z), and Z is worm axis direction, is machine tool rotary main shaft axis direction, and X is worm screw radial direction, and Y is the direction vertical with X, Z, so f (x₁,y₁,z₁)=0 can represent

f(X,Y,Z)=0(12)

Ii) on flank of tooth mathematical model basis, definition according to helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation, sets up the mathematical model of helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation.

A) helical line error mathematical model

Such as Fig. 3 and Fig. 4, worm indexing annulus face equation is

${(140-\sqrt{X^2+Y^2})}^2+Z^2={112.5}^2---\left(13\right)$

Wherein R₂Being worm gear reference radius, formula (12) obtains helical line error mathematical model with (13) connection is vertical:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ {(140-\sqrt{X^2+Y^2})}^2+Z^2={112.5}^2\end{array}\right.---\left(14\right)$

B) axial profile of tooth error mathematic model

As shown in Figure 5, the profile of tooth measured is the axial profile of tooth of larynx planimetric position on symmetrical plane, therefore will determine the axial cross section of symmetrical plane position, and the angle that the axial cross section of symmetrical plane position is corresponding isAxial profile of tooth error mathematic model is obtained by formula (12):

C) normal direction profile of tooth error mathematic model

The method vector of the larynx plane place left and right flank of tooth is oppositely parallel, at larynx plane place, got true origin and is normal direction profile of tooth with the plane of this method vector normal and the friendship line of the flank of tooth, and plane equation is

67.839X+-77.450Y+12.725Z=0 the direction vector that (16) wherein (A, B, C) is method vector. Stand by formula (2) and (7) connection and obtain normal direction profile of tooth error mathematic model:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ 67.839X+-77.450Y+12.725Z=0\end{array}\right.---\left(17\right)$

D) error of division mathematical model

Angle intervals �� '=360 �� between each head of worm screw, wherein Z₁For worm screw head number, theoretical �� ' is the error of division with the difference of actual �� '.

E) axial tooth thickness deviation mathematical model

The transverse tooth thickness measured is the axial tooth thickness of larynx planimetric position on symmetrical plane, so transverse tooth thickness measurement point be worm shaft in profile of tooth with the intersection point in worm indexing annulus face, by formula (13) with (15) connection is vertical obtains intersecting point coordinate.

Iii) set up X, the contacting of Y and ��: sin ��=X/Y, by ii) in mathematical model carry out coordinate transform, with (X, Z, ��) represent, �� be along worm shaft to rotation, be C axle, Z along worm shaft to movement, X is along the movement of worm screw radial direction.

Iv) utilize the method for iteration to obtain the numerical solution of (X, Z, ��) three coordinates, compile array stand-by;

$\left(\begin{array}{ccc}{X}_1& Z_1& {\mathrm{\θ}}_1\\ .& .& .\\ .& .& .\\ .& .& .\\ X_n& Z_n& {\mathrm{\θ}}_n\end{array}\right)$

S2: utilize worm measuring machine to determine worm screw larynx planimetric position

I) being arranged on worm measuring machine by tested worm screw, then utilize survey head to determine transverse plane position, worm screw is processed by benchmark of this end face, according to endface position, drafts worm screw larynx plane starting position Z_h0, based on initial larynx planimetric position, worm screw is carried out helical line error measurement, obtains helical line error f_{h1_0};

Ii), after having measured for the first time, initial larynx planimetric position is moved axially 5��10 ��m or-5��-10 ��m, and this position is decided to be worm screw larynx planimetric position Z_h1, again worm screw is carried out helical line error and measures f_{h1_1};

Iii) repeating step ii) 10 times so that about the worm screw larynx planimetric position that 10 times are measured is evenly distributed on initial larynx planimetric position, with helical line error minimum value min{f_{h1_0},f_{h1_1},��,f_{h1_11}Time position as by measurement worm screw larynx planimetric position Z_hi;

S3: helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation are measured by control worm measuring machine.

1. the method measuring helical line error is as follows:

I) step S1 is input to digital control system according to the array that spiral-line mathematical model is tried to achieve, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), helical line error is carried out sweep measurement, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the scanning coordinate of process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves helical line error, and rendering error curve, finally complete helical line error and measure.

2. the method measuring tooth error is as follows:

I) array that step S1 tries to achieve according to axial profile of tooth or normal tooth shape mathematical model is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), tooth error is carried out sweep measurement, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the scanning coordinate of process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves tooth error, and rendering error curve, finally complete tooth error and measure.

3. the method for worm indexing error is measured, such as Fig. 6:

I) flank of tooth mathematical model set up according to step S1, solve the point coordinate of each head of worm screw on larynx plane punishment degree annulus, these points are carried out coordinate transform, with (X, Z, ��) represent, and solve (X, Z, ��) the numerical solution of coordinate, it is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), the error of division is measured, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the coordinate of measuring process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves the error of division, and rendering error curve, finally complete the error of division and measure.

4. the method for worm shaft to tooth pitch error is measured, such as Fig. 7:

I) the transverse tooth thickness measurement point coordinate figure obtained in step S1 is input to digital control system, carries out surveying head radius and compensate, then control survey machine motion;

Ii) based on i), axial tooth thickness deviation is measured, synchronous acquisition (X, Z, ��) three axle grating reading and survey head data;

Iii) according to the coordinate of measuring process each point and method vector direction and size, the take off data that data collecting system obtains is carried out error correction, then solves axial tooth thickness deviation, and rendering error curve, finally complete axial tooth thickness deviation and measure.

S4: measuring error correction

In measuring process, the method vector at each point place projection �� Y along the Y direction is change, and worm measuring machine survey head does not move along the Y direction in measuring process, and the change of Y-direction projection causes Z-direction to introduce measuring error �� Z. The lead angle �� at each point place is utilized to calculate the magnitude of error of Z-direction introducing, �� Z=�� Y �� tan7.086 ��, it is achieved to project, to surveying head radius, the correction changing the measuring error caused in the Y direction.

Detailed measurement procedure is as shown in Figure 9.

Claims (6)

1. planar double-enveloping worm measuring method, it is characterized in that: according to space meshing principle, set up worm tooth-surface mathematical model, with helical line error, axial tooth error, normal direction tooth error, the error of division and axial tooth thickness deviation are defined as constraint, draw the mathematical model of above-mentioned each error term, the mathematical model of error term is carried out coordinate transform, with (X, Z, ��) represent, X-axis is along worm screw radial direction, Z axle is along worm screw axial direction due, �� axle is the rotation axis around worm screw rotating shaft Z axle, it is C axle, obtain (X, Z, ��) the numerical solution of three coordinates, compile array and it is input to digital control system, control survey machine is along X-axis, Z axle moves and rotates around Z axle, error is carried out sweep measurement, synchronous acquisition (X, Z, ��) three axle grating readings and survey head data, error correction is carried out by take off data data collecting system obtained, obtain error term, and rendering error curve, complete error to measure,

The survey head that described measuring method uses is scanning probe, each point coordinate figure on scanning pattern and theoretical value is contrasted, draws error term;

Described measuring method is applied on horizontal measuring engine or vertical measuring engine;

The foundation of described flank of tooth mathematical model, set up flank of tooth mathematical model according to space meshing principle:

Wherein S₁(O₁-x₁,y₁,z₁) and S₂(O₂-x₂,y₂,z₂) it is the moving coordinate system being connected with worm and worm wheel respectively, z₁With z₂Overlap with the revolution axis of worm gear respectively at worm screw,It is worm screw corner,Being worm gear corner, set up the circular cone that an axis overlaps with worm gear axis, and female plane and this circular cone are tangent, u is that in female plane, point is to the distance of female plane and circular cone tangent line, and t is the coordinate figure on the axle that in female plane, this some place is vertical with u, i₁₂Being transmitting ratio, a is worm screw and the width between centers of worm gear axis, r_bBeing main base radius, �� is female plane camber angle, and formula (1) is simplified shown as f (x₁,y₁,z₁)=0, sets up lathe coordinate system S (O-X, Y, Z), and Z is worm axis direction, is machine tool rotary main shaft axis direction, and X is worm screw radial direction, and Y is the direction vertical with X, Z, so f (x₁,y₁,z₁)=0 represents

F (X, Y, Z)=0 (2).

2. planar double-enveloping worm measuring method according to claim 1, is characterized in that: in planar double-enveloping worm flank of tooth mathematical model, the foundation of helical line error mathematical model, and worm indexing annulus face equation is

${(a-\sqrt{X^2+Y^2})}^2+Z^2={R_2}^2---\left(3\right)$

Wherein R₂Being worm gear reference radius, formula (2) obtains helical line error mathematical model with (3) connection is vertical:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ {(a-\sqrt{X^2+Y^2})}^2+Z^2={R_2}^2\end{array}\right.---\left(4\right).$

3. planar double-enveloping worm measuring method according to claim 1, it is characterized in that: the foundation of axial profile of tooth error mathematic model, the profile of tooth measured is the axial profile of tooth of larynx planimetric position on symmetrical plane, the axial cross section of symmetrical plane position need to be determined, the angle that the axial cross section of symmetrical plane position is correspondingFor

Wherein �� is pressure angle, ��=0.45 �� ��/Z₂, Z₂For the worm gear number of teeth, obtain axial profile of tooth error mathematic model by formula (2) and (5) connection are vertical:

4. planar double-enveloping worm measuring method according to claim 1, it is characterized in that: in planar double-enveloping worm flank of tooth mathematical model, the foundation of normal direction profile of tooth error mathematic model, the method vector of the larynx plane place left and right flank of tooth is oppositely parallel, at larynx plane place, getting true origin and be normal direction profile of tooth with the plane of this method vector normal and the friendship line of the flank of tooth, this plane equation is

AX+BY+CZ=0 (7)

Wherein (A, B, C) is method vectorDirection vector, by formula (2) and (7) connection stand obtain normal direction profile of tooth error mathematic model:

$\left\{\begin{array}{c}f(X,Y,Z)=0\\ AX+BY+CZ=0\end{array}\right.---\left(8\right).$ ��

5. planar double-enveloping worm measuring method according to claim 1, is characterized in that: utilize worm measuring machine to determine worm screw larynx planimetric position:

I) tested worm screw is arranged on worm measuring machine, then utilizes survey head to determine transverse plane position, draft worm screw larynx plane starting position by benchmark of this transverse plane position, based on initial larynx planimetric position, worm screw is carried out helical line error measurement;

Ii) move axially 5��10 ��m or-5��-10 ��m, and position after movement is decided to be worm screw larynx planimetric position, again worm screw is carried out helical line error measurement;

Iii) repeating step ii) 10 times so that about the worm screw larynx planimetric position that 10 times are measured is evenly distributed on initial larynx planimetric position, position time minimum using helical line error is as by measurement worm screw larynx planimetric position.

6. planar double-enveloping worm measuring method according to claim 1, it is characterized in that: described error correcting method is, in measuring process, the method vector at each point place projection �� Y along the Y direction is change, and worm measuring machine survey head does not move along the Y direction in measuring process, the change that survey head radius projects in the Y direction causes Z-direction to introduce measuring error �� Z, utilizes formula (2) to obtain the method vector of each point on the flank of tooth

Thus derive each point lead angle ��,

$\mathrm{\γ}=\arccos \frac{\sqrt{A^{\′2}+B^{\′2}}}{\sqrt{A^{\′2}+B^{\′2}+C^{\′2}}}---\left(10\right)$

Wherein

(A ', B ', C ') for spiral-line is at (x₁,y₁,z₁) the direction vector of tangent line put, calculate the magnitude of error �� Z=�� Ytan �� that Z-direction is introduced, it is achieved to the correction of measuring error surveyed head radius and project change in the Y direction and cause.