CN113704899B - Gear pair transmission error calculation method based on gear point cloud data - Google Patents

Gear pair transmission error calculation method based on gear point cloud data Download PDF

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CN113704899B
CN113704899B CN202110811848.2A CN202110811848A CN113704899B CN 113704899 B CN113704899 B CN 113704899B CN 202110811848 A CN202110811848 A CN 202110811848A CN 113704899 B CN113704899 B CN 113704899B
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tooth surface
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driven wheel
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CN113704899A (en
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于渤
寇寒林
石照耀
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Beijing University of Technology
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Abstract

The invention discloses a gear pair transmission error calculation method based on gear point cloud data, and belongs to the technical field of precise measurement. The method utilizes the point cloud data on the surface of the gear to simulate the gear meshing process on a computer to obtain the position information when the gear is meshed, thereby calculating the transmission error curve of the gear pair. Firstly, establishing a gear coordinate system; secondly, determining the initial position of the tooth profile; then, determining the meshing position of the gears; finally, solving the transmission error of the gear pair. The method combines non-contact measurement with calculation of gear transmission and tooth surface contact analysis, obtains the transmission error of the gear pair through a computer, can analyze the influence of a single tooth surface on the integral transmission error of the gear pair, and provides a new way for selecting gears, controlling the transmission quality of the gears and reducing gear vibration and noise.

Description

Gear pair transmission error calculation method based on gear point cloud data
Technical Field
The invention relates to a gear pair transmission error calculation method based on gear point cloud data, and belongs to the technical field of precise measurement.
Background
With the development of contemporary industry, higher demands are placed on the vibration and noise levels of gears. Transmission errors are one of the primary excitations of gear vibration and noise. The traditional mode of obtaining the transmission error of the gear pair can only be measured through experiments and can only be applied to medium-modulus gear measurement. For the extremely small module gear and the extremely large module gear, the transmission errors of the gear pair are difficult to measure through experiments due to reasons such as volume, installation errors, rigidity, inertia and the like. Meanwhile, when the transmission error is measured, since the gear overlap ratio is larger than 1, two adjacent pairs (or more than two pairs) of gear teeth are measured simultaneously, so that each error point on the unclean transmission error curve represents the error of which part on which pair of tooth surfaces.
The gear measurement technology mainly measures the tooth pitch deviation, tooth profile deviation, spiral line deviation and the like of gears from die comparison measurement to mechanical generation measurement to electronic generation measurement. Measuring gears using optical means is now becoming a reality from theory. Compared with the traditional method, the method for measuring the gear by using the optical method can quickly obtain the shape information of the gear surface with high precision and high density.
The gear surface point cloud data is used for simulating the gear meshing process on a computer to obtain a gear pair transmission error, so that not only can the result of the interaction of errors of a main gear and a driven gear in the meshing process be reflected, but also the complete process of each meshing tooth pair on the main gear and the driven gear is reflected, and particularly, how the errors of two pairs of gear teeth which participate in meshing together in a double meshing area are mutually influenced and interacted is disclosed; and the calculated error values on the transmission error curve of the gear pair correspond to the contact points on the main wheel and the slave wheel one by one relative to experimental measurement, so that the error values can be clearly determined to represent the errors of the part on the tooth surface. The non-contact measurement is combined with the calculation of gear transmission and the tooth surface contact analysis, so that the method is a trend of future gear detection and gear evaluation, provides a new way for gear selection, gear transmission quality control and gear vibration and noise reduction, and is an improvement in the gear measurement field.
Disclosure of Invention
The invention discloses a method which can obtain the transmission error of a gear pair according to the point cloud data of the surface of a gear. On the basis, a gear tooth surface contact judgment algorithm is provided based on the idea of the meshing principle. And obtaining the position information of the driven wheel by calculating the contact positions of the driving wheel at different positions. And analyzing the position information of the driving wheel and the driven wheel to obtain the transmission error of the gear pair and the influence of a single tooth surface on the transmission error of the gear pair.
The method can be applied to all parallel axis gear transmissions. The method adopted by the invention comprises the following steps.
S1, establishing a gear coordinate system
And establishing a rectangular space coordinate system according to the measured gear parameters. The driving wheel and the driven wheel are both gear models constructed by point cloud data of the gear surface.
As shown in fig. 1, a coordinate system (O 1 -x 1 ,y 1 ,z 1 ) Is a driven wheel coordinate system, and the driven wheel rotates anticlockwise; coordinate system (O) 2 -x 2 ,y 2 ,z 2 ) Is a driving wheel coordinate system, and the driving wheel rotates clockwise. Noodles (O) 1 ,x 1 ,y 1 ) Dough mixing (O) 2 ,x 2 ,y 2 ) On the same plane, the axis x 1 With axis x 2 On the same straight line, O 1 O 2 The distance between the driving wheel and the driven wheel is the sum of the pitch circle radius of the driving wheel and the pitch circle radius of the driven wheel.
S2, determining the initial position of the tooth profile
(1) Initial position of driven wheel
At (O) 1 -x 1 ,y 1 ,z 1 ) In the coordinate system epsilon 1 Is an ideal tooth surface, and the equation is
p 1 Is the spiral parameter of the driven wheel; r is (r) b1 Is a base circle parameter of the driven wheel; u is the spread angle of the involute; z is an equation parameter.
Epsilon as shown in figure 2 1 Is the ideal tooth surface, and the point cloud data epsilon of the first tooth surface of the driven wheel 1,1 The fitted standard tooth surface rotates anticlockwise by alpha 1,1 Degree and ε 1 And (5) overlapping. Point cloud data epsilon of the first tooth surface of the driven wheel 1,1 And taking the initial position as the initial position to rotate to engage.
The point cloud data of all tooth surfaces of the driven wheel are processed, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Counter-clockwise rotation alpha 1,i And when the initial position is reached, the point cloud data of each tooth surface of the driven wheel takes the initial position as a starting point, and the driven wheel rotates to participate in meshing.
(2) Initial position of driving wheel
At (O) 2 -x 2 ,y 2 ) In the coordinate system epsilon 2 Is an ideal tooth surface, and the equation is
p 2 Is the spiral parameter of the driving wheel; r is (r) b2 Is a base circle parameter of the gear point cloud data; u is the expansion angle of the involute and is an equation parameter; z is an equation parameter.
As shown in fig. 3, the point cloud data epsilon of the 1 st tooth surface of the driving wheel 2,1 The fitted standard tooth surface rotates clockwise by alpha 2,1 And epsilon 2 And (5) overlapping. Point cloud data epsilon of 1 st tooth surface of driving wheel 2,1 With this as the initial position, the rotation takes part in the engagement.
The point cloud data of all tooth surfaces of the driving wheel are processed, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 2,i Clockwise rotation alpha 2,i And when the initial position is reached, the point cloud data of each tooth surface of the driving wheel is taken as a starting point from the initial position, and the driving wheel is rotationally engaged.
S3, determining the meshing position of the gear
Epsilon as shown in figure 4 1,i The point cloud data epsilon of the ith tooth surface of the driving wheel is the point cloud data epsilon of the ith tooth surface of the driven wheel 2,i Clockwise rotation from an initial positionThe degree reaches the position at the moment, B is the point cloud data epsilon of the ith tooth surface of the driving wheel 2,i After rotation at (O) 2 -x 2 ,y 2 ,z 2 ) Any one coordinate point B (x B ,y B ,z B ). C is z 2 ＝z B Is arranged in the axial section of the bearing.
Point cloud data epsilon for the ith tooth surface of driven wheel 1,i Interpolation processing is performed to obtain a result in (O 1 -x 1 ,y 1 ,z 1 ) In the coordinate system, the ith tooth surface z of the driven theory 1 ＝z B Is a tooth profile of (a).
As shown in fig. 5, fig. 5 is a sectional view of the central axis section C in fig. 4. L (L) 1 Is the tooth profile of the driven wheel on the section C of the shaft, L 2 Is the tooth profile of the driving wheel on the axial section C, and the point B reaches z 1 Distance R of axis B . At L by interpolation method 1 Find A point, let R A ＝R B 。
As shown in FIG. 6, FIG. 6 shows the tooth profile L of the driven wheel on the axial section C 1 The spanned angle u is the abscissa and the radius R is the ordinate.
The spread angle u is interpolated to obtain an interpolation value,find exhibition u A When r=r B . Normal error corresponding to the point
Spread angle u passing through point A A Sum-of-phase error e A Obtain A point at (O 1 -x 1 ,y 1 ,z 1 ) The following coordinates are: a (x) A ,y A ,z A )。
At this time, the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Clockwise rotation BO 1 Degree A, point B is in contact with point A.
Point cloud data epsilon for ith tooth surface of driving wheel 2,i All points on the driven wheel are processed as above, and the minimum value of the rotation angle of the driven wheel is selected asI.e. the driven wheel rotates clockwise from the initial position +.>The driven wheel is in contact with the driving wheel at one point, and the two gears are in a meshed state. By constantly changing->Repeating the above method to find the corresponding angle
Point cloud data epsilon of ith tooth surface of driven wheel 1,i Clockwise rotation from an initial positionDegree, point cloud data epsilon of ith tooth surface of driving wheel 2,i Clockwise rotation from the initial position->The two tooth surfaces are in engagement with each other only at a point.
Considering the rotation angle of the i-th tooth surface of the driven wheel, the total rotation angle of the i-th tooth surface of the driven wheel
Considering the rotation angle of the i-th tooth surface of the driving wheel, the total rotation angle of the i-th tooth surface of the driving wheel
HandleSequentially arranging the values of i from small to large to form +.>I.e. the point cloud data of the tooth surface of the driving wheel is clockwise rotated +.>Degree, point cloud data wheel rotation of driven wheel tooth surface +.>After the degree, the two gears are in the meshed state. The angle of the first pair of tooth surface point cloud data when the tooth enters into engagement for the first time can be obtained>
S4, solving transmission error of gear pair
Point cloud data of driving wheel rotates clockwiseDegree, point cloud data of driven wheel rotates anticlockwise +.>After the degree, the two gears are in the meshed state. The transmission error TE of gear engagement is
r d1 For the radius of the index circle of the driven wheel, i 12 Is the transmission ratio of the driven wheel to the driving wheel.
The invention provides a method for calculating a gear pair transmission error according to point cloud data on the surface of a gear pair, which can calculate a gear pair transmission error curve according to the point cloud data on the surface of the gear pair and predict the transmission performance of the gear; reflecting the result of error interaction of the driving wheel and the driven wheel in the meshing process; the complete process of each meshing tooth pair on the driving wheel and the driven wheel is shown; the interaction and interaction of errors of two pairs of co-engaged gear teeth in a double-meshed region is disclosed.
Drawings
Fig. 1 establishes a gear space coordinate system.
Fig. 2 illustrates the initial position of the capstan.
Figure 3 driven wheel initial position.
Fig. 4 determines the gear mesh position.
Fig. 5 is a sectional view of section C.
FIG. 6 is a graph of the driven axle cross-sectional profile u-R.
Detailed Description
The invention is illustrated below in connection with specific examples of processing:
driven wheel parameters: normal pressure angle α=20°, normal modulus m=1, tooth number z=23, tooth width l=6mm, tooth top height h a =1 mm, tooth root height h f =1.25 mm, right-handed, helix angle β=15°.
Driving wheel parameters: normal pressure angle a=20°, normal modulus m=1, number of teeth z=45, tooth width l=6 mm,tooth top height h a =1 mm, tooth root height h f =1.25 mm, left-hand, helix angle β=15°.
S1, establishing a gear coordinate system
And establishing a rectangular space coordinate system according to the measured gear parameters. The driving wheel and the driven wheel are both gear models constructed by point cloud data of the gear surface.
As shown in fig. 1, a coordinate system (O 1 -x 1 ,y 1 ,z 1 ) Is a driven wheel coordinate system, and the driven wheel rotates anticlockwise; coordinate system (O) 2 -x 2 ,y 2 ,z 2 ) Is a driving wheel coordinate system, and the driving wheel rotates clockwise. Noodles (O) 1 ,x 1 ,y 1 ) Dough mixing (O) 2 ,x 2 ,y 2 ) On the same plane, the axis x 1 With axis x 2 On the same straight line, O 1 O 2 The distance between the driving wheel and the driven wheel is the sum of the pitch circle radius of the driving wheel and the pitch circle radius of the driven wheel.
S2, determining the initial position of the tooth profile
(2) Initial position of driven wheel
At (O) 1 -x 1 ,y 1 ,z 1 ) In the coordinate system epsilon 1 Is an ideal tooth surface, and the equation is
p 1 Is the spiral parameter of the driven wheel; r is (r) b1 Is a base circle parameter of the driven wheel; u is the spread angle of the involute; z is an equation parameter.
Epsilon as shown in figure 2 1 Is the ideal tooth surface, and the point cloud data epsilon of the first tooth surface of the driven wheel 1,1 The fitted standard tooth surface rotates anticlockwise by alpha 1,1 Degree and ε 1 And (5) overlapping. Point cloud data epsilon of the first tooth surface of the driven wheel 1,1 And taking the initial position as the initial position to rotate to engage.
The point cloud data of all tooth surfaces of the driven wheel are processed, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Counter-clockwise rotation alpha 1,i And when the initial position is reached, the point cloud data of each tooth surface of the driven wheel takes the initial position as a starting point, and the driven wheel rotates to participate in meshing.
(2) Initial position of driving wheel
At (O) 2 -x 2 ,y 2 ) In the coordinate system epsilon 2 Is an ideal tooth surface, and the equation is
p 2 Is the spiral parameter of the driving wheel; r is (r) b2 Is a base circle parameter of the gear point cloud data; u is the expansion angle of the involute and is an equation parameter; z is an equation parameter.
As shown in fig. 3, the point cloud data epsilon of the 1 st tooth surface of the driving wheel 2,1 The fitted standard tooth surface rotates clockwise by alpha 2,1 And epsilon 2 And (5) overlapping. Point cloud data epsilon of 1 st tooth surface of driving wheel 2,1 With this as the initial position, the rotation takes part in the engagement.
The point cloud data of all tooth surfaces of the driving wheel are processed, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 2,i Clockwise rotation alpha 2,i And when the initial position is reached, the point cloud data of each tooth surface of the driving wheel is taken as a starting point from the initial position, and the driving wheel is rotationally engaged.
S3, determining the meshing position of the gear
Epsilon as shown in figure 4 1,i And the point cloud data of the ith tooth surface of the driven wheel. Point cloud data epsilon of ith tooth surface of driving wheel 2,i Clockwise rotation from an initial positionThe degree reaches the position at the moment, B is the point cloud data epsilon of the ith tooth surface of the driving wheel 2,i After rotation at (O) 2 -x 2 ,y 2 ,z 2 ) Any one coordinate point B (x B ,y B ,z B ). C is z 2 ＝z B Is arranged in the axial section of the bearing.
Point cloud data epsilon for the ith tooth surface of driven wheel 1,i Interpolation processing is performed to obtain a result in (O 1 -x 1 ,y 1 ,z 1 ) In the coordinate system, the ith tooth surface z of the driven theory 1 ＝z B Is a tooth profile of (a).
As shown in fig. 5, fig. 5 is a sectional view of the central axis section C in fig. 4. L (L) 1 Is the tooth profile of the driven wheel on the section C of the shaft, L 2 Is the tooth profile of the driving wheel on the axial section C, and the point B reaches z 1 Distance R of axis B . At L by interpolation method 1 Find A point, let R A ＝R B 。
As shown in FIG. 6, FIG. 6 shows the tooth profile L of the driven wheel on the axial section C 1 The spanned angle u is the abscissa and the radius R is the ordinate.
Interpolation is carried out on the expansion angle u to find the expansion angle u A When r=r B . Normal error corresponding to the point
Spread angle u passing through point A A Sum-of-phase error e A Obtain A point at (O 1 -x 1 ,y 1 ,z 1 ) The following coordinates are: a (x) A ,y A ,z A )。
At this time, the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Clockwise rotation BO 1 Degree A, point B is in contact with point A.
Point cloud data epsilon for ith tooth surface of driving wheel 2,i All points on the driven wheel are processed as above, and the minimum value of the rotation angle of the driven wheel is selected asI.e. the driven wheel rotates clockwise from the initial position +.>The driven wheel is in contact with the driving wheel at one point only, and the two gears are positionedEngagement state. By constantly changing->Repeating the above method to find the corresponding angle
Point cloud data epsilon of ith tooth surface of driven wheel 1,i Clockwise rotation from an initial positionDegree, point cloud data epsilon of ith tooth surface of driving wheel 2,i Clockwise rotation from the initial position->The two tooth surfaces are in engagement with each other only at a point.
Considering the rotation angle of the i-th tooth surface of the driven wheel, the total rotation angle of the i-th tooth surface of the driven wheel
Considering the rotation angle of the i-th tooth surface of the driving wheel, the total rotation angle of the i-th tooth surface of the driving wheel
HandleSequentially arranging the values of i from small to large to form +.>I.e. the point cloud data of the tooth surface of the driving wheel is clockwise rotated +.>Degree, point cloud data wheel rotation of driven wheel tooth surface +.>After the degree, the two gears are in the meshed state. The angle of the first pair of tooth surface point cloud data when the tooth enters into engagement for the first time can be obtained>
S4, solving transmission error of gear pair
Point cloud data of driving wheel rotates clockwiseDegree, point cloud data of driven wheel rotates anticlockwise +.>After the degree, the two gears are in the meshed state. The transmission error TE of gear engagement is
r d1 For the radius of the index circle of the driven wheel, i 12 Is the transmission ratio of the driven wheel to the driving wheel.

Claims (3)

1. The gear pair transmission error calculation method based on the gear point cloud data is characterized by comprising the following steps of: comprises the following steps of the method,
s1, establishing a gear coordinate system;
establishing a rectangular space coordinate system according to the measured gear parameters; the driving wheel and the driven wheel are both gear models constructed by point cloud data on the surface of the gear;
coordinate system (O) 1 -x 1 ,y 1 ,z 1 ) Is a driven wheel coordinate system, and the driven wheel rotates anticlockwise; coordinate system (O) 2 -x 2 ,y 2 ,z 2 ) Is a driving wheel coordinate system, and the driving wheel rotates clockwise; noodles (O) 1 ,x 1 ,y 1 ) Dough mixing (O) 2 ,x 2 ,y 2 ) On the same plane, the axis x 1 With axis x 2 On the same straight line, O 1 O 2 The distance between the driving wheel and the driven wheel is the sum of the dividing circle radius of the driving wheel and the dividing circle radius of the driven wheel;
s2, determining the initial position of the tooth profile;
(1) Initial position of driven wheel
At (O) 1 -x 1 ,y 1 ,z 1 ) In the coordinate system epsilon 1 Is an ideal tooth surface, and the equation is
p 1 Is the spiral parameter of the driven wheel; r is (r) b1 Is a base circle parameter of the driven wheel; u is the spread angle of the involute; z is an equation parameter;
ε 1 is the ideal tooth surface, and the point cloud data epsilon of the first tooth surface of the driven wheel 1,1 The fitted standard tooth surface rotates anticlockwise by alpha 1,1 Degree and ε 1 Overlapping; point cloud data epsilon of the first tooth surface of the driven wheel 1,1 Taking the initial position as the initial position to rotate to participate in engagement;
processing the point cloud data of all tooth surfaces of the driven wheel, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Counter-clockwise rotation alpha 1,i The point cloud data of each tooth surface of the driven wheel is taken as a starting point from the initial position to participate in meshing in a rotating way;
(2) An initial position of the driving wheel;
at (O) 2 -x 2 ,y 2 ) In the coordinate system epsilon 2 Is an ideal tooth surface, and the equation is
p 2 Is the spiral parameter of the driving wheel; r is (r) b2 Is a base circle parameter of the gear point cloud data; u (u)The expansion angle of the involute is an equation parameter; z is an equation parameter;
point cloud data epsilon of 1 st tooth surface of driving wheel 2,1 The fitted standard tooth surface rotates clockwise by alpha 2,1 And epsilon 2 Overlapping; point cloud data epsilon of 1 st tooth surface of driving wheel 2,1 Taking the initial position as the initial position, and rotating to engage in engagement;
the point cloud data of all tooth surfaces of the driving wheel are processed, namely the point cloud data epsilon of the ith tooth surface of the driven wheel 2,i Clockwise rotation alpha 2,i When the initial position is reached, the point cloud data of each tooth surface of the driving wheel is taken as a starting point from the initial position, and the driving wheel is rotated to participate in engagement;
s3, determining the meshing position of the gear
ε 1,i The point cloud data of the ith tooth surface of the driven wheel; point cloud data epsilon of ith tooth surface of driving wheel 2,i Clockwise rotation from an initial positionThe degree reaches the position at the moment, B is the point cloud data epsilon of the ith tooth surface of the driving wheel 2,i After rotation at (O) 2 -x 2 ,y 2 ,z 2 ) Any one coordinate point B (x B ,y B ,z B ) The method comprises the steps of carrying out a first treatment on the surface of the C is z 2 ＝z B Is arranged on the outer surface of the bearing;
point cloud data epsilon for the ith tooth surface of driven wheel 1,i Interpolation processing is performed to obtain a result in (O 1 -x 1 ,y 1 ,z 1 ) In the coordinate system, the ith tooth surface z of the driven theory 1 ＝z B Is a tooth profile of (a);
L 1 is the tooth profile of the driven wheel on the section C of the shaft, L 2 Is the tooth profile of the driving wheel on the axial section C, and the point B reaches z 1 Distance R of axis B The method comprises the steps of carrying out a first treatment on the surface of the At L by interpolation method 1 Find A point, let R A ＝R B ；
The spreading angle u is an abscissa, and the radius R is an ordinate;
interpolation is carried out on the expansion angle u to find the expansion angle u A When r=r B The method comprises the steps of carrying out a first treatment on the surface of the Corresponding normal error
Spread angle u passing through point A A Sum-of-phase error e A Obtain A point at (O 1 -x 1 ,y 1 ,z 1 ) The following coordinates are: a (x) A ,y A ,z A )；
At this time, the point cloud data epsilon of the ith tooth surface of the driven wheel 1,i Clockwise rotation BO 1 Degree A, point B contacts point A;
point cloud data epsilon for ith tooth surface of driving wheel 2,i All points on the driven wheel are processed as above, and the minimum value of the rotation angle of the driven wheel is selected asI.e. the driven wheel rotates clockwise from the initial position +.>The driven wheel is in contact with the driving wheel at one point, and the two gears are in a meshed state; by constantly changing->Is repeated to find the corresponding +.>
Point cloud data epsilon of ith tooth surface of driven wheel 1,i Clockwise rotation from an initial positionDegree, point cloud data epsilon of ith tooth surface of driving wheel 2,i Clockwise rotation from the initial position->The two tooth surfaces are in meshing state, and only one point of the two tooth surfaces are contacted;
considering the rotation angle of the i-th tooth surface of the driven wheel, the total rotation angle of the i-th tooth surface of the driven wheel
Considering the rotation angle of the i-th tooth surface of the driving wheel, the total rotation angle of the i-th tooth surface of the driving wheel
HandleSequentially arranging the values of i from small to large to form +.>I.e. the point cloud data of the tooth surface of the driving wheel is clockwise rotated +.>Degree, point cloud data wheel rotation of driven wheel tooth surface +.>After the degree, the two gears are in a meshed state; obtaining the angle of the first pair of tooth surface point cloud data when the tooth surface point cloud data enters into engagement for the first time>S4, solving a gear pair transmission error;
point cloud data of driving wheel rotates clockwiseDegree, point cloud data of driven wheel anticlockwiseRotate->After the degree, the two gears are in a meshed state; the transmission error TE of gear engagement is
r d1 For the radius of the index circle of the driven wheel, i 12 Is the transmission ratio of the driven wheel to the driving wheel.
2. The gear pair transmission error calculation method based on the gear point cloud data according to claim 1, wherein the method is used for spur gear transmission and helical gear transmission.
3. The gear pair transmission error calculation method based on the gear point cloud data according to claim 1, wherein the influence of a single tooth on the gear pair transmission error is analyzed, and the gear pair transmission performance is predicted.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101915667A (en) * 2010-07-23 2010-12-15 北京工业大学 Integrated error measuring technology and method thereof of gear pair
CN108645323A (en) * 2018-06-21 2018-10-12 北京工业大学 Involute spur gear wheel total profile deviation assessment method under the influence of installation error

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5000459B2 (en) * 2007-11-14 2012-08-15 本田技研工業株式会社 Hypoid gear meshing position adjustment method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101915667A (en) * 2010-07-23 2010-12-15 北京工业大学 Integrated error measuring technology and method thereof of gear pair
CN108645323A (en) * 2018-06-21 2018-10-12 北京工业大学 Involute spur gear wheel total profile deviation assessment method under the influence of installation error

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
机器人RV减速器摆线针轮传动轮齿接触分析;梁帅锋等;《机械传动》;第17-22页 *

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