CN115824113A - Method for measuring tooth surface error of face gear - Google Patents
Method for measuring tooth surface error of face gear Download PDFInfo
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- CN115824113A CN115824113A CN202211542394.4A CN202211542394A CN115824113A CN 115824113 A CN115824113 A CN 115824113A CN 202211542394 A CN202211542394 A CN 202211542394A CN 115824113 A CN115824113 A CN 115824113A
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Abstract
The invention discloses a method for measuring the tooth surface error of a face gear, which comprises the following steps: the method comprises the following steps: dividing a face gear scanning area: 11 Utilizing the meshing relation of the virtual gear shaper cutter during processing of the face gear to construct and obtain a face gear tooth surface equation, and performing discrete processing on the face gear tooth surface equation to obtain a face gear theoretical tooth surface; 12 Obtaining a face gear scanning area according to face gear theoretical tooth surface division; step two: measuring the face gear tooth surface by using a gear measuring center: 21 Measured face gear: acquiring data points by adopting a scanning type measuring head to face the tooth surface of the gear; 22 Data processing: converting a measurement coordinate system of the tooth surface of the face gear to a theoretical coordinate system; 23 Surface fitting: fitting the face gear tooth surface data points by adopting a high-order polynomial to obtain a curved surface polynomial between the face gear tooth surface data and a measuring position; step three: and mapping the tooth surface points of the theoretical tooth surface of the face gear to a curved surface polynomial to obtain the tooth surface error of the face gear.
Description
Technical Field
The invention belongs to the technical field of gear detection, and particularly relates to a method for measuring a tooth surface error of a face gear.
Background
The face gear transmission is successfully applied to the speed reducer, the quality of the main speed reducer can be greatly reduced, and the power-weight ratio of the main speed reducer is improved. Compared with a bevel gear transmission pair, the face gear transmission pair has the advantages of light weight, small volume, compact structure, longer service life, higher bearing capacity, insensitivity to installation errors and the like. The main difficulty of face gear manufacturing is reflected in the problems of immature face gear machining process, low machining efficiency, low machining precision and the like. At present, how to evaluate the precision of face gears is a new problem, the tooth surfaces of the face gears are obviously different from the tooth surfaces of straight gears and bevel gears, and the tooth surfaces of the face gears are complex space curved surfaces. The tooth surface precision of the face gear cannot be accurately evaluated by adopting the traditional detection means, the tooth surface precision measurement efficiency is low, the measurement cost is high, the measurement method is complex, and the tooth surface precision of the face gear cannot be measured on general detection equipment.
Disclosure of Invention
In view of this, the present invention aims to provide a method for measuring a tooth surface error of a face gear, which can not only meet the measurement requirement of the tooth surface error of the face gear, but also has the advantages of simple operation, high measurement accuracy and high measurement speed.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for measuring the tooth surface error of a face gear comprises the following steps:
the method comprises the following steps: dividing a face gear scanning area
11 Utilizing the meshing relation of the virtual gear shaper cutter during processing the face gear, constructing a tooth surface equation of the face gear by using the tooth surface equation of the virtual gear shaper cutter to obtain a tooth surface equation of the face gear, and then performing discrete processing on the tooth surface equation of the face gear to obtain a theoretical tooth surface of the face gear;
12 Obtaining a face gear scanning area according to face gear theoretical tooth surface division;
step two: measuring face gear tooth surface by using gear measuring center
21 Measured face gear: installing a face gear on a workbench of a gear measurement center, and acquiring data points on the tooth surface of the face gear by adopting a scanning type measuring head;
22 Data processing: converting a measurement coordinate system of the tooth surface of the face gear to a theoretical coordinate system;
23 Surface fitting: fitting the face gear tooth surface data points by adopting a high-order polynomial to obtain a curved surface polynomial between the face gear tooth surface data and a measuring position;
step three: and mapping the tooth surface points of the theoretical tooth surface of the face gear to a curved surface polynomial to obtain the tooth surface error of the face gear.
Further, in the step 11), a tooth surface equation of the virtual gear shaper cutter is obtained by a standard involute equation:
wherein r is s (x s0 ,y s0 ,z s0 ) Represents the tooth surface equation of a virtual slotting cutter, and O s0 -x s0 y s0 z s0 A fixed coordinate system representing the slotting cutter; r is bs Is the base radius of the pinion cutter, and
m is the module of the pinion cutter; alpha is a pressure angle of the slotting cutter; n is a radical of s The number of teeth of the gear shaping cutter is shown; theta.theta. s Is an involute spread angle parameter; theta s0 The included angle between the involute starting point and the tooth socket midpoint; u. of s Parameters of the virtual gear shaper cutter along the z direction are obtained; '+/-'Is an involute symmetrical along the y-axis;
by utilizing the meshing relation of the virtual gear shaper cutter during processing the face gear, the equation of the tooth surface of the face gear is obtained as follows:
[r f (x f ,y f ,z f )，1] T ＝M fs ·[r s (x s ,y s ,z s ),1] T
wherein r is f (x f ,y f ,z f ) Representing the tooth surface equation of a face gear, O f -x f y f z f Representing a fixed coordinate system of the face gear; r is s (x s ,y s ,z s ) Representing the tooth surface equation O in the fixed coordinate system of the slotting cutter s -x s y s z s Representing a fixed connection coordinate system of the slotting cutter; m fs A coordinate transformation matrix representing a virtual slotting cutter to face gear;
for involute spread angle parameter theta s And a parameter u of the virtual slotting cutter in the z direction s And dispersing to obtain the theoretical tooth surface of the face gear.
Further, in the step 12), a face gear scanning area is obtained by face gear theoretical face shrinkage, wherein: the distance of downward contraction in the tooth crest direction is aH v (ii) a The distance of the upward contraction of the transition circle in the tooth root direction is bH v (ii) a The distance of inward contraction in both sides of the tooth width is cW h (ii) a Wherein H v Indicating face gear tooth height; w h Representing face gear tooth width; a. b and c represent scale factors, respectively.
Further, in the step 21), during the process of measuring the data of the face gear tooth surface point, the scanning measuring head moves along the tooth profile, and the face gear rotates along with the workbench.
Further, in the step 22), a method for converting the measurement coordinate system of the tooth surface of the face gear into the theoretical coordinate system comprises the following steps:
[r fc (x fc ,y fc ,z fc )，1] T ＝M fc_f0 ·[r f0 (x f0 ,y f0 ,z f0 ),1] T
wherein r is fc (x fc ,y fc ,z fc ) Representing the tooth surface equation, O, of the gear under the measurement coordinate system fc -x fc y fc z fc A measurement coordinate system representing the face gear; r is f0 (x f0 ,y f0 ,z f0 ) Representing the face gear tooth surface equation, O, in the design coordinate system f0 -x f0 y f0 z f0 A design coordinate system representing the face gear; m fc_f0 Is a transformation matrix from a measured coordinate system to a theoretical coordinate system of a face gear tooth face, and:
wherein gamma is the angle of the face gear rotating along with the gear measurement center workbench in the rotating process; omega is the rotation angle from the face gear measurement coordinate system to the design coordinate system; and:
wherein, beta represents the angle that the graduation circular arc corresponds between two adjacent tooth homonymy flank profiles, just:
N s the number of teeth of the gear shaping cutter is shown;
Further, in the step 23), fitting the measurement data with a matlab curved surface Fitting Tool current Fitting Tool to obtain a curved surface polynomial, wherein the curved surface polynomial is as follows:
f(x,y)＝p 00 +p 10 ·x+p 01 ·y+p 20 ·x 2 +p 11 ·x·y+p 02 ·y 2 +p 21 ·x 2 ·y+p 12 ·x·y 2 +p 03 ·y n
wherein p is 00 、p 10 、p 01 、p 20 、p 11 、p 02 、p 21 、p 12 And p 03 All represent polynomial coefficients.
Further, in the third step, the tooth surface error of the face gear is as follows:
wherein D (i, j) represents an error value of a j-th tooth surface point on an i-th scanning track line; (x) i ',y i ',z i ') is the face coordinates of the face gear determined by a polynomial equation (x) i ,y i ,z i ) Is the theoretical tooth surface coordinate of the face gear.
The invention has the beneficial effects that:
according to the method for measuring the tooth surface error of the face gear, firstly, a face gear tooth surface equation is constructed and obtained based on the meshing relation of the virtual gear shaper cutter during processing of the face gear, and the theoretical tooth surface of the face gear is obtained through the face gear tooth surface equation, so that a measurement scanning area can be divided according to the theoretical tooth surface of the face gear; after a scanning area is defined, measuring a face gear by using a gear measuring center, and performing surface fitting after converting a measuring coordinate system into a theoretical coordinate system to obtain a surface polynomial between the data of the tooth surface of the face gear and a measuring position; and finally, mapping the tooth surface points of the theoretical tooth surface of the face gear to the curved surface polynomial to obtain the tooth surface error of the face gear, so that the measurement requirement of the tooth surface error of the face gear can be met, and the method has the advantages of simplicity in operation, high measurement precision and high measurement speed.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a flow chart of a face gear tooth surface error measurement method of the present invention;
FIG. 2 is a diagram of a tooth profile of a virtual shaper cutter;
FIG. 3 is a diagram showing the meshing relationship between the virtual slotting cutter and the face gear;
FIG. 4 is a theoretical tooth profile view of a face gear;
FIG. 5 is a physical diagram of a P26 gear measurement center;
FIG. 6 is a sectional view of a probe scanning area of the gear measurement center;
FIG. 7 is a pictorial view of a face gear mounted to a gear measurement center table;
FIG. 8 is an interface diagram of a gear measurement center with a measurement start point;
FIG. 9 is a measurement interface of a measurement center of a P26 type gear;
FIG. 10 is a data point diagram obtained by fitting under a measurement coordinate system;
FIG. 11 is a data point diagram after the measured coordinate system is transformed to the design coordinate system;
FIG. 12 is an interface diagram of the Curve Fitting Tool;
FIG. 13 is a data point diagram of a problem;
FIG. 14 is a measurement point surface fit;
FIG. 15 is a comparison of a theoretical surface and a fitted surface;
FIG. 16 is a schematic illustration of theoretical tooth flank points of a face gear;
FIG. 17 is a tooth face error topology diagram for a face gear.
Detailed Description
The present invention is further described below in conjunction with the drawings and the embodiments so that those skilled in the art can better understand the present invention and can implement the present invention, but the embodiments are not to be construed as limiting the present invention.
As shown in fig. 1, the method for measuring the tooth surface error of the face gear of the present embodiment includes the following steps.
The method comprises the following steps: dividing a face gear scanning area
11 Utilizing the meshing relation of the virtual gear shaper cutter during processing the face gear, constructing a tooth surface equation of the face gear by using the tooth surface equation of the virtual gear shaper cutter to obtain a tooth surface equation of the face gear, and then performing discrete processing on the tooth surface equation of the face gear to obtain a theoretical tooth surface of the face gear;
the virtual gear shaper cutter for machining face gears is of a standard involute profile. As shown in fig. 2, is the involute profile, parameters and fixed-link coordinate system of the virtual gear shaper cutter.
The tooth surface equation of the virtual gear shaper cutter is obtained by a standard involute equation:
wherein r is s (x s0 ,y s0 ,z s0 ) Represents the tooth surface equation of a virtual slotting cutter, and O s0 -x s0 y s0 z s0 Representing a fixed coordinate system of the slotting cutter as shown in figure 2; r is bs Is the base radius of the pinion cutter, and
m is the module of the pinion cutter; alpha is a pressure angle of the slotting cutter; n is a radical of hydrogen s The number of teeth of the gear shaping cutter is shown; theta s Is an involute spread angle parameter; theta s0 The included angle between the involute starting point and the tooth socket midpoint; u. of s Parameters of the virtual gear shaper cutter along the z direction are obtained; '+/-' is an involute symmetrical along the y axis;
as shown in fig. 3, the meshing relationship between the virtual slotting cutter and the face gear is shown. In the figure
Is the rotation angle of the virtual gear shaper cutter and the face gear in the meshing process. The meshing relation of the virtual gear shaper cutter during processing of the face gear is utilized to obtain a face gear tooth surface equation as follows:
[r f (x f ,y f ,z f )，1] T ＝M fs ·[r s (x s ,y s ,z s ),1] T
wherein r is f (x f ,y f ,z f ) Representing the tooth surface equation of a face gear, O f -x f y f z f Representing a fixed connection coordinate system of the face gear; r is s (x s ,y s ,z s ) Representing the tooth surface equation O in the fixed coordinate system of the slotting cutter s -x s y s z s A fixed connection coordinate system of the pinion cutter is shown as figure 3; m fs A coordinate transformation matrix representing a virtual slotting cutter to face gear;
for involute spread angle parameter theta s And a parameter u of the virtual slotting cutter in the z direction s The discretization is performed to obtain the face gear theoretical tooth surface, as shown in fig. 4.
12 Obtaining a face gear scan area based on face gear theoretical tooth surface division
As shown in fig. 5, the present embodiment measures the face gear tooth surface using the P26 type gear measurement center. In order to avoid the interference of the tooth space tooth profile boundary on the measuring result of the measuring head and the scratch of the measuring head in the whole measuring process, the measuring area is contracted. In this embodiment, the face gear scanning area is obtained from the face gear theoretical tooth face shrinkage, as shown in fig. 6. Wherein: the distance of downward contraction in the tooth crest direction is aH v (ii) a The distance of the upward contraction of the transition circle in the tooth root direction is bH v (ii) a The distance of inward contraction in both sides of the tooth width is cW h (ii) a Wherein H v Indicating face gear tooth height; w h Representing face gear tooth width; a. b and c represent scale factors, respectively. In the present example, a =0.05, b =0.05, c =0.1.
Gear tooth height of face contracted downwards in tooth top directionH v 5% of; tooth root direction transition circle upwards contraction face gear tooth height H v 5% of; the tooth width W of the face gear is contracted inwards in the direction of both sides of the tooth width h 10% of the total.
Step two: face gear tooth surface measurement using gear measurement center
21 Measured face gear: the face gear was mounted on the table of the gear measurement center as shown in fig. 7. And acquiring data points by adopting a scanning type measuring head to face the tooth surface of the gear. As shown in fig. 8, the measurement starting point of this embodiment is (0,0,87.4000), unit: mm. The measuring head scans data points along the profile of the face gear, the P26 type gear measuring center measures the face gear and collects data points on the tooth surface of the face gear by adopting the scanning measuring head, and a tooth surface point coordinate is collected every 50 ms. In the process of measuring the tooth surface point data of the face gear, the scanning measuring head moves along the tooth profile, and the face gear rotates along with the workbench. As shown in fig. 9, is a measurement interface of a measurement center of a gear of P26 type.
22 Data processing: converting the measuring coordinate system of the tooth surface of the face gear to the theoretical coordinate system
A measuring head of a P26 type gear measuring center scans along the tooth profile of a face gear to measure the tooth face precision of the face gear, a contact type measuring head is always ensured to be in contact with the tooth face of the face gear in the measuring process, and the face gear rotates at a small angle in the measuring process, so that a measuring point needs to be rotated to a theoretical coordinate system. The result of the gear measurement center is imported into matlab to obtain measurement data without coordinate transformation, as shown in fig. 10.
In the process of measuring the tooth surface accuracy of the face gear in the gear measurement of P26, the measuring head scans nine lines along the face gear at high intervals, and the tooth profile scanning sequence is shown in fig. 11. Since the face gear rotates with the table during the measurement, the measured coordinate system of the face gear does not coincide with the theoretical coordinate system, as shown in fig. 11. In this embodiment, the 5 th scanning track is a central scanning track line, and the face gear measurement coordinate system is subjected to coordinate transformation. Specifically, the method for converting the measurement coordinate system of the tooth surface of the face gear into the theoretical coordinate system comprises the following steps:
[r fc (x fc ,y fc ,z fc )，1] T ＝M fc_f0 ·[r f0 (x f0 ,y f0 ,z f0 ),1] T
wherein r is fc (x fc ,y fc ,z fc ) Representing the tooth surface equation, O, of the gear under the measurement coordinate system fc -x fc y fc z fc A measurement coordinate system representing the face gear, and measurement results in the measurement coordinate system are shown in fig. 10; r is a radical of hydrogen f0 (x f0 ,y f0 ,z f0 ) Representing the face gear tooth surface equation, O, in the design coordinate system f0 -x f0 y f0 z f0 A design coordinate system of the face gear is shown, and the measurement result in the design coordinate system is shown in fig. 11; m fc_f0 Is a transformation matrix from a measured coordinate system to a theoretical coordinate system of a face gear tooth face, and:
wherein gamma is the angle of the face gear rotating along with the gear measurement center worktable in the rotating process; omega is the rotation angle from the face gear measurement coordinate system to the design coordinate system; and:
wherein, β represents the angle corresponding to the indexing arc between the tooth profiles on the same sides of two adjacent teeth, and:
N s the number of teeth of the gear shaping cutter is shown;
In this example, R =91.133mm First stage ＝-32.758mm，x Powder = 24.002mm. Take ω =90 °, rotate 90 ° counterclockwise about the Z axis.
23 Surface fitting: and fitting the face gear tooth surface data points by adopting a high-order polynomial to obtain a curved surface polynomial between the face gear tooth surface data and the measurement position. The function expression of the polynomial fitting surface model is as follows:
ζ(x,y)＝p 00 +p 10 ·x+p 01 ·y+p 20 ·x 2 +p 11 ·x·y+p 02 ·y 2 +...+p 0n y n
as shown in fig. 12, the measurement data is fitted with matlab surface Fitting Tool, and the obtained surface polynomial is:
f(x,y)＝p 00 +p 10 ·x+p 01 ·y+p 20 ·x 2 +p 11 ·x·y+p 02 ·y 2 +p 21 ·x 2 ·y+p 12 ·x·y 2 +p 03 ·y n
wherein p is 00 、p 10 、p 01 、p 20 、p 11 、p 02 、p 21 、p 12 And p 03 All represent polynomial coefficients.
In this example, fitting accuracy evaluation: SSE =0.1366 (and variance), R-Square =0.9998 (deterministic coefficient), adjusted R-Square =0.9998 (adjustment Square), RMSE =0.02754 (root mean Square).
Wherein: p is a radical of 00 ＝-72.96，p 10 ＝3.753，p 01 ＝-66.99，p 20 ＝-0.01966，p 11 ＝1.327，p 02 ＝0.3535，p 21 ＝-0.006758，p 12 ＝-0.004652，p 03 ＝-0.01084。
As shown in fig. 13, error points are easy to occur at positions close to the tooth grooves during measurement, and the error points should be eliminated. Tooth surface fitting of problematic data points was excluded as shown in fig. 14. The fitting of the curved surface and the theoretical curved surface is better than that shown in fig. 15.
Step three: and mapping the tooth surface points of the theoretical tooth surface of the face gear to a curved surface polynomial to obtain the tooth surface error of the face gear.
Firstly, the tooth surface error of the face gear is solved, and the tooth surface point of the face gear is mapped to the fitting curved surface, and the theoretical tooth surface point of the face gear is shown as 16. Based on the Gleason tooth surface measuring point planning standard, more uniformly distributed tooth surface measuring points of the face gear are obtained, and the theoretical tooth surface coordinate of the face gear is shown in Table 1.
TABLE 1 theoretical tooth flank point diagram of a gear
And (3) substituting the tooth surface points of the theoretical face gear into a fitted polynomial to obtain the tooth surface deviation of the face gear:
wherein D (i, j) represents an error value of a j-th tooth surface point on the ith scanning track line; (x) i ',y i ',z i ') is composed ofCoordinates of the tooth surface of the face gear (x) determined by a polynomial i ,y i ,z i ) Is the theoretical tooth surface coordinate of the face gear.
And then a topological graph of the tooth surface error of the face gear is obtained, as shown in fig. 17.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (7)
1. A method for measuring the tooth surface error of a face gear is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: dividing a face gear scanning area
11 Utilizing the meshing relation of the virtual gear shaper cutter during processing the face gear, constructing a tooth surface equation of the face gear by using the tooth surface equation of the virtual gear shaper cutter to obtain a tooth surface equation of the face gear, and then performing discrete processing on the tooth surface equation of the face gear to obtain a theoretical tooth surface of the face gear;
12 Obtaining a face gear scanning area according to face gear theoretical tooth surface division;
step two: face gear tooth surface measurement using gear measurement center
21 Measured face gear: installing a face gear on a workbench of a gear measurement center, and acquiring data points on the tooth surface of the face gear by adopting a scanning type measuring head;
22 Data processing: converting a measurement coordinate system of the tooth surface of the face gear to a theoretical coordinate system;
23 Surface fitting: fitting the face gear tooth surface data points by adopting a high-order polynomial to obtain a curved surface polynomial between the face gear tooth surface data and a measuring position;
step three: and mapping the tooth surface points of the theoretical tooth surface of the face gear to a curved surface polynomial to obtain the tooth surface error of the face gear.
2. The method of measuring face gear tooth face error of claim 1, characterized by: in the step 11), a tooth surface equation of the virtual gear shaper cutter is obtained by a standard involute equation:
wherein r is s (x s0 ，y s0 ，z s0 ) Represents the tooth surface equation of a virtual gear shaper cutter, and O s0 -x s0 y s0 z s0 A fixed coordinate system representing the slotting cutter; r is bs Is the base radius of the pinion cutter, and
m is the module of the pinion cutter; alpha is a pressure angle of the slotting cutter; n is a radical of s The number of teeth of the gear shaping cutter is shown; theta s Is an involute spread angle parameter; theta.theta. s0 The included angle between the involute starting point and the tooth socket midpoint; u. of s Parameters of the virtual gear shaper cutter along the z direction are obtained; '+/-' is an involute symmetrical along the y axis;
the meshing relation of the virtual gear shaper cutter during processing of the face gear is utilized to obtain a face gear tooth surface equation as follows:
[r f (x f ，y f ，z f )，1] T ＝M fs ·[r s (x s ，y s ，z s )，1] T
wherein r is f (x f ，y f ，z f ) Representing the tooth surface equation of a face gear, O f -x f y f z f Representing a fixed coordinate system of the face gear; r is a radical of hydrogen s (x s ，y s ，z s ) Representing the tooth surface equation O in the fixed coordinate system of the slotting cutter s -x s y s z s Representing a fixed connection coordinate system of the slotting cutter; m fs Representing a fixed connection coordinate transformation matrix from a virtual gear shaper cutter fixed connection coordinate system to a face gear;
for involute spread angle parameter theta s And a parameter u of the virtual gear shaper cutter in the z direction s And dispersing to obtain the theoretical tooth surface of the face gear.
3. The method of measuring a tooth face error of a face gear according to claim 1, wherein: in the step 12), a face gear scanning area is obtained by face gear theoretical tooth surface shrinkage, wherein: the distance of downward contraction in the tooth crest direction is aH v (ii) a The distance of the upward contraction of the transition circle in the tooth root direction is bH v (ii) a The distance of inward contraction in both sides of the tooth width is cW h (ii) a Wherein H v Indicating face gear tooth height; w h Representing face gear tooth width; a. b and c represent scale factors, respectively.
4. The method of measuring face gear tooth face error of claim 1, characterized by: in the step 21), in the process of measuring the data of the face gear and the gear surface point, the scanning measuring head moves along the tooth profile, and the face gear rotates along with the workbench.
5. The method of measuring face gear tooth face error of claim 1, characterized by: in the step 22), the method for converting the measurement coordinate system of the tooth surface of the face gear into the theoretical coordinate system comprises the following steps:
[r fc (x fc ，y fc ，z fc )，1] T ＝M fc_f′0 ·[r f0 (x f0 ，y f0 ，z f0 )，1] T
wherein r is fc (x fc ，y fc ，z fc ) Representing the tooth surface equation, O, of the gear under the measurement coordinate system fc -x fc y fc z fc A measurement coordinate system representing the face gear; r is f0 (x f0 ，y f0 ，z f0 ) Representing the face gear tooth surface equation, O, in the design coordinate system f0 -x f0 y f0 z f0 A design coordinate system representing the face gear; m fc_f0 A transformation matrix for a measurement coordinate system to a design coordinate system for a face gear tooth face, and:
wherein gamma is the angle of the face gear rotating along with the gear measurement center worktable in the rotating process; omega is the rotation angle from the face gear measurement coordinate system to the design coordinate system; and:
wherein, β represents the angle corresponding to the indexing arc between the tooth profiles on the same sides of two adjacent teeth, and:
N s the number of teeth of the gear shaping cutter is shown;
6. The method of measuring face gear tooth face error of claim 1, characterized by: in the step 23), fitting the measurement data with a matlab curved surface Fitting Tool, and obtaining a curved surface polynomial as follows:
f(x，y)＝p 00 +p 10 ·x+p 01 ·y+p 20 ·x 2 +p 11 ·x·y+p 02 ·y 2 +p 21 ·x 2 ·y+p 12 ·x·y 2 +p 03 ·y n
wherein p is 00 、p 10 、p 01 、p 20 、p 11 、p 02 、p 21 、p 12 And p 03 All represent polynomial coefficients.
7. The method of measuring face gear tooth face error of claim 1, characterized by: in the third step, the tooth surface error of the face gear is as follows:
wherein D (i, j) represents an error value of a j-th tooth surface point on an i-th scanning track line; (x' i ，y′ i ，z′ i ) Is a face gear tooth face coordinate (x) obtained by a polynomial i ，y i ，z i ) Is the theoretical tooth surface coordinate of the face gear.
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