CN110587038A - Tooth profile error compensation method for gear scraping machining - Google Patents
Tooth profile error compensation method for gear scraping machining Download PDFInfo
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- CN110587038A CN110587038A CN201910873575.7A CN201910873575A CN110587038A CN 110587038 A CN110587038 A CN 110587038A CN 201910873575 A CN201910873575 A CN 201910873575A CN 110587038 A CN110587038 A CN 110587038A
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- 238000007790 scraping Methods 0.000 title claims abstract description 51
- 238000000034 method Methods 0.000 title claims abstract description 30
- 238000003754 machining Methods 0.000 title claims abstract description 17
- 238000005520 cutting process Methods 0.000 claims abstract description 36
- 230000005540 biological transmission Effects 0.000 claims abstract description 8
- 238000013507 mapping Methods 0.000 claims abstract description 6
- 230000009466 transformation Effects 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 abstract description 5
- 238000010586 diagram Methods 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F1/00—Making gear teeth by tools of which the profile matches the profile of the required surface
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F23/00—Accessories or equipment combined with or arranged in, or specially designed to form part of, gear-cutting machines
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Numerical Control (AREA)
- Gear Processing (AREA)
Abstract
The invention provides a method for compensating errors of a tooth profile processed by scraping teeth, which comprises the following steps of; considering a local motion transmission chain of a gear shaving machine tool, establishing a powerful gear shaving space coordinate system to obtain a theoretical tooth surface and an actual tooth surface of a workpiece, then calculating a pose deviation e of a tooth surface meshing point, establishing a mapping relation between the pose deviation and a tooth profile normal error to obtain a workpiece tooth profile normal error delta M, obtaining a virtual calculation tooth profile relative to the theoretical tooth profile by taking the delta M as an error reverse compensation value, obtaining a cutting edge profile of a gear shaving cutter by calculating the virtual calculation tooth profile, finally obtaining a compensated workpiece tooth profile by reverse calculation, and if the compensated tooth profile error does not meet the precision requirement, performing iterative compensation according to the method until the precision requirement is met. The method effectively reduces parameter variables, is simple to calculate, and improves the machining precision of the scraping teeth.
Description
Technical Field
The invention relates to the field of numerical control machining error compensation, in particular to a tooth profile error compensation method for gear scraping machining
Background
The powerful gear scraping is to use a gear scraping cutter to machine a gear, and the gear is meshed like a pair of staggered shaft gears. In the gear scraping process, a cutter shaft and a workpiece shaft have a certain shaft intersection angle, a cutting side edge of a cutter tooth which starts to process the workpiece is a cutting edge, a side edge which participates in cutting at last is a cutting edge, and a tooth top is a top edge. The tooth root of the cutter tooth firstly participates in the cutting of a workpiece, the edge section participating in the cutting on the cutting edge gradually moves towards the tooth top, and the tooth top of the cutter cuts the tooth root part of the workpiece; after the cutting of the root portion is completed, the cutting edge section moves to the cutting side edge on the other side, and finally the cutting is released from the root of the cutting edge side edge. In the cutting process, chips are always on the front tool face before chip breaking, and the chips are discharged from the tooth height direction, so that the machining of the non-through internal teeth is realized. The cutting edge of the tool cuts into the workpiece point by point, cutting a small section of strip material from the blank, and forming a groove in the workpiece. The cutter carries out similar cutting for dozens of thousands of times along the tooth trace to finish the whole tooth surface processing, and the tooth surface is cut on the tooth blank.
According to the principle, the dynamic and static characteristics of the gear scraping machine tool have great influence on the machining quality of the gear in the gear scraping machining, and the cutting force and the cutting heat generated in the gear scraping process, the eccentricity of a cutter, the eccentricity of a workpiece and the like all influence the tooth profile precision of the final machining of the gear. However, the error compensation of the tooth profile for the gear scraping processing at present is to compensate each motion axis, and has more parameters and more complex calculation.
Disclosure of Invention
In view of the above, the present invention provides a method for compensating tooth profile error in a scraped tooth process. The method utilizes the normal error Delta M of the tooth profile as an error reverse compensation value to obtain a virtual calculation tooth profile relative to a theoretical tooth profile, then obtains a tooth profile of a tooth scraping knife through the virtual calculation tooth profile, obtains a workpiece tooth profile after error compensation through reverse calculation of the tooth profile of the tooth scraping knife, and can carry out iterative compensation according to the method until the accuracy requirement is met if the compensated tooth profile error does not meet the accuracy requirement,
a method for compensating errors of a tooth profile for shaving processing comprises the following steps:
establishing a powerful tooth scraping space coordinate system according to a local motion transmission chain of a tooth scraping machine tool to obtain a theoretical tooth surface and an actual tooth surface;
step (2) obtaining a pose deviation e according to the pose relation between the theoretical meshing point and the actual meshing point obtained in the step (1);
step (3) establishing a mapping relation between the pose deviation e obtained in the step (2) and the tooth profile normal error delta M to obtain the tooth profile normal error delta M;
step (4) obtaining a virtual calculation tooth profile relative to the theoretical tooth profile by taking the tooth profile normal error delta M obtained in the step (3) as an error reverse compensation value;
step (5) calculating the virtual calculated tooth profile obtained in the step (4) to obtain the cutting edge profile of the gear scraping cutter;
and (6) reversely calculating the profile of the scraping tooth cutter obtained in the step (5) to obtain the compensated workpiece tooth profile.
In the step (1), the local motion transmission chain of the gear scraping machine tool is only based on three parts: the device comprises a cutter assembly, a workpiece rotary table and a lathe bed; and establishing a powerful tooth scraping space coordinate system to obtain a theoretical tooth surface and an actual tooth surface.
In the step (3), a mapping relation between the pose deviation e and the tooth profile normal error is established by combining the pose relation between the theoretical meshing point and the actual meshing point in the workpiece coordinate system, and the tooth profile normal error is obtained by:
ΔM＝ex sinαcosβm+ey cosαcosβm+ez sinβm (1)
wherein: alpha is the reference circle pressure angle of the gear workpiece, betamHelix angle of mesh point, exIs a deviation of the attitude in the x' direction, eyIs a deviation of the pose in the y' direction, ezIs the pose deviation in the z' direction.
In the step (4), the virtual calculated tooth profile relative to the theoretical tooth profile with the Δ M as the error reverse compensation value is obtained, which specifically includes the following steps;
i, establishing a gear involute model, and setting the coordinates of theoretical tooth profile points as M (x)a,ya) Corresponding actual tooth profile point coordinates are M' (x)b,yb) And the normal error of the tooth profile is delta M, the corresponding point on the obtained virtual calculated tooth profile is M ', and the coordinate is expressed as M' (x)c,yc)，
The equation for obtaining the normal virtual calculated tooth profile is as follows:
in the step (5), the cutting edge profile of the tooth scraping cutter calculated by the virtual calculated tooth profile is obtained, a cutting edge equation of the tooth scraping cutter is obtained, and a normal cutting edge equation can be obtained at the same time, and the method specifically comprises the following steps;
obtaining a cutter cutting edge profile in a cutter coordinate system according to a coordinate transformation principle;
II. And (4) obtaining a normal cutting edge equation according to the geometrical shape characteristics of the tooth scraping cutter and by combining the front angle and the shaft intersection angle of the cutter.
In the step (6), the profile of the gear scraping cutter is reversely calculated, the profile coordinate of the gear scraping cutter is converted into a workpiece coordinate system, and an error-compensated workpiece tooth profile equation is obtained by combining a meshing equation of contact points, wherein the step comprises the following steps;
obtaining the tooth profile of the scraping tooth knife in a tool coordinate system:
II. And after coordinate transformation, obtaining a workpiece tooth profile equation by a meshing equation.
The step (6) is followed by: and (7) if the compensated tooth profile error does not meet the precision requirement, performing iterative compensation according to the steps (2) to (6) until the precision requirement is met.
The invention has the beneficial effects that:
the invention effectively reduces the number of calculation parameters and improves the precision of gear scraping processing.
Drawings
Fig. 1 is a flow chart of the tooth profile error compensation method for the scraping tooth machining of the invention.
FIG. 2 is a partial motion transmission chain diagram of the gear scraping machine of the invention
Fig. 3 is a space coordinate system diagram of the power scraping tooth of the invention.
Fig. 4 is a schematic diagram of the scraping tooth processing pose deviation of the invention.
FIG. 5 is a diagram of an involute model of a gear according to the present invention.
Fig. 6 is a graph comparing the theoretical tooth profile and the actual tooth profile after error compensation according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings and embodiments:
referring to fig. 1 to 6, fig. 1 is a flow chart of a tooth scraping tooth processing tooth profile error compensation method of the present invention, and fig. 2 is a flow chart illustrating a tooth scraping tooth processing tooth profile error compensation method by using a numerical control tooth scraping machine of a certain type to process a workpiece, only considering a tool assembly, a workpiece turntable and a motion transmission chain of a lathe bed.
Step (1), according to a local motion transmission chain of a machine tool, considering displacement and corner errors of a cutter assembly, a workpiece rotary table and a machine body, and establishing a powerful tooth scraping space coordinate system (figure 3) to obtain a theoretical tooth surface and an actual tooth surface;
step (2), obtaining a pose deviation e according to the pose relation between the theoretical meshing point and the actual meshing point;
step (3), a local coordinate system is established at a tooth surface meshing point, a mapping relation (figure 4) between pose deviation and tooth profile normal error is established, and the obtained tooth profile normal error delta M is as follows:
ΔM＝ex sinαcosβm+ey cosαcosβm+ez sinβm (1)
step (4), obtaining a virtual calculation tooth profile relative to a theoretical tooth profile by taking the delta M as an error reverse compensation value, and comprising the following steps;
i, establishing a gear involute model (figure 5), and setting the coordinates of theoretical tooth profile points as M (x)a,ya) Corresponding actual tooth profile point coordinates are M' (x)b,yb) And the normal error of the tooth profile is delta M, the corresponding point on the obtained virtual calculated tooth profile is M ', and the coordinate is expressed as M' (x)c,yc)，
The equation for obtaining the normal virtual calculated tooth profile is as follows:
step (5), obtaining a cutter cutting edge profile calculated by the virtual calculated tooth profile to obtain a cutter cutting edge equation, and simultaneously obtaining a normal cutting edge equation, wherein the method comprises the following steps;
according to the coordinate transformation principle, the cutting edge profile of the cutter obtained in the cutter coordinate system is as follows:
r2(x2，y2，z2) (4)
II. According to the geometrical characteristics of the scraping tooth cutter, the front angle gamma of the cutter is combinedzAnd the intersection angle sigma of the axis, and obtaining a normal cutting edge equation as follows:
rn(x2，y2，Σ，γz) (5)
and (6) reversely calculating the profile of the gear scraping cutter, transforming the profile coordinate of the cutter to a workpiece coordinate system, and acquiring an error-compensated workpiece tooth profile equation by combining a meshing equation of a contact point, wherein the method comprises the following steps:
obtaining the tooth profile of the scraping tooth knife in a tool coordinate system:
II. After coordinate transformation, obtaining a workpiece tooth profile equation by a meshing equation:
and (7) if the compensated tooth profile error does not meet the precision requirement, performing iterative compensation according to the steps (2) to (6) until the precision requirement is met.
And (8) in order to verify the effectiveness of the tooth profile error compensation method for the scraped tooth machining, carrying out numerical simulation (figure (6)) by using MATLAB according to the steps to obtain a theoretical tooth profile and an actual tooth profile generated by generating envelope by a tooth scraping cutter, then obtaining a virtual calculated tooth profile, and obtaining a compensated workpiece tooth profile through reverse calculation.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (7)
1. A method for compensating errors of a tooth profile for shaving processing is characterized by comprising the following steps:
establishing a powerful tooth scraping space coordinate system according to a local motion transmission chain of a tooth scraping machine tool to obtain a theoretical tooth surface and an actual tooth surface;
step (2) obtaining a pose deviation e according to the pose relation between the theoretical meshing point and the actual meshing point obtained in the step (1);
step (3) establishing a mapping relation between the pose deviation e obtained in the step (2) and the tooth profile normal error delta M to obtain the tooth profile normal error delta M;
step (4) obtaining a virtual calculation tooth profile relative to the theoretical tooth profile by taking the tooth profile normal error delta M obtained in the step (3) as an error reverse compensation value;
step (5) calculating the virtual calculated tooth profile obtained in the step (4) to obtain the cutting edge profile of the gear scraping cutter;
and (6) reversely calculating the profile of the scraping tooth cutter obtained in the step (5) to obtain the compensated workpiece tooth profile.
2. The method for tooth profile error compensation for scraped tooth machining of claim 1, wherein: in the step (1), the local motion transmission chain of the gear scraping machine tool is only based on three parts: the device comprises a cutter assembly, a workpiece rotary table and a lathe bed; and establishing a powerful tooth scraping space coordinate system to obtain a theoretical tooth surface and an actual tooth surface.
3. The method for tooth profile error compensation for scraped tooth machining of claim 1, wherein: in the step (3), a mapping relation between the pose deviation e and the tooth profile normal error is established by combining the pose relation between the theoretical meshing point and the actual meshing point in the workpiece coordinate system, and the tooth profile normal error is obtained by:
ΔM＝exsinαcosβm+eycosαcosβm+ezsinβm (1)
wherein: alpha is the reference circle pressure angle of the gear workpiece, betamHelix angle of mesh point, exIs a deviation of the attitude in the x' direction, eyIs a deviation of the pose in the y' direction, ezIs the pose deviation in the z' direction.
4. The method for tooth profile error compensation for scraped tooth machining of claim 1, wherein: in the step (4), the virtual calculated tooth profile relative to the theoretical tooth profile with the Δ M as the error reverse compensation value is obtained, which specifically includes the following steps;
i, establishing a gear involute model, and setting the coordinates of theoretical tooth profile points as M (x)a,ya) Corresponding actual tooth profile point coordinates are M' (x)b,yb) And the normal error of the tooth profile is delta M, the corresponding point on the obtained virtual calculated tooth profile is M ', and the coordinate is expressed as M' (x)c,yc)，
The equation for obtaining the normal virtual calculated tooth profile is as follows:
5. the method for tooth profile error compensation for scraped tooth machining of claim 1, wherein:
in the step (5), the cutting edge profile of the tooth scraping cutter calculated by the virtual calculated tooth profile is obtained, a cutting edge equation of the tooth scraping cutter is obtained, and a normal cutting edge equation can be obtained at the same time, and the method specifically comprises the following steps;
obtaining a cutter cutting edge profile in a cutter coordinate system according to a coordinate transformation principle;
II. And (4) obtaining a normal cutting edge equation according to the geometrical shape characteristics of the tooth scraping cutter and by combining the front angle and the shaft intersection angle of the cutter.
6. The method for tooth profile error compensation for scraped tooth machining of claim 1, wherein: in the step (6), the profile of the gear scraping cutter is reversely calculated, the profile coordinate of the gear scraping cutter is converted into a workpiece coordinate system, and an error-compensated workpiece tooth profile equation is obtained by combining a meshing equation of contact points, wherein the step comprises the following steps;
obtaining the tooth profile of the scraping tooth knife in a tool coordinate system:
II. And after coordinate transformation, obtaining a workpiece tooth profile equation by a meshing equation.
7. The method for tooth profile error compensation for scraped tooth machining of claim 1, wherein:
after the step (6), further comprising: and (7) if the compensated tooth profile error does not meet the precision requirement, performing iterative compensation according to the steps (2) to (6) until the precision requirement is met.
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| CN112580160A (en) * | 2020-12-03 | 2021-03-30 | 南京工业大学 | Calibration method for on-machine measurement system of forming gear grinding machine |
| CN112719467A (en) * | 2020-12-21 | 2021-04-30 | 武汉理工大学 | Face gear scraping machining method |
| CN113127986A (en) * | 2021-03-30 | 2021-07-16 | 南京工业大学 | Method for analyzing influence of cutter error on tooth profile of machined gear |
| CN113419488A (en) * | 2021-06-08 | 2021-09-21 | 湖北工业大学 | Method for eliminating variable-displacement modification over-cutting of non-circular fan |
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| CN113419488B (en) * | 2021-06-08 | 2022-07-08 | 湖北工业大学 | Method for eliminating variable-displacement modification over-cutting of non-circular fan |
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Effective date of registration: 20220803 Address after: 210000 No. 18, Qing'an Road, Jiangbei new area, Nanjing, Jiangsu Patentee after: NANJING GONGDA CNC TECHNOLOGY Co.,Ltd. Address before: 210000, No. 5, new exemplary Road, Nanjing, Jiangsu Patentee before: Nanjing Tech University Patentee before: NANJING GONGDA CNC TECHNOLOGY Co.,Ltd. |