CN113510616B - Method for dressing grinding wheel formed by cycloid wheel - Google Patents
Method for dressing grinding wheel formed by cycloid wheel Download PDFInfo
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- CN113510616B CN113510616B CN202110485235.4A CN202110485235A CN113510616B CN 113510616 B CN113510616 B CN 113510616B CN 202110485235 A CN202110485235 A CN 202110485235A CN 113510616 B CN113510616 B CN 113510616B
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- 238000000034 method Methods 0.000 title claims abstract description 26
- 229910003460 diamond Inorganic materials 0.000 claims abstract description 40
- 239000010432 diamond Substances 0.000 claims abstract description 40
- -1 hydrogen Chemical class 0.000 claims description 4
- 239000001257 hydrogen Substances 0.000 claims description 4
- 125000000217 alkyl group Chemical group 0.000 claims description 3
- 238000009966 trimming Methods 0.000 abstract description 21
- 238000003754 machining Methods 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 4
- 230000004048 modification Effects 0.000 description 4
- 238000012986 modification Methods 0.000 description 4
- 239000003638 chemical reducing agent Substances 0.000 description 3
- 238000002679 ablation Methods 0.000 description 2
- 230000005540 biological transmission Effects 0.000 description 2
- PCTMTFRHKVHKIS-BMFZQQSSSA-N (1s,3r,4e,6e,8e,10e,12e,14e,16e,18s,19r,20r,21s,25r,27r,30r,31r,33s,35r,37s,38r)-3-[(2r,3s,4s,5s,6r)-4-amino-3,5-dihydroxy-6-methyloxan-2-yl]oxy-19,25,27,30,31,33,35,37-octahydroxy-18,20,21-trimethyl-23-oxo-22,39-dioxabicyclo[33.3.1]nonatriaconta-4,6,8,10 Chemical compound C1C=C2C[C@@H](OS(O)(=O)=O)CC[C@]2(C)[C@@H]2[C@@H]1[C@@H]1CC[C@H]([C@H](C)CCCC(C)C)[C@@]1(C)CC2.O[C@H]1[C@@H](N)[C@H](O)[C@@H](C)O[C@H]1O[C@H]1/C=C/C=C/C=C/C=C/C=C/C=C/C=C/[C@H](C)[C@@H](O)[C@@H](C)[C@H](C)OC(=O)C[C@H](O)C[C@H](O)CC[C@@H](O)[C@H](O)C[C@H](O)C[C@](O)(C[C@H](O)[C@H]2C(O)=O)O[C@H]2C1 PCTMTFRHKVHKIS-BMFZQQSSSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 238000007493 shaping process Methods 0.000 description 1
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B53/00—Devices or means for dressing or conditioning abrasive surfaces
- B24B53/06—Devices or means for dressing or conditioning abrasive surfaces of profiled abrasive wheels
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
Abstract
The invention relates to a method for trimming a grinding wheel formed by a cycloid wheel, belonging to the technical field of processing of cycloid wheels. The trimming method comprises the following steps: acquiring profile curves before and after the grinding wheel is dressed and the grinding amount in unit time; calculating the projection distance corresponding to each interpolation point; the interpolation points are each point on a contour curve after the grinding wheel is dressed, and the projection distance is the projection distance of the connecting line of each interpolation point and the corresponding intersection point in the normal vector direction of the interpolation points; the intersection point is the intersection point of the diamond wheel and the contour curve before finishing; and obtaining the interpolation speed of each interpolation point according to the projection distance corresponding to each interpolation point and the grinding amount in unit time. The invention reasonably distributes the interpolation speed of each interpolation point based on the idea that the grinding wheel dressing amount in unit time is the same, so that the output power and dressing force of the diamond wheel in the whole grinding wheel dressing process are kept relatively stable, the instantaneous impact of the diamond wheel on the grinding wheel in the dressing process is reduced, and the dressing precision is improved.
Description
Technical Field
The invention relates to a method for trimming a grinding wheel formed by a cycloid wheel, belonging to the technical field of processing of cycloid wheels.
Background
The RV reducer is widely applied to industries such as industrial robots, cranes and medical instruments as a precise transmission device. The key component of the RV reducer is a cycloidal gear pin wheel planetary gear train, and the precision of a cycloidal gear in the cycloidal gear pin wheel planetary gear train directly determines the transmission efficiency of the RV reducer.
At present, the cycloidal gear is processed mainly by a forming grinding method, namely, the axial truncation of a grinding wheel is trimmed into a specific shape to grind a gear tooth groove surface to be processed, and then the cycloidal gear is manufactured. However, the grinding wheel is worn during the machining process of the cycloid wheel, and the grinding wheel needs to be dressed.
The traditional dressing method of the grinding wheel comprises the following steps: the diamond wheel finishes the grinding wheel at a constant speed according to a certain motion track. However, the constant speed dressing can cause large fluctuation of dressing force of the grinding wheel in the dressing process, and the dressing precision of the grinding wheel is influenced, and further the processing precision of the cycloid wheel is influenced.
Disclosure of Invention
The application aims to provide a method for trimming a cycloidal gear forming grinding wheel, which is used for solving the problems that the conventional trimming method has large trimming force fluctuation and influences the trimming precision.
In order to achieve the purpose, the application provides a technical scheme of a dressing method of a cycloidal gear forming grinding wheel, which comprises the following steps:
1) acquiring profile curves before and after the grinding wheel is dressed and the grinding amount in unit time;
2) calculating the projection distance corresponding to each interpolation point; the interpolation points are each point on a contour curve after the grinding wheel is dressed, and the projection distance is the projection distance of a connecting line of each interpolation point and the corresponding intersection point in the normal vector direction of the interpolation point; the intersection point is the intersection point of the diamond wheel and the contour curve before finishing;
3) and obtaining the interpolation speed of each interpolation point according to the projection distance corresponding to each interpolation point and the grinding amount in unit time.
The technical scheme of the method for trimming the grinding wheel formed by the cycloid wheel has the beneficial effects that: the interpolation speed under each interpolation point is stably and reversely deduced based on the trimming force: the method has the advantages that the dressing force is stable, namely the output power of the diamond wheel is stable, the output power is stable, namely the dressing amount of the grinding wheel in unit time is the same, therefore, based on the thought that the dressing amount of the grinding wheel in unit time is the same and the contour curves before and after the grinding wheel is dressed, the projection distance corresponding to each interpolation point is determined, the interpolation speed of each interpolation point is further obtained, the interpolation speed of each interpolation point is reasonably distributed, the output power and the dressing force of the diamond wheel in the whole grinding wheel dressing process are kept relatively stable, the instantaneous impact of the diamond wheel on the grinding wheel in the dressing process is reduced, the dressing precision is improved, and the machining precision of the cycloid wheel is further improved.
Further, the profile curve after the grinding wheel is dressed is as follows:
wherein X is the coordinate value of the profile curve after the grinding wheel is dressed on the X axis; y is a coordinate value of the profile curve after the grinding wheel is dressed on the Y axis; r iszIs a first constant and is equal to the radius of a pin wheel distribution circle of the cycloid wheel in numerical value;
is an angle parameter; a is the eccentricity; zbIs a second constant equal in value to the number of pinwheels of the cycloid wheel; r iszIs a third constant, numerically equal to the pinwheel radius of the cycloidal gear; k is1Is a short amplitude coefficient; z is a linear or branched memberaIs a fourth constant equal in value to the number of teeth of the cycloid gear.
Further, the trajectory curve of the diamond wheel center is as follows:
wherein x isfIs the track X-axis coordinate of the center of the diamond wheel; y isfIs the track Y-axis coordinate of the center of the diamond wheel; x is a coordinate value of the profile curve trimmed by the grinding wheel on the X axis; y is a coordinate value of the profile curve trimmed by the grinding wheel on the Y axis; r is0Is the radius of the diamond wheel; n isd1The unit normal vector of the profile curve trimmed by the grinding wheel in the X direction is shown; n isd2The unit normal vector of the profile curve of the grinding wheel after dressing in the Y direction is shown.
Further, the interpolation speed is calculated as follows:
wherein v is an interpolation speed; k is a proportionality coefficient; dsIs the trim amount per unit time; dhIs the projection distance.
Drawings
FIG. 1 is a schematic view of the dressing of a cycloidal gear form grinding wheel of the present invention;
FIG. 2 is a schematic area diagram of the trim amount of the present invention;
fig. 3 is a variation curve of interpolation point-interpolation speed according to the present invention.
Detailed Description
The embodiment of the dressing method of the cycloidal gear forming grinding wheel comprises the following steps:
the main idea of the invention is that based on the problem of trimming force fluctuation caused by constant-speed interpolation trimming, the invention stably and reversely deduces the interpolation speed under each interpolation point based on the trimming force: the dressing force is stable, namely the output power of the diamond wheel is stable, the output power is stable, namely the dressing amount of the grinding wheel in unit time is the same, therefore, based on the idea that the dressing amount of the grinding wheel in unit time is the same, the projection distance under each interpolation point is determined by determining the profile curve before and after dressing of the grinding wheel and the track curve of the center of the diamond wheel, the interpolation speed of each interpolation point is further determined according to the projection distance and the grinding amount in unit time, the interpolation speed when the diamond wheel dresses the grinding wheel is reasonably distributed, the stability of the dressing force is ensured, and the dressing precision of the grinding wheel is improved.
The interpolation speed calculation principle is as shown in fig. 1 and 2, when the diamond wheel moves along the track center, the edge of the diamond wheel moves from the position AD to the position BC, the trimming amount per unit time multiplied by the interpolation period is substantially the area ABCD, however, when the trimming amount per unit time and the interpolation period Δ T are small, the interpolation distance AB' in actual machining may be approximately equal to AB. The interpolation distance AB 'is a projection distance of the line segment AB in the ablation direction of the point a, and the interpolation distance AB'/the interpolation period Δ T is a distance actually moved by the diamond wheel in unit time, that is, an interpolation speed.
As shown in fig. 2, point B ' is a projection point of point B in the ablation direction along point a, and at this time, the actual interpolation distance is the mode length of vector AB ', and the dressing amount of the grinding wheel can also be approximately expressed as the area of quadrangle AB ' CD. Because AD and B ' C are in a translation relation, AB ' can be obtained to be approximately equal to FE, wherein point E is the intersection point of a normal vector of a point B ' and a line segment CD, point F is the intersection point of the normal vector of the point A and an extension line of the line segment CD, AF is the normal projection of the line segment AD on a point A of a tooth profile curve of the trimmed cycloid wheel, AB ' can be obtained to be approximately equal to DC, FD is equal to EC, therefore, the area of B ' EC is equal to the area of AFD, when an interpolation period is very small, the model length of the vector AB ' is approximately used for replacing an arc length AB, the area of an irregular quadrangle AB ' CD can be approximately equal to the area of a rectangle AB ' EF, and the amount of a rigid wheel trimming grinding wheel in each interpolation period can be approximately regarded as the area of the rectangle AB ' EF.
Therefore, after the grinding amount per unit time is determined, the projection distance of each interpolation point is calculated, and the interpolation speed at each interpolation point can be obtained. The interpolation points are each point on the trimmed contour curve, and the projection distance of each interpolation point is the projection distance of the connecting line of each interpolation point and the corresponding intersection point in the normal vector direction of the interpolation point; the intersection point is the intersection point of the diamond wheel and the contour curve before finishing.
Taking point a as an example, since the grinding amount per unit time is determined, the grinding amount per unit time is determined by multiplying the interpolation period, that is, the area of AB 'EF is determined, the intersection point of the diamond wheel and the contour curve before trimming is point D, the projection distance is AF, the length of AB' is equal to the area of AB 'EF divided by the line segment AF, and the interpolation speed of point a is obtained according to the interpolation distance AB' and the interpolation period Δ T. Due to the irregularity of the contour curve before the dressing of the grinding wheel, the projection distance of each interpolation point is different, and therefore, the interpolation speed of each interpolation point is different.
Regarding the position of the interpolation point, it is determined before calculation, and the interpolation point is about 400 to 500 points. The time period from one interpolation point (corresponding to point a) to the next interpolation point (corresponding to point B) is an interpolation period Δ T.
Specifically, the dressing method of the cycloidal gear forming grinding wheel comprises the following steps:
1) obtaining the profile curves before and after dressing of the grinding wheel and the grinding amount D per unit times。
The profile curve of the grinding wheel before dressing, namely the profile curve of the worn grinding wheel, is assumed to be a translation curve of the profile curve after dressing, and the translation distance is determined according to the grinding distance.
The grinding wheel is used for carrying out shaping grinding processing on the cycloidal gear during grinding, so that a profile curve after the grinding wheel is trimmed is the same as a tooth profile curve of the cycloidal gear, and the profile curve after the grinding wheel is trimmed is an equidistant curve of a track curve of the center of the diamond wheel; which may also be referred to as a translation curve, the distance of translation is d.
The expression of the profile curve after the grinding wheel is dressed is as follows:
wherein X is an X-axis coordinate value; y is a Y-axis coordinate value; r iszIs a first constant and is equal to the radius of a pin wheel distribution circle of the cycloid wheel in numerical value;
is an angle parameter; a is the eccentricity; zbThe number of the second constant is equal to the number of the pinwheels of the cycloid wheel; r is a radical of hydrogenzIs a third constant and is numerically equal to the radius of the pinwheel of the cycloid wheel; k1Is a short amplitude coefficient; zaIs a fourth constant, numerically equal to the number of teeth of the cycloid gears.
The pair of the profile curves after the grinding wheel is dressed
And (3) obtaining a unit normal vector of the trimmed contour curve by derivation:
wherein n isd1A unit normal vector of a profile curve trimmed by a grinding wheel in the X direction; n isd2A unit normal vector of a profile curve trimmed by a grinding wheel in the Y direction; d is a radical ofyDeriving a profile curve trimmed by a grinding wheel in the Y direction; d is a radical ofxThe derivative is obtained in the X direction for the profile curve after the grinding wheel is dressed.
And then obtaining the following track curve of the center of the diamond wheel:
wherein x isfIs the track X-axis coordinate of the center of the diamond wheel; y isfIs the track Y-axis coordinate of the center of the diamond wheel; x is a coordinate value of the profile curve trimmed by the grinding wheel on the X axis; y is a coordinate value of the profile curve trimmed by the grinding wheel on the Y axis; r is a radical of hydrogen0Is the radius of the diamond wheel; n is a radical of an alkyl radicald1A unit normal vector of a profile curve trimmed by a grinding wheel in the X direction; n isd2The unit normal vector is in the Y direction for the profile curve after the grinding wheel is dressed.
2) Calculating the projection distance d corresponding to each interpolation pointhThe interpolation points are each point on a contour curve after the grinding wheel is dressed, and the projection distance is the projection distance of the connecting line of each interpolation point and the corresponding intersection point in the normal vector direction of the interpolation point; the corresponding intersection point is the intersection point of the diamond wheel and the contour curve before finishing under each interpolation point.
Because the profile curve after the grinding wheel is dressed and the track curve of the diamond wheel are in a translation relationship, the interpolation points can be points on the profile curve after the grinding wheel is dressed and can also be points on the track curve of the diamond wheel.
The calculation process of the projection distance is described by taking the interpolation point A as an example:
the tooth profile curve of the cycloidal gear before trimming is a translation curve of the tooth profile curve of the cycloidal gear after trimming, and the translation distance is the trimming depth. According to the relationship between the profile curve of the rigid wheel and the profile curve of the cycloidal gear before and after trimming in the graph 1, the method comprises the following steps: and (3) the curve of the tooth profile of the cycloidal gear after the modification is tangent to the curve of the tooth profile of the cycloidal gear before the modification is intersected with the curve of the tooth profile of the cycloidal gear before the modification, and when a position point A is given, the coordinate of an intersection point D is calculated by utilizing the relation, wherein the point A represents any point on the curve of the tooth profile of the cycloidal gear after the modification.
Similarly, the coordinates of the intersection points corresponding to other interpolation points can be calculated according to a Newton iteration method.
The coordinates (x) at a given point A can be determined by Matlab software based on the above geometric relationshipa,ya) The coordinate (x) of the D point is obtained by time calculationd,yd) The available segment AD vector is:
the normal vector n of a point A on a profile curve after the grinding wheel is dressed is as follows:
the projection distance d of the line segment AD on the normal vector of the contour curve point A after the grinding wheel is dressedhComprises the following steps:
3) and obtaining the interpolation speed of each interpolation point according to the projection distance corresponding to each interpolation point and the grinding amount in unit time.
Grinding amount per unit time DsAfter obtaining, the grinding amount d of each interpolation period can be obtainedsIs ds＝DsX Δ T, setting the grinding amount d of the diamond wheel in an interpolation period from the interpolation point AsApproximately the area of the rectangle AB' EF, the length of the diamond wheel in an interpolation period is dl：
And d islD is satisfied depending on the interpolation period DeltaT and the interpolation speed vl＝△T×v；
Further obtain
It is deduced that,
k is a proportionality coefficient which is used for adjusting the size of an initial value in a diamond wheel speed change rule graph; d is a radical ofhAnd the curvature change rule of the trimmed profile curve.
Therefore, when DsAfter the interpolation speed of the point A is determined, the interpolation speed is derived according to the relation, and the dressing amount of the grinding wheel in one interpolation period from the point A can be a constant value. The change rule graph of the interpolation speed in the dressing process of the grinding wheel can be obtained, wherein the points on the tooth profile curve of the dressed cycloidal gear and the points on the track curve of the diamond wheel meet the corresponding relation, so that the distribution of the interpolation speed is realized, and the vibration in the machining process is further reduced. When given the proportionality coefficient K is 1 × 106Grinding amount per unit time Ds＝0.0001mm2Then, a graph of the variation law of interpolation speed of the diamond wheel as shown in FIG. 3 is obtained.
Based on the idea that the grinding amount in unit time is the same, the interpolation speed of each interpolation point is reasonably distributed, so that the output power and the dressing force of a diamond wheel in the whole dressing process of the grinding wheel are kept relatively stable, the instantaneous impact of the diamond wheel on the grinding wheel in the dressing process is reduced, the dressing precision is improved, and the machining precision of the cycloid wheel is further improved.
Claims (1)
1. A method for dressing a grinding wheel formed by a cycloid wheel is characterized by comprising the following steps:
1) acquiring profile curves before and after the grinding wheel is dressed and the grinding amount in unit time;
2) calculating the projection distance corresponding to each interpolation point; the interpolation points are each point on a contour curve after being dressed by the grinding wheel, and the projection distance is the projection distance of a connecting line of each interpolation point and the corresponding intersection point in the normal vector direction of the interpolation point; the intersection point is the intersection point of the diamond wheel and the contour curve before finishing;
3) obtaining the interpolation speed of each interpolation point according to the projection distance corresponding to each interpolation point and the grinding amount in unit time; the profile curve after the grinding wheel is dressed is as follows:
wherein, X is the coordinate value of the profile curve after the grinding wheel is dressed on the X axis; y is the coordinate value of the profile curve after the grinding wheel is dressed on the Y axis; r iszIs a first constant and is equal to the radius of a pin wheel distribution circle of the cycloid wheel in numerical value;
is an angle parameter; a is the eccentricity; zbThe number of the second constant is equal to the number of the pinwheels of the cycloid wheel; r is a radical of hydrogenzIs a third constant and is numerically equal to the radius of the pinwheel of the cycloid wheel; k1Is a short amplitude coefficient; z is a linear or branched memberaIs a fourth constant, numerically equal to the number of teeth of the cycloid gears;
the track curve of the center of the diamond wheel is as follows:
wherein x isfIs the track X-axis coordinate of the center of the diamond wheel; y isfIs the track Y-axis coordinate of the center of the diamond wheel; x is a coordinate value of the profile curve trimmed by the grinding wheel on the X axis; y is a coordinate value of the profile curve trimmed by the grinding wheel on the Y axis; r is a radical of hydrogen0Is the radius of the diamond wheel; n is a radical of an alkyl radicald1A unit normal vector of a profile curve trimmed by a grinding wheel in the X direction; n is a radical of an alkyl radicald2The unit normal vector of the profile curve trimmed by the grinding wheel in the Y direction is shown;
the interpolation speed is calculated as follows:
wherein v is an interpolation speed; k is a proportionality coefficient; dsIs the trim amount per unit time; dhIs the projected distance.
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| DE19940686A1 (en) * | 1999-08-27 | 2001-03-01 | Mikrosa Werkzeugmaschinen Gmbh | Method and device for CNC-controlled dressing of a regulating wheel of a grinding machine for a centerless grinding process on a workpiece, method for centerless grinding and a grinding machine |
| CN101767314B (en) * | 2010-01-28 | 2011-08-31 | 洛阳轴研科技股份有限公司 | Grinding wheel dressing method used for grinding processing of raceway of outer ring of bearing |
| CN101913115A (en) * | 2010-07-29 | 2010-12-15 | 南京钢铁股份有限公司 | Method for machining double circular caliber of roll collar of rolling mill |
| CN105234776A (en) * | 2015-09-02 | 2016-01-13 | 无锡市普森精密机床制造有限公司 | Method for machining rolling way of inner ring of bearing and convexity degree of roller |
| CN107081678B (en) * | 2017-07-04 | 2020-01-07 | 河南科技大学 | Method for dressing grinding wheel for forming and grinding cycloid wheel |
| CN109531425A (en) * | 2018-12-29 | 2019-03-29 | 厦门创云精智机械设备股份有限公司 | A kind of full-automatic abrasive wheel finishing machine and its finishing grinding wheel method |
| CN109968204B (en) * | 2019-03-21 | 2021-05-14 | 华南理工大学 | Numerical control grinding shape error self-adaptive compensation method for mutual abrasion of grinding wheel workpieces |
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Application publication date: 20211019 Assignee: Ruihong Machinery Processing Factory in Xigong District, Luoyang City Assignor: HENAN University OF SCIENCE AND TECHNOLOGY Contract record no.: X2024980002613 Denomination of invention: A Dressing Method for Cycloidal Wheel Forming Grinding Wheel Granted publication date: 20220722 License type: Exclusive License Record date: 20240312 |
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