CN112729206B - Detection method for tooth profile of non-involute gear turning cutter - Google Patents
Detection method for tooth profile of non-involute gear turning cutter Download PDFInfo
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- CN112729206B CN112729206B CN202011521529.XA CN202011521529A CN112729206B CN 112729206 B CN112729206 B CN 112729206B CN 202011521529 A CN202011521529 A CN 202011521529A CN 112729206 B CN112729206 B CN 112729206B
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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Abstract
A non-involute form-turning cutter tooth profile detection method, adopt the gear measuring instrument, 1, obtain a set involute form-turning cutter tooth profile through the non-involute form-turning cutter tooth profile, and its set parameter; 2. obtaining a set error between the tooth profile of the non-involute tooth turning tool and the tooth profile of the set involute tooth turning tool through set parameters; 3. inputting a set parameter, and detecting the tooth profile of the non-involute tooth turning cutter to obtain the actual error between the tooth profile of the non-involute tooth turning cutter and the tooth profile of the set involute tooth turning cutter; 4. and comparing the actual error with the planned error to obtain a detection result of the non-involute gear cutting tool. Because the proposed parameters for the tooth profile of the proposed involute threading cutter are introduced, the detection of the non-involute threading cutter can be implemented by adopting the existing gear measuring instrument and inputting the corresponding proposed parameters through the conventional operation of the gear measuring instrument. The whole detection process is simple to operate, additional equipment or software development is not needed, and the problem of evaluating the non-involute gear turning tool is solved.
Description
Technical Field
The invention belongs to the technical field of cutter detection, and relates to a method for detecting the tooth profile of a non-involute threading cutter.
Background
With the application and popularization of the gear turning technology, non-involute tooth-shaped gear turning technologies such as harmonic waves and tooth-shaped chains are more and more favored by the gear processing industry. Corresponding non-involute tooth turning tools are also subject to increasingly higher detection requirements. The detection instruments commonly used at present include two types: one is a gear measuring instrument, and the other is a universal work display. But the tooth profile precision of the non-involute lathe tool cannot be effectively evaluated by the existing detection instrument and the detection method. The reason is as follows:
the gear measuring instrument is a special instrument for detecting involute tooth profile gears and cutters. The software matched with the gear measuring instrument can not judge the non-involute tooth profile.
And the industrial display is detected by using an optical projection technology. The non-involute pinion cutter can detect because the non-involute pinion cutter does not have a helix angle, and light can penetrate through the maximum profile of the tooth profile to compare the actual profile with the theoretical tooth profile. For the non-involute pinion cutter, the detection is performed by using a universal tool and display, so that the operation is simple, and the detection result is intuitive and understandable. But is not applicable to non-involute facing cutters. As shown in fig. 1 and 2, the non-involute cutting tool is generally bowl-shaped or taper shank shaped in configuration with a generally helical tooth flank and a leading edge facet perpendicular to the helix. Because non-involute tooth turning cutters generally have a large helix angle, light cannot penetrate the maximum profile of the tooth profile. The industrial display detection can only supplement light from the end face, and the detection is very difficult. And the projection method is more difficult to detect for the non-involute tooth cutting tool with larger modulus and larger rake angle. The main reason is that the blunt edge and the sharp edge of the non-involute gear turning cutter are not on the same section, so that the focal lengths of the tooth surfaces on two sides are not consistent. In the measuring process, the tooth profile of the cutter can be acquired only by respectively adjusting the focal lengths, and the operation difficulty is high. And the detection results of different operators are greatly different, and finally the detection results of the non-involute tooth turning tools are easily inconsistent.
Disclosure of Invention
In view of this, the invention provides a method for detecting the tooth profile of a non-involute tooth turning tool, which can detect the non-involute tooth turning tool by matching a gear measuring instrument with original measurement software, and solves the problem that the existing non-involute tooth turning tool cannot be effectively detected.
The technical scheme adopted by the invention is as follows: a non-involute tooth turning cutter tooth profile detection method adopts a gear measurement instrument to detect, and is characterized in that:
step 1, obtaining a similar tooth profile of a proposed involute threading tool through the known tooth profile parameters of a non-involute threading tool, wherein the proposed involute threading tool tooth profile has corresponding proposed parameters;
step 2, a series of set errors between the theoretical tooth profile of the non-involute tooth turning tool and the tooth profile of the set involute tooth turning tool can be obtained through the set parameters obtained in the step 1;
step 3, inputting the set parameters obtained in the step 1 into a gear measuring instrument, and detecting the actual tooth profile of the non-involute tooth turning tool through the gear measuring instrument to obtain a series of actual errors between the actual tooth profile of the non-involute tooth turning tool and the tooth profile of the set involute tooth turning tool;
and 4, comparing the actual error in the step 3 with the corresponding set error in the step 2 to finally obtain a detection result of the actual tooth profile of the non-involute gear turning tool.
Further, the step 1 of drawing up the drawing-up parameters of the involute tooth turning tool comprises drawing up a pressure angle alpha t Modulus M t Number of teeth Z, base diameter d b And addendum diameter d a 。
Further, the set pressure angle α t The determination method is specifically as follows:
in the formula: alpha is alpha y Is any round pressure angle on the involute; d y Is any circle diameter; s y Is any arc tooth thickness; s is the indexing circular arc tooth thickness; r is y Is any circle radius; r is the reference circle radius; theta is a reference circle groove width half angle;
determination of alpha t Then, iterative computation is required, at α t Calculating the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter, comparing the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter with the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter, and when the tooth thickness difference is less than 0.01mm, considering the alpha t A pressure angle is drawn up;
the base diameter d b ＝M t *Z*cosα t ；
The modulus
D f The diameter of a reference circle of the non-involute gear turning cutter; the tooth number Z is consistent with the tooth number of the tooth shape of the non-involute gear turning cutter;
diameter of the addendum circled a The diameter of the tooth crest circle of the tooth profile of the non-involute threading cutter is consistent.
Further, the calculation of α t When α is greater than t Is set to 0 deg., incrementing with an accuracy of 0.0001 deg. each time.
Further, the proposed error is Δ ρ, and the determination method is specifically as follows:
one point M ' (X ') is arbitrarily selected from the tooth profile of the non-involute tooth cutter ' yM ，Y′ yM ) Arbitrary circular pressure angle alpha corresponding to M' point y The involute development length of M 'is rho';
arbitrary circular pressure angle alpha corresponding to M' point y The corresponding point on the planned involute is M (X) M ，Y M ) The involute development length of M is rho;
as can be seen from the involute theorem, the set error Δ ρ is ρ — ρ':
in the formula: eta b The width of the tooth groove is base circle.
Further, a set error curve can be drawn by the set errors obtained in the step 2, an actual tooth profile curve can be drawn by the actual errors obtained in the step 3, and the set errors and the actual tooth profile curve can be visually compared.
The invention has the beneficial effects that: because the proposed parameters of the tooth profile of the proposed involute tooth turning tool are introduced, the detection of the non-involute tooth turning tool can be implemented by adopting the existing gear measuring instrument and inputting the corresponding proposed parameters through the conventional operation of the gear measuring instrument. The whole detection process is simple to operate, additional equipment or development software is not needed, and the problem of evaluation of the non-involute tooth turning tool is solved.
Drawings
FIG. 1 is a perspective view of a non-involute tooth cutting tool;
FIG. 2 is a side view of a non-involute tooth cutting tool;
FIG. 3 is a schematic diagram of a non-involute facing tool detected by a probe of a gear measuring instrument;
FIG. 4 is a schematic diagram of a non-involute tooth turning tool tooth profile that is intended to be an involute tooth profile;
FIG. 5 is a schematic diagram of a proposed involute and a proposed error curve;
FIG. 6 is a schematic diagram of a proposed error curve and an actual tooth profile curve.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.
The detection equipment adopted by the invention is the existing gear measuring instrument, and the measurement software is the common software in the existing gear measuring instrument.
When the non-involute gear turning tool is definitely machined, corresponding parameters are known, for example, a series of parameters such as a module, the number of teeth, the tooth thickness, the diameter of a tooth crest circle, the diameter of a reference circle and the like.
The core idea of the invention is that the non-involute tooth profile is formulated into an involute tooth profile, and then the formulated error between the non-involute tooth profile and the formulated involute tooth profile can be obtained theoretically through the formulated calculation of the involute tooth profile. The actual error between the non-involute tooth profile and the proposed involute tooth profile can be obtained through the actual measurement of the gear measuring instrument. The actual error of the corresponding position is compared with the set error, and the detection of the tooth profile of the non-involute gear-turning cutter on the gear measuring instrument can be realized. The set-up error is a series of data, and a set-up error curve can be drawn. And comparing the drawn error curve with the actual tooth profile curve of the non-involute gear-turning cutter obtained by actual measurement to obtain a more intuitive evaluation result.
For ease of understanding and description, the known parameters of the non-involute tooth turning tool referred to in this invention are illustrated:
M t -a modulus; z-number of teeth; d f -a reference circle diameter; d a -addendum circle diameter.
Wherein:
the detection instrument adopts a gear measuring instrument, and the specific detection method comprises the following steps:
step 1, obtaining a similar tooth profile of a proposed involute threading tool through the known tooth profile parameters of a non-involute threading tool, wherein the proposed involute threading tool tooth profile has corresponding proposed parameters. The proposed parameters include a modulus M consistent with the tooth profile parameters of the non-involute cutting tool t Number of teeth Z, base diameter d b And addendum diameter d a And also an important nominal pressure angle alpha t . Only the intended pressure angle alpha is determined t The subsequent proposed error can be calculated.
This is because the pressure angle α needs to be determined in order to obtain an involute tooth cutting edge profile close to a non-involute tooth cutting edge profile t And calculating the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter. Then comparing the calculated tooth top circular arc tooth thickness and any circular arc tooth thickness of the involute gear cutter with the known tooth top circular arc tooth thickness and any circular arc tooth thickness of the non-involute gear cutter, and when the tooth thickness difference is less than 0.01mm, considering that the pressure angle alpha is t I.e. the pressure angle of the involute tooth turning cutter.
Drawing up a pressure angle alpha t The determination method specifically comprises the following steps:
pressure angle alpha of any circle of involute gear y Comprises the following steps:
in the formula: d y For any circle diameter, the diameter of the corresponding circle is only needed to be replaced when the pressure angle of the addendum circle and the base circle needs to be calculated.
Arbitrary arc tooth thickness S y The calculation formula of (2) is as follows:
inv alpha is an involute function, and the calculation formula is as follows:
in the formula: r is y Is any circle radius; r is the reference circle radius, i.e.
Referring to the coordinate system in fig. 4, the calculation formula of the reference circular arc tooth thickness S is:
in the formula: theta is the half angle of the width of the reference circular groove,
D 0 the point corresponding to the diameter of the middle part of the tooth height of the involute tooth profile is drawn up, and the coordinate is D 0 (X y0 ，Y y0 )；
D 0 On the reference circle, the reference circle is,
the determination of the proposed pressure angle alpha is made by the equations (1-1), (1-2) and (1-3) t 。
Calculating a proposed pressure angle alpha t When it is neededPerforming iterative computation to obtain alpha t Setting the initial value of the angle alpha to be 0 degree, then gradually increasing with the precision of 0.0001 degree each time, then calculating the tooth top arc tooth thickness under the corresponding pressure angle and the arc tooth thickness value of any given circle, comparing the actual tooth top arc tooth thickness of the non-involute lathe tooth cutter with the non-involute arc tooth thickness of any given circle, and determining the alpha when the difference between the two is less than 0.01mm t The pressure angle is drawn up and then the next calculation is performed.
And 2, obtaining a series of determined errors of the tooth profile of the non-involute tooth turning tool relative to the tooth profile of the determined involute tooth turning tool through the determined parameters of the determined involute tooth turning tool obtained in the step 1.
The specific method for obtaining the proposed error is as follows:
the parameters obtained in step 1 include tooth number Z and modulus M t And drawing up the pressure angle alpha t . The tooth profile of the involute lathe tool can be determined through the set parameters. At this time, the base circle diameter d of the involute gear cutting tool is determined b ＝M t *Z*cosα t 。
As shown in the coordinate system of FIG. 4, let M '(X' yM ，Y′ yM ) The radius of the circle where M' is located is as follows:
when M 'is positioned on the involute tooth profile of the tooth turning cutter with the designed involute, the corresponding arbitrary circle pressure angle alpha of M' is determined y Comprises the following steps:
according to the basic theorem of the involute, the developed length rho 'of the involute of the point M' is as follows:
however, in practice, any circular pressure angle is α y The corresponding point on the proposed involute is M (X) M ，Y M ) The involute spread length ρ of the M point is:
in the formula: eta b The width of the tooth groove is base circle.
Also from the basic theorem of involutes, M' and M lie on the same straight line, i.e. both on the tangent of point M to the base circle, at the same base circle and pressure angle. Thus, the distance Δ ρ from point M' to point M can be expressed as
Δρ＝ρ-ρ′
This Δ ρ can be considered as the proposed error of point M. The proposed error Δ ρ is a theoretical value.
And 3, inputting the formulated parameters obtained in the step 1 into a gear measuring instrument, and detecting the non-involute tooth turning tool through the gear measuring instrument, as shown in fig. 3. The actual error between the detection position of the non-involute gear-turning cutter and the tooth profile of the planned involute can be obtained. The input proposed parameters include M t 、Z、α t 、d b 、d a 。
And 4, comparing the actual error in the step 3 with the planned error in the step 2 to finally obtain a detection result of the tooth shape of the non-involute turning tooth cutter.
As shown in fig. 5, a series of Δ ρ on the non-involute is calculated according to the above process, and a drawn error curve can be drawn. As shown in fig. 6, whether the tooth profile of the manufactured non-involute tooth turning tool is qualified or not is visually judged through a set-up error calculated theoretically, an actual error obtained through detection, and a set-up error curve and an actual tooth profile curve which are drawn, so that the detection problem of the non-involute tooth turning tool is solved.
Practical application shows that the tooth profile error of the non-involute threading tool detected by the method is consistent with the practical machining error of a workpiece, and the method is feasible and can guide production.
Claims (4)
1. A non-involute tooth turning cutter tooth profile detection method adopts a gear measuring instrument to detect, and is characterized in that:
step 1, obtaining a similar tooth profile of a proposed involute tooth turning tool through the known tooth profile parameters of a non-involute tooth turning tool, wherein the proposed involute tooth turning tool tooth profile has corresponding proposed parameters; the parameter comprises a pressure angle alpha t Modulus M t Number of teeth Z, base diameter d b And addendum diameter d a (ii) a Drawing up a pressure angle alpha t The determination method of (d) is specifically as follows:
in the formula: alpha (alpha) ("alpha") y Is any round pressure angle on the involute; d y Is any circle diameter; s y Is any arc tooth thickness; s is the indexing circular arc tooth thickness; r is y Is any circle radius; r is the reference circle radius; theta is a reference circle groove width half angle;
determining alpha t Then, iterative computation is required, at α t Calculating the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter, comparing the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter with the tooth top arc tooth thickness and any arc tooth thickness of the involute gear turning cutter, and when the tooth thickness difference is less than 0.01mm, considering the alpha t A pressure angle is drawn up;
the base circle diameter d b ＝M t *Z*cosα t ；
The modulus
D f The diameter of a reference circle of the non-involute gear turning cutter; the tooth number Z is consistent with the tooth number of the tooth shape of the non-involute gear turning cutter;
diameter d of the addendum circle a The diameter of the tooth crest circle of the tooth profile of the non-involute gear turning cutter is consistent;
step 2, a series of set errors between the theoretical tooth profile of the non-involute tooth turning tool and the tooth profile of the set involute tooth turning tool can be obtained through the set parameters obtained in the step 1;
step 3, inputting the set parameters obtained in the step 1 into a gear measuring instrument, and detecting the actual tooth profile of the non-involute tooth turning tool through the gear measuring instrument to obtain a series of actual errors between the actual tooth profile of the non-involute tooth turning tool and the tooth profile of the set involute tooth turning tool;
and 4, comparing the actual error in the step 3 with the corresponding set error in the step 2 to finally obtain a detection result of the actual tooth profile of the non-involute gear turning tool.
2. The method for detecting the tooth profile of the non-involute threading tool as claimed in claim 1, characterized in that: said calculation of alpha t When is, will alpha t Is set to 0 deg., increments with an accuracy of 0.0001 deg. each time.
3. The method for detecting the tooth profile of the non-involute turning gear cutter as claimed in claim 1, characterized in that: the proposed error is Δ ρ, and the determination method is as follows:
one point M ' (X ') is arbitrarily selected from the tooth profile of the non-involute tooth cutter ' yM ，Y′ yM ) Arbitrary circular pressure angle alpha corresponding to M' point y The involute development length of M 'is rho';
arbitrary circular pressure angle alpha corresponding to M' point y The corresponding point on the proposed involute is M (X) M ，Y M ) The involute development length of M is rho;
as can be seen from the involute theorem, the error Δ ρ ═ ρ — ρ':
in the formula: eta b The width of the tooth groove is the base circle.
4. The method for detecting the tooth profile of the non-involute threading tool as claimed in claim 1, characterized in that: a set error curve can be drawn by the set errors obtained in the step 2, an actual tooth profile curve can be drawn by the set errors obtained in the step 3, and the set errors and the actual tooth profile curve can be visually compared.
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| CN113819874B (en) * | 2021-09-01 | 2024-04-02 | 宜昌长机科技有限责任公司 | Method for checking speed ratio and speed ratio crowned tooth sector machining precision |
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| GB160447A (en) * | 1920-03-13 | 1921-12-08 | Vickers Electrical Co Ltd | Improvements in hobs for cutting gear teeth |
| US5271289A (en) * | 1992-12-16 | 1993-12-21 | Baxter Jr Meriwether L | Non-involute gear |
| KR100458161B1 (en) * | 2001-12-18 | 2004-11-26 | 학교법인 포항공과대학교 | Method for measuring shape error of spiral bevel gear |
| JP3774740B2 (en) * | 2002-09-05 | 2006-05-17 | 大阪精密機械株式会社 | Tooth profile measuring machine verification method |
| CN101391324B (en) * | 2008-10-30 | 2011-01-26 | 吉林大学 | Spherical involute spiral Archimedes spiral bevel gear cutting method and machine tool |
| CN102184301A (en) * | 2011-05-24 | 2011-09-14 | 上海理工大学 | Virtual detection method for tooth error of involute bevel gear model |
| DE102012221034A1 (en) * | 2012-11-19 | 2014-05-22 | Zf Friedrichshafen Ag | Method for automatic measurement and evaluation of non-involute tooth profiles of gear wheel, involves comparing quasi-involute tooth profile with approximate involute tooth profile for evaluation of non-involute tooth profile |
| CN104063605A (en) * | 2014-06-30 | 2014-09-24 | 西安北方光电科技防务有限公司 | Method for checking gear involute tooth profile error |
| CN104896061B (en) * | 2015-06-08 | 2017-05-24 | 中车戚墅堰机车车辆工艺研究所有限公司 | Non-full-symmetry involute gear and machining method thereof |
| CN111981951B (en) * | 2020-08-31 | 2021-11-02 | 重庆青山工业有限责任公司 | Method for measuring gear parameters of involute cylindrical gear |
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