CN107704429B - Method for calculating length of convex angle of double-contact gear hob - Google Patents
Method for calculating length of convex angle of double-contact gear hob Download PDFInfo
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- CN107704429B CN107704429B CN201710962286.5A CN201710962286A CN107704429B CN 107704429 B CN107704429 B CN 107704429B CN 201710962286 A CN201710962286 A CN 201710962286A CN 107704429 B CN107704429 B CN 107704429B
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- G—PHYSICS
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
Abstract
The invention discloses a method for calculating the length of a convex angle of a double-contact gear hob, which comprises the following steps: determining the original tooth profile of the hob teeth, obtaining related parameters of the original tooth profile according to the requirements of the double-contact gear to be processed, and drawing the original tooth profile according to the related parameters of the original tooth profile; determining the tooth shape of the hob teeth of the removed hob, horizontally removing the original convex angle arc line outwards by a displacement amount T to obtain a removed convex angle arc line, making an inclined tangent line of the removed convex angle intersect with the original tooth shape line and tangent with an extension line of the removed convex angle arc line, and making an included angle between the inclined tangent line of the removed convex angle and the vertical direction; the shift-out lobe length is determined. By adopting the method for calculating the length of the convex angle of the double-contact gear hob, the length of the convex angle of the hob tooth can be quickly obtained, the calculation is simple and convenient, the precision is high, the reasonable design and selection of the gear hob are facilitated, and the problem of interference between a transition curve and an involute when the double-contact gear is in rotating engagement is effectively solved.
Description
Technical Field
The invention relates to a method for calculating the hobbing tooth shape of a convex angle type hobbing cutter, in particular to a method for calculating the length of a convex angle of a special hobbing cutter for a double-contact gear.
Background
The traditional cylindrical gear is in pure involute mesh, and the cylindrical gear with the pure involute tooth surface has the advantages of simple structure and easiness in processing, and is widely applied to mechanical transmission. The cylindrical gear with a pure involute tooth surface has no over-high requirement on the precision of the tooth form transition curve part; the double-contact gear is a gear with tooth surfaces provided with double-position meshing of an involute and a transition curve, the tooth surfaces have good fatigue strength and bending resistance strength, low noise during meshing, high strength and long service life, but the tooth surfaces formed by the involute and the transition curve have interference of the transition curve and the involute during gear rotating meshing, so that the double-contact gear tooth transition curve has high requirements on the precision.
Disclosure of Invention
The invention aims to provide a method for calculating the length of a convex angle of a double-contact tooth hobbing cutter, which aims to solve the problems in the background technology.
In order to achieve the purpose, the invention provides a method for calculating the length of a convex angle of a double-contact gear hob, which comprises the following steps:
s1, determining the original tooth profile of the hob teeth:
obtaining related parameters of an original tooth profile according to the requirements of a double-contact gear to be processed: the fillet radius R1 of the original convex angle arc line MQ, the end face pressure angle alpha of the original tooth profile line MS and the cutter tooth thickness Ss; drawing an original tooth profile according to the related parameters of the original tooth profile, wherein the original convex arc line MQ is tangent to the original tooth profile line MS at a point M, and the central point of the original convex arc line MQ is a point O;
s2, determining the tooth profile of the hob teeth after removal:
horizontally moving the original convex angle arc line MQ outwards by a displacement T to obtain a moved convex angle arc line M 'P and a central point O' point; making a shifting-out convex angle inclined tangent line AB and the original tooth profile line MS to intersect at a point A, and making the shifting-out convex angle inclined tangent line AB and an extension line of the shifting-out convex angle circular arc line M' P to be tangent at a point B, wherein an included angle between the shifting-out convex angle inclined tangent line AB and the vertical direction is beta;
s3, calculating the length h of the convex angle of the hob teeth after the hob teeth are removed:
the point crossing O and the point crossing O 'are taken as a line segment OO' and are extended to intersect with the inclined tangent AB of the shifting-out convex angle, the perpendicular line from the point crossing M to the extension line of the line segment OO 'is intersected with the point D and is extended to intersect with the plane where the point A is located at the point G, the perpendicular line from the point crossing M' to the extension line of the line segment OO 'is intersected with the point H and is extended to intersect with the plane where the point A is located at the point F, and the perpendicular line from the point B to the extension line of the line segment OO' is intersected with the point C and is extended to intersect with the plane where the point A is located at; and calculating the vertical distance from the tooth top of the hob teeth to the horizontal plane where the point A is located to obtain the length h of the convex angle of the removed hob teeth.
Preferably, in step S3:
(1) in the case of. DELTA.BCO',
d1＝R1cosβ 1)，
d2＝R1sinβ 2)，
wherein d1 is the length of side CO', d2 is the length of side BC;
(2) in Δ MDO and Δ M 'HO', Δ MDO ≡ Δ M 'HO', so that:
d3＝d4＝R1cosα 3)，
d5＝d6＝R1sinα 4)，
wherein d3 is the length of side DO, d4 is the length of side HO ', d5 is the length of side MD, d6 is the length of M' H;
(3) in Δ BAE,. DELTA.M' AF and. DELTA.MAG,
d7＝d6-d2+h1 5)，
d8＝(h1tgβ+T+d1-d4)/tgα 6)，
the following formula 1) to formula 6) are solved simultaneously:
d7＝R1sinα-R1sinβ+h1 7)，
d8＝(h1tgβ+T+R1cosβ-R1cosα)/tgα 8)，
the length of the side M' F is equal to that of the side MG, and is obtained by the simultaneous solution of the equations 7) and 8):
h1＝{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 9)，
wherein h1 is the length of side BE, d7 is the length of side M' F, and d8 is the length of side MG;
(5)、h＝R1+h1-d4 10)；
the following equations 3), 9), and 10) are solved simultaneously:
h＝R1(1-sinβ)+{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 11)。
compared with the prior art, the invention has the following beneficial effects:
the invention discloses a method for calculating the length of a convex angle of a double-contact gear hob, which comprises the following steps: determining the original tooth profile of the hob teeth, obtaining related parameters of the original tooth profile according to the requirements of the double-contact gear to be processed, and drawing the original tooth profile according to the related parameters of the original tooth profile; determining the tooth shape of the hob teeth of the removed hob, horizontally removing the original convex angle arc line outwards by a displacement amount T to obtain a removed convex angle arc line, making an inclined tangent line of the removed convex angle intersect with the original tooth shape line and tangent with an extension line of the removed convex angle arc line, and making an included angle between the inclined tangent line of the removed convex angle and the vertical direction; the shift-out lobe length is determined. By adopting the method for calculating the length of the convex angle of the double-contact gear hob, the length of the convex angle of the hob tooth can be quickly obtained, the calculation is simple and convenient, the precision is high, the reasonable design and selection of the gear hob are facilitated, and the problem of interference between a transition curve and an involute when the double-contact gear is in rotating engagement is effectively solved.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of the original tooth profile structure of a double-contact gear hob tooth of the present invention (before the original convex angle arc line MQ is not removed);
FIG. 2 is a schematic view of the tooth profile structure of a hob tooth after the double contact gear of the present invention is removed (after the original convex angle arc line MQ is removed);
FIG. 3 is an enlarged partial view of the tooth profile of the hob teeth of FIG. 2 after removal.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Referring to fig. 1 to 3, a method for calculating the lobe length of a double-contact gear hob includes the following steps:
s1, determining the original tooth profile of the hob teeth: the designer obtains relevant parameters of the original tooth profile according to experience and the requirement of the double-contact gear to be processed: the fillet radius R1 of the original convex angle arc line MQ, the end face pressure angle alpha of the original tooth profile line MS and the cutter tooth thickness Ss; and drawing an original tooth profile according to the related parameters of the original tooth profile, wherein the original convex arc line MQ is tangent to the original tooth profile line MS at the point M, and the central point of the original convex arc line MQ is the point O.
S2, determining the tooth profile of the hob teeth after removal: horizontally moving the original convex angle arc line MQ outwards by the displacement T to obtain a moved convex angle arc line M 'P and a central point O'; and making a shifting-out convex angle inclined tangent line AB and an original tooth profile line MS to intersect at a point A, and making an extension line of a shifting-out convex angle circular arc line M' P to be tangent at a point B, wherein an included angle between the shifting-out convex angle inclined tangent line AB and the vertical direction is beta, and the shifting-out displacement amount T and the inclination angle beta of the shifting-out convex angle inclined tangent line AB are selected by a designer according to experience.
S3, calculating the length h of the convex angle of the hob teeth after the hob teeth are removed: the point crossing O and the point crossing O 'are taken as a line segment OO' and are extended to intersect with the inclined tangent AB of the shifting-out convex angle, the perpendicular line from the point crossing M to the extension line of the line segment OO 'is intersected with the point D and is extended to be intersected with the plane where the point A is located at the point G, the perpendicular line from the point crossing M' to the extension line of the line segment OO 'is intersected with the point H and is extended to be intersected with the plane where the point A is located at the point F, and the perpendicular line from the point B to the extension line of the line segment OO' is intersected with the point C and is extended to be intersected with the plane where the point; and calculating the vertical distance from the tooth top of the hob teeth to the horizontal plane where the point A is located to obtain the length h of the convex angle of the removed hob teeth.
In a specific embodiment, the specific steps for calculating the lobe length h of the hob after the step S3 is removed are as follows:
(1) in the case of. DELTA.BCO',
d1＝R1cosβ 1)，
d2＝R1sinβ 2)，
wherein d1 is the length of side CO', d2 is the length of side BC;
(2) in Δ MDO and Δ M 'HO', Δ MDO ≡ Δ M 'HO', so that:
d3＝d4＝R1cosα 3)，
d5＝d6＝R1sinα 4)，
wherein d3 is the length of side DO, d4 is the length of side HO ', d5 is the length of side MD, d6 is the length of M' H;
(3) in Δ BAE,. DELTA.M' AF and. DELTA.MAG,
d7＝d6-d2+h1 5)，
d8＝(h1tgβ+T+d1-d4)/tgα 6)，
the following formula 1) to formula 6) are solved simultaneously:
d7＝R1sinα-R1sinβ+h1 7)，
d8＝(h1tgβ+T+R1cosβ-R1cosα)/tgα 8)，
the length of the side M' F is equal to that of the side MG, and is obtained by the simultaneous solution of the equations 7) and 8):
h1＝{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 9)，
wherein h1 is the length of side BE, d7 is the length of side M' F, and d8 is the length of side MG;
(5)、h＝R1+h1-d4 10)；
the following equations 3), 9), and 10) are solved simultaneously:
h＝R1(1-sinβ)+{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 11)。
from expression 11), it can be known that the lobe length h of the hob after being removed can be quickly calculated only according to the fillet radius R1 of the original lobe of the hob teeth, the end face pressure angle α of the original tooth profile line, the inclination angle of the inclined tangent of the removed lobe and the outward horizontal removal displacement T of the original lobe arc line. The double-contact gear hob designed by the calculation method is simple and convenient to calculate, high in precision and convenient to operate.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A method for calculating the length of a convex angle of a double-contact gear hob is characterized by comprising the following steps:
s1, determining the original tooth profile of the hob teeth:
obtaining related parameters of an original tooth profile according to the requirements of a double-contact gear to be processed: the fillet radius R1 of the original convex angle arc line MQ, the end face pressure angle alpha of the original tooth profile line MS and the cutter tooth thickness Ss; drawing an original tooth profile according to the related parameters of the original tooth profile, wherein the original convex arc line MQ is tangent to the original tooth profile line MS at a point M, and the central point of the original convex arc line MQ is a point O;
s2, determining the tooth profile of the hob teeth after removal:
horizontally moving the original convex angle arc line MQ outwards by a displacement T to obtain a moved convex angle arc line M 'P and a central point O' point; making a shifting-out convex angle inclined tangent line AB and the original tooth profile line MS to intersect at a point A, and making the shifting-out convex angle inclined tangent line AB and an extension line of the shifting-out convex angle circular arc line M' P to be tangent at a point B, wherein an included angle between the shifting-out convex angle inclined tangent line AB and the vertical direction is beta;
s3, calculating the length h of the convex angle of the hob teeth after the hob teeth are removed:
the point crossing O and the point crossing O 'are taken as a line segment OO' and are extended to intersect with the inclined tangent AB of the shifting-out convex angle, the perpendicular line from the point crossing M to the extension line of the line segment OO 'is intersected with the point D and is extended to intersect with the plane where the point A is located at the point G, the perpendicular line from the point crossing M' to the extension line of the line segment OO 'is intersected with the point H and is extended to intersect with the plane where the point A is located at the point F, and the perpendicular line from the point B to the extension line of the line segment OO' is intersected with the point C and is extended to intersect with the plane where the point A is located at; and calculating the vertical distance from the tooth top of the hob cutter tooth to the horizontal plane where the point A is located to obtain the lobe length h of the removed hob cutter tooth, wherein the lobe length h is R1(1-sin beta) + { T + R1[ (cos beta-cos alpha) -tg alpha (sin alpha-sin beta) ] }/(tg alpha-tg beta).
2. The method for calculating the lobe length of a double contact gear hob according to claim 1, wherein in step S3:
(1) in the case of. DELTA.BCO',
d1＝R1cosβ 1)，
d2＝R1sinβ 2)，
wherein d1 is the length of side CO', d2 is the length of side BC;
(2) in Δ MDO and Δ M 'HO', Δ MDO ≡ Δ M 'HO', so that:
d3＝d4＝R1cosα 3)，
d5＝d6＝R1sinα 4)，
wherein d3 is the length of side DO, d4 is the length of side HO ', d5 is the length of side MD, d6 is the length of M' H;
(3) in Δ BAE,. DELTA.M' AF and. DELTA.MAG,
d7＝d6-d2+h1 5)，
d8＝(h1tgβ+T+d1-d4)/tgα 6)，
the following formula 1) to formula 6) are solved simultaneously:
d7＝R1sinα-R1sinβ+h1 7)，
d8＝(h1tgβ+T+R1cosβ-R1cosα)/tgα 8)，
the length of the side M' F is equal to that of the side MG, and is obtained by the simultaneous solution of the equations 7) and 8):
h1＝{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 9)，
wherein h1 is the length of side BE, d7 is the length of side M' F, and d8 is the length of side MG;
(5)、h＝R1+h1-d4 10)；
the following equations 3), 9), and 10) are solved simultaneously:
h＝R1(1-sinβ)+{T+R1[(cosβ-cosα)-tgα(sinα-sinβ)]}/(tgα-tgβ) 11)。
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20050006165A (en) * | 2002-04-22 | 2005-01-15 | 제네시스 파트너스 엘.피. | Gear tooth profile |
| CN102672284A (en) * | 2012-06-01 | 2012-09-19 | 株洲齿轮有限责任公司 | Double contact gear hobbing cutter |
| CN104889505A (en) * | 2015-06-08 | 2015-09-09 | 南车戚墅堰机车车辆工艺研究所有限公司 | Asymmetrical hob and design method thereof |
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2017
- 2017-10-16 CN CN201710962286.5A patent/CN107704429B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20050006165A (en) * | 2002-04-22 | 2005-01-15 | 제네시스 파트너스 엘.피. | Gear tooth profile |
| CN102672284A (en) * | 2012-06-01 | 2012-09-19 | 株洲齿轮有限责任公司 | Double contact gear hobbing cutter |
| CN104889505A (en) * | 2015-06-08 | 2015-09-09 | 南车戚墅堰机车车辆工艺研究所有限公司 | Asymmetrical hob and design method thereof |
Non-Patent Citations (2)
| Title |
|---|
| 磨前齿轮滚刀齿形优化设计;潘起;《中国优秀硕士学位论文全文数据库》;20080315(第3期);第B022-162页 * |
| 齿轮磨前滚刀的齿形研究;梁嫣蕊;《机械工程与自动化》;20040430(第2期);第33-36页 * |
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