EP1688202A1 - Meule pour détalonner un outil-pignon réaffûtable - Google Patents

Meule pour détalonner un outil-pignon réaffûtable Download PDF

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Publication number
EP1688202A1
EP1688202A1 EP06002184A EP06002184A EP1688202A1 EP 1688202 A1 EP1688202 A1 EP 1688202A1 EP 06002184 A EP06002184 A EP 06002184A EP 06002184 A EP06002184 A EP 06002184A EP 1688202 A1 EP1688202 A1 EP 1688202A1
Authority
EP
European Patent Office
Prior art keywords
type cutter
pinion type
shape profile
cutting edge
relief
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP06002184A
Other languages
German (de)
English (en)
Inventor
Hiroshi Harmonic Drive Systems Inc. Yamazaki
Yoshitaro Harmonic Drive Systems Inc. Yoshida
Yoshihide Harmonic Drive Systems Inc. KIYOSAWA
Satoshi Kishi
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harmonic Drive Systems Inc
Original Assignee
Harmonic Drive Systems Inc
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Filing date
Publication date
Application filed by Harmonic Drive Systems Inc filed Critical Harmonic Drive Systems Inc
Publication of EP1688202A1 publication Critical patent/EP1688202A1/fr
Ceased legal-status Critical Current

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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
    • B24B3/00—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools
    • B24B3/34—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools of turning or planing tools or tool bits, e.g. gear cutters

Definitions

  • the present invention relates to a grinding wheel for relief machining for a resharpenable pinion-type cutter having an arbitrary tooth profile for cutting the internal gear or the like of a wave gear device, and more particularly relates to method for designing the tooth shape profile of a grinding wheel for relief machining for a pinion-type cutter having a relief surface capable of reproducing a tooth shape profile required for the resultant gear even when pinion-type cutter is resharpened.
  • a gearing mechanism there is a wave gear mechanism known by the trade name "Harmonic Drive” owned by the present applicant, and the wave gear mechanism is comprised of three components: a rigid internal gear, a flexible external gear, and a wave generator, enabling a simple reduction gear mechanism with high reduction gear ratio to be realized.
  • involute gearings have been used in wave gear mechanisms, but currently non-involute, specially shaped gears are adopted in order to improve performance characteristics.
  • the pinion type cutter is generally used for the internal gear; however, when the pinion-type cutter is resharpened, a problem arises that a tooth shape profile required for a resultant gear cannot be reproduced.
  • An object of the present invention is to provide a grinding wheel for relief machining for a pinion-type cutter that can prevent generating tooth shape errors in an obtained gear by using the resharpened pinion type cutter.
  • the tooth shape of the pinion type cutter machined by the grinding wheel for relief machining designed in accordance with the present invention is a continuum of cutting edge shapes with different radii, capable of cutting a gear that has the required tooth shape profile.
  • the external peripheral relief surface can be a conical surface or a rotational surface.
  • the lateral relief surface can be a tapered helical surface.
  • Tooth shape profile of the pinion type cutter is defined as follows. Namely, in a coordinate system in which a pinion type cutter having a number of teeth zp is employed to cut and obtain an internal gear with a number of teeth z, an axially perpendicular tooth shape profile contour for the internal gear is given as a series of dispersive points, the given series of axially perpendicular cross-sectional tooth shape profile points for the internal gear is interpolated by the Akima method, and the axially perpendicular cross-sectional tooth shape profile for the internal gear is defined by the following formula, where t is a variable for expressing the profile,
  • the axially perpendicular cross-sectional tooth shape profile is defined by the following formula, in which the coordinate system has been transformed to a fixed coordinate system that rotates integrally with the pinion type cutter
  • the cutting edge shape profile of the pinion type cutter is determined by projecting the envelope onto the cone of the rake surface of the pinion type cutter.
  • the grinding wheel for relief machining for a pinion type cutter provided with such a profile in accordance with the present invention has a cutting edge shape profile defined as follows.
  • a coordinate system op-uvw of a pinion type cutter rotating around an axis w a stationary coordinate system o 0 - ⁇ 0 ⁇ 0 ⁇ 0 on the relief grinding wheel side, and a coordinate system o G - ⁇ that is fixed to the relief grinding wheel in which the axis ⁇ 0 and grinding wheel axis ⁇ form a setting angle ⁇ G .
  • the grinding wheel moves diagonally by an amount equal to stan ⁇ in the positive direction of the axis ⁇ 0 while moving by an amount of an "s" in the positive direction of the axis ⁇ 0 along the outside radial relief angle ⁇ of the pinion type cutter as the pinion type cutter rotates by an angle of ⁇ p .
  • the right-side relief surface of the cutting edge peak shape thus obtained is shaped as a tapered helical surface having a right-hand helix
  • the left-side relief surface is a tapered helical surface having a left-hand helix.
  • the generating line that connects the cutting edge tip points in the axially perpendicular cross-sections of the pinion type cutter forms a straight line along the peaks of the cone
  • the generating line that connects the pitch points of the pinion type cutter also forms a straight line along the peaks of the cone.
  • the helix angle ⁇ of the tapered helical surface at the radius of the pitch circle of the pinion type cutter is approximated by the following formula from the geometric relationship whereby the generating lines are projected on the axis-containing horizontal plane of the pinion type cutter, where r Pc is the radius of the pitch circle of the pinion type cutter, v c is the coordinate value of the cutting edge in the pitch circle, and ⁇ c is the relief angle ⁇ , reduced with r Pc , of the outside diameter.
  • the helix angle ⁇ of the tapered helical surface is determined in the following range.
  • the movement amount s is determined by the following expression, where r Pk is the outside radius of the pinion type cutter.
  • This profile is expressed by the following formula in the fixed coordinate system o G - ⁇ ⁇ ⁇ on the grinding wheel side in relief motion.
  • a relief surface can be machined with good precision after resharpening the pinion type cutter if a grinding wheel for relief machining designed in accordance with the present invention is used.
  • the cutting edge shape of a pinion type cutter is defined by a continuum of pinion type cutter cutting edge shapes with different radii that can correctly cut a cylindrical internal spur gear with a required tooth shape in order to provide the pinion type cutter with an optimum relief surface.
  • FIG. 1 is a perspective view showing the pinion type cutter
  • FIG. 2 is a schematic diagram showing the internal gear, which is the resultant gear after cutting by the pinion type cutter, and the cutting edge shape in three different axially perpendicular cross-sections of the pinion type cutter.
  • each of the cutting edge shapes in the respective axially perpendicular cross-sections is one that can correctly cut an internal gear 2 with the required tooth shape, and such cutting edge profiles appear as relief surfaces after resharpening.
  • the tooth shape of an internal gear which is a resultant gear after cutting by the pinion type cutter, is obtained from a rack tooth shape.
  • Designating the profile-expressing mediating variable as t, the rack tooth shape profile can be given by the following formula (tertiary equation of the Akima method).
  • Eq. (1•4-1) expresses a group of curves related to t and ⁇ , so the envelope of this group is the tooth shape profile of the intended internal gear.
  • the condition formula of the envelope is the following Jacobian matrix.
  • a cusp is a type of singular point of a function at which a slope of a tangent is undefined on the curve, so the validity limits of the tooth shape profile of a cylindrical internal spur gear can be known by identifying the undefined position. From this result, a cylindrical internal spur gear in which interference does not occur can be designed.
  • Eq. (1•4-1) that expresses the tooth shape profile of a cylindrical internal spur gear leads to a formula for determining the validity range.
  • the formula for the tangent to the gear tooth shape profile of the cylindrical internal spur gear can be written in the following manner from Eqs. (1•4-1) and (1•5-2).
  • the point at which the two are zero at the same time is an undefined point, and its presence shows that there is a point in which the tooth shape profile of the cylindrical internal spur gear is invalid.
  • Eq. (1• 7 ) for deriving U G and V G is the formula for determining the validity limits of the tooth shape profile of the cylindrical internal spur gear.
  • FIG. 3 Shown in FIG. 3 is a coordinate system for a theoretical analysis to determine the cutting edge shape of a pinion type cutter.
  • This diagram shows a coordinate system in which an internal gear with a number of teeth z is cut with a pinion type cutter that has a number of teeth zp.
  • the coordinate system o-xy is fixed to the internal gear and rotates at an angle ⁇ .
  • the coordinate system o P -u 0 v 0 is a stationary coordinate system on the pinion type cutter side, and the coordinate system Op-uv is fixed to the pinion type cutter that rotates at the angle ⁇ / i .
  • the series of tooth shape profile points in the axially perpendicular cross-section of a given internal gear is interpolated by the Akima method and is given by the following formula.
  • t is a profile-expressing variable.
  • Eq. (2) expresses a group of curves for which t and ⁇ are variables, and the envelope of this group of curves is the required cutting edge shape profile of the pinion type cutter.
  • a conditional formula for the envelope can be derived by computing the following Jacobian matrix for Eq. (2).
  • the cutting edge shape profile of a pinion type cutter calculated using the aforementioned theoretical formulae may have a cusp (singular point in which the tangent slope is undefined), and interference phenomenon may occur. In this case, the cutting edge shape profile of the pinion type cutter in not valid.
  • the following formulae can be derived from Eqs. (2) and (4) in order to verify the presence of a cusp.
  • a coordinate system O P -uvw of a pinion type cutter rotating around an axis w a stationary coordinate system O 0 - ⁇ 0 ⁇ 0 ⁇ 0 on the relief grinding wheel side, and a coordinate system O G - ⁇ that is fixed to the relief grinding wheel in which the axis ⁇ 0 and grinding wheel axis (form a setting angle ⁇ G , as shown in FIG. 4.
  • the grinding wheel moves diagonally by an amount equal to stan ⁇ in the positive direction of the axis ⁇ 0 while moving in the form of an "s" in the positive direction of the axis ⁇ 0 along the outside radial relief angle ⁇ of the pinion type cutter as the pinion type cutter rotates by an angle of ⁇ P .
  • the right-side relief surface of the cutting edge peak shape thus obtained is shaped as a tapered helical surface having a right-hand helix
  • the left-side relief surface is a tapered helical surface having a left-hand helix.
  • the generating line that connects the cutting edge tip points in the axially perpendicular cross-sections of the pinion type cutter forms a straight line along the peaks of the cone.
  • the generating line that connects the pitch points of the pinion type cutter also forms a straight line along the peaks of the cone.
  • the helix angle ⁇ of the tapered helical surface at the radius of the pitch circle of the pinion type cutter is approximated by the following formula from the geometric relationship whereby the generating lines are projected on the axis-containing horizontal plane of the pinion type cutter, as shown in FIG. 5, where r Pc is the radius of the pitch circle of the pinion type cutter, v c is the coordinate value of the cutting edge in the pitch circle, and ⁇ c is the relief angle ⁇ , reduced with r Pc , of the outside diameter.
  • the helix angle ⁇ of the tapered helical surface is determined in the following range with consideration given to the helix angle ⁇ c thus obtained and the characteristics of the tooth shape.
  • This profile is expressed by the following formula in the fixed coordinate system o G - ⁇ ⁇ ⁇ on the grinding wheel side in relief motion.
  • an arbitrary radius of the relief grinding wheel is designated as p
  • the cutting edge shape profile of the grinding wheel in axial cross-section is expressed by the following formula.
  • Eq. (10) expresses a group of curves in which t and ⁇ P are variables, and the cutting edge shape profile of the relief grinding wheel in axial cross-section can be obtained as the envelope of this group of curves.
  • the condition formula of the envelope is obtained by calculating the following Jacobian matrix with respect to Eq. (10).
  • the pinion type cutter of the present invention in addition to being applicable to internal gears, may also be applied to the cutting of cylindrical gears, internal and external bevel gears, face gears, circular and non-circular gears of worm gears, and other gears.
  • the grinding wheel can be fed linearly, or the shafts of the grinding wheel and pinion type cutter can be fed in threadable fashion, when a relief surface is formed on the pinion type cutter.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Polishing Bodies And Polishing Tools (AREA)
  • Gear Processing (AREA)
EP06002184A 2005-02-03 2006-02-02 Meule pour détalonner un outil-pignon réaffûtable Ceased EP1688202A1 (fr)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP2005027173A JP4688510B2 (ja) 2005-02-03 2005-02-03 研ぎ直し可能な任意歯形を有するピニオンカッタの二番面加工用砥石の刃形輪郭設計方法

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EP1688202A1 true EP1688202A1 (fr) 2006-08-09

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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015038334A2 (fr) * 2013-09-12 2015-03-19 The Gleason Works Engrenage intérieur conique
CN108349029A (zh) * 2016-03-25 2018-07-31 三菱重工工作机械株式会社 车齿加工用刀具以及使用其的齿轮制造方法
CN108406621A (zh) * 2017-02-10 2018-08-17 蓝思科技（长沙）有限公司 烧结砂轮棒及其使用方法
CN111638682A (zh) * 2020-05-26 2020-09-08 四川新迎顺信息技术股份有限公司 一种使用磨损砂轮磨削周齿螺旋刃后刀面的补偿方法
CN112123038A (zh) * 2020-08-03 2020-12-25 西安交通大学 一种插齿刀后刀面双参数单面成形磨削方法
CN113124811A (zh) * 2021-04-21 2021-07-16 泸州高新中航传动转向系统有限公司 一种剃齿刀修磨参数精确控制方法
CN113486476A (zh) * 2021-08-11 2021-10-08 重庆大学 一种磨削双圆弧谐波减速器刚轮插刀的砂轮齿廓设计方法

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5880040B2 (ja) * 2011-12-28 2016-03-08 住友電気工業株式会社 切削刃の刃形状の設計方法、設計プログラム、設計装置、及び、切削刃の製造方法
HUP1900107A1 (hu) * 2019-04-02 2020-10-28 Maform Kft Kétlépcsõs gyorsító hajtómû-elrendezés, valamint hajtáslánc órához
CN115507769B (zh) * 2022-05-24 2023-09-22 北京工业大学 融合视觉和光学原理的齿轮快速测量方法
CN114912228B (zh) * 2022-07-12 2023-03-24 广东鼎泰高科技术股份有限公司 开槽砂轮廓形设计方法、装置及计算机可读存储介质

Citations (6)

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Publication number Priority date Publication date Assignee Title
US1790609A (en) * 1931-01-27 Geab cutteb
US2801459A (en) * 1954-03-15 1957-08-06 Fellows Gear Shaper Co Gear shaper cutter
DE1527110A1 (de) * 1963-11-13 1969-09-04 Hurth Masch Zahnrad Carl Schabzahnrad mit schraeg verlaufenden Schneidnuten zur Verwendung zum Balligschaben
US3720989A (en) * 1970-05-25 1973-03-20 Renault Gear cutting methods
EP0037909A2 (fr) * 1980-04-10 1981-10-21 Maag-Zahnräder und -Maschinen Aktiengesellschaft Outil pignon hélicoidal à affûtage en escalier
EP1504838A1 (fr) * 2003-08-04 2005-02-09 Harmonic Drive Systems Inc. Outil-pignon susceptible d'être affûté avec une forme de dents arbitraire

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1790609A (en) * 1931-01-27 Geab cutteb
US2801459A (en) * 1954-03-15 1957-08-06 Fellows Gear Shaper Co Gear shaper cutter
DE1527110A1 (de) * 1963-11-13 1969-09-04 Hurth Masch Zahnrad Carl Schabzahnrad mit schraeg verlaufenden Schneidnuten zur Verwendung zum Balligschaben
US3720989A (en) * 1970-05-25 1973-03-20 Renault Gear cutting methods
EP0037909A2 (fr) * 1980-04-10 1981-10-21 Maag-Zahnräder und -Maschinen Aktiengesellschaft Outil pignon hélicoidal à affûtage en escalier
EP1504838A1 (fr) * 2003-08-04 2005-02-09 Harmonic Drive Systems Inc. Outil-pignon susceptible d'être affûté avec une forme de dents arbitraire

Cited By (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105531058B (zh) * 2013-09-12 2019-01-08 格里森工场 机加工内锥齿轮的方法
WO2015038334A3 (fr) * 2013-09-12 2015-05-07 The Gleason Works Engrenage intérieur conique
CN105531058A (zh) * 2013-09-12 2016-04-27 格里森工场 机加工内锥齿轮的方法
US10016825B2 (en) 2013-09-12 2018-07-10 The Gleason Works Internal bevel gear
WO2015038334A2 (fr) * 2013-09-12 2015-03-19 The Gleason Works Engrenage intérieur conique
US10751818B2 (en) 2016-03-25 2020-08-25 Mitsubishi Heavy Industries Machine Tool Co., Ltd. Cutter for skiving and gear manufacturing method using same
CN108349029B (zh) * 2016-03-25 2019-06-28 三菱重工工作机械株式会社 车齿加工用刀具以及使用其的齿轮制造方法
CN108349029A (zh) * 2016-03-25 2018-07-31 三菱重工工作机械株式会社 车齿加工用刀具以及使用其的齿轮制造方法
CN108406621A (zh) * 2017-02-10 2018-08-17 蓝思科技（长沙）有限公司 烧结砂轮棒及其使用方法
CN111638682A (zh) * 2020-05-26 2020-09-08 四川新迎顺信息技术股份有限公司 一种使用磨损砂轮磨削周齿螺旋刃后刀面的补偿方法
CN111638682B (zh) * 2020-05-26 2023-04-28 四川新迎顺信息技术股份有限公司 一种使用磨损砂轮磨削周齿螺旋刃后刀面的补偿方法
CN112123038A (zh) * 2020-08-03 2020-12-25 西安交通大学 一种插齿刀后刀面双参数单面成形磨削方法
CN112123038B (zh) * 2020-08-03 2022-07-12 西安交通大学 一种插齿刀后刀面双参数单面成形磨削方法
CN113124811A (zh) * 2021-04-21 2021-07-16 泸州高新中航传动转向系统有限公司 一种剃齿刀修磨参数精确控制方法
CN113124811B (zh) * 2021-04-21 2023-03-31 泸州高新中航传动转向系统有限公司 一种剃齿刀修磨参数精确控制方法
CN113486476A (zh) * 2021-08-11 2021-10-08 重庆大学 一种磨削双圆弧谐波减速器刚轮插刀的砂轮齿廓设计方法

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Publication number Publication date
JP4688510B2 (ja) 2011-05-25
JP2006212733A (ja) 2006-08-17

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