JP4763611B2 - Evaluation method of edge profile of re-sharpened pinion cutter - Google Patents
Evaluation method of edge profile of re-sharpened pinion cutter Download PDFInfo
- Publication number
- JP4763611B2 JP4763611B2 JP2006532587A JP2006532587A JP4763611B2 JP 4763611 B2 JP4763611 B2 JP 4763611B2 JP 2006532587 A JP2006532587 A JP 2006532587A JP 2006532587 A JP2006532587 A JP 2006532587A JP 4763611 B2 JP4763611 B2 JP 4763611B2
- Authority
- JP
- Japan
- Prior art keywords
- pinion cutter
- profile
- edge
- error
- pinion
- 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.)
- Active
Links
- 238000011156 evaluation Methods 0.000 title claims description 10
- 238000000034 method Methods 0.000 claims description 33
- 230000009466 transformation Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 description 3
- 238000002474 experimental method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
Images
Classifications
-
- 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
- B24B49/00—Measuring or gauging equipment for controlling the feed movement of the grinding tool or work; Arrangements of indicating or measuring equipment, e.g. for indicating the start of the grinding operation
-
- 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
-
- 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
- B24B3/346—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 of gear shaper cutter
Landscapes
- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Gear Processing (AREA)
- Finish Polishing, Edge Sharpening, And Grinding By Specific Grinding Devices (AREA)
- Length Measuring Devices With Unspecified Measuring Means (AREA)
- Constituent Portions Of Griding Lathes, Driving, Sensing And Control (AREA)
- Length Measuring Devices By Optical Means (AREA)
Description
本発明は、研ぎ直ししたピニオンカッタに生ずる刃形誤差を評価する方法に関し、特に、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿うねじ運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を評価する方法に関するものである。 The present invention relates to a method for evaluating a cutting edge error generated in a re-sharpened pinion cutter, and in particular, using a second-handing grindstone and performing second-handing grinding by a screw motion along the outer diameter second-angle of the pinion cutter. The present invention relates to a method for evaluating the error of the edge profile of the obtained sharpened pinion cutter.
研ぎ直ししたピニオンカッタを用いて内歯車などの歯切り加工を行う場合には、研ぎ直し後のピニオンカッタの刃形輪郭の誤差を測定して、精度良く歯切り加工ができるか否かを確認する必要がある。ピニオンカッタの刃形誤差の測定方法はＪＩＳに規定されている。 When gears such as internal gears are cut using a re-honed pinion cutter, the error of the edge profile of the pinion cutter after re-grinding is measured to check whether the gear can be cut with high accuracy. There is a need to. The measuring method of the pinion cutter blade shape error is defined in JIS.
しかしながら、ＪＩＳに規定されている測定方法は、対象がインボリュート歯車用のピニオンカッタに限定されている。また、すくい面から約１ｍｍ隔たった軸直角断面において誤差を測定するように規定されており、すくい角が考慮されていない。 However, the measurement method defined in JIS is limited to pinion cutters for involute gears. Moreover, it is prescribed | regulated that an error should be measured in the cross section orthogonal to an axis about 1 mm away from the rake face, and the rake angle is not taken into consideration.
一方、現在は、各種性能の向上のために非インボリュートの特殊形状歯形が広く用いられている。しかしながら、非インボリュート歯車用のピニオンカッタの研ぎ直しによる刃形誤差の測定あるいは評価の方法については具体的な提案がなされていない。 On the other hand, a non-involute special shape tooth profile is widely used at present to improve various performances. However, no specific proposal has been made for a method of measuring or evaluating the edge shape error by re-sharpening a pinion cutter for a non-involute gear.
本発明の目的は、このような点に鑑みて、非インボリュート歯形などの任意歯形を持つピニオンカッタを研ぎ直しした場合に生ずる刃形輪郭の誤差を評価する方法を提案することにある。 In view of the above, an object of the present invention is to propose a method for evaluating an error of a blade profile generated when a pinion cutter having an arbitrary tooth shape such as a non-involute tooth shape is sharpened.
さらに詳しくは、本発明の目的は、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿うねじ運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を評価する方法を提案することにある。 More specifically, the object of the present invention is to provide an error in the edge profile of a re-sharpened pinion cutter obtained by performing a second grinding by a screw motion along a second corner of the outer diameter of the pinion cutter using a second grinding wheel. It is to propose a method for evaluating the above.
また、本発明の目的は、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿う直線運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を評価する方法を提案することにある。 In addition, the object of the present invention is to evaluate the error of the edge profile of a re-sharpened pinion cutter obtained by performing a second grinding by a linear motion along a second corner of the outer diameter of the pinion cutter using a second grinding wheel. It is to propose a method to do.
上記の目的を達成するために、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿うねじ運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を評価する本発明の方法では、まず、二番取り砥石の軸断面輪郭に基づき、座標変換により研ぎ直し後のピニオンカッタ刃形を決定する。次に、研ぎ直しピニオンカッタと同一外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、これを研ぎ直しピニオンカッタの理想刃形とする。次に、得られた研ぎ直しピニオンカッタの刃形上の点から当該理想刃形に法線を立て、その足の長さを求め、これを研ぎ直し誤差としている。 In order to achieve the above-mentioned purpose, the error of the edge profile of the re-sharpened pinion cutter obtained by performing the second grinding with the screw motion along the outer diameter second corner of the pinion cutter using the second grinding wheel. In the method of the present invention to be evaluated, first, a pinion cutter blade shape after sharpening by coordinate conversion is determined based on the axial cross-sectional profile of the second grinding wheel. Next, a pinion tooth shape having the same outer diameter as the re-sharpened pinion cutter and correctly meshing with the tooth shape of the internal gear to be cut is obtained, and this is re-sharpened to be the ideal edge shape of the pinion cutter. Next, a normal is made to the ideal edge shape from the point on the edge shape of the obtained sharpening pinion cutter, the length of the foot is obtained, and this is taken as the error of sharpening.
ここで、前記研ぎ直しピニオンカッタの刃形輪郭を決定する工程では、
前記二番取り砥石の軸断面輪郭形状を離散的数値の点列で与え、
与えられた前記二番取り砥石の軸断面輪郭形状をアキマの方法で補間し、軸ζを回転軸とする二番取り砥石に固着の固着座標系ＯG−ξηζにおいて、当該軸断面輪郭上の各座標点を、輪郭を表す媒介変数ｔを用いて（式Ａ）により与え、Here, in the step of determining the edge profile of the re-sharp pinion cutter,
The shaft section profile of the second grinding wheel is given as a discrete numerical point sequence,
Interpolate the given axial section contour shape of the second grinding wheel by the Akima method, and in the fixed coordinate system O G -ξηζ fixed to the second grinding wheel with the axis ζ as the rotation axis, Each coordinate point is given by (Equation A) using a parameter t representing the contour,
（式Ａ）
（式Ａ）で与えられる砥石の軸断面輪郭を軸ζ回りに角φで旋回させることにより形成される砥石面を（式Ｂ）により規定し、 (Equation B) defines the grindstone surface formed by turning the axial cross-sectional profile of the grindstone given by (Equation A) around the axis ζ at an angle φ,
（式Ｂ）
当該砥石面を備えた二番取り砥石による二番取り研削作業の動作を、当該砥石の静止座標系Ｏ0−ξ0η0ζ0で表し、
次に、軸ｗ回りに角θPで回転するピニオンカッタに固着の固着座標系Ｏp−ｕｖｗで表し、
しかる後に、当該座標系に対して軸ｗの正方向にτだけ離れた座標系Ｏτ−ｕτｖτｗτにおいて、すくい角εのついた研ぎ直しピニオンカッタの切れ刃面の範囲内における任意の軸直角平面（ｗτ＝ｃ）における当該ピニオンカッタ二番面の軸直角断面輪郭上の各座標点（ｕτ、ｖτ）を（式Ｃ）により規定することを特徴としている。The operation of the second grinding operation by the second grinding wheel provided with the grinding wheel surface is represented by the stationary coordinate system O 0 -ξ 0 η 0 ζ 0 of the grinding wheel,
Next, it is expressed by a fixed coordinate system O p -uvw fixed to the pinion cutter rotating around the axis w at an angle θ P.
Thereafter, in the coordinate system O τ −u τ v τ w τ that is separated from the coordinate system by τ in the positive direction of the axis w, within the range of the cutting edge surface of the re-sharp pinion cutter with the rake angle ε. Each coordinate point (u τ , v τ ) on the cross-sectional profile perpendicular to the axis of the second pinion cutter plane in an arbitrary axis perpendicular plane (w τ = c) is defined by (Expression C).
（式Ｃ）
上記のｃの値は、研ぎ直し後のピニオンカッタ外半径をｒPT、当該ピニオンカッタの円錐形状切れ刃面のすくい角をε、ｗτ＝０の断面における歯形の座標値をｕτ0、ｖτ0とし、（式Ｄ）から求めることができる。The value of c described above is defined as the outer radius of the pinion cutter after sharpening, r PT , the rake angle of the conical cutting edge surface of the pinion cutter, ε, and the coordinate value of the tooth profile in the cross section of w τ = 0, u τ0 , v It can be obtained from (Equation D) as τ0 .
（式Ｄ）
次に、本発明のピニオンカッタの研ぎ直し限界の算出方法は、上記の誤差評価方法を用いて、各研ぎ直し量における刃形輪郭の誤差を算出し、研ぎ直しピニオンカッタの刃形輪郭の許容誤差を設定し、当該許容誤差以内の誤差で研ぎ直しピニオンカッタの刃形輪郭が得られる研ぎ直し量の最大値を研ぎ直し限界とすることを特徴としている。 Next, the pinion cutter re-grinding limit calculation method according to the present invention uses the error evaluation method described above to calculate the error of the edge profile at each re-grinding amount and tolerate the edge profile of the re-sharp pinion cutter. It is characterized in that an error is set, and the maximum value of the re-grinding amount at which the edge profile of the pinion cutter is obtained with an error within the permissible error is defined as the re-sharpening limit.
本発明の方法によれば、二番取り砥石を用いて、ピニオンカッタの外周二番面に沿うねじ運動により二番取り研削を行う場合に、インボリュート歯車用および非インボリュート歯車用のいずれかを問わず、当該ピニオンカッタの研ぎ直し後の刃形輪郭誤差を求めることができる。 According to the method of the present invention, when the second grinding is performed by the screw motion along the second circumferential surface of the pinion cutter using the second grinding wheel, it is possible to use either an involute gear or a non-involute gear. First, the edge profile error after reshaping of the pinion cutter can be obtained.
また、傾斜したすくい面に形成される研ぎ直しピニオンカッタの刃形輪郭を決定して、当該刃形輪郭上の各点における誤差を算出しているので、現行上においてＪＩＳに規定されている軸直角断面上における刃形輪郭に基づき誤差を測定する場合とは異なり、すくい角を考慮して正確に誤差を算出することができる。 In addition, since the edge profile of the sharpened pinion cutter formed on the inclined rake face is determined, and the error at each point on the edge profile is calculated, the axis defined in JIS at present Unlike the case where the error is measured based on the edge profile on the right-angled section, the error can be accurately calculated in consideration of the rake angle.
さらに、これまでは、実際にピニオンカッタを研ぎ直し、さらに歯切り実験を行うことで研ぎ直し量の限界を決定していたが、本発明によれば、刃形誤差を設定し研ぎ直し限界を特定することが可能になる。 Furthermore, until now, the pinion cutter was actually sharpened, and the limit of the re-sharpening amount was determined by conducting a gear cutting experiment.However, according to the present invention, the edge error is set and the sharpening limit is set. It becomes possible to specify.
次に、本発明は、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿う直線運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を算出する方法であって、まず、二番取り砥石の軸断面輪郭を基に座標変換により研ぎ直し後のピニオンカッタ刃形を決定する。次に、研ぎ直しピニオンカッタと同一外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、これを研ぎ直しピニオンカッタの理想刃形とする。次に、得られた研ぎ直しピニオンカッタの刃形上の点から当該理想刃形に法線を立て、その足の長さを求め、これを研ぎ直し誤差としている。 Next, the present invention calculates the error of the edge profile of the re-sharpened pinion cutter obtained by performing the second grinding by the linear motion along the outer diameter second angle of the pinion cutter using the second grinding wheel. In this method, first, the pinion cutter blade shape after sharpening by coordinate transformation is determined based on the axial cross-sectional contour of the second grinding wheel. Next, a pinion tooth shape having the same outer diameter as the re-sharpened pinion cutter and correctly meshing with the tooth shape of the internal gear to be cut is obtained, and this is re-sharpened to be the ideal edge shape of the pinion cutter. Next, a normal is made to the ideal edge shape from the point on the edge shape of the obtained sharpening pinion cutter, the length of the foot is obtained, and this is taken as the error of sharpening.
ここで、前記研ぎ直し後のピニオンカッタ刃形を決定する工程では、前記二番取り砥石の軸断面輪郭形状を離散的数値の点列で与える。また、与えられた前記二番取り砥石の軸断面輪郭形状をアキマの方法で補間し、軸ζを回転軸とする二番取り砥石に固着の座標系ＯG−ξηζにおいて、当該軸断面輪郭上の各座標点を、輪郭を表す媒介変数ｔを用いて次の（式Ｅ）により与える。Here, in the step of determining the pinion cutter blade shape after the re-sharpening, the axial cross-sectional contour shape of the second grinding wheel is given as a discrete numerical point sequence. Further, the given axial section contour shape of the second grinding wheel is interpolated by the Akima method, and in the coordinate system O G -ξηζ fixed to the second grinding wheel with the axis ζ as the rotation axis, Are given by the following (Equation E) using a parameter t representing the contour.
（式Ｅ）
次に、（式Ｅ）で与えられる砥石の軸断面輪郭に座標変換を施して、軸ｗを回転軸とするピニオンカッタに固着の座標系ＯP−ｕｖｗに対して軸ｗの正方向にτだけ離れた座標系Ｏτ−ｕτｖτｗτにおいて、すくい角εのついた研ぎ直しピニオンカッタの切れ刃面の範囲内における任意の軸直角平面（ｗτ＝ｃ）における当該ピニオンカッタ二番面の軸直角断面輪郭上の各座標点を次の（式Ｆ）により規定する。Next, coordinate transformation is performed on the axial cross-sectional contour of the grindstone given by (Equation E), and τ is in the positive direction of the axis w with respect to the coordinate system O P -uvw fixed to the pinion cutter with the axis w as the rotation axis. In the coordinate system O τ −u τ v τ w τ that is far away from each other, the
（式Ｆ）
次に、幾何学的関係から、（式Ｆ）のｃの値は、次の（式Ｇ）から求めることができる。 Next, from the geometrical relationship, the value of c in (Expression F) can be obtained from the following (Expression G).
（式Ｇ）
求まった値を（式Ｆ）に代入して、研ぎ直し後のピニオンカッタ刃形輪郭を求めることができる。 By substituting the obtained value into (Formula F), the pinion cutter edge profile after reshaping can be obtained.
次に、本発明は、ピニオンカッタの研ぎ直し限界の算出方法に関するものであり、上記の誤差算出方法を用いて、各研ぎ直し量における刃形輪郭の誤差を算出し、研ぎ直しピニオンカッタの刃形輪郭の許容誤差を設定し、当該許容誤差以内の誤差で研ぎ直しピニオンカッタの刃形輪郭が得られる研ぎ直し量の最大値を研ぎ直し限界とすることを特徴としている。 Next, the present invention relates to a calculation method for a pinion cutter re-sharpening limit. Using the error calculation method described above, an error of the edge profile at each re-sharpening amount is calculated, and the blade of the re-sharp pinion cutter is calculated. It is characterized in that an allowable error of the shape contour is set, and the maximum value of the re-sharpening amount at which the edge shape of the pinion cutter is obtained with an error within the allowable error is defined as the re-sharpening limit.
本発明の方法によれば、二番取り砥石を外周二番面に沿って直線運動させることにより製作したピニオンカッタについて、インボリュート歯車用および非インボリュート歯車用のいずれかを問わず、その研ぎ直し後の刃形輪郭誤差を求めることができる。また、傾斜したすくい面に形成される研ぎ直しピニオンカッタの刃形輪郭を決定して、当該刃形輪郭上の各点における誤差を算出しているので、現行上においてＪＩＳに規定されている軸直角断面上における刃形輪郭に基づき誤差を測定する場合とは異なり、すくい角を考慮して正確に誤差を算出することができる。 According to the method of the present invention, a pinion cutter manufactured by linearly moving a second picking grindstone along the outer peripheral second surface, regardless of whether it is for an involute gear or a non-involute gear, Can be obtained. In addition, since the edge profile of the sharpened pinion cutter formed on the inclined rake face is determined, and the error at each point on the edge profile is calculated, the axis defined in JIS at present Unlike the case where the error is measured based on the edge profile on the right-angled section, the error can be accurately calculated in consideration of the rake angle.
また、これまでは、実際にピニオンカッタを研ぎ直し、さらに歯切り実験を行うことで研ぎ直し量の限界を決定していたが、本発明によれば、刃形誤差を設定し研ぎ直し限界を特定することが可能になる。 In the past, the pinion cutter was actually sharpened again, and the limit of the amount of sharpening was determined by performing a gear cutting experiment.However, according to the present invention, the edge error is set and the sharpening limit is set. It becomes possible to specify.
以下に、図面を参照して本発明の方法を詳細に説明する。 Hereinafter, the method of the present invention will be described in detail with reference to the drawings.
（実施の形態１）
二番取り砥石を用いてピニオンカッタの外径二番角に沿うねじ運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を評価する方法を説明する。(Embodiment 1)
A method for evaluating the error of the edge profile of the re-sharpened pinion cutter obtained by performing the second grinding by the screw movement along the outer diameter second corner of the pinion cutter using the second grinding wheel will be described.
まず、二番取り砥石の軸断面輪郭が離散的数値の点列で与えられた場合に、この砥石により研削されたピニオンカッタの二番面の形状を求める解析手順を説明する。 First, an analysis procedure for obtaining the shape of the second surface of the pinion cutter ground by the grindstone when the axial cross-sectional contour of the second grindstone is given by a discrete numerical point sequence will be described.
図１は、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿うねじ運動により二番取り研削を行う場合の座標系を示す説明図である。ＯG−ξηζは軸ζを回転軸とする二番取り砥石に固着の固着座標系である。Ｏ0−ξ0η0ζ0は、砥石軸ζとζ0軸とが砥石取付角ΓGをなす二番取り砥石側の静止座標系である。ＯP−ｕｖｗは軸ｗを回転軸とするピニオンカッタに固着して軸ｗ回りに角θPで回転する固着座標系である。Ｏτ−ｕτｖτｗτは、固着座標系ＯP−ｕｖｗから軸ｗ方向にτだけ離れたピニオンカッタの研ぎ直し座標系である。τはピニオンカッタ外径で軸方向に測った研ぎ直し量であり、ｂは二番取り砥石軸とピニオンカッタ軸との設計軸間距離であり、角εはピニオンカッタの円錐形状切れ刃面のすくい角である。FIG. 1 is an explanatory diagram showing a coordinate system in the case of performing second grinding by screw motion along the second outer diameter of the pinion cutter using a second grinding wheel. O G −ξηζ is a fixed coordinate system fixed to the second grinding wheel with the axis ζ as the rotation axis. O 0 −ξ 0 η 0 ζ 0 is a stationary coordinate system on the second grinding wheel side in which the grinding wheel axis ζ and the ζ 0 axis form a grinding wheel mounting angle Γ G. O P -uvw is a fixed coordinate system that is fixed to a pinion cutter having the axis w as a rotation axis and rotates around the axis w by an angle θ P. O τ -u τ v τ w τ is a re-sharpened coordinate system of a pinion cutter that is separated from the fixed coordinate system O P -uvw by τ in the axis w direction. τ is the re-grinding amount measured in the axial direction at the pinion cutter outer diameter, b is the distance between the design axes of the second grinding wheel shaft and the pinion cutter shaft, and the angle ε is the conical cutting edge surface of the pinion cutter It is a rake angle.
二番取り研削作業においては、ピニオンカッタが角θPだけ回転する間に砥石は外径二番角γに沿って、軸η0の正方向へｓ移動しつつ、軸ξ0の正方向へｓｔａｎγだけ斜行移動する。このようにピニオンカッタの外径二番角に沿うねじ運動により研削された二番面は、切れ刃山形の右側は右ねじれのテーパねじ面形状を呈し、左側は左ねじれのテーパねじ面形状を呈する。ピニオンカッタの刃先外形状を円錐体の一部と考えるならば、ピニオンカッタの各々の軸直角断面における刃先点を連ねた母線は円錐の頂点に集合する直線となる。In the second grinding operation, the grindstone moves s in the positive direction of the axis η 0 along the outer diameter second angle γ while the pinion cutter rotates by the angle θ P, while moving in the positive direction of the axis ξ 0 . It moves diagonally by stan γ. In this way, the second surface ground by the screw motion along the outer diameter of the pinion cutter has a right-handed tapered thread shape on the right side of the cutting edge chevron and a left-handed tapered thread shape on the left side. Present. If the outside shape of the pinion cutter is considered as a part of the cone, the generatrix line connecting the cutting edge points in the cross-section perpendicular to each axis of the pinion cutter is a straight line that gathers at the apex of the cone.
そこで、図２に示すように、これらの母線をピニオンカッタの含軸水平面に投影した幾何学的関係から考察し、ｒPCをピニオンカッタのピッチ円半径、ｖCをピッチ円における刃形の座標値、γCを外径二番面γのｒPCでの換算値とすれば、ピニオンカッタのピッチ円半径におけるテーパねじ面のねじれ角βCは近似的に（式１−１）で与えられる。Therefore, as shown in FIG. 2, these buses are considered from the geometrical relationship projected onto the axial plane of the pinion cutter, r PC is the pitch circle radius of the pinion cutter, and v C is the coordinates of the blade shape in the pitch circle. if the value, gamma C to the converted value at r PC outer diameter double-dip surface gamma, helix angle beta C tapered thread surface in the pitch circle radius of the pinion cutter is given by an approximation (equation 1-1) .
（式１−１）
求めたねじれ角βCと歯形の特長を考慮し、テーパねじ面のねじれ角βを次の範囲で定める。Considering the obtained torsion angle β C and the characteristics of the tooth profile, the torsion angle β of the tapered thread surface is determined within the following range.
（式１−２）
また、ｒPｋをピニオンカッタの外半径とすると、砥石の軸方向移動距離ｓと回転角θPの間に（式２）の関係が成り立つ。When r Pk is the outer radius of the pinion cutter, the relationship of (Equation 2) is established between the axial movement distance s of the grindstone and the rotation angle θ P.
（式２）
ここで、与えられた二番取り砥石の軸断面輪郭を、点列を滑らかに補間することで評価の高いアキマの方法で補間し、各区間を座標系ＯG−ξηζにより（式３）で与える。ｔは輪郭を表すための媒介変数である。Here, the axial cross-sectional contour of the given second grinding wheel is interpolated by the highly acclaimed method by smoothly interpolating the point sequence, and each section is expressed by (Equation 3) using the coordinate system O G -ξηζ. give. t is a parameter for representing the contour.
（式３）
この砥石の軸断面輪郭を、軸ζ回りに角φで旋回させて砥石面を形成すると、（式４）となる。 When the grinding wheel surface is formed by turning the axial cross-sectional contour of the grinding wheel about the axis ζ at an angle φ, (Formula 4) is obtained.
（式４）
そこで、前述した二番取り研削作業における砥石の動作を、砥石の静止座標系Ｏ0−ξ0η0ζ0で表し、次に、ピニオンカッタの固着座標系ＯP−ｕｖｗで表し、さらにピニオンカッタの研ぎ直しを想定した座標系Ｏτ−ｕτｖτｗτで表すという手順により（式５）を得る。Therefore, the movement of the grindstone in the above-described second grinding operation is represented by the stationary coordinate system O 0 -ξ 0 η 0 ζ 0 of the grindstone, and then by the fixed coordinate system O P -uvw of the pinion cutter, and further the pinion (Expression 5) is obtained by a procedure of expressing the coordinate system O τ -u τ v τ w τ assuming reshaping of the cutter.
（式５）
（式５）は二番取り砥石の曲線群を表し、この曲線群の包絡面がピニオンカッタの二番面を表す。いま、この座標系系Ｏτ−ｕτｖτｗτにより研ぎ直し後の刃形を表すことを考え、すくい角のついた研ぎ直し後の切れ刃面の範囲で、任意平面ｗτ＝ｃにより（式５）で表される砥石の曲線群を切断し（式６）を得る。(Equation 5) represents a curve group of the second grinding wheel, and the envelope surface of this curve group represents the second surface of the pinion cutter. Now, considering that the coordinate system O τ -u τ v τ w τ represents the edge shape after re-sharpening, an arbitrary plane w τ = c in the range of the cutting edge surface after re-sharpening with a rake angle. By cutting the curve group of the grindstone represented by (Equation 5), (Equation 6) is obtained.
（式６）
これと（式２）に基づき、（式７）を得る。 Based on this and (Expression 2), (Expression 7) is obtained.
（式７）
（式６）を（式５）に代入して次の（式８）を得る。 Substituting (Expression 6) into (Expression 5), the following (Expression 8) is obtained.
（式８）
（式７）を併せて考えると、（式８）はｔとφとを変数とする曲線群を表し、この曲線群の包絡線としてピニオンカッタ二番面のｗτ＝ｃ平面による軸直角断面輪郭が求められる。包絡線の条件式は（式８）に対して次の（式９）のヤコビアンを計算して求められる。Considering (Equation 7) together, (Equation 8) represents a group of curves having t and φ as variables, and an axis perpendicular to the w τ = c plane of the second surface of the pinion cutter is used as an envelope of this group of curves. A contour is required. The conditional expression of the envelope is obtained by calculating the following Jacobian of (Expression 9) with respect to (Expression 8).
（式９）
（式１０）
そこで、すくい角のついた研ぎ直し後のピニオンカッタ刃形を求めるために、幾何学的関係から式（８）の中のｃを計算する次の（式１１）を得る。式中のｒPTは研ぎ直し後のピニオンカッタ外半径、ｕτ0、ｖτ0はｗτ＝０の断面における刃形の座標値である。Therefore, in order to obtain the pinion cutter blade shape after the sharpening with a rake angle, the following (Expression 11) for calculating c in Expression (8) is obtained from the geometric relationship. In the equation, r PT is the outside radius of the pinion cutter after reshaping , and u τ0 and v τ0 are the coordinate values of the blade shape in the cross section of w τ = 0.
（式１１）
以上のことから研ぎ直し後のピニオンカッタ刃形は、次に示す手順を繰り返すことにより計算することができる。
（i）各諸元ｂ、γ、εなどを与える。
（ii）研ぎ直し量τを設定する。
（iii）座標点番号ｊを定めてｔを与え、式（１）によってｇ（ｔ）、ｈ（ｔ）を与える。
（iv）ｃ＝０とおいて式（９）、（１０）、（７）によりｆ（ｔ，φ）＝０を満足するφを試行錯誤的に求める。
（v）これらを式（１１）に代入して、ｕτ0、ｖτ0を求め、ｃを定める。
（vi）求められたｃを用いて、式（９）、（１０）、（７）によりｆ（ｔ，φ）＝０を満足するφを試行錯誤的に求める。
（vii）これらを式（８）に代入して、ｕτ、ｖτとして刃形上の一点を求める。
（viii）iii〜viiを繰り返す。From the above, the pinion cutter blade shape after reshaping can be calculated by repeating the following procedure.
(I) Give each item b, γ, ε, etc.
(Ii) Set the sharpening amount τ.
(Iii) The coordinate point number j is determined and given t, and g (t) and h (t) are given by the equation (1).
(Iv) With c = 0, φ satisfying f (t, φ) = 0 is determined by trial and error from the equations (9), (10), and (7).
(V) By substituting these into equation (11), u τ0 and v τ0 are obtained, and c is determined.
(Vi) Using the obtained c, φ satisfying f (t, φ) = 0 is obtained by trial and error using the equations (9), (10), and (7).
(Vii) By substituting these into equation (8), one point on the blade shape is obtained as u τ and v τ .
(Viii) Repeat iii to vii.
ここで、刃形の研ぎ直し誤差は次のように定義する。まず、研ぎ直しピニオンカッタと同じ外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、これをピニオンカッタの理想刃形とする。次に、得られた研ぎ直しピニオンカッタの刃形上の点からこの理想刃形に法線を立て、その足の長さを求めて、研ぎ直し誤差とする。 Here, the sharpening error of the blade shape is defined as follows. First, a pinion tooth profile having the same outer diameter as that of the re-sharpened pinion cutter and correctly meshing with the tooth profile of the internal gear to be cut is obtained, and this is defined as the ideal blade shape of the pinion cutter. Next, a normal is made to this ideal edge shape from the point on the edge shape of the obtained sharpening pinion cutter, the length of the foot is obtained, and this is taken as an error for sharpening.
（実施の形態２）
次に、二番取り砥石を用いてピニオンカッタの外径二番角に沿う直線運動により二番取り研削を行って得られる研ぎ直しピニオンカッタの刃形輪郭の誤差を算出するための方法を説明する。(Embodiment 2)
Next, a method for calculating the error of the edge profile of the re-sharpened pinion cutter obtained by performing the second grinding by the linear motion along the second outer diameter of the pinion cutter using the second grinding wheel To do.
まず、二番取り砥石の軸断面輪郭が離散的数値の点列で与えられた場合に、この砥石により研削されたピニオンカッタの二番面の形状を求める解析手順を説明する。 First, an analysis procedure for obtaining the shape of the second surface of the pinion cutter ground by the grindstone when the axial cross-sectional contour of the second grindstone is given by a discrete numerical point sequence will be described.
図３は、二番取り砥石を用いて、ピニオンカッタの外径二番角に沿う直線運動により、二番取り研削を行う場合の座標系を示す説明図である。ＯG−ξηζは軸ζを回転軸とする二番取り砥石に固着の座標系、Ｏ0−ξ0η0ζ0は二番取り砥石側の静止座標系である。また、ＯP−ｕｖｗは軸ｗを回転軸とするピニオンカッタに固着の座標系であり、Ｏτ−ｕτｖτｗτは、軸ｗの正方向にτだけ離れた座標系である。ここで、τはピニオンカッタ外径で軸方向に測った研ぎ直し量であり、ｂは二番取り砥石軸とピニオンカッタ軸との設計軸間距離であり、角εはピニオンカッタの円錐形状切れ刃面のすくい角である。FIG. 3 is an explanatory diagram showing a coordinate system in the case of performing second-hand grinding using a second-hand grindstone by linear motion along the second outer diameter of the pinion cutter. O G −ξηζ is a coordinate system fixed to the second grinding wheel with the axis ζ as a rotation axis, and O 0 −ξ 0 η 0 ζ 0 is a stationary coordinate system on the second grinding wheel side. Further, O P -uvw is a coordinate system fixed to the pinion cutter with the axis w as the rotation axis, and O τ -u τ v τ w τ is a coordinate system separated by τ in the positive direction of the axis w. Here, τ is the re-grinding amount measured in the axial direction with the pinion cutter outer diameter, b is the designed inter-axis distance between the second grinding wheel shaft and the pinion cutter shaft, and the angle ε is the conical shape of the pinion cutter. The rake angle of the blade surface.
いま、与えられた二番取り砥石の軸断面輪郭を、点列を滑らかに補間することで評価の高いアキマの方法で補間し、各区間を座標系ＯG−ξηζにより次の（式２１）で与える。ここで、ｔは輪郭を表す媒介変数である。Now, the axial section profile of the given second grinding wheel is interpolated by the highly acclaimed method by smoothly interpolating the point sequence, and each section is expressed by the coordinate system O G -ξηζ as follows (Equation 21) Give in. Here, t is a parameter representing the contour.
（式２１）
この砥石の軸断面輪郭を、軸ζ回りに角φで旋回させて砥石面を形成すると、次の（式２２）となる。 When the grinding wheel surface is formed by turning the axial cross section contour of the grinding wheel about the axis ζ at an angle φ, the following (Expression 22) is obtained.
（式２２）
二番取り研削加工においては、砥石はピニオンカッタの外径二番角γに沿って軸ηの正方向へｓ移動しつつ軸ξの正方向へｓｔａｎγだけ斜行移動する。この動きを砥石の静止座標Ｏ0−ξ0η0ζ0で表し、次にピニオンカッタの固着座標ＯP−ｕｖｗで表すという手順で考え、次の（式２３）を得る。In the second grinding process, the grindstone moves obliquely by stan γ in the positive direction of the axis ξ while moving s in the positive direction of the axis η along the outer diameter second angle γ of the pinion cutter. This movement is expressed by the procedure of expressing the stationary coordinates O 0 -ξ 0 η 0 ζ 0 of the grindstone and then expressing the fixed coordinates O P -uvw of the pinion cutter, and the following (Equation 23) is obtained.
（式２３）
さらに、この（式２３）をピニオンカッタの研ぎ直しを想定した座標系Ｏτ−ｕτｖτｗτで表すと次の（式２４）となる。Further, when this (Equation 23) is expressed by a coordinate system O τ -u τ v τ w τ assuming reshaping of the pinion cutter, the following (Equation 24) is obtained.
（式２４）
（式２４）は二番取り砥石の曲線群を表し、この曲線群の包絡面がピニオンカッタの二番面を表す。いま、この座標系Ｏτ−ｕτｖτｗτにより研ぎ直し後の刃形を表すことを考え、すくい角のついた研ぎ直し後の切れ刃面の範囲で、任意平面ｗτ＝ｃにより（式２４）で表される砥石曲線群を切断し次の（式２５）を得る。(Equation 24) represents a curve group of the second grinding wheel, and the envelope surface of this curve group represents the second surface of the pinion cutter. Now, considering that the edge shape after reshaping is expressed by this coordinate system O τ -u τ v τ w τ , in the range of the cutting edge surface after reshaping with a rake angle, by an arbitrary plane w τ = c The grindstone curve group represented by (Expression 24) is cut to obtain the following (Expression 25).
（式２５）
これを（式２４）に代入して次の（式２６）を得る。 By substituting this into (Equation 24), the following (Equation 26) is obtained.
（式２６）
（式２６）はｔとφとを変数とする曲線群を表し、この曲線群の包絡線としてピニオンカッタ二番面のｗτ＝ｃ平面による軸直角断面輪郭が求められる。包絡線の条件式は（式２６）に対してヤコビアンを計算して求められる。(Equation 26) represents a group of curves having t and φ as variables, and an axis-perpendicular cross-sectional profile by the w τ = c plane of the second surface of the pinion cutter is obtained as an envelope of this group of curves. The conditional expression of the envelope is obtained by calculating the Jacobian with respect to (Expression 26).
（式２７）
これにより次の（式２８）を得る。 As a result, the following (formula 28) is obtained.
（式２８）
これを（式２６）に代入して次の（式２９）を得る。 By substituting this into (Equation 26), the following (Equation 29) is obtained.
（式２９）
ここで、ピニオンカッタの切れ刃上の輪郭は、ピニオンカッタの二番面と円錐すくい面との立体的な交差曲線で表される。この交差曲線をｗ軸方向からピニオンカッタ軸直角断面を含む断面へ投影した曲線がピニオンカッタの刃形である。ピニオンカッタの切れ刃上の輪郭を２つの面の交差曲線から計算することは困難である。そこで、研ぎ直し座標系Ｏτ−ｕτｖτｗτのピニオンカッタ軸直角断面上の任意の点（ｕτ0ｖτ0）と対応するすくい面までの距離ｃを、幾何学的関係から、次の（式３０）により表す。式中のｒPTは研ぎ直し後のピニオンカッタ外半径である。Here, the contour on the cutting edge of the pinion cutter is represented by a three-dimensional intersection curve between the second surface of the pinion cutter and the conical rake face. A curve obtained by projecting the intersecting curve from the w-axis direction onto a cross section including a cross section perpendicular to the pinion cutter axis is the blade shape of the pinion cutter. It is difficult to calculate the contour on the cutting edge of the pinion cutter from the intersection curve of the two surfaces. Therefore, the distance c to the rake face corresponding to an arbitrary point (u τ0 v τ0 ) on the cross-section perpendicular to the pinion cutter axis of the re-sharpened coordinate system O τ -u τ v τ w τ is expressed by the following geometrical relationship. (Equation 30). In the equation, r PT is an outside radius of the pinion cutter after reshaping.
（式３０）
このｃ点を通るピニオンカッタの軸直角断面輪郭は（式２９）で計算できる。また、点（ｕτ0ｖτ0）に対応する当該軸直角断面輪郭上の点（ｕτｖτ）が切れ刃上の点となる。The cross-sectional profile perpendicular to the axis of the pinion cutter passing through the point c can be calculated by (Equation 29). A point on the axis perpendicular cross-sectional profile corresponding to the point (u τ0 v τ0) (u τ v τ) becomes a point on the cutting edge is.
以上のことから研ぎ直し後のピニオンカッタ刃形は、次に示す手順を繰り返すことにより計算することができる。
（i）各諸元ｂ、γ、εなどを与える。
（ii）研ぎ直し量τを設定する。
（iii）座標点番号ｊを定めて式（１）によってｇ（ｔ）、ｈ（ｔ）を与える。
（iv）（式３０）に代入してｃを求める。
（v）（式２９）に代入して刃形上の一点を求める。
（vi）iii〜vを繰り返す。From the above, the pinion cutter blade shape after reshaping can be calculated by repeating the following procedure.
(I) Give each item b, γ, ε, etc.
(Ii) Set the sharpening amount τ.
(Iii) A coordinate point number j is determined and g (t) and h (t) are given by equation (1).
(Iv) Substituting into (Equation 30) to find c.
(V) Substituting into (Equation 29) to find one point on the blade shape.
(Vi) Repeat iii to v.
ここで、刃形の研ぎ直し誤差は次のように定義する。まず、研ぎ直しピニオンカッタと同じ外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、これをピニオンカッタの理想刃形とする。次に、得られた研ぎ直しピニオンカッタの刃形上の点からこの理想刃形に法線を立て、その足の長さを求めて、研ぎ直し誤差とする。 Here, the sharpening error of the blade shape is defined as follows. First, a pinion tooth profile having the same outer diameter as that of the re-sharpened pinion cutter and correctly meshing with the tooth profile of the internal gear to be cut is obtained, and this is defined as the ideal blade shape of the pinion cutter. Next, a normal is made to this ideal edge shape from the point on the edge shape of the obtained sharpening pinion cutter, the length of the foot is obtained, and this is taken as an error for sharpening.
（数値解析例）
表１に示す内歯車とピニオンカッタおよび二番取り砥石の諸元により数値解析を行った。まず、研ぎ直し量をτ＝０〜４ｍｍと設定して、研ぎ直しピニオンカッタの刃形を計算し、上述の手順により研ぎ直しによる刃形誤差を求めた。(Numerical analysis example)
Numerical analysis was performed using the specifications of the internal gear, the pinion cutter and the second grinding wheel shown in Table 1. First, the re-grinding amount was set to τ = 0 to 4 mm, the blade shape of the re-sharp pinion cutter was calculated, and the blade shape error due to re-sharping was determined by the above procedure.
（表１）
図４はその結果を示すグラフである。この図から、τ＝０の場合は研ぎ直し刃形誤差が生じておらず、研ぎ直しピニオンカッタ刃形と理想刃形とが一致したことが解り、上述した研ぎ直し刃形誤差を求める解析理論の妥当性が確認された。 FIG. 4 is a graph showing the results. From this figure, it can be seen that when τ = 0, there is no re-sharpening edge error, and that the re-sharpening pinion cutter edge shape matches the ideal edge shape, and the analysis theory for obtaining the above-mentioned re-sharpening edge error The validity of was confirmed.
また、図４から、τ＝１ｍｍの場合の刃形誤差は、点ｊ＝４２で−３．９μｍ、点ｊ＝７３で８．９μｍ、したがって幅で１２．８μｍとなる。同様に、τ＝２ｍｍでは２５．９μｍ、τ＝３ｍｍでは３９．３μｍ、τ＝４ｍｍでは５３．０μｍとなることが見て取れる。 From FIG. 4, the blade shape error when τ = 1 mm is −3.9 μm at point j = 42, 8.9 μm at point j = 73, and therefore 12.8 μm in width. Similarly, it can be seen that 25.9 μm at τ = 2 mm, 39.3 μm at τ = 3 mm, and 53.0 μm at τ = 4 mm.
したがって、これまでは、実際にピニオンカッタを研ぎ直し、さらに歯切り実験を行うことで研ぎ直し量の限界を決定していたが、本発明によれば、刃形誤差を設定し研ぎ直し限界を特定することが可能になる。 Therefore, until now, the limit of the amount of re-sharpening was determined by actually re-sharpening the pinion cutter and further performing a gear cutting experiment.However, according to the present invention, the blade shape error is set and the re-sharpening limit is set. It becomes possible to specify.
Claims (8)
二番取り砥石の軸断面輪郭に基づき、研ぎ直しピニオンカッタの刃形輪郭を決定し、
研ぎ直しピニオンカッタと同じ外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、当該歯形を研ぎ直しピニオンカッタの理想刃形とし、
前記研ぎ直しピニオンカッタの前記刃形輪郭上の点から前記理想刃形に立てた法線の長さを、当該刃形輪郭の誤差として規定することを特徴とする研ぎ直しピニオンカッタの歯形輪郭の誤差評価方法。A method for evaluating the error of the edge profile of a re-sharpened pinion cutter obtained by performing second-hand grinding by screw movement along the outer diameter second corner of the pinion cutter using a second-hand grindstone,
Based on the shaft cross-sectional profile of the second grinding wheel, determine the edge profile of the re-sharpened pinion cutter,
Find the pinion tooth profile that has the same outer diameter as the re-sharpened pinion cutter and meshes correctly with the tooth profile of the internal gear to be cut, re-grind the tooth profile to the ideal blade shape of the pinion cutter,
The length of a normal line set up in the ideal edge shape from a point on the edge shape of the sharpened pinion cutter is defined as an error of the edge shape outline, and the tooth shape outline of the sharpened pinion cutter is characterized in that Error evaluation method.
前記研ぎ直しピニオンカッタの刃形輪郭を決定する工程では、
前記二番取り砥石の軸断面輪郭形状を離散的数値の点列で与え、
与えられた前記二番取り砥石の軸断面輪郭形状をアキマの方法で補間し、軸ζを回転軸とする二番取り砥石に固着の固着座標系ＯG−ξηζにおいて、当該軸断面輪郭上の各座標点を、輪郭を表す媒介変数ｔを用いて（式Ａ）により与え、
（式Ａ）
（式Ｂ）
次に、軸ｗ回りに角θPで回転するピニオンカッタに固着の固着座標系ＯP−ｕｖｗで表し、
しかる後に、当該座標系に対して軸ｗの正方向にτだけ離れた座標系Ｏτ−ｕτｖτｗτにおいて、すくい角εのついた研ぎ直しピニオンカッタの切れ刃面の範囲内における任意の軸直角平面（ｗτ＝ｃ）における当該ピニオンカッタ二番面の軸直角断面輪郭上の各座標点（ｕτ、ｖτ）を（式Ｃ）により規定することを特徴とする研ぎ直しピニオンカッタの刃形輪郭の誤差評価方法。
（式Ｃ）
In the step of determining the edge profile of the re-sharp pinion cutter,
The shaft section profile of the second grinding wheel is given as a discrete numerical point sequence,
Interpolate the given axial section contour shape of the second grinding wheel by the Akima method, and in the fixed coordinate system O G -ξηζ fixed to the second grinding wheel with the axis ζ as the rotation axis, Each coordinate point is given by (Equation A) using a parameter t representing the contour,
(Formula A)
(Formula B)
Next, it is expressed by a fixed coordinate system O P -uvw fixed to the pinion cutter that rotates about the axis w at an angle θ P.
Thereafter, in the coordinate system O τ −u τ v τ w τ that is separated from the coordinate system by τ in the positive direction of the axis w, within the range of the cutting edge surface of the re-sharp pinion cutter with the rake angle ε. Re -sharpening characterized in that each coordinate point (u τ , v τ ) on the axial cross-sectional profile of the second pinion cutter second surface in an arbitrary axis perpendicular plane (w τ = c) is defined by (Equation C) Error evaluation method for pinion cutter edge profile.
(Formula C)
研ぎ直し後のピニオンカッタ外半径をｒPT、当該ピニオンカッタの円錐形状切れ刃面のすくい角をε、ｗτ＝０の断面における歯形の座標値をｕτ0、ｖτ0とし、前記ｃの値を（式Ｄ）から求め、
（式Ｄ）
The outer radius of the pinion cutter after re-sharpening is r PT , the rake angle of the conical cutting edge surface of the pinion cutter is ε, and the coordinate values of the tooth profile in the cross section of w τ = 0 are u τ0 and v τ0, and the value of c Is obtained from (Formula D),
(Formula D)
研ぎ直しピニオンカッタの刃形輪郭の許容誤差を設定し、
当該許容誤差以内の誤差で研ぎ直しピニオンカッタの刃形輪郭が得られる研ぎ直し量の最大値を研ぎ直し限界とすることを特徴とするピニオンカッタの研ぎ直し限界の算出方法。Using the error evaluation method according to claim 1, 2 or 3, the error of the edge profile at each regrind amount is calculated,
Set the tolerance of the edge profile of the re-sharpened pinion cutter,
A method for calculating a re-grinding limit of a pinion cutter, wherein the re-sharpening limit is a maximum value of the re-sharpening amount at which an edge shape of the re-pinion cutter is obtained with an error within the permissible error.
二番取り砥石の軸断面輪郭に基づき、研ぎ直しピニオンカッタの刃形輪郭を決定し、
研ぎ直しピニオンカッタと同じ外径を持ち、切削すべき内歯車の歯形と正しく噛み合うピニオンの歯形を求め、当該歯形を研ぎ直しピニオンカッタの理想刃形とし、
前記研ぎ直しピニオンカッタの刃形輪郭上の点から前記理想刃形に立てた法線の長さを、当該研ぎ直し後のピニオンカッタ刃形輪郭の誤差として規定することを特徴とする研ぎ直しピニオンカッタの刃形輪郭の誤差評価方法。A method of calculating an error of the edge profile of a re-sharpened pinion cutter obtained by performing second-hand grinding by linear motion along the outer diameter second angle of the pinion cutter using a second-hand grindstone,
Based on the shaft cross-sectional profile of the second grinding wheel, determine the edge profile of the re-sharpened pinion cutter,
Find the pinion tooth profile that has the same outer diameter as the re-sharpened pinion cutter and meshes correctly with the tooth profile of the internal gear to be cut, re-grind the tooth profile to the ideal blade shape of the pinion cutter,
A re-pinion pinion characterized in that a length of a normal line established from the point on the edge shape of the re-sharp pinion cutter to the ideal edge shape is defined as an error of the pinion cutter edge shape after the re-sharpening Error evaluation method for cutter edge profile.
前記研ぎ直し後のピニオンカッタ刃形を決定する工程では、
前記二番取り砥石の軸断面輪郭形状を離散的数値の点列で与え、
与えられた前記二番取り砥石の軸断面輪郭形状をアキマの方法で補間し、軸ζを回転軸とする二番取り砥石に固着の座標系ＯG−ξηζにおいて、当該軸断面輪郭上の各座標点を、輪郭を表す媒介変数ｔを用いて（式Ｅ）により与え、
（式Ｅ）
（式Ｆ）
In the step of determining the pinion cutter blade shape after the re-sharpening,
The shaft section profile of the second grinding wheel is given as a discrete numerical point sequence,
A given axial cross-sectional contour shape of the second grinding wheel is interpolated by the Akima method, and in the coordinate system O G -ξηζ fixed to the second grinding wheel with the axis ζ as the rotation axis, The coordinate point is given by (Equation E) using a parameter t representing the contour,
(Formula E)
(Formula F)
研ぎ直し後のピニオンカッタ外半径をｒPTとし、前記ｃの値を次の（式Ｇ）から求め、
（式Ｇ）
The outer radius of the pinion cutter after reshaping is defined as rPT, and the value of c is calculated from the following (formula G).
(Formula G)
研ぎ直しピニオンカッタの刃形輪郭の許容誤差を設定し、
当該許容誤差以内の誤差で研ぎ直しピニオンカッタの刃形輪郭が得られる研ぎ直し量の最大値を研ぎ直し限界とすることを特徴とするピニオンカッタの研ぎ直し限界の算出方法。Using the error evaluation method according to any one of claims 5 to 7, an error of the edge profile at each re-sharpening amount is calculated,
Set the tolerance of the edge profile of the re-sharpened pinion cutter,
A method for calculating a re-grinding limit of a pinion cutter, wherein the re-sharpening limit is a maximum value of the re-sharpening amount at which an edge shape of the re-pinion cutter is obtained with an error within the permissible error.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2006532587A JP4763611B2 (en) | 2004-08-27 | 2005-08-25 | Evaluation method of edge profile of re-sharpened pinion cutter |
Applications Claiming Priority (6)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2004248623 | 2004-08-27 | ||
| JP2004248623 | 2004-08-27 | ||
| JP2004338045 | 2004-11-22 | ||
| JP2004338045 | 2004-11-22 | ||
| PCT/JP2005/015447 WO2006022336A1 (en) | 2004-08-27 | 2005-08-25 | Method of evaluating cutting edge profile of re-sharpening pinion cutter |
| JP2006532587A JP4763611B2 (en) | 2004-08-27 | 2005-08-25 | Evaluation method of edge profile of re-sharpened pinion cutter |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPWO2006022336A1 JPWO2006022336A1 (en) | 2008-05-08 |
| JP4763611B2 true JP4763611B2 (en) | 2011-08-31 |
Family
ID=35967543
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP2006532587A Active JP4763611B2 (en) | 2004-08-27 | 2005-08-25 | Evaluation method of edge profile of re-sharpened pinion cutter |
Country Status (3)
| Country | Link |
|---|---|
| EP (1) | EP1792690B1 (en) |
| JP (1) | JP4763611B2 (en) |
| WO (1) | WO2006022336A1 (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102018102271A1 (en) | 2017-02-03 | 2018-08-09 | Jtekt Corporation | Gear cutter processing apparatus, gear cutter processing method, tool profile simulation apparatus and tool profile simulation method |
| CN109834551A (en) * | 2019-01-28 | 2019-06-04 | 湖北工业大学 | A kind of method of arc diamond wheel grinding circular arc straight trough |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN100562403C (en) * | 2008-09-13 | 2009-11-25 | 东方电气集团东方汽轮机有限公司 | The modification method of error of knife tool integral relief grinding emery cutter line and device |
| CN112123038B (en) * | 2020-08-03 | 2022-07-12 | 西安交通大学 | Double-parameter single-side forming grinding method for rear cutter face of slotting cutter |
| 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 |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS49103293A (en) * | 1973-02-02 | 1974-09-30 | ||
| US4139327A (en) * | 1977-06-16 | 1979-02-13 | Barber-Colman Company | Roughing gear shaper cutter |
| CH647445A5 (en) * | 1980-04-10 | 1985-01-31 | Maag Zahnraeder & Maschinen Ag | BEVEL CUTTING WHEEL WITH STAIR SHARPENING. |
| JPS61109654A (en) * | 1984-10-29 | 1986-05-28 | Karatsu Tekkosho:Kk | Re-polishing machine of pinion cutter |
| JPS6272024U (en) * | 1985-10-25 | 1987-05-08 | ||
| JPH0732215A (en) * | 1993-07-21 | 1995-02-03 | Kobe Steel Ltd | Pinion cutter and its manufacture |
| JP3391058B2 (en) * | 1993-09-09 | 2003-03-31 | 株式会社ニコン | Method and apparatus for measuring shape parameters of constrained multidimensional shape |
| JP3080824B2 (en) * | 1993-11-17 | 2000-08-28 | エムエムシーコベルコツール株式会社 | Pinion cutter grinding method |
| JPH09212222A (en) | 1996-02-02 | 1997-08-15 | Honda Motor Co Ltd | Machining simulation system for gear and simulation method |
-
2005
- 2005-08-25 EP EP05780973A patent/EP1792690B1/en active Active
- 2005-08-25 JP JP2006532587A patent/JP4763611B2/en active Active
- 2005-08-25 WO PCT/JP2005/015447 patent/WO2006022336A1/en active Application Filing
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102018102271A1 (en) | 2017-02-03 | 2018-08-09 | Jtekt Corporation | Gear cutter processing apparatus, gear cutter processing method, tool profile simulation apparatus and tool profile simulation method |
| CN109834551A (en) * | 2019-01-28 | 2019-06-04 | 湖北工业大学 | A kind of method of arc diamond wheel grinding circular arc straight trough |
| CN109834551B (en) * | 2019-01-28 | 2020-08-07 | 湖北工业大学 | Method for grinding arc straight groove by arc grinding wheel |
Also Published As
| Publication number | Publication date |
|---|---|
| WO2006022336A1 (en) | 2006-03-02 |
| EP1792690A4 (en) | 2011-01-12 |
| JPWO2006022336A1 (en) | 2008-05-08 |
| EP1792690B1 (en) | 2012-03-07 |
| EP1792690A1 (en) | 2007-06-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JP4688510B2 (en) | Edge shape design method of grinding wheel for second face machining of pinion cutter with arbitrary tooth shape that can be re-sharpened | |
| CN102470466B (en) | Method and tool for manufaturing face gears | |
| CN109063326B (en) | Gear accurate modeling method considering microscopic shape correction and actual machining errors | |
| JP5650762B2 (en) | Continuous process for producing face gears | |
| CN111644909B (en) | Method for solving grinding track of rear cutter face of woodworking forming milling cutter | |
| JP4763611B2 (en) | Evaluation method of edge profile of re-sharpened pinion cutter | |
| US10816336B2 (en) | Measurement of worm gears | |
| Zheng et al. | Research on the tooth modification in gear skiving | |
| CN112705794A (en) | Tooth cutting tool for machining cycloid gear and design method thereof | |
| CN106312850A (en) | Design method for screw grinding tool | |
| CN112989517A (en) | Trajectory solving method for grinding rear cutter face of ball head by adopting parallel grinding wheel | |
| CN106735612B (en) | A method of improving gear honing processing | |
| Boral et al. | Machining of spur gears using a special milling cutter | |
| CN108256174B (en) | Shaving engagement modeling method for analyzing influence of shaving process on tooth profile quality | |
| JP4606042B2 (en) | Pinion cutter blade contour design method | |
| CN113065205A (en) | Track solving method for grinding rear cutter face of arc head by adopting parallel grinding wheel | |
| Wasif et al. | An accurate approach to determine the cutting system for the face milling of hypoid gears | |
| CN115026354A (en) | Reverse envelope design method for complex-tooth-shaped turning cutter | |
| CN106815399B (en) | Non-equilateral shaving cutter tooth shape design method based on negative deflection balance shaving | |
| Radzevich | A novel design of cylindrical hob for machining of precision involute gears | |
| Chlost et al. | A new method of the positioning and analysis of the roughness deviation in five-axis milling of external cylindrical gear | |
| Várkuli et al. | Determination of tooth surface points on bevel gears for checking on a coordinate measuring machine | |
| JP5872532B2 (en) | Gear grinding correction data creation method | |
| Huang et al. | Novel third-order correction for a helical gear shaping cutter made by a lengthwise-reciprocating grinding process | |
| CN113145943A (en) | Design method of equal-front-angle tooth cutting knife for machining cycloid wheel |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| A621 | Written request for application examination |
Free format text: JAPANESE INTERMEDIATE CODE: A621 Effective date: 20080409 |
|
| TRDD | Decision of grant or rejection written | ||
| A01 | Written decision to grant a patent or to grant a registration (utility model) |
Free format text: JAPANESE INTERMEDIATE CODE: A01 Effective date: 20110607 |
|
| A01 | Written decision to grant a patent or to grant a registration (utility model) |
Free format text: JAPANESE INTERMEDIATE CODE: A01 |
|
| A61 | First payment of annual fees (during grant procedure) |
Free format text: JAPANESE INTERMEDIATE CODE: A61 Effective date: 20110609 |
|
| FPAY | Renewal fee payment (event date is renewal date of database) |
Free format text: PAYMENT UNTIL: 20140617 Year of fee payment: 3 |
|
| R150 | Certificate of patent or registration of utility model |
Ref document number: 4763611 Country of ref document: JP Free format text: JAPANESE INTERMEDIATE CODE: R150 Free format text: JAPANESE INTERMEDIATE CODE: R150 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |
|
| R250 | Receipt of annual fees |
Free format text: JAPANESE INTERMEDIATE CODE: R250 |