JP3986320B2 - Gear machining method and apparatus - Google Patents

Description

【００２５】
【数２】

【００２６】
【数３】

【００２７】
このような解析結果から、歯すじ方向誤差ΔＬを修正するにはリード誤差の補正量ΔＰのみを用い、まず始めにこのリード補正量ΔＰを測定された歯すじ方向誤差ΔＬから２分法を用いて算出する。次に、このリード補正量ΔＰを考慮し、圧力角誤差ΔｆａL ，ΔｆａR 及び歯厚誤差Δｔｈを修正するような砥石中心位置補正量ΔＸ，ΔＹと砥石取付角補正量ΔΣを滑降シンプレックス法を用いて算出する。そして、この滑降シンプレックス法では、左歯面圧力角誤差ΔｆａL の２乗値と右歯面圧力角誤差ΔｆａR の２乗値と歯厚誤差Δｔｈの２乗値の加算値を評価関数とし、この評価関数を用いて最小化することで、圧力角誤差ΔｆａL ，ΔｆａR 及び歯厚誤差Δｔｈを同時に修正できる砥石中心位置誤差の補正量ΔＸ，ΔＹ及び砥石取付角誤差の補正量ΔΣを設定する。
【００２８】
例えば、ヘリカルギヤにおいて、まず、歯すじ方向誤差ΔＬを修正するには、リード誤差の補正量ΔＰを求める必要がある。歯筋誤差伝播解析にて、歯すじ方向誤差ΔＬはＺ−Ｙ座標上で表されるものであるため、図２に示すように、歯幅方向における各端部での歯形曲線（一点鎖線で表示）を求め、各歯形曲線がピッチ円付近どれだけ誤差があるかを求めて歯筋チャートが得られ、歯すじ方向誤差ΔＬが求められる。ここで、リード誤差ΔＰが発生したときにこの歯筋チャートがどのように変化するかを、前述した数式２を用いて求める。
【００２９】
歯形誤差伝播解析にて、インボリュート歯形の点列（Ｘ₀ ，Ｙ₀ ）は、図４(ａ)に示すものとなっており、砥石中心位置誤差ΔＸ＝０，ΔＹ＝０であるときは加工目標値通りの歯形チャートとなる。従って、この数式２のΔＰに適当な数値を入力していくことで、歯幅方向の各端部にてそれぞれ図４(ａ)に示すインボリュート歯形の点列（Ｘ₀ ′，Ｙ₀ ′）を求める。この場合、
ΔＸ＝Ｘ₀ ′−Ｘ₀
ΔＹ＝Ｙ₀ ′−Ｙ₀
であり、ΔＸ，ΔＹから歯幅方向の上端と下端での歯すじ方向誤差ΔＬ_T ′，ΔＬ_B ′が求められ、このΔＬ_T ′，ΔＬ_B ′の合計がピッチ円付近での歯すじ方向誤差ΔＬ′となり、図４(ｂ)に示すような歯形チャートとなる。
【００３０】
このようにして求められた歯すじ方向誤差ΔＬ′から２分法を用いてリード誤差の補正量ΔＰを求める。つまり、この歯すじ方向誤差ΔＬ′と測定された歯すじ方向誤差ΔＬとの差が０となれば、実際のリード誤差ΔＰが正確に推定されたものであり、実際には、最小となる補正量ΔＰを求めることとなる。
【００３１】
このようにしてリード誤差の補正量ΔＰが設定されると、次に、左右の歯面の圧力角誤差Δｆａ_L ，Δｆａ_R 及び歯厚誤差Δｔｈから砥石中心位置補正量ΔＸ，ΔＹと砥石取付角誤差ΔΣを求めるが、この場合、リード誤差の補正量ΔＰによる圧力角誤差Δｆａ_L ，Δｆａ_R と歯厚誤差Δｔｈの影響を考慮する必要がある。つまり、前述した数式２を用いてリード誤差ΔＰからΔＸ₀ ，ΔＹ₀ を求めておく。
【００３２】
歯形誤差伝播解析にて、インボリュート歯形の点列（Ｘ₀ ，Ｙ₀ ）は、図４(ａ)に示すものとなっており、砥石中心位置誤差ΔＸ＝０，ΔＹ＝０であるときは加工目標値通りの歯形チャートとなり、圧力角誤差Δｆａ_L ＝０，Δｆａ_R ＝０である。ここで、砥石中心位置誤差ΔＸ，ΔＹが発生したときにこの歯形チャートがどのように変化するかを、前述した数式１を用いて求める。つまり、この数式１のΔＸ，ΔＹに適当な数値を入力していくことで、図４(ａ)に示すインボリュート歯形の点列（Ｘ₀ ′，Ｙ₀ ′）を求める。この場合、
Ｘ₀ ′＝Ｘ₀ ＋ΔＸ
Ｙ₀ ′＝Ｙ₀ ＋ΔＹ
であるが、Ｘ₀ ′，Ｙ₀ ′にはリード誤差ΔＰから数式２にて求めたΔＸ₀ ，ΔＹ₀ を加算する。すると、求めたデータ（Ｘ₀ ′，Ｙ₀ ′）から図４(ｃ)に示すような歯形チャートが得られ、圧力角誤差Δｆａ_L ′（Δｆａ_R ′）を求めることができる。
【００３３】
また、同様に、前述した数式３を用いて砥石取付角誤差ΔΣに適当な数値を入力していくことで、インボリュート歯形の点列（Ｘ₀ ′，Ｙ₀ ′）を求め、求めたデータ（Ｘ₀ ′，Ｙ₀ ′）から歯形チャートを得て歯厚誤差Δｔｈ′を求める。
【００３４】
このようにして求められた圧力角誤差Δｆａ_L ′，Δｆａ_R ′及び歯厚誤差Δｔｈ′から滑降シンプレックス法を用いて砥石中心位置誤差の補正量ΔＸ，ΔＹ及び砥石取付角誤差の補正量ΔΣを求める。この場合、評価関数ｆは、下記式により与えられる。
ｆ＝（Δｆａ_L ′−Δｆａ_L ）² ＋（Δｆａ_R ′−Δｆａ_R ）²
＋（Δｔｈ′−Δｔｈ）²
この数式を用いて推定した補正量ΔＸ，ΔＹ，ΔΣに対して、評価関数ｆ＝０となれば、実際の砥石中心位置誤差ΔＸ，ΔＹ、砥石取付角誤差ΔΣが正確に推定されたものであり、実際には、評価関数ｆが最小となる補正量ΔＸ，ΔＹ，ΔΣを求めることとなる。
【００３５】
このような演算はＮＣ装置１５内で行われるものであり、図５に示すように、ＮＣ装置１５の表示部２５に被加工物Ｗの測定データとして左歯形圧力角誤差Δｆａ_L 、右歯形圧力角誤差Δｆａ_R 、歯すじ方向誤差ΔＬ、歯厚誤差Δｔｈが表示され、パソコン１８の操作により砥石中心位置誤差（Ｘ，Ｙ軸誤差）の補正量ΔＸ，ΔＹ、砥石取付角誤差（Ａ軸誤差）の補正量ΔΣ、リード誤差の補正量ΔＰがそれぞれ演算されて表示される。従って、ＮＣ装置１５はこの各補正量ΔＸ，ΔＹ、ΔΣ、ΔＰに基づいて砥石車１４の位置を修正することで、例えば、被加工物Ｗの歯形形状において、図６に示すように、加工目標値に近似した加工を行うことができる。
【００３６】
このように本実施形態の歯車加工装置にあっては、研削加工終了後、測定子１７が被加工物（歯車）Ｗにおける左右の圧力角誤差ΔｆａL ，ΔｆａR 、歯すじ方向誤差ΔＬ、歯厚誤差Δｔｈを測定演算し、まず、測定された歯すじ方向誤差ΔＬから２分法を用いてリード補正量ΔＰを算出し、次に、このリード補正量ΔＰを考慮し、測定された圧力角誤差ΔｆａL ，ΔｆａR 及び歯厚誤差Δｔｈから評価関数ｆが最小となるよう滑降シンプレックス法を用いて砥石中心位置補正量ΔＸ，ΔＹと砥石取付角補正量ΔΣを算出するようにしている。
【００３７】
従って、歯車Ｗにおける左右の圧力角誤差ΔｆａL ，ΔｆａR 、歯すじ方向誤差ΔＬ、歯厚誤差Δｔｈにおける互いの影響度を考慮して砥石中心位置補正量ΔＸ，ΔＹ、リード補正量ΔＰ、砥石取付角補正量ΔΣを求めることとなり、早期に、且つ、高精度な砥石車１４の位置修正を行うことができ、作業性を向上することができる。
【００３８】
なお、上述の実施形態では、ヘリカルギヤにおいて、圧力角誤差ΔｆａL ，ΔｆａR 、歯すじ方向誤差ΔＬ、歯厚誤差Δｔｈから砥石中心位置補正量ΔＸ，ΔＹ、リード補正量ΔＰ、砥石取付角補正量ΔΣを求める手法について説明したが、スパーギヤの場合には、リード補正量ΔＰを考慮せずに、圧力角誤差ΔｆａL ，ΔｆａR 、歯すじ方向誤差ΔＬ、歯厚誤差Δｔｈから砥石中心位置補正量ΔＸ，ΔＹ、砥石取付角補正量ΔΣを求めればよい。
【００３９】
また、上述の実施形態では、砥石台１２の近傍に設けられた測定ヘッド１６を誤差測定手段としたが、圧力角誤差、歯すじ方向誤差、歯厚を予め測定する外部測定機としてもよい。
【００４０】
【発明の効果】
以上、実施形態において詳細に説明したように第１の発明の歯車加工方法によれば、総形砥石を用いた成形研削による歯車加工方法において、加工した歯車における圧力角誤差と歯厚誤差を測定あるいは測定値に基づいて算出する一方、前記圧力角誤差が砥石中心位置誤差と砥石取付角誤差により受ける影響と、前記歯厚誤差が砥石中心位置誤差と砥石取付角誤差により受ける影響と、を予め解析しておき、該解析結果に基づいて圧力角誤差と歯厚誤差が減少するような砥石中心位置と砥石取付角の各補正量をそれぞれ設定し、該各補正量を加味して再度歯車を加工するので、被加工物における圧力角誤差と歯厚誤差における互いの影響度を考慮して砥石中心位置補正量と砥石取付角補正量を求めることとなり、早期に、且つ、高精度な砥石車の位置修正を行うことができ、作業性を向上することができる。
【００４１】
また、第２の発明の歯車加工方法によれば、総形砥石を用いた成形研削による歯車加工方法において、加工した歯車における圧力角誤差、歯すじ方向誤差及び歯厚誤差を測定あるいは測定値に基づいて算出する一方、前記圧力角誤差が砥石中心位置誤差、リード誤差及び砥石取付角誤差により受ける影響と、前記歯すじ方向誤差がリード誤差により受ける影響と、前記歯厚誤差が砥石中心位置誤差、リード誤差及び砥石取付角誤差により受ける影響と、を予め解析しておき、該解析結果に基づいて圧力角誤差、歯すじ方向誤差及び歯厚誤差が減少するような砥石中心位置、リード及び砥石取付角の各補正量をそれぞれ設定し、該各補正量を加味して再度歯車を加工するので、被加工物における圧力角誤差、歯すじ方向誤差及び歯厚誤差における互いの影響度を考慮して砥石中心位置補正量、リード補正量及び砥石取付角補正量を求めることとなり、早期に、且つ、高精度な砥石車の位置修正を行うことができ、作業性を向上することができる。
【００４２】
第３の発明の歯車加工方法によれば、リード補正量を歯すじ方向誤差から２分法を用いて算出するので、影響を受けない誤差項目を除外することで、容易にリード補正量を算出することができる。
【００４３】
第４の発明の歯車加工方法によれば、前記砥石中心位置補正量と前記砥石取付角補正量は、前記圧力角誤差と歯厚誤差から滑降シンプレックス法を用いて算出するので、各誤差項目の影響度を十分に考慮して高精度な演算を実行することができる。
【００４４】
第５の発明の歯車加工方法によれば、前記滑降シンプレックス法は、前記圧力角誤差の２乗値と前記歯厚誤差の２乗値の加算値を評価関数とし、この評価関数を用いて最小化することで、前記砥石中心位置補正量と前記砥石取付角補正量を設定するので、評価関数を用いることで容易に高精度な演算を実行することができる。
【００４５】
また、第６の発明の歯車加工装置によれば総形砥石を用いた成形研削による歯車加工装置において、
回転可能で且つ互いに直交する３方向に移動自在に支持された砥石と、
該砥石の回転及び移動を制御する駆動制御手段と、
前記砥石により研削加工された歯車における圧力角誤差と歯厚誤差（及び歯すじ方向誤差）を測定あるいは測定値に基づいて算出する誤差測定手段と、
前記圧力角誤差が砥石中心位置誤差と砥石取付角誤差により受ける影響と、前記歯厚誤差が砥石中心位置誤差と砥石取付角誤差により受ける影響（及び前記歯すじ方向誤差がリード誤差により受ける影響）と、を予め解析した解析結果に基づいて該圧力角誤差と歯厚誤差（及び歯すじ方向誤差）が減少するような砥石中心位置と砥石取付角（及びリード）の各補正量をそれぞれ設定する補正量演算手段と、
該補正量演算手段により算出された前記砥石中心位置と砥石取付角（及びリード）の各補正量に基づいて前記砥石中心位置と砥石取付角（及びリード）を修正する修正制御手段と、
を具えたので、被加工物における圧力角誤差と歯厚誤差（及び歯すじ方向誤差）における互いの影響度を考慮して砥石中心位置補正量と砥石取付角補正量（及びリード補正量）を求めることとなり、早期に、且つ、高精度な砥石車の位置修正を行うことができ、作業性を向上することができると共に、装置の簡素化を図ることができる。
【００４６】
第７の発明の歯車加工装置によれば、誤差測定手段を砥石の近傍に設けてワークを支持位置で前記各種誤差を測定あるいは算出可能としたので、計測精度を向上することができると共に、計測作業を短時間で行うことができ、また、装置の小型化に寄与することができる。
【００４７】
第８の発明の歯車加工装置によれば、誤差測定手段を前記各種誤差を予め測定する外部測定機としたので、作業を短時間で行うことができると共に、装置を小型化することができる。
【図面の簡単な説明】
【図１】本発明の一実施形態に係る歯車加工装置の概略図である。
【図２】歯車形状測定装置の概略図である。
【図３】ＮＣ装置の制御ブロック図である。
【図４】歯形誤差伝播解析を説明するためのインボリュート歯形及び歯形チャートである。
【図５】ＮＣ装置における表示部の概略図である。
【図６】本実施形態の歯車加工装置による補正前後の歯形形状を表す歯形チャートである。
【符号の説明】
１１ 主軸台
１２ 砥石台
１４ 砥石車
１５ ＮＣ装置
１６ 測定ヘッド
１７ 測定子
１８ パソコン
２１ 補正量演算部
２２ 誤差演算部
２３ リード補正部
２４ Ｘ・Ｙ・Ａ補正部
２５ 表示部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a gear machining method and a gear machining apparatus (gear grinding machine) using a grinding wheel.
[0002]
[Prior art]
The gear grinding machine is supported by a table on a bed so that a headstock and a tailstock can move freely, and a grinding wheel along the vertical and horizontal directions intersecting the moving direction of the headstock and the tailstock on the bed. A whetstone base having a slidable support is movably supported. A grinding wheel that rotates at a predetermined speed by supporting the workpiece by the spindle stock and the tailstock and giving cutting and feeding to the grinding wheel platform in a state in which the workpiece is rotated by the spindle. Thus, gear grinding can be performed on the outer peripheral surface of the workpiece.
[0003]
[Problems to be solved by the invention]
A predetermined tooth profile is formed by grinding the outer peripheral surface of the workpiece with the above-described conventional gear grinding machine. Generally, however, a pressure tooth error or tooth is formed as a gear tooth profile for each processing. The streak direction error is measured, and the position and angle of the grinding wheel, the cutting amount, the feed amount, etc. are corrected so as to eliminate these errors.
[0004]
However, the pressure angle error and the tooth trace direction error of this gear influence each other in relation to the position and angle of the grinding wheel. For example, the synchronous movement of the grinding wheel and the table shaft so as to eliminate the tooth trace direction error. If the position of the grinding wheel is corrected so that the pressure angle error is eliminated, the tooth thickness error may be increased. For this reason, the worker relies on intuition for many years to consider the effect of the correction amount of the grinding wheel position, angle, and synchronous motion on the pressure angle error, tooth direction error, and tooth thickness, and the grinding wheel position, angle, and synchronization. The movement is adjusted and each error is eliminated by several adjustments, and there is a problem that the work is difficult, the work time is long, and the work efficiency is not good.
[0005]
The present invention solves such problems, and an object of the present invention is to provide a gear machining method and apparatus that improve workability in gear grinding work.
[0006]
[Means for Solving the Problems]
Gear cutting method of the first invention for achieving the above object, in the gear cutting method according to profile grinding with form-grinding wheel, processed in the measurement or measurements the difference erroneous pressure angle and tooth thickness error in gear while calculated based, the influence of the pressure angle errors experienced by the grindstone center position error and the grindstone mounting angle error, the tooth thickness error in advance by analyzing the influence received by the grindstone center position error and the grindstone mounting angle error, the previously , the difference erroneous pressure angle on the basis of the analysis result and the tooth thickness error of the correction amount of the grinding wheel center position and the grindstone mounting angle so as to reduce set respectively, to process the re-gear in consideration of the respective correction amount It is characterized by.
[0007]
Further, the gear machining method of the second invention is a gear machining method by forming grinding using a general-purpose grindstone. In the gear machining method, the pressure angle error, the tooth line direction error and the tooth thickness error in the machined gear are measured or based on the measured value. On the other hand, the pressure angle error is affected by the wheel center position error, the lead error, and the wheel mounting angle error, the influence of the tooth streak direction error by the lead error, and the tooth thickness error is the wheel center position error, the lead. Analyzing the error and the influence of the wheel mounting angle error in advance, and based on the analysis result, the wheel center position, the lead and the wheel mounting angle that reduce the pressure angle error, tooth direction error and tooth thickness error Each correction amount is set, and the gear is processed again in consideration of each correction amount.
[0008]
In the third gear cutting method of the invention, the lead correction amount is characterized in that calculated using the bisection method from the tooth trace direction error.
[0009]
In gear machining method of the fourth invention, the grindstone mounting angle correction amount and the grinding wheel center position correction amount is characterized in that calculated using the downhill simplex procedure from the pressure angle error and tooth thickness error .
[0010]
In the gear machining method according to a fifth aspect of the present invention, the downhill simplex method uses the square value of the pressure angle error and the square value of the tooth thickness error as an evaluation function, and minimizes it using this evaluation function. Thus, the grinding wheel center position correction amount and the grinding wheel mounting angle correction amount are set .
[0011]
The gear machining apparatus of the sixth invention is
In gear processing equipment by forming grinding using a general grinding wheel,
A grindstone supported so as to be rotatable and movable in three directions orthogonal to each other;
Drive control means for controlling the rotation and movement of the grindstone;
And error measuring means for calculating, based on the measurement or measurements of the pressure angle erroneous difference and the tooth thickness error (and the tooth trace direction error) in Grinding processed gear by said grinding wheel,
The effect of the pressure angle error due to the wheel center position error and the wheel mounting angle error, and the effect of the tooth thickness error due to the wheel center position error and the wheel mounting angle error (and the effect of the tooth line direction error due to the lead error) setting the respective correction amounts of based on previously analyzed analysis result pressure angle erroneous difference and the tooth thickness error (and the tooth trace direction error) grinding wheel center position and the grindstone mounting angle as to decrease (and lead), respectively Correction amount calculating means to perform,
Correction control means for correcting the grindstone center position and the grindstone mounting angle (and lead) based on the respective correction amounts of the grindstone center position and the grindstone mounting angle (and lead) calculated by the correction amount calculating means;
It is characterized by comprising.
[0012]
In a gear machining apparatus according to a seventh aspect of the present invention, the error measuring means is provided in the vicinity of the grindstone, and the various errors can be measured at a position where the workpiece is supported .
[0013]
In the gear machining apparatus according to an eighth aspect of the invention, the error measuring means is an external measuring machine that measures the various errors in advance .
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0015]
FIG. 1 is an outline of a gear machining apparatus according to an embodiment of the present invention, FIG. 2 is an outline of a gear shape measuring apparatus, FIG. 3 is a control block of an NC apparatus, and FIG. 4 is an involute tooth profile for explaining tooth profile error propagation analysis. FIG. 5 shows an outline of the display unit in the NC device, and FIG. 6 shows a tooth profile chart showing the tooth profile before and after correction by the gear machining device of this embodiment.
[0016]
In the gear machining apparatus (gear grinding machine) of the present embodiment, as shown in FIG. 1, a headstock 11 disposed on a bed (not shown) has a spindle (not shown) that can be driven and rotated by a drive motor. The workpiece W is supported together with the tailstock that does not, and can rotate in the C direction at a predetermined speed. On the other hand, a grindstone platform 12 is disposed adjacent to the headstock 11 and is supported so as to be movable in the X, Y, and Z directions. A grinding wheel 14 that can be driven and rotated by a drive motor 13 is mounted on the grinding wheel base 12. The grinding wheel base 12 is driven and controlled by an NC device 15, and a cutting amount (X direction) and a feeding amount (Z) with respect to the workpiece W are provided. Direction) is set. The grinding wheel base 12 is rotatable in the direction A, and the mounting angle of the grinding wheel 14 can be adjusted.
[0017]
Further, a measuring head (error measuring means) 16 having a gate shape is rotatably attached to the grindstone 12, and a measuring element 17 is attached to the measuring head 16. As shown in FIG. 2, the measuring element 17 moves the measuring element 17 and the gear W as a workpiece along the processing target value, so that the contact of the tip portion and the surface of the gear W makes contact with the gear W. The left and right pressure angle errors Δfa _L and Δfa _R (tooth profile error), tooth line direction error ΔL (tooth trace error), and tooth thickness (stripe thickness) th can be measured. In this case, the pressure angle errors Δfa _L and Δfa _R are represented by a point sequence of a maximum of 100 points on the XY coordinate, and the tooth direction error ΔL is represented by a point sequence of a maximum of 100 points on the Z-Y coordinate. Then, the measurement result of the probe 17 is output to the personal computer 18 as the operation unit via the NC device 15. The NC device 15 calculates a tooth thickness error Δth from the tooth thickness (spanning tooth thickness) th.
[0018]
By the way, in the gear machining apparatus according to the present embodiment, the NC device 15 performs the rotation speed of the workpiece W, the cutting amount (X direction) and the feed amount (Z) by the grinding wheel 14 based on the machining target value input from the personal computer 18. by controlling the direction), but grinding the workpiece W by the grinding wheel 14, after the processing end, the measuring element 17 is a workpiece (gear) the pressure angle of the left and right in the W error .delta.fa _L, .delta.fa _R The tooth trace direction error ΔL and the tooth thickness th are measured and output to the NC device 15, and the NC device 15 grinds so that the pressure angle errors Δfa _L and Δfa _R , the tooth trace direction error ΔL and the tooth thickness error Δth decrease. The correction amounts ΔX, ΔY, ΔP, and ΔΣ for the center position, the lead, and the grindstone mounting angle are set, respectively, and the position of the grinding wheel 14 is corrected based on the respective correction amounts and the workpiece W is ground again. ing.
[0019]
Here, a calculation method of the correction amount ΔX, ΔY of the grindstone center position error, the correction amount ΔP of the lead error, and the correction amount ΔΣ of the grindstone mounting angle error by the NC device 15 will be described. The lead error is a synchronization error between the vertical movement of the grindstone table 12 and the rotational movement of the worktable W around the spindle of the spindle table 11.
[0020]
As shown in FIG. 3, when the measuring element 17 measures the left and right pressure angle errors Δfa _L and Δfa _R , the tooth streak direction error ΔL, and the tooth thickness th in the workpiece (gear) W, the measurement result is used as the NC device 15. Is output to the correction amount calculation unit 21. This correction amount calculation unit 21 calculates an error calculation unit 22 that calculates a tooth thickness error Δth from the target tooth thickness and the measured tooth thickness th, and a lead correction that sets a correction amount ΔP of the lead error based on the tooth line direction error ΔL. X, Y, A correction unit 24 for setting the correction amount ΔX, ΔY of the grindstone center position error and the correction amount ΔΣ of the grindstone mounting angle error based on the pressure angle errors Δfa _L , Δfa _R and the tooth thickness error th. And have.
[0021]
In this case, in the lead correction unit 23 and the X / Y / A correction unit 24, the wheel center position errors ΔX and ΔY, the lead error ΔP, and the wheel mounting angle error ΔΣ are the pressure angle errors Δfa _L and Δfa _R , and the tooth trace direction error ΔL. , The mutual influence on the tooth thickness error Δth is analyzed in advance, and based on the analysis result, the wheel center is set so that the pressure angle errors Δfa _L and Δfa _R , the tooth line direction error ΔL, and the tooth thickness error Δth are reduced. A position error correction amount ΔX, ΔY, a lead error correction amount ΔP, and a grinding wheel mounting angle error correction amount ΔΣ are set.
[0022]
The applicant firstly determines how the pressure angle errors ΔfaL and ΔfaR, the tooth line direction error ΔL, and the tooth thickness error Δth affect the wheel center position errors ΔX and ΔY, the lead error ΔP, and the wheel mounting angle error ΔΣ. Was investigated by forming grinding simulation. Then, the pressure angle errors ΔfaL and ΔfaR are affected by all items, but the tooth line direction error ΔL is affected only by the lead error ΔP, the tooth thickness error Δth is the wheel center position error ΔX, the lead error ΔP, and the wheel mounting. It was found that it was affected by the angular error ΔΣ.
[0023]
Next, in the tooth profile error propagation analysis, the errors of the gear machining apparatus to be used (grinding wheel center position errors ΔX, ΔY, lead error ΔP, wheel mounting angle error ΔΣ) are converted into tooth profile errors (pressure angle error Δfa _L , It was analyzed how Δfa _R , tooth line direction error ΔL, and tooth thickness error Δth) were propagated. Then, in the helical gear, the tooth profile error propagation equations 1 to 3 for the respective error amounts could be obtained as follows. In the spur gear, the tooth profile error propagation equations for the respective error amounts are 1 and 3.
[0024]
[Expression 1]

[0025]
[Expression 2]

[0026]
[Equation 3]

[0027]
From such an analysis result, only the lead error correction amount ΔP is used to correct the tooth trace direction error ΔL, and first, this lead correction amount ΔP is first divided into two from the measured tooth direction error ΔL. To calculate. Next, considering the lead correction amount ΔP, the wheel center position correction amounts ΔX and ΔY and the wheel mounting angle correction amount ΔΣ that correct the pressure angle errors ΔfaL and ΔfaR and the tooth thickness error Δth are calculated using the downhill simplex method. calculate. In this downhill simplex method, the evaluation value is the sum of the square value of the left tooth surface pressure angle error ΔfaL, the square value of the right tooth surface pressure angle error ΔfaR, and the square value of the tooth thickness error Δth. By minimizing using the function, the correction amounts ΔX and ΔY of the grindstone center position error and the correction amount ΔΣ of the grindstone mounting angle error that can simultaneously correct the pressure angle errors ΔfaL and ΔfaR and the tooth thickness error Δth are set.
[0028]
For example, in a helical gear, first, in order to correct the tooth trace direction error ΔL, it is necessary to obtain a lead error correction amount ΔP. In the tooth trace error propagation analysis, the tooth trace direction error ΔL is expressed on the Z-Y coordinate, and therefore, as shown in FIG. 2, the tooth profile curve at each end in the tooth width direction (indicated by a one-dot chain line) Display), how much error each tooth profile curve has in the vicinity of the pitch circle is obtained, a tooth trace chart is obtained, and the tooth trace direction error ΔL is obtained. Here, how the tooth trace chart changes when the read error ΔP occurs is obtained using the above-described formula 2.
[0029]
At tooth profile error propagation analysis, point sequence of involute tooth (X _0, Y ₀₎ is adapted to that shown in FIG. 4 (a), the grinding wheel center position error [Delta] X = 0, when it is [Delta] Y = 0 is processed It becomes a tooth profile chart according to the target value. Therefore, by inputting an appropriate numerical value to ΔP in Equation 2, the involute tooth profile point sequence (X ₀ ′, Y ₀ ′) shown in FIG. 4A is obtained at each end in the tooth width direction. Ask for. in this case,
ΔX = X ₀ ′ −X ₀
ΔY = Y ₀ ′ −Y ₀
The tooth trace direction errors ΔL _T ′ and ΔL _B ′ at the upper and lower ends in the tooth width direction are obtained from ΔX and ΔY, and the sum of these ΔL _T ′ and ΔL _B ′ is the direction of the tooth trace in the vicinity of the pitch circle. The error ΔL ′ results in a tooth profile chart as shown in FIG.
[0030]
A correction amount ΔP of the lead error is obtained from the tooth direction error ΔL ′ thus obtained using a bisection method. In other words, if the difference between the tooth trace direction error ΔL ′ and the measured tooth trace direction error ΔL becomes zero, the actual read error ΔP is accurately estimated, and in practice, the minimum correction is performed. The amount ΔP is obtained.
[0031]
When the lead error correction amount ΔP is set in this way, the grinding wheel center position correction amounts ΔX and ΔY and the wheel mounting angle are then calculated from the pressure angle errors Δfa _L and Δfa _{R of} the left and right tooth surfaces and the tooth thickness error Δth. The error ΔΣ is obtained. In this case, it is necessary to consider the effects of the pressure angle errors Δfa _L and Δfa _R and the tooth thickness error Δth due to the lead error correction amount ΔP. That is, ΔX ₀ and ΔY ₀ are obtained from the read error ΔP using Equation 2 described above.
[0032]
In the tooth profile error propagation analysis, the point sequence (X ₀ , Y ₀ ) of the involute tooth profile is as shown in FIG. 4 (a). When the grinding wheel center position error ΔX = 0, ΔY = 0, machining is performed. become tooth profile chart of the desired value as the pressure angle error .delta.fa _L = 0, a Δfa _R = 0. Here, how the tooth profile chart changes when the whetstone center position errors ΔX and ΔY are generated is obtained using the above-described equation (1). That is, by inputting appropriate numerical values to ΔX and ΔY in Equation 1, the involute tooth profile point sequence (X ₀ ′, Y ₀ ′) shown in FIG. in this case,
X ₀ ′ = X ₀ + ΔX
Y ₀ ′ = Y ₀ + ΔY
However, ΔX ₀ and ΔY ₀ obtained from Formula 2 from the read error ΔP are added to X ₀ ′ and Y ₀ ′. Then, a tooth profile chart as shown in FIG. 4C is obtained from the obtained data (X ₀ ′, Y ₀ ′), and the pressure angle error Δfa _L ′ (Δfa _R ′) can be obtained.
[0033]
Similarly, by inputting an appropriate numerical value to the grindstone mounting angle error ΔΣ using the above-described Equation 3, the involute tooth profile (X ₀ ′, Y ₀ ′) is obtained, and the obtained data ( Tooth profile error Δth ′ is obtained by obtaining a tooth profile chart from X ₀ ′, Y ₀ ′).
[0034]
From the pressure angle errors Δfa _L ′, Δfa _R ′ and the tooth thickness error Δth ′ thus determined, the correction amounts ΔX, ΔY of the grindstone center position error and the correction amount ΔΣ of the grindstone mounting angle error are calculated using the downhill simplex method. Ask. In this case, the evaluation function f is given by the following equation.
f = (Δfa _L ′ −Δfa _L ) ² + (Δfa _R ′ −Δfa _R ) ²
+ (Δth′−Δth) ²
If the evaluation function f = 0 with respect to the correction amounts ΔX, ΔY, ΔΣ estimated using this mathematical formula, the actual wheel center position error ΔX, ΔY and the wheel mounting angle error ΔΣ are accurately estimated. In fact, correction amounts ΔX, ΔY, ΔΣ that minimize the evaluation function f are obtained.
[0035]
Such calculation is performed in the NC device 15, and as shown in FIG. 5, the left tooth profile pressure angle error Δfa _L and the right tooth profile pressure are measured on the display unit 25 of the NC device 15 as measurement data of the workpiece W. The angle error Δfa _R , the tooth line direction error ΔL, and the tooth thickness error Δth are displayed, and the correction amount ΔX, ΔY of the wheel center position error (X, Y axis error) and the wheel mounting angle error (A axis error) are operated by the personal computer 18. ) And the read error correction amount ΔP are calculated and displayed. Therefore, the NC device 15 corrects the position of the grinding wheel 14 based on the correction amounts ΔX, ΔY, ΔΣ, ΔP, for example, in the tooth profile shape of the workpiece W, as shown in FIG. Processing close to the target value can be performed.
[0036]
As described above, in the gear machining apparatus according to the present embodiment, after the grinding process is finished, the measuring element 17 causes the right and left pressure angle errors ΔfaL and ΔfaR in the workpiece (gear) W, the tooth trace direction error ΔL, and the tooth thickness error. Δth is measured and calculated. First, a lead correction amount ΔP is calculated from the measured tooth line direction error ΔL using a bisection method. Next, the measured pressure angle error ΔfaL is calculated in consideration of the lead correction amount ΔP. , and to calculate the grinding wheel center position correction amount [Delta] X, [Delta] Y and the grindstone mounting angle correction amount ΔΣ using downhill simplex method so that the evaluation function f is minimized from ΔfaR and tooth thickness error .DELTA.th.
[0037]
Accordingly, the wheel center position correction amounts ΔX and ΔY, the lead correction amount ΔP, and the wheel mounting angle in consideration of the mutual influences of the left and right pressure angle errors ΔfaL and ΔfaR, the tooth direction error ΔL, and the tooth thickness error Δth in the gear W. Since the correction amount ΔΣ is obtained, the position of the grinding wheel 14 can be corrected early and with high accuracy, and workability can be improved.
[0038]
In the above-described embodiment, in the helical gear, the wheel center position correction amounts ΔX and ΔY, the lead correction amount ΔP, and the wheel mounting angle correction amount ΔΣ are calculated from the pressure angle errors ΔfaL and ΔfaR, the tooth line direction error ΔL, and the tooth thickness error Δth. In the case of the spur gear, the lead correction amount ΔP is not considered, but the pressure angle errors ΔfaL, ΔfaR, the tooth line direction error ΔL, and the tooth thickness error Δth are used to calculate the wheel center position correction amounts ΔX, ΔY , The grindstone mounting angle correction amount ΔΣ may be obtained.
[0039]
In the above-described embodiment, the measurement head 16 provided in the vicinity of the grindstone table 12 is used as an error measurement unit. However, an external measurement device that measures a pressure angle error, a tooth line direction error, and a tooth thickness in advance may be used.
[0040]
【The invention's effect】
As described above, according to the gear cutting method of the first invention, as described in detail in embodiments, the gear cutting method according to profile grinding with form-grinding wheel, processed difference and tooth thickness error erroneous pressure angle at the gear While measuring or calculating based on the measured value, the influence of the pressure angle error due to the wheel center position error and the wheel mounting angle error, and the influence of the tooth thickness error due to the wheel center position error and the wheel mounting angle error , previously analyzed, the correction amount of the grinding wheel center position and the grindstone mounting angle as erroneous difference and tooth thickness error is reduced pressure angle, based on the analysis results are respectively set, again in consideration of the respective correction amount since processing the gear, it becomes possible to obtain a grinding wheel center position correction amount in consideration of the mutual impact and the grindstone mounting angle correction amount at a pressure angle erroneous difference and the tooth thickness error in the workpiece, early, and precision a grinding wheel Can perform the position fix, it is possible to improve workability.
[0041]
Further, according to the gear machining method of the second invention, in the gear machining method by forming grinding using the general-purpose grindstone, the pressure angle error, the tooth line direction error and the tooth thickness error in the machined gear are measured or measured values. while calculated based, the pressure angle error grindstone center position error, lead error and the influence received by the grindstone mounting angle error, the effect of the tooth trace direction error is subjected by the read error, the tooth thickness error grindstone center position error The effect of the lead error and the wheel mounting angle error is analyzed in advance, and the wheel center position, the lead and the wheel are such that the pressure angle error, the tooth line direction error and the tooth thickness error are reduced based on the analysis result. each correction amount of the mounting angle was set respectively, since the processing again gear in consideration of the respective correction amount, put in pressure angle error, tooth trace direction error and tooth thickness error in the workpiece Grindstone center position correction amount in consideration of the mutual influence, it becomes possible to obtain a lead correction amount and the grindstone mounting angle correction amount, early, and can perform position correction of the high precision grinding wheel, the workability Can be improved.
[0042]
According to the gear machining method of the third aspect of the invention, the lead correction amount is calculated from the tooth direction error using the bisection method, so that the lead correction amount can be easily calculated by excluding the error items that are not affected. can do.
[0043]
According to the gear machining method of the fourth invention, the grinding wheel center position correction amount and the grinding wheel mounting angle correction amount are calculated using the downhill simplex method from the pressure angle error and the tooth thickness error. It is possible to perform highly accurate calculations with sufficient consideration of the degree of influence.
[0044]
According to the gear machining method of the fifth invention, the downhill simplex method uses the sum of the square value of the pressure angle error and the square value of the tooth thickness error as an evaluation function, and uses this evaluation function to minimize Therefore, since the grinding wheel center position correction amount and the grinding wheel mounting angle correction amount are set, highly accurate calculation can be easily executed by using the evaluation function.
[0045]
Further, according to the gear machining apparatus of the sixth aspect of the present invention, in the gear machining apparatus by forming grinding using the overall shape grindstone,
A grindstone supported so as to be rotatable and movable in three directions orthogonal to each other;
Drive control means for controlling the rotation and movement of the grindstone;
And error measuring means for calculating, based on the measurement or measurements of the pressure angle erroneous difference and the tooth thickness error (and the tooth trace direction error) in Grinding processed gear by said grinding wheel,
The effect of the pressure angle error due to the wheel center position error and the wheel mounting angle error, and the effect of the tooth thickness error due to the wheel center position error and the wheel mounting angle error (and the effect of the tooth line direction error due to the lead error) setting the respective correction amounts of based on previously analyzed analysis result pressure angle erroneous difference and the tooth thickness error (and the tooth trace direction error) grinding wheel center position and the grindstone mounting angle as to decrease (and lead), respectively Correction amount calculating means to perform,
And correction control means for correcting the grinding wheel center position and the grindstone mounting angle based on the correction amount of the grinding wheel center position and the grindstone mounting angle is calculated (and read) (and read) by the correction amount calculation means,
Therefore, the wheel center position correction amount and the wheel mounting angle correction amount ( and lead correction amount) are calculated in consideration of the mutual effects of the pressure angle error and tooth thickness error (and tooth trace direction error) on the workpiece. As a result, the position of the grinding wheel can be corrected at an early stage and with high accuracy, workability can be improved, and the apparatus can be simplified.
[0046]
According to the gear machining apparatus of the seventh aspect of the invention, the error measurement means is provided in the vicinity of the grindstone so that the various errors can be measured or calculated at the work support position, so that the measurement accuracy can be improved and the measurement can be performed. Work can be performed in a short time, and it can contribute to size reduction of an apparatus.
[0047]
According to the gear machining apparatus of the eighth invention, since the error measuring means is an external measuring machine that measures the various errors in advance, the operation can be performed in a short time and the apparatus can be miniaturized.
[Brief description of the drawings]
FIG. 1 is a schematic view of a gear machining apparatus according to an embodiment of the present invention.
FIG. 2 is a schematic view of a gear shape measuring apparatus.
FIG. 3 is a control block diagram of the NC device.
FIG. 4 is an involute tooth profile and a tooth profile chart for explaining tooth profile error propagation analysis;
FIG. 5 is a schematic view of a display unit in the NC apparatus.
FIG. 6 is a tooth profile chart showing tooth profile shapes before and after correction by the gear machining apparatus of the present embodiment.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 11 Headstock 12 Grinding wheel base 14 Grinding wheel 15 NC device 16 Measuring head 17 Measuring element 18 Personal computer 21 Correction amount calculation part 22 Error calculation part 23 Lead correction part 24 X, Y, A correction part 25 Display part

Claims (9)

In gear cutting method according to profile grinding with form-grinding wheel, processed while calculating on the basis of the pressure angle erroneous difference and tooth thickness errors in the measurement or measurements in gear, the pressure angle error grindstone center position error and the grindstone mounting and influence received by the angular errors, the tooth thickness error in advance by analyzing the influence received by the grindstone center position error and the grindstone mounting angle error, in advance, erroneous difference and tooth thickness error is reduced pressure angle on the basis of the analysis result gear cutting method characterized by the correction amount of the grinding wheel center position and the grindstone mounting angle as the respectively set, to process the re-gear in consideration of the respective correction amounts. In gear cutting method according to profile grinding with form-grinding wheel, the pressure angle error at the processed gear, while calculating on the basis of the measurement or measurements of the tooth trace direction error and tooth thickness error, the pressure angle error grindstone center position Error, lead error and grinding wheel mounting angle error, influence of tooth direction error due to lead error, and influence of tooth thickness error due to grinding wheel center position error, lead error and grinding wheel mounting angle error. Analyze in advance, and set each correction amount of the wheel center position, lead and wheel mounting angle so that the pressure angle error, tooth direction error and tooth thickness error are reduced based on the analysis results. A gear machining method, wherein the gear is machined again in consideration of the amount.   3. The gear machining method according to claim 2, wherein the lead correction amount is calculated from the tooth line direction error using a bisection method. 3. The gear machining method according to claim 1, wherein the grinding wheel center position correction amount and the grinding wheel mounting angle correction amount are calculated by using a downhill simplex method from the pressure angle error and the tooth thickness error. Processing method. 5. The gear machining method according to claim 4, wherein the downhill simplex method uses an addition value of the square value of the pressure angle error and the square value of the tooth thickness error as an evaluation function, and minimizes the evaluation function. Thus, the gear processing method is characterized in that the grinding wheel center position correction amount and the grinding wheel mounting angle correction amount are set. In gear processing equipment by forming grinding using a general grinding wheel,
A grindstone supported so as to be rotatable and movable in three directions orthogonal to each other;
Drive control means for controlling the rotation and movement of the grindstone;
And error measuring means for calculating on the basis of the pressure angle erroneous difference and tooth thickness errors in the measurement or measurements at ground machined gear by said grinding wheel,
Based on the analysis results obtained by analyzing in advance the influence of the pressure angle error due to the wheel center position error and the wheel mounting angle error and the influence of the tooth thickness error due to the wheel center position error and the wheel mounting angle error. a correction amount calculation means for setting the correction amount of the grinding wheel center position and the grindstone mounting angle as erroneous difference and tooth thickness error is reduced, respectively,
And correction control means for correcting the grinding wheel center position and the grindstone mounting angle based on the correction amount of the grinding wheel center position and the grindstone mounting angle calculated by the correction amount calculation means,
A gear machining apparatus characterized by comprising: In gear processing equipment by forming grinding using a general grinding wheel,
A grindstone supported so as to be rotatable and movable in three directions orthogonal to each other;
Drive control means for controlling the rotation and movement of the grindstone;
Error measurement means for measuring a pressure angle error, a tooth line direction error and a tooth thickness error in a gear ground by the grinding wheel or calculating based on a measurement value ;
The effect of the pressure angle error due to the wheel center position error, the lead error and the wheel mounting angle error, the effect of the tooth direction error due to the lead error, and the tooth thickness error as the wheel center position error, the lead error and the wheel mounting error. Based on the analysis results obtained by analyzing in advance the effects of angle errors, the correction values for the wheel center position, lead and wheel mounting angle are set to reduce the pressure angle error, tooth direction error and tooth thickness error. Correction amount calculating means to perform,
Correction control means for correcting the grindstone center position, the lead and the grindstone mounting angle based on the correction amounts of the grindstone center position, the lead and the grindstone mounting angle calculated by the correction amount calculating means;
A gear machining apparatus characterized by comprising: 8. The gear machining apparatus according to claim 6, wherein the error measuring means is provided in the vicinity of the grindstone, and the various errors can be measured at a position where the workpiece is supported. 8. The gear machining apparatus according to claim 6, wherein the error measuring means is an external measuring machine that measures the various errors in advance.

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