WO2011125533A1 - 歯車測定装置の校正方法 - Google Patents
歯車測定装置の校正方法 Download PDFInfo
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- WO2011125533A1 WO2011125533A1 PCT/JP2011/057279 JP2011057279W WO2011125533A1 WO 2011125533 A1 WO2011125533 A1 WO 2011125533A1 JP 2011057279 W JP2011057279 W JP 2011057279W WO 2011125533 A1 WO2011125533 A1 WO 2011125533A1
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- gear
- tooth profile
- measured
- tooth
- error
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B5/00—Measuring arrangements characterised by the use of mechanical techniques
- G01B5/20—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures
- G01B5/202—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures of gears
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/021—Gearings
Definitions
- the present invention relates to a method for calibrating a gear measuring device, which is devised so that the position of the probe can be calibrated without using a mechanical reference member such as a reference block.
- the gear processing machine is a machine for processing a gear to be processed, and specifically, there are a gear shaper and hobbing machine for producing a gear by cutting, a gear grinding machine for grinding a gear after quenching, and the like.
- a gear shaper and hobbing machine for producing a gear by cutting
- a gear grinding machine for grinding a gear after quenching, and the like.
- Tooth shape measurement and tooth thickness measurement for a gear to be processed are performed by a gear measuring device including a measuring instrument having a probe (probe).
- a gear measuring device is generally configured as a separate device from the gear processing machine.
- the gear measuring device is separate from the gear processing machine, it is necessary to replace the gear to be processed from the gear processing machine to the gear measuring device.
- the gear measuring device has been installed so that the tooth profile measurement and the tooth thickness measurement can be performed on the machined gear after machining.
- Various gear processing machines provided as a unit have been proposed (see, for example, Patent Document 1).
- the measuring element (probe) of the measuring instrument when the measuring element (probe) of the measuring instrument is brought into contact with the workpiece gear, the position of the measuring element in contact with the workpiece gear is indicated. A position signal is output from the measuring instrument.
- the tooth profile and the tooth thickness can be measured by changing the position at which the probe contacts the gear to be processed and calculating the position signal at each position.
- FIG. 8 shows a gear measuring device 1 for measuring a small or medium gear.
- a guide rail 3 extending along the X-axis direction
- a rotary table 4 and a support column 5 are arranged on the base 2 of the gear measuring device 1.
- the moving body 6 can move along the X-axis direction along the guide rail 3.
- the moving body 6 is provided with a guide rail 7 extending in the Y-axis direction (perpendicular to the paper surface in FIG. 8), and the moving body 8 can move along the Y-axis direction.
- a guide rail 9 extending along the Z-axis direction is disposed on the moving body 8, and the moving body 10 can move along the Z-axis direction.
- the measuring device 30 including the measuring element 31 is attached to the moving body 10.
- any one of a reference block 21, a test bar 22, and a master work 23, which are mechanical reference members, is installed at a predetermined reference position.
- the reference block 21 is installed on the support arm portion of the support column 5. In this case, the position where the reference block 21 is installed is used as the reference position.
- the test bar 22 is coaxially installed on the upper surface of the turntable 4, and in this case, the position where the test bar 22 is installed is used as the reference position.
- the master work 23 is coaxially installed on the upper surface of the turntable 4. In this case, the position where the master work 23 is installed is used as the reference position.
- the probe 31 When the position of the probe 31 is calibrated, the probe 31 is brought into contact with a mechanical reference member (any one of the reference block 21, the test bar 22, and the master work 23) installed at the reference position. At this time, the position signal output from the measuring device 30 is inspected. When the position signal does not indicate the reference position, calibration is performed so that the position signal output at this time indicates the reference position.
- a mechanical reference member any one of the reference block 21, the test bar 22, and the master work 23
- a mechanical reference member (reference block 21, test bar 22, master work 23) is required, and the reference member is attached. There is a problem that it takes work time to remove or remove.
- FIG. 9 shows a gear measuring device 11 for measuring a large gear.
- 12 is a base
- 13 and 19 are guide rails extending along the X-axis direction, Y-axis direction and Z-axis direction, respectively
- 14 is a rotary table
- 16, 18 and 20 are respectively X-axis direction.
- 30 is a measuring instrument attached to the moving body 20
- 31 is a measuring element.
- a support column is not provided in order to reduce the installation space.
- the present invention has been made in view of the above prior art, and an object of the present invention is to provide a gear measuring device calibration method that can calibrate the position of a probe without a mechanical reference member.
- a position signal indicating the position at which the measuring element contacts the gear to be measured is output, and each direction in the three-dimensional direction is output.
- a measuring instrument driven along In the gear measuring device having arithmetic means for measuring the gear to be measured by calculating the position signal, When the measuring element comes into contact with the tooth surface of the gear to be measured by rotating the measured gear around its rotation axis in synchronization with moving the measuring element in the tangential direction of the basic circle.
- Calculating the tooth profile of the gear to be measured by calculating the output position signal, and determining the tooth profile gradient error ( ⁇ 1) of the gear to be measured from the tooth profile;
- the measuring element contacts the tooth surface of the measured gear by rotating the measured gear around its rotation axis in synchronization with moving the measuring element in a direction other than the tangential direction of the basic circle.
- Calculating a tooth profile of the gear to be measured by calculating a position signal output when the gear is measured, and obtaining a tooth profile gradient error ( ⁇ 2) of the gear to be measured from the tooth profile; Calculating a difference ( ⁇ ) in the tooth profile gradient error which is a difference between the tooth profile gradient error ( ⁇ 1) and the tooth profile gradient error ( ⁇ 2); Determining the position error ( ⁇ x) of the probe using the difference in the tooth profile gradient error ( ⁇ ) and the gear specifications of the gear to be measured; And calibrating the position of the measuring element based on the position error ( ⁇ x).
- the position error ( ⁇ x) is calculated using the following equation:
- ⁇ A is the tooth tip measurement offset angle
- ⁇ B is the tooth root measurement offset angle
- ⁇ 21 tan ⁇ 1 [(Do 2 ⁇ Dg 2 ) 0.5 + d] / Dg]
- ⁇ 22 tan ⁇ 1 [(Dr 2 ⁇ Dg 2 ) 0.5 + d] / Dg].
- the tooth tip measurement offset angle ⁇ A and the tooth root measurement offset angle ⁇ B are angles shown in FIG.
- the position of the measuring element can be calibrated by arithmetic processing from the difference in the tooth profile gradient error of the tooth profile measurement obtained in two steps. Further, if the same tooth is measured in two steps, Since the cause of the tooth profile error can be canceled, calibration using the gear to be machined is also a candidate. If it can be calibrated using the gear to be machined, it is not necessary to use mechanical reference members (reference block, test bar, master work), and the time required for mounting / removing mechanical reference members Can be eliminated.
- the block diagram which shows the gear measuring apparatus to which this invention method is applied The perspective view which shows a part of workpiece
- work (measuring gear, to-be-processed gear).
- FIG. 1 shows a gear measuring apparatus 101 to which the method of the present invention is applied.
- a guide rail 103 extending along the X-axis direction and a rotary table 104 are arranged on a base 102 of the gear measuring device 101.
- the rotary table 104 can rotate around the rotation axis C.
- the moving body 106 can move along the X-axis direction along the guide rail 103.
- a guide rail 107 extending in the Y-axis direction (perpendicular to the paper surface in FIG. 1) is disposed on the moving body 106, and the moving body 108 can move along the Y-axis direction.
- a guide rail 109 extending along the Z-axis direction (vertical direction) is disposed on the moving body 108, and the moving body 110 can move along the Z-axis direction.
- a measuring instrument 130 having a measuring element 131 is attached to the moving body 110.
- a large workpiece (measuring gear, workpiece gear) W (see FIG. 2) after grinding is placed coaxially.
- the measuring instrument 130 (measuring element 131) is driven (moved) along each three-dimensional direction by driving the moving bodies 106, 108, and 110 along the X-axis, Y-axis, and Z-axis directions, respectively.
- the measuring device 130 outputs a position signal indicating the contact position.
- the control calculation device 140 is a device that controls the entire gear measurement device 101 in an integrated manner and calculates the position signal. That is, the control arithmetic unit 140 moves the moving bodies 106 and 108 based on the gear specifications of the workpiece W, the position (coordinates) of the measuring element 131, the tooth profile measurement position, and the tooth thickness measurement position that are set and stored in advance. , 110 in the X, Y, and Z axis directions are controlled to control the movement of the measuring instrument 130 (measuring element 131) in the X, Y, and Z axis directions, and the rotary table 104 on which the workpiece W is placed. The rotation around the rotation axis C is controlled. Further, the control arithmetic device 140 measures the tooth profile and the tooth thickness based on the position signal output from the measuring instrument 130 and calibrates the position of the measuring element 131.
- L represents a tangent to the basic circle.
- the tangential direction of the basic circle as the scanning direction is the horizontal direction in a normal gear measuring machine, but may be an oblique direction, and this figure is drawn in an oblique direction.
- the workpiece W is first rotated slightly around the rotation axis C as shown in FIG. After the tooth gap is made to face the measuring instrument 130, the measuring instrument 130 is driven in the X-axis, Y-axis, and Z-axis directions, and the measuring element 131 contacts the intersection with the root circle on the tooth surface of the workpiece W. Let That is, this intersection is the measurement start position # 1 on the tooth surface.
- the measuring instrument 130 is driven in the X-axis and Y-axis directions so as to move the measuring element 131 along the tangent L of the basic circle from the state in which the measuring element 131 is in contact with the measurement start position # 1.
- the rotary table 104 is driven to rotate the workpiece W around the rotation axis C.
- the probe 131 is an analog probe
- the probe 131 is continuously in contact with the tooth surface of the workpiece W.
- the probe 131 is a digital type (on-off type)
- the probe 131 is used.
- each position where the tooth surface of the workpiece W intersects the tangent line L of the basic circle is determined.
- a position signal shown is output from the measuring instrument 130.
- the control operation device 140 performs an arithmetic process on the position signal output from the measuring instrument 130 when the measuring element 131 moves from the measurement start position # 1 to the measurement end position # 2, so that the workpiece W
- the tooth profile can be determined. Based on the tooth profile obtained by calculation, the tooth profile gradient error ⁇ 1 of the workpiece W can be obtained.
- the contact angle at the measurement start position # 1 is ⁇ 12
- the contact angle at the measurement end position # 2 is ⁇ 11
- the position error (positional deviation in the X-axis direction) is ⁇ x.
- the contact angle between the tooth surface of the workpiece W and the measuring element 131 does not substantially change, that is, ⁇ 11 and ⁇ 12 are substantially equal. Even if there is a position error (position shift in the X-axis direction) ⁇ x, there is a characteristic that the measurement error e1 of the tooth profile gradient error ⁇ 1 hardly occurs.
- the workpiece W is slightly rotated around the rotation axis C, and the tooth groove of the workpiece W is formed.
- the measuring device 130 is driven in the X-axis, Y-axis, and Z-axis directions, and the measuring element 131 is brought into contact with the intersection with the root circle on the tooth surface of the workpiece W. That is, this intersection is the measurement start position # 3 on the tooth surface.
- the rotary table 104 is driven to rotate the workpiece W around the rotation axis C.
- the probe 131 is an analog probe
- the probe 131 is continuously in contact with the tooth surface of the workpiece W.
- the probe 131 is a digital type (on-off type)
- the probe 131 is used.
- the control arithmetic device 140 performs arithmetic processing on the position signal output from the measuring instrument 130 when the measuring element 131 moves from the measurement start position # 3 to the measurement end position # 4, so that the workpiece W
- the tooth profile can be determined. Based on the tooth profile obtained by calculation, the tooth profile gradient error ⁇ 2 of the workpiece W can be obtained.
- the contact angle at the measurement start position # 3 is ⁇ 22
- the contact angle at the measurement end position # 4 is ⁇ 21
- there is a position error in the probe 131 is ⁇ x
- the position error (positional deviation in the X-axis direction) is ⁇ x.
- the contact angle between the tooth surface of the workpiece W and the measuring element 131 changes, that is, ⁇ 21 and ⁇ 22 are different.
- the measurement error e2 of the tooth profile gradient error ⁇ 2 is larger than the measurement error e1 in the first method (basic circle tangential direction scanning method).
- the measuring device 130 is driven in the X-axis, Y-axis, and Z-axis directions, and the measuring element 131 is brought into contact with the intersection intersecting the pitch circle on the right tooth surface WR of the workpiece W.
- the control arithmetic device 140 performs arithmetic processing on the position signal output from the measuring instrument 130, and detects the position at this time.
- the measuring device 130 is driven in the X-axis, Y-axis, and Z-axis directions, and the measuring element 131 is brought into contact with the intersection intersecting the pitch circle on the left tooth surface WL of the workpiece W.
- the control arithmetic device 140 performs arithmetic processing on the position signal output from the measuring instrument 130, and detects the position at this time.
- the tooth thickness of the workpiece W can be measured based on the position of the intersection on the right tooth surface WL and the position of the intersection on the left tooth surface WR.
- the control arithmetic device 140 obtains the tooth profile of the workpiece W by using the above-described first method for measuring the tooth profile of the workpiece W (the tangential direction scanning method of the basic circle), and calculates the workpiece W from the tooth profile of the workpiece W obtained by computation.
- the tooth profile gradient error ⁇ 1 is obtained (step S1).
- the obtained tooth profile gradient error ⁇ 1 includes the measurement error e1.
- ⁇ 1 ⁇ w1 + e1 ( ⁇ w1 is a true value of the tooth profile gradient error).
- the control arithmetic device 140 obtains the tooth profile of the workpiece W using the above-described second method (radial scanning method) of the tooth profile measurement of the workpiece W, and calculates the tooth profile gradient error of the workpiece W from the tooth profile of the workpiece W obtained by computation.
- ⁇ 2 is obtained (step S2).
- the obtained tooth profile gradient error ⁇ 2 includes a measurement error e2.
- ⁇ 2 ⁇ w2 + e2 ( ⁇ w2 is a true value of the tooth profile gradient error).
- step S1 and step S2 may be reversed.
- the control arithmetic unit 140 calculates a difference ⁇ of the tooth profile gradient error, which is the difference between the tooth profile gradient error ⁇ 1 obtained in step S1 and the tooth profile gradient error ⁇ 2 obtained in step S2 (step S3).
- the difference ⁇ of the tooth profile gradient error is expressed by the following equation (3).
- ⁇ w1 ⁇ w2
- e1 hardly occurs (e1 ⁇ 0).
- ⁇ e2 ⁇ x (tan ⁇ 21 ⁇ tan ⁇ 22) (4) It can be.
- the control calculation device 140 calculates the position error (position shift in the X-axis direction) ⁇ x of the measuring element 131 using the following formula (5) obtained by modifying the formula (4) (step S4).
- ⁇ x ⁇ / (tan ⁇ 21 ⁇ tan ⁇ 22) (5)
- the basic circle diameter of the workpiece W is Dg
- the outer diameter is Do
- the root diameter is Dr
- the ball diameter of the measuring element is d (see FIG. 6)
- ⁇ 21 and ⁇ 22 in the equation (4) are expressed by the following equations: It is a value given by (6) and (7) (that is, a value given by gear specifications).
- ⁇ 21 tan ⁇ 1 [(Do 2 ⁇ Dg 2 ) 0.5 + d] / Dg] (6)
- ⁇ 22 tan ⁇ 1 [(Dr 2 ⁇ Dg 2 ) 0.5 + d] / Dg] (7)
- the control device 140 calculates the position error (position shift in the X-axis direction) ⁇ x at the position of the probe 131 by the above equation (5), the position signal output from the detector 130 corresponds to the value corresponding to the position error ⁇ x. Is determined to be included. Then, the control device 140 calibrates the stored position (coordinates) of the measuring element 131 according to the position error ⁇ x (step S5). Thereby, the position of the detector 131 can be calibrated.
- the position signal output from the detector 130 indicates an accurate position that does not include a position error. Therefore, if tooth thickness measurement is performed after this calibration, The tooth thickness can be accurately measured (step S6).
- the calibration method of the gear measuring device has a large measurement error e2 included in the tooth profile gradient error ⁇ 2 obtained by the second method (radial scanning method), and the first method (tangent to the basic circle).
- e1 included in the tooth profile gradient error ⁇ 1 obtained by the direction scanning method
- the position error ⁇ x of the measuring element 131 is calculated based on the difference ⁇ in the tooth profile gradient error, and calibration is performed so that the calculated position error ⁇ x is eliminated.
- the influence is the same if the tooth surfaces measured by the two methods are made the same tooth surface because of the influence of the tooth profile shape. ) Can be cancelled. Therefore, the gear required for calibration does not need to be highly accurate like the master gear, and a gear in the middle of processing can be used.
- the position of the probe 131 can be calibrated only by calculation processing, so that it is not necessary to use a mechanical reference member, and time for attaching / detaching the mechanical reference member is eliminated. be able to.
- the scanning direction of the second method (scanning method in a direction other than the tangential direction of the basic circle) may be other than the radius, and according to the method described below, the calibration accuracy can be further improved.
- ⁇ 21 and ⁇ 22 are values determined by the gear specifications according to the equations (6) and (7), but (tan ⁇ 21 ⁇ tan ⁇ 22) means a difference in contact angle between the probe 131 and the workpiece W.
- the difference in the contact angle between the probe 131 and the workpiece W may be increased.
- the difference in the contact angle between the probe 131 and the workpiece W can be increased. That is, ⁇ A is the tooth tip measurement offset angle, ⁇ B is the tooth root measurement offset angle, tan ⁇ 21 is increased to (tan ⁇ 21 + ⁇ A), tan ⁇ 22 is decreased to (tan ⁇ 22 ⁇ B), and the sensitivity is ⁇ tan ( ⁇ 21 + ⁇ A) ⁇ tan ( ⁇ 22 ⁇ ⁇ B) ⁇ .
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Abstract
Description
このような歯車加工機械により、小型の被加工歯車を量産加工する場合には、加工した初品の被加工歯車に対して、歯形測定や歯厚測定をした後、その精度を確認し、精度が良好である場合には残りの未加工ロットを加工し、精度が不良である場合には加工精度の修正をしてから残りの未加工ロットを加工するようにしている。歯車測定機能を持たない歯車加工機械では、またぎ歯厚、オーバーピン径の確認しかできないために、初品は精度不良になることがある。
このような歯車測定装置は、従前では、歯車加工機械とは別体の装置として構成することが一般的であった。歯車測定装置を歯車加工機械とは別体とした場合には、被加工歯車を、歯車加工機械から歯車測定装置に付け替える作業が必要である。
一方、近年では上記の付け替え作業を省略し作業性の向上を図ることを目的として、加工後の被加工歯車に対して、機上で歯形測定や歯厚測定ができるように、歯車測定装置を一体として備えた歯車加工機械が種々提案されている(例えば、特許文献1参照)。
しかし、周囲の温度や被加工歯車の加工時に発生する熱等により、測定器を含む歯車測定装置に熱変形が生じると、測定子が測定器に対しては基準位置に位置していたとしても、被加工歯車に対する位置に対して誤差が生じ、測定時の測定位置がずれてしまうことがある。
ここで、従来の校正方法を、図8を参照して説明する。
移動体6は、ガイドレール3に沿いX軸方向に沿い移動することができる。移動体6にはY軸方向(図8では紙面に垂直方向)に延在したガイドレール7が配置されており、移動体8はY軸方向に沿い移動することができる。移動体8にはZ軸方向に沿い延在したガイドレール9が配置されており、移動体10はZ軸方向に沿い移動することができる。
測定子31を具備した測定器30は、移動体10に取り付けられている。
基準ブロック21は、サポートコラム5のサポートアーム部に設置しており、この場合には、基準ブロック21を設置した位置を基準位置としている。
テストバー22は、回転テーブル4の上面に同軸に設置しており、この場合には、テストバー22を設置した位置を基準位置としている。
マスターワーク23は、回転テーブル4の上面に同軸に設置しており、この場合には、マスターワーク23を設置した位置を基準位置としている。
図9は、大形の歯車の測定をする歯車測定装置11である。同図において、12は基台、13,17,19はそれぞれX軸方向,Y軸方向,Z軸方向に沿い延在したガイドレール、14は回転テーブル、16,18,20はそれぞれX軸方向,Y軸方向,Z軸方向に沿い移動することができる移動体、30は移動体20に取り付けられている測定器、31は測定子である。
なお、この歯車測定装置11では、設置スペースを削減するためサポートコラムは備えられていない。
また、測定子31を回転テーブル14の中心までストロークすることができないので、テストバー22aとしては、大きなものが必要である。
また、マスターワーク23aとしては、大きなものが必要である。
このようにテストバー22aやマスターワーク23aとして大きなものを用意しておかなければならないため、その作製費用や保管費用が大きくなるという問題及び校正を実施するたびにテストバー22aやマスターワーク23aを取り付けたり取り外したりする作業時間を要するという問題がある。
前記位置信号を演算処理することにより、前記被測定歯車の測定をする演算手段とを有する歯車測定装置において、
前記測定子を基礎円の接線方向に移動させるのと同期して前記被測定歯車をその回転軸周りで回転させていくことにより、前記被測定歯車の歯面に前記測定子が接触したときに出力される位置信号を演算処理して前記被測定歯車の歯形を求め、この歯形から前記被測定歯車の歯形こう配誤差(α1)を求める工程と、
前記測定子を基礎円の接線方向以外の方向に移動させるのと同期して前記被測定歯車をその回転軸周りで回転させていくことにより、前記被測定歯車の歯面に前記測定子が接触したときに出力される位置信号を演算処理して前記被測定歯車の歯形を求め、この歯形から前記被測定歯車の歯形こう配誤差(α2)を求める工程と、
前記歯形こう配誤差(α1)と前記歯形こう配誤差(α2)との差である歯形こう配誤差の差(Δα)を算出する工程と、
前記測定子の位置誤差(Δx)を、前記歯形こう配誤差の差(Δα)と前記被測定歯車の歯車諸元を用いて求める工程と、
前記位置誤差(Δx)を基に、前記測定子の位置を校正する工程と、を有することを特徴とする。
次式を用いて位置誤差(Δx)を求めることを特徴とする歯車測定装置の校正方法。
Δx=Δα/{tan(α21+αA)-tan(α22-αB)}
但し、αAは歯先計測オフセット角度、αBは歯元計測オフセット角度であり、
被測定歯車の基礎円直径をDg、外径をDo、歯底直径をDr、測定子のボール径をdとしたときに、
α21=tan-1〔(Do2-Dg2)0.5+d〕/Dg〕
α22=tan-1〔(Dr2-Dg2)0.5+d〕/Dg〕である。
なお、歯先計測オフセット角度αA、歯元計測オフセット角度αBは、図7に示す角度である。
また、測定子を基礎円の接線方向以外の方向に移動させる方向として、半径方向とした場合は、αA=0、αB=0になる(図6参照)。
回転テーブル104は、回転軸C周りに回転することができる。
測定器130(測定子131)は、移動体106,108,110がそれぞれX軸,Y軸,Z軸方向に沿い駆動されることにより、三次元の各方向に沿い駆動(移動)される。測定器130は、測定子131がワークWに接触すると、接触した位置を示す位置信号を出力する。
即ち、制御演算装置140は、予め設定・記憶されている、ワークWの歯車諸元や、測定子131の位置(座標)、歯形測定位置及び歯厚測定位置に基づいて、移動体106,108,110のX,Y,Z軸方向の移動を制御して測定器130(測定子131)のX,Y,Z軸方向の移動を制御し、また、ワークWが載置された回転テーブル104の回転軸C周りの回転を制御する。
更に、制御演算装置140は、測定器130から出力された位置信号を基に、歯形や歯厚を測定すると共に、測定子131の位置の校正をする。
測定子131がアナログ式のプローブである場合には測定子131をワークWの歯面に連続的に接触しつつ、また、測定子131がデジタル式(オンオフ式)である場合には測定子131をワークWの歯面に間欠的に接触しつつ、測定子131が基礎円の接線Lに沿い移動していくことで、ワークWの歯面と基礎円の接線Lとが交差する各位置を示す位置信号が、測定器130から出力される。
e1=Δx(tanα11-tanα12) ・・・(1)
測定子131がアナログ式のプローブである場合には測定子131をワークWの歯面に連続的に接触しつつ、また、測定子131がデジタル式(オンオフ式)である場合には測定子131をワークWの歯面に間欠的に接触しつつ、測定子131が半径方向(X軸方向)に移動していくことで、ワークWの歯面とX軸(測定子131の移動軌跡)とが交差する各位置を示す位置信号が、測定器130から出力される。
e2=Δx(tanα21-tanα22) ・・・(2)
歯厚測定をするには、測定器130をX軸,Y軸,Z軸方向に駆動させて、測定子131を、ワークWの右歯面WR上においてピッチ円と交差する交点に接触させる。このとき測定器130から出力される位置信号を制御演算装置140が演算処理して、このときの位置を検出する。
なお、測定子131の位置に位置誤差(X軸方向の位置ずれ)Δxがある場合には、求めた歯形こう配誤差α1には計測誤差e1が含まれる。ここで、α1=αw1+e1(αw1は歯形こう配誤差の真値)とする。
なお、測定子131の位置に位置誤差(X軸方向の位置ずれ)Δxがある場合には、求めた歯形こう配誤差α2には計測誤差e2が含まれる。ここで、α2=αw2+e2(αw2は歯形こう配誤差の真値)とする。
この歯形こう配誤差の差Δαは、次式(3)により表される。
Δα=α2-α1=(αw1+e1)-(αw2+e2) ・・・(3)
つまり、歯形こう配誤差の差Δαは、「歯形こう配誤差α2」と「歯形こう配誤差α1」の差を示すものとなる。
ここで、ステップ1とステップ2で、同じ歯面を計測すれば、αw1=αw2になること、e1はほとんど生じない(e1≒0)ことを考慮すれば、
Δα≒e2=Δx(tanα21-tanα22) ・・・(4)
とすることができる。
Δx=Δα/(tanα21-tanα22) ・・・(5)
ここにおいて、ワークWの基礎円直径をDg、外直径をDo、歯底直径をDr、測定子のボール径をdとすると(図6参照)、式(4)におけるα21とα22は、次式(6),(7)により与えられる値(即ち、歯車諸元により与えられる値)である。
α21=tan-1〔(Do2-Dg2)0.5+d〕/Dg〕 ・・・(6)
α22=tan-1〔(Dr2-Dg2)0.5+d〕/Dg〕 ・・・(7)
そして、制御装置140は、位置誤差Δxの値に応じて、記憶されている測定子131の位置(座標)に対して校正をする(ステップS5)。これにより検出子131の位置を校正することができる。
このようにして位置誤差があると判定した場合には、歯形こう配誤差の差Δαを基に、測定子131の位置誤差Δxを演算し、演算した位置誤差Δxが無くなるように校正する。
歯形こう配誤差α1、α2の演算において、歯形形状の影響を受けることに対しては、2つの手法で測定する歯面を同じ歯面とすれば、影響が同じになるので、これも式(3)の演算においてキャンセルさせることができる。よって、校正に必要な歯車はマスターギヤのような高精度なものは必要ではなく、加工途中の歯車も使用できる。
式(5)より、測定子131の位置誤差Δxに対する歯形こう配誤差の差Δαの感度は、
Δα/Δx=(tanα21-tanα22)である。
α21とα22は式(6)、(7)により歯車諸元で決まる値であるが、(tanα21-tanα22)は、測定子131とワークWの接触角の差を意味する。感度を高めるには、測定子131とワークWの接触角の差を大きくすれば良い。
(Δα/Δx)={tan(α21+αA)-tan(α22-αB)} ・・・(8)
Δx=Δα/{tan(α21+αA)-tan(α22-αB)} ・・・(9)
つまり、式(9)は位置誤差Δxを示す一般式であり、式(5)は測定子131の移動方向を半径方向に特定したときの位置誤差Δxを示す特定式である。
2,12,102 基台
3,7,9,13,17,19,103,107,109 ガイドレール
4,14,104 回転テーブル
5 サポートコラム
6,8,19,16,18,20,106,108,110 移動体
21 基準ブロック
22 テストバー
23 マスターワーク
30,130 測定器
31,131 測定子
140 制御演算装置
W ワーク
Claims (2)
- 測定子を被測定歯車の歯面に接触させると、前記測定子が前記被測定歯車に接触した位置を示す位置信号を出力すると共に、三次元方向の各方向に沿い駆動される測定器と、
前記位置信号を演算処理することにより、前記被測定歯車の測定をする演算手段とを有する歯車測定装置において、
前記測定子を基礎円の接線方向に移動させるのと同期して前記被測定歯車をその回転軸周りで回転させていくことにより、前記被測定歯車の歯面に前記測定子が接触したときに出力される位置信号を演算処理して前記被測定歯車の歯形を求め、この歯形から前記被測定歯車の歯形こう配誤差(α1)を求める工程と、
前記測定子を基礎円の接線方向以外の方向に移動させるのと同期して前記被測定歯車をその回転軸周りで回転させていくことにより、前記被測定歯車の歯面に前記測定子が接触したときに出力される位置信号を演算処理して前記被測定歯車の歯形を求め、この歯形から前記被測定歯車の歯形こう配誤差(α2)を求める工程と、
前記歯形こう配誤差(α1)と前記歯形こう配誤差(α2)との差である歯形こう配誤差の差(Δα)を算出する工程と、
前記測定子の位置誤差(Δx)を、前記歯形こう配誤差の差(Δα)と前記被測定歯車の歯車諸元を用いて求める工程と、
前記位置誤差(Δx)を基に、前記測定子の位置を校正する工程と、
を有することを特徴とする歯車測定装置の校正方法。 - 請求項1において、
前記測定子の位置誤差(Δx)を、前記歯形こう配誤差の差(Δα)と前記被測定歯車の歯車諸元を用いて求める工程では、
次式を用いて位置誤差(Δx)を求めることを特徴とする歯車測定装置の校正方法。
Δx=Δα/{tan(α21+αA)-tan(α22-αB)}
但し、αAは歯先計測オフセット角度、αBは歯元計測オフセット角度であり、
被測定歯車の基礎円直径をDg、外径をDo、歯底直径をDr、測定子のボール径をdとしたときに、
α21=tan-1〔(Do2-Dg2)0.5+d〕/Dg〕
α22=tan-1〔(Dr2-Dg2)0.5+d〕/Dg〕である。
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CN113427088A (zh) * | 2021-07-07 | 2021-09-24 | 合肥工业大学 | 一种基于数控滚齿机的齿轮在机误差测算装置 |
CN113427088B (zh) * | 2021-07-07 | 2023-06-30 | 合肥工业大学 | 一种基于数控滚齿机的齿轮在机误差测算装置 |
CN114295063A (zh) * | 2021-12-16 | 2022-04-08 | 中国航空工业集团公司北京长城计量测试技术研究所 | 一种花键量规参数测量方法及装置 |
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BR112012021245A2 (ja) | 2018-04-03 |
TWI474891B (zh) | 2015-03-01 |
CN102782441A (zh) | 2012-11-14 |
US20130054172A1 (en) | 2013-02-28 |
EP2554938B1 (en) | 2017-09-27 |
TW201141655A (en) | 2011-12-01 |
EP2554938A4 (en) | 2016-11-02 |
US9212891B2 (en) | 2015-12-15 |
JP2011215090A (ja) | 2011-10-27 |
CN102782441B (zh) | 2015-02-04 |
EP2554938A1 (en) | 2013-02-06 |
JP5255012B2 (ja) | 2013-08-07 |
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