JP2022513552A - How to determine the grindstone trajectory by polishing the complicated tip pocket of the tool - Google Patents
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Abstract
本発明は、工具の複雑なチップポケット研磨による砥石軌跡の決定方法を開示する。当該方法は、砥石の型番、サイズ及び目的工具径ＤＴを決定するステップ（１）と、チップポケット数学モデルｒｓｉを確立するステップ（２）と、砥石半径拘束方程式ｆｃｏｎ１を確立するステップ（３）と、時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップ（４）と、ステップ（４）の目的関数、ステップ（３）の砥石半径拘束方程式ｆｃｏｎ１から、時刻ｔにおける砥石の位置・姿勢を解くステップ（５）と、時刻ｔの値を変えてステップ（３）～ステップ（５）を繰り返し、複雑なチップポケットの砥石軌跡を解くステップ（６）と、を含む。当該方法は、工具の複雑なチップポケット研磨工程に適用可能であり、工具の複雑なチップポケット研磨工程の決定の技術及び方法の面からサポートし、精度が高く、信頼性に優れる。【選択図】図１The present invention discloses a method for determining a grindstone trajectory by polishing a complicated tip pocket of a tool. The method includes a step (1) for determining the model number, size and target tool diameter DT of the grindstone, a step (2) for establishing the chip pocket mathematical model rsi, and a step (3) for establishing the grindstone radius constraint equation fcon1. , The position / orientation of the grindstone at time t from the step (4) for establishing the objective function for solving the position / orientation of the grindstone at time t, the objective function of step (4), and the grindstone radius constraint equation fcon1 in step (3). The step (5) of solving the above step (5) and the step (6) of solving the grindstone trajectory of the complicated tip pocket by repeating steps (3) to (5) by changing the value at time t are included. This method is applicable to the complicated tip pocket polishing process of the tool, supports in terms of the technique and method of determining the complicated tip pocket polishing process of the tool, and has high accuracy and excellent reliability. [Selection diagram] Fig. 1
Description
本発明は、砥石軌跡の決定方法に関し、より具体的には、工具の複雑なチップポケット研磨による砥石軌跡の決定方法に関する。 The present invention relates to a method for determining a grindstone trajectory, and more specifically, to a method for determining a grindstone trajectory by polishing a complicated tip pocket of a tool.
工具の複雑なチップポケットは、すくい角、コア径、溝幅、螺旋角などの構造パラメータが工具軸線に沿って変化することで、工具の剛性、強度、切削性能を効果的に向上させることができ、高性能超硬エンドミルに広く応用されている。しかし、複雑なチップポケット研磨は、いくつかの難点に直面している。第１に、複雑なチップポケットの幾何構造は、砥石形状及び運動軌跡の両方で決められ、工程の求解に係る変数及び拘束条件が多く、「チップポケット構造パラメータ」と「砥石形状＋運動軌跡」との関数関係を直接確立することができない。第２に、従来のチップポケット幾何成形の理論基礎である空間単一パラメータ曲面族包絡理論は、接触線を橋掛けとして砥石と溝の形状との間の関係を確立し、研磨中に接触線が一定である。しかし、接触線が変化し続ける複雑なチップポケット研磨に適用できず、複雑なチップポケット研磨成形の理論基礎に欠ける。従って、従来の包絡理論又は試行錯誤方法に基づいてチップポケット研磨における砥石運動軌跡を求める方法は、複雑な形状のチップポケットに適用できず、複雑なチップポケット製造過程では、砥石軌跡の求解が難しいというネックに直面している。 Complex tip pockets for tools can effectively improve tool rigidity, strength and cutting performance by changing structural parameters such as rake angle, core diameter, groove width and spiral angle along the tool axis. It can be used and is widely applied to high-performance carbide end mills. However, complex chip pocket polishing faces some drawbacks. First, the complex geometric structure of the chip pocket is determined by both the grindstone shape and the motion locus, and there are many variables and constraint conditions related to the solution of the process, "chip pocket structure parameter" and "grindstone shape + motion locus". It is not possible to directly establish a functional relationship with. Second, the spatial single-parameter curved surface group envelope theory, which is the basis of the conventional theory of chip pocket geometry, establishes the relationship between the grindstone and the shape of the groove by bridging the contact line, and the contact line during polishing. Is constant. However, it cannot be applied to complicated chip pocket polishing in which the contact line keeps changing, and lacks the theoretical basis of complicated chip pocket polishing molding. Therefore, the method of obtaining the grindstone motion trajectory in chip pocket polishing based on the conventional envelope theory or trial and error method cannot be applied to a chip pocket having a complicated shape, and it is difficult to solve the grindstone trajectory in a complicated chip pocket manufacturing process. I am facing the neck.
本発明の目的は、工具の複雑なチップポケット研磨工程に適用可能であり、且つ高精度及び信頼性を有する工具を用いた複雑なチップポケット研磨による砥石軌跡の決定方法を提供することである。 An object of the present invention is to provide a method for determining a grindstone trajectory by complicated tip pocket polishing using a tool which is applicable to a complicated tip pocket polishing process of a tool and has high accuracy and reliability.
本発明は、工具の複雑なチップポケット研磨による砥石軌跡の決定方法を提供し、砥石の型番、サイズ及び目的工具径ＤＴを決定するステップ（１）と、チップポケット数学モデルｒｓｉを確立するステップ（２）と、砥石半径拘束方程式ｆｃｏｎ１を確立するステップ（３）と、時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップ（４）と、ステップ（４）の目的関数、ステップ（３）の砥石半径拘束方程式ｆｃｏｎ１から、時刻ｔにおける砥石の位置・姿勢を解くステップ（５）と、時刻ｔの値を変えてステップ（３）～ステップ（５）を繰り返し、複雑なチップポケットの砥石軌跡を解くステップ（６）とを含む。 The present invention provides a method for determining a grindstone trajectory by polishing a complicated tip pocket of a tool, a step (1) for determining a model number, a size and a target tool diameter DT of the grindstone, and a step for establishing a tip pocket mathematical model r si . (2), the step (3) for establishing the grindstone radius constraint equation f con1 , the step (4) for establishing the objective function for solving the position and orientation of the grindstone at time t, and the objective function and step of step (4). From the grindstone radius constraint equation f con1 of (3), the step (5) for solving the position and orientation of the grindstone at time t and the steps (3) to (5) for changing the value at time t are repeated to make a complicated chip. This includes step (6) of solving the grindstone trajectory of the pocket.
ステップ（２）において、
ｒｓｉ＝［ｘｓｉ，ｙｓｉ，ｚｓｉ］＝［ｘｓｉ（θｉ），ｙｓｉ（θｉ），ｚｓｉ（θｉ）］
ｉ＝１、２、３、４は、それぞれ、複雑なチップポケットを表現するためのエッジ曲線、すくい角線、コア径線、背面線を示し、ｘｓｉ、ｙｓｉ、ｚｓｉは、それぞれ、エッジ曲線、すくい角線、コア径線、背面線の工具座標系における座標値であり、θｉは、エッジ曲線、すくい角線、コア径線、背面線のパラメータ方程式を表現する変数である。ｒｓ２とｒｓ１との距離は、０．０５ＤＴ未満であり、ｒｓ３から工具軸線までの距離は、ｒｓ１、ｒｓ２又はｒｓ４から工具軸線までの距離よりも小さい。
In step (2)
r si = [x si , y si , z si ] = [x si (θ i ), y si (θ i ), z si (θ i )]
i = 1, 2, 3, 4 indicate an edge curve, a rake angle line, a core diameter line, and a back line for expressing a complicated chip pocket, respectively, and x si , y si , and z si are, respectively. It is a coordinate value in the tool coordinate system of the edge curve, the rake angle line, the core diameter line, and the back line, and θ i is a variable expressing the parameter equation of the edge curve, the rake angle line, the core diameter line, and the back line. The distance between r s2 and r s1 is less than 0.05 DT, and the distance from r s3 to the tool axis is less than the distance from r s1 , r s2 or r s4 to the tool axis.
ステップ（３）で砥石半径拘束方程式ｆｃｏｎ１を確立するステップは、
（ａ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心座標ｒｏｗを解く。
ｒｏｗ＝［ｘｏｗ，ｙｏｗ，ｚｏｗ］＝［ｘｏｗ（θ１＿ｔ，θ２，θ３），ｙｏｗ（θ１＿ｔ，θ２，θ３），zｏｗ（θ１＿ｔ，θ２，θ３）］
ｘｏｗ、ｙｏｗ、ｚｏｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心の工具座標系における座標値であり、θ１＿ｔは、時刻ｔにおける研磨加工砥石のエッジ曲線上の一点のパラメータ値であり、θ２，θ３は、それぞれ、すくい角線、コア径線パラメータ方程式の変数。
（ｂ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径を解く。
Ｒｗｃ=Ｒｗｃ（θ１＿ｔ，θ２，θ３）
Ｒｗｃは、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径。
（ｃ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルｎｗを解く。
ｎｗ＝［ｘｎｗ，ｙｎｗ，ｚｎｗ］＝［ｘｎｗ（θ１＿ｔ，θ２，θ３），ｙｎｗ（θ１＿ｔ，θ２，θ３），ｚｎｗ（θ１＿ｔ，θ２，θ３）］
ｘｎｗ、ｙｎｗ、ｚｎｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルの工具座標系における座標値。
（ｄ）砥石大端円半径拘束方程式を確立する。
ｆｃｏｎ１＝Ｒｃｗ（θ１＿ｔ，θ２，θ３）－Ｒｗ＝０
Ｒｗは、砥石大端円半径であり、Ｒｗ≧１５ＤＴ、である。
The step of establishing the grindstone radius constraint equation fcon1 in step (3) is
(A) Solve the center coordinates row of a circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
r ow = [x ow , y ow , z ow ] = [x ow (θ 1_t , θ 2 , θ 3 ), y ow (θ 1_t , θ 2 , θ 3 ), z ow (θ 1_t , θ 2 ), θ 3 )]
x ow , you ow , and z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively, and θ 1_t is the polishing at time t. It is a parameter value of one point on the edge curve of the machined grindstone, and θ 2 and θ 3 are variables of the rake angle line and the core diameter line parameter equation, respectively.
(B) Solve the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
R wc = R wc (θ 1_t , θ 2 , θ 3 )
R wc is the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at time t.
(C) Solve the axis vector nw of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at an arbitrary time t.
n w = [x nw , y nw , z nw ] = [x nw (θ 1_t , θ 2 , θ 3 ), y nw (θ 1_t , θ 2 , θ 3 ), z nw (θ 1_t , θ 2 ), θ 3 )]
x nw , y nw , and z nw are coordinate values in the tool coordinate system of the axis vector of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively.
(D) Establish the grindstone large end circular radius constraint equation.
f con1 = R cw (θ 1_t , θ 2 , θ 3 ) -R w = 0
R w is the radius of the large end circle of the grindstone, and R w ≧ 15DT.
ステップ（４）で時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップは、
（ａ）背面線と砥石軸線との間の距離方程式を確立する。
ｄａｘｉｓ＝ｄａｘｉｓ（θ１＿ｔ，θ２，θ３，θ４）
（ｂ）背面線と砥石底面との間の距離方程式を確立する。
ｄｐｌａｎｅ＝ｄｐｌａｎｅ（θ１＿ｔ，θ２，θ３，θ４）
（ｃ）背面線と砥石回転面との間の距離方程式を確立する。
ｄＧＷ＝ｄａｘｉｓ－ｄｐｌａｎｅ／ｔａｎ（θｗ）
θｗは、砥石円錐角である。π／２≧θｗ＞π／６である。
（ｄ）砥石の位置・姿勢の求解目的関数を確立する。
ｆｏｂｊ＝ｍｉｎ（ｄＧＷ（θ１＿ｔ，θ２，θ３，θ４））
(A) Establish a distance equation between the back line and the grindstone axis.
d axis = d axis (θ 1_t , θ 2 , θ 3 , θ 4 )
(B) Establish a distance equation between the back line and the bottom of the grindstone.
d plane = d plane (θ 1_t , θ 2 , θ 3 , θ 4 )
(C) Establish a distance equation between the back line and the surface of revolution of the grindstone.
d GW = d axis -d plane / tan (θ w )
θ w is a grindstone cone angle. π / 2 ≧ θ w > π / 6.
(D) Establish a function for solving the position and orientation of the grindstone.
f obj = min (d GW (θ 1_t , θ 2 , θ 3 , θ 4 ))
ステップ（５）で時刻ｔにおける砥石の位置・姿勢を解くステップとして、ステップ（３）の方程式ｆｃｏｎ１とステップ（４）の砥石の位置・姿勢の求解目的関数から、時刻ｔに対応するエッジ曲線、すくい角線、コア径線及び背面線パラメータθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔを解き、θ１＿ｔ、θ２＿ｔ、θ３＿ｔをステップ（３）の砥石半径方程式ｆｃｏｎ１に代入して時刻ｔにおける砥石の位置・姿勢を解く。時刻ｔに対応するθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔなどのパラメータ値は、直前時刻に対応するパラメータ値以上である。 As a step to solve the position / orientation of the grindstone at time t in step (5), the edge curve corresponding to time t is obtained from the equation f con1 of step (3) and the solution objective function of the position / orientation of the grindstone in step (4). , Scoop angle line, core diameter line and back line parameters θ 1_t , θ 2_t , θ 3_t , θ 4_t are solved, and θ 1_t , θ 2_t , θ 3_t are substituted into the grindstone radius equation f con1 in step (3). Solve the position and posture of the grindstone at t. The parameter values such as θ 1_t , θ 2_t , θ 3_t , and θ 4_t corresponding to the time t are equal to or higher than the parameter values corresponding to the immediately preceding time.
ここで、砥石に１Ａ１又は１Ｖ１型のダイヤモンド砥石を採用し、砥石の径は、１００ｍｍ～２００ｍｍである。 Here, a 1A1 or 1V1 type diamond grindstone is used as the grindstone, and the diameter of the grindstone is 100 mm to 200 mm.
１．工具の複雑なチップポケット研磨工程に適用可能であり、工具の複雑なチップポケット研磨工程の決定技術及び方法の面からサポートする。２．精度が高い。３．信頼性に優れる。 1. 1. It can be applied to the complicated tip pocket polishing process of the tool, and supports the determination technique and method of the complicated tip pocket polishing process of the tool. 2. 2. High accuracy. 3. 3. Excellent reliability.
砥石運動軌跡の全体的な求解フローは、図１に示すように、以下のステップを含む。
（１）１Ｖ１型の標準砥石を採用し、図２に示すように、砥石の厚さＢｗは、１２ｍｍであり、砥石円錐角θｗ＝１．２２１７ｒａｄであり、砥石大端円径ＤＷ＝１１６ｍｍであり、フライスリードＰＴ＝６０ｍｍであり、フライス径ＤＴ＝２０ｍｍである。
The overall solution flow of the grindstone motion locus includes the following steps, as shown in FIG.
(1) A 1V1 type standard grindstone is adopted, and as shown in FIG. 2, the grindstone thickness B w is 12 mm, the grindstone cone angle θ w = 1.2217 rad, and the grindstone large end circular diameter D W. = 116 mm, milling lead PT = 60 mm, and milling diameter DT = 20 mm.
（２）チップポケット数学モデルｒｓｉを確立する。
（３）砥石半径拘束方程式ｆｃｏｎ１を確立するステップは、具体的に以下を含む。
（ａ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心座標ｒｏｗを解く。
ｒｏｗ＝［ｘｏｗ，ｙｏｗ，ｚｏｗ］＝［ｘｏｗ（θ１＿ｔ，θ２，θ３），ｙｏｗ（θ１＿ｔ，θ２，θ３），zｏｗ（θ１＿ｔ，θ２，θ３）］
ここで、ｘｏｗ、ｙｏｗ、ｚｏｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心の工具座標系における座標値であり、θ１＿ｔは、時刻ｔにおける研磨加工砥石のエッジ曲線上の一点のパラメータ値である。
（ｂ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径を解く。
Ｒｗｃ=Ｒｗｃ（θ１＿ｔ，θ２，θ３）
ここで、Ｒｗｃは、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径である。
（ｃ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルｎｗを解く。
ｎｗ＝［ｘｎｗ，ｙｎｗ，ｚｎｗ］＝［ｘｎｗ（θ１＿ｔ，θ２，θ３），ｙｎｗ（θ１＿ｔ，θ２，θ３），ｚｎｗ（θ１＿ｔ，θ２，θ３）］
ここで、ｘｎｗ、ｙｎｗ、ｚｎｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルの工具座標系における座標値である。
（ｄ）砥石大端円半径拘束方程式を確立する。
ｆｃｏｎ１＝Ｒｃｗ（θ１＿ｔ，θ２，θ３）－Ｒｗ＝０
ここで、Ｒｗは、砥石大端円半径である。
(3) The step of establishing the grindstone radius constraint equation f con1 specifically includes the following.
(A) Solve the center coordinates row of a circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
r ow = [x ow , y ow , z ow ] = [x ow (θ 1_t , θ 2 , θ 3 ), y ow (θ 1_t , θ 2 , θ 3 ), z ow (θ 1_t , θ 2 ), θ 3 )]
Here, x ow , y ow , and z ow are coordinate values in the tool coordinate system of the center of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively, and θ 1_t is the time. It is a parameter value of one point on the edge curve of the polished grindstone at t.
(B) Solve the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
R wc = R wc (θ 1_t , θ 2 , θ 3 )
Here, R wc is the radius of a circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t.
(C) Solve the axis vector nw of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at an arbitrary time t.
n w = [x nw , y nw , z nw ] = [x nw (θ 1_t , θ 2 , θ 3 ), y nw (θ 1_t , θ 2 , θ 3 ), z nw (θ 1_t , θ 2 ), θ 3 )]
Here, x nw , y nw , and z nw are coordinate values in the tool coordinate system of the axis vector of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively.
(D) Establish the grindstone large end circular radius constraint equation.
f con1 = R cw (θ 1_t , θ 2 , θ 3 ) -R w = 0
Here, R w is the radius of the large end circle of the grindstone.
（４）時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立する。
（ａ）背面線と砥石軸線との間の距離方程式を確立する。
ｄａｘｉｓ＝ｄａｘｉｓ（θ１＿ｔ，θ２，θ３，θ４）
（ｂ）背面線と砥石底面との間の距離方程式を確立する。
ｄｐｌａｎｅ＝ｄｐｌａｎｅ（θ１＿ｔ，θ２，θ３，θ４）
（ｃ）背面線と砥石回転面との間の距離方程式を確立する。
ｄＧＷ＝ｄａｘｉｓ－ｄｐｌａｎｅ／ｔａｎ（θｗ）
ここで、θｗは、砥石円錐角である。
（ｄ）砥石の位置・姿勢の求解目的関数を確立する。
ｆｏｂｊ＝ｍｉｎ（ｄＧＷ（θ１＿ｔ，θ２，θ３，θ４））
(A) Establish a distance equation between the back line and the grindstone axis.
d axis = d axis (θ 1_t , θ 2 , θ 3 , θ 4 )
(B) Establish a distance equation between the back line and the bottom of the grindstone.
d plane = d plane (θ 1_t , θ 2 , θ 3 , θ 4 )
(C) Establish a distance equation between the back line and the surface of revolution of the grindstone.
d GW = d axis -d plane / tan (θ w )
Here, θ w is a grindstone cone angle.
(D) Establish a function for solving the position and orientation of the grindstone.
f obj = min (d GW (θ 1_t , θ 2 , θ 3 , θ 4 ))
（５）ステップ（３）の方程式ｆｃｏｎ１とステップ（４）の方程式ｆｏｂｊ、ｆｃｏｎ２、ｆｃｏｎ３、ｆｃｏｎ４から、時刻ｔに対応するパラメータθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔを解き、θ１＿ｔ、θ２＿ｔ、θ３＿ｔをステップ（３）の式ｒｏｗとｎｗに代入して、図３に示す時刻ｔにおける砥石の位置・姿勢を解く。 (5) Solving the parameters θ 1_t , θ 2_t , θ 3_t , and θ 4_t corresponding to the time t from the equations f con1 in step (3) and the equations f obj , f con2 , f con3 , and f con4 in step (4). , Θ 1_t , θ 2_t , and θ 3_t are substituted into the equations row and n w in step (3), and the position and orientation of the grindstone at time t shown in FIG. 3 are solved.
（６）時刻ｔの値を変えてステップ（３）～ステップ（５）を繰り返し、複雑なチップポケットの砥石運動軌跡を解く。
上記の解いた軌跡を採用し、複雑なチップポケット研磨結果が得られる。図４に示すように、ｒｓ１、ｒｓ２、ｒｓ３、ｒｓ４は、それぞれ工具のエッジ、すくい角、コア径、溝幅を制御する曲線である。図４、図５によると、刃先から５ｍｍ、１０ｍｍ、１５ｍｍの３か所で、工具軸線に垂直な平面でチップポケット形状を切り出し、工具軸線に沿ってすくい角及び溝幅が一定であり、コア径が変化し続けるチップポケットを得る。 By adopting the above-solved trajectory, a complicated chip pocket polishing result can be obtained. As shown in FIG. 4, r s1 , r s2 , r s3 , and r s4 are curves that control the edge, rake angle, core diameter, and groove width of the tool, respectively. According to FIGS. 4 and 5, the tip pocket shape is cut out in a plane perpendicular to the tool axis at three points of 5 mm, 10 mm, and 15 mm from the cutting edge, the rake angle and the groove width are constant along the tool axis, and the core. Get a tip pocket whose diameter keeps changing.
（付記）
（付記１）
工具の複雑なチップポケット研磨による砥石軌跡の決定方法であって、
砥石の型番、サイズ及び目的工具径ＤＴを決定するステップ（１）と、
チップポケット数学モデルｒｓｉを確立するステップ（２）と、
砥石半径拘束方程式ｆｃｏｎ１を確立するステップ（３）と、
時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップ（４）と、
ステップ（４）の目的関数、ステップ（３）の砥石半径拘束方程式ｆｃｏｎ１から、時刻ｔにおける砥石の位置・姿勢を解くステップ（５）と、
時刻ｔの値を変えてステップ（３）～ステップ（５）を繰り返し、複雑なチップポケットの砥石軌跡を解くステップ（６）と、を含むことを特徴とする、
工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Additional note)
(Appendix 1)
It is a method of determining the grindstone trajectory by polishing the complicated tip pocket of the tool.
Step (1) to determine the model number, size and target tool diameter DT of the grindstone,
Step (2) to establish the chip pocket mathematical model r si ,
Step (3) to establish the grindstone radius constraint equation f con1 and
Step (4) to establish the solution objective function of the position and orientation of the grindstone at time t, and
From the objective function of step (4) and the grindstone radius constraint equation f con1 of step (3), the step (5) of solving the position and orientation of the grindstone at time t and
It is characterized by including a step (6) of solving a grindstone locus of a complicated chip pocket by repeating steps (3) to (5) by changing the value of time t.
A method for determining the grindstone trajectory by polishing a complicated tip pocket of a tool.
（付記２）
前記ステップ（２）において、
ｒｓｉ＝［ｘｓｉ，ｙｓｉ，ｚｓｉ］＝［ｘｓｉ（θｉ），ｙｓｉ（θｉ），ｚｓｉ（θｉ）］
ｉ＝１、２、３、４は、それぞれ、複雑なチップポケットを表現するためのエッジ曲線、すくい角線、コア径線、背面線を示し、ｘｓｉ、ｙｓｉ、ｚｓｉは、それぞれ、エッジ曲線、すくい角線、コア径線、背面線の工具座標系における座標値であり、θｉは、エッジ曲線、すくい角線、コア径線、背面線のパラメータ方程式を表現する変数、であることを特徴とする、
付記１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 2)
In the step (2),
r si = [x si , y si , z si ] = [x si (θ i ), y si (θ i ), z si (θ i )]
i = 1, 2, 3, 4 indicate an edge curve, a rake angle line, a core diameter line, and a back line for expressing a complicated chip pocket, respectively, and x si , y si , and z si are, respectively. It is a coordinate value in the tool coordinate system of the edge curve, the rake angle line, the core diameter line, and the back line, and θ i is a variable expressing the parameter equation of the edge curve, the rake angle line, the core diameter line, and the back line. Characterized by that,
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 1.
（付記３）
前記ステップ（２）におけるｒｓ２とｒｓ１との距離は、０．０５ＤＴ未満であり、ｒｓ３から工具軸線までの距離は、ｒｓ１、ｒｓ２又はｒｓ４から工具軸線までの距離よりも小さいことを特徴とする、
付記２に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 3)
The distance between r s2 and r s1 in step (2) is less than 0.05 DT, and the distance from r s3 to the tool axis is smaller than the distance from r s1 , r s2 or r s4 to the tool axis. Characterized by that,
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 2.
（付記４）
前記ステップ（３）で砥石半径拘束方程式ｆｃｏｎ１を確立するステップは、
（ａ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心座標ｒｏｗを解く、
ｒｏｗ＝［ｘｏｗ，ｙｏｗ，ｚｏｗ］＝［ｘｏｗ（θ１＿ｔ，θ２，θ３），ｙｏｗ（θ１＿ｔ，θ２，θ３），zｏｗ（θ１＿ｔ，θ２，θ３）］
ｘｏｗ、ｙｏｗ、ｚｏｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心の工具座標系における座標値であり、θ１＿ｔは、時刻ｔにおける研磨加工砥石のエッジ曲線上の一点のパラメータ値であり、θ２、θ３は、それぞれ、すくい角線、コア径線パラメータ方程式の変数、
（ｂ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径を解く、
Ｒｗｃ=Ｒｗｃ（θ１＿ｔ，θ２，θ３）
Ｒｗｃは、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径、
（ｃ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルｎｗを解く、
ｎｗ＝［ｘｎｗ，ｙｎｗ，ｚｎｗ］＝［ｘｎｗ（θ１＿ｔ，θ２，θ３），ｙｎｗ（θ１＿ｔ，θ２，θ３），ｚｎｗ（θ１＿ｔ，θ２，θ３）］
ｘｎｗ、ｙｎｗ、ｚｎｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルの工具座標系における座標値、
（ｄ）砥石大端円半径拘束方程式を確立する、
ｆｃｏｎ１＝Ｒｃｗ（θ１＿ｔ，θ２，θ３）－Ｒｗ＝０
Ｒｗは、砥石大端円半径、であることを特徴とする、
付記１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 4)
The step of establishing the grindstone radius constraint equation f con1 in step (3) is
(A) Solve the center coordinates row of the circles that intersect at the same time as the edge curve, rake angle line, and core diameter line at any time t.
r ow = [x ow , y ow , z ow ] = [x ow (θ 1_t , θ 2 , θ 3 ), y ow (θ 1_t , θ 2 , θ 3 ), z ow (θ 1_t , θ 2 ), θ 3 )]
x ow , you ow , and z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively, and θ 1_t is the polishing at time t. It is a parameter value of one point on the edge curve of the machined grindstone, and θ 2 and θ 3 are the rake angle line and the variable of the core diameter line parameter equation, respectively.
(B) Solve the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at any time t.
R wc = R wc (θ 1_t , θ 2 , θ 3 )
R wc is the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at time t.
(C) Solve the axis vector nw of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
n w = [x nw , y nw , z nw ] = [x nw (θ 1_t , θ 2 , θ 3 ), y nw (θ 1_t , θ 2 , θ 3 ), z nw (θ 1_t , θ 2 ), θ 3 )]
x nw , y nw , and z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively.
(D) Establish the grindstone large end circle radius constraint equation,
f con1 = R cw (θ 1_t , θ 2 , θ 3 ) -R w = 0
R w is a grindstone large end circular radius.
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 1.
（付記５）
前記ステップ（３）でＲｗ≧１５ＤＴであることを特徴とする、
付記４に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 5)
It is characterized in that R w ≧ 15DT in the step (3).
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 4.
（付記６）
前記ステップ（４）で時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップは、
（ａ）背面線と砥石軸線との間の距離方程式を確立する、
ｄａｘｉｓ＝ｄａｘｉｓ（θ１＿ｔ，θ２，θ３，θ４）
（ｂ）背面線と砥石底面との間の距離方程式を確立する、
ｄｐｌａｎｅ＝ｄｐｌａｎｅ（θ１＿ｔ，θ２，θ３，θ４）
（ｃ）背面線と砥石回転面との間の距離方程式を確立する、
ｄＧＷ＝ｄａｘｉｓ－ｄｐｌａｎｅ／ｔａｎ（θｗ）
θｗは、砥石円錐角、
（ｄ）砥石の位置・姿勢の求解目的関数を確立する、
ｆｏｂｊ＝ｍｉｎ（ｄＧＷ（θ１＿ｔ，θ２，θ３，θ４））
付記１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 6)
In step (4), the step of establishing the solution objective function of the position / orientation of the grindstone at time t is
(A) Establish a distance equation between the back line and the grindstone axis,
d axis = d axis (θ 1_t , θ 2 , θ 3 , θ 4 )
(B) Establish a distance equation between the back line and the bottom of the grindstone,
d plane = d plane (θ 1_t , θ 2 , θ 3 , θ 4 )
(C) Establish a distance equation between the back line and the surface of revolution of the grindstone,
d GW = d axis -d plane / tan (θ w )
θw is the grindstone cone angle,
(D) Establish a solution objective function for the position and orientation of the grindstone,
f obj = min (d GW (θ 1_t , θ 2 , θ 3 , θ 4 ))
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 1.
（付記７）
前記ステップ（４）でπ／２≧θｗ＞π／６であることを特徴とする、
付記６に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 7)
It is characterized in that π / 2 ≧ θ w > π / 6 in the step (4).
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 6.
（付記８）
前記ステップ（５）で時刻ｔにおける砥石の位置・姿勢を解くステップは、
ステップ（３）の方程式ｆｃｏｎ１とステップ（４）の砥石の位置・姿勢の求解目的関数から、時刻ｔに対応するエッジ曲線、すくい角線、コア径線及び背面線パラメータθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔを解き、θ１＿ｔ、θ２＿ｔ、θ３＿ｔをステップ（３）の砥石半径方程式ｆｃｏｎ１に代入して時刻ｔにおける砥石の位置・姿勢を解くことを特徴とする、
付記６に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 8)
In step (5), the step of solving the position / posture of the grindstone at time t is
From the equation f con1 in step (3) and the objective function for solving the position / orientation of the grindstone in step (4), the edge curve, rake angle line, core diameter line and back line parameters θ 1_t , θ 2_t , corresponding to time t, It is characterized in that θ 3_t and θ 4_t are solved, and θ 1_t , θ 2_t and θ 3_t are substituted into the grindstone radius equation f con1 in step (3) to solve the position and posture of the grindstone at time t.
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 6.
（付記９）
前記ステップ（５）で時刻ｔに対応するθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔのパラメータ値は、直前時刻に対応するパラメータ値以上であることを特徴とする、
付記８に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 9)
The parameter values of θ 1_t , θ 2_t , θ 3_t , and θ 4_t corresponding to the time t in the step (5) are equal to or greater than the parameter values corresponding to the immediately preceding time.
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 8.
（付記１０）
前記ステップ（１）で砥石に１Ａ１又は１Ｖ１型のダイヤモンド砥石を採用し、砥石の径は、１００ｍｍ～２００ｍｍであることを特徴とする、
付記１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。
(Appendix 10)
A 1A1 or 1V1 type diamond grindstone is adopted as the grindstone in the step (1), and the diameter of the grindstone is 100 mm to 200 mm.
A method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to Appendix 1.
Claims (10)
砥石の型番、サイズ及び目的工具径ＤＴを決定するステップ（１）と、
チップポケット数学モデルｒｓｉを確立するステップ（２）と、
砥石半径拘束方程式ｆｃｏｎ１を確立するステップ（３）と、
時刻ｔにおける砥石の位置・姿勢の求解目的関数を確立するステップ（４）と、
ステップ（４）の目的関数、ステップ（３）の砥石半径拘束方程式ｆｃｏｎ１から、時刻ｔにおける砥石の位置・姿勢を解くステップ（５）と、
時刻ｔの値を変えてステップ（３）～ステップ（５）を繰り返し、複雑なチップポケットの砥石軌跡を解くステップ（６）と、を含むことを特徴とする、
工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 It is a method of determining the grindstone trajectory by polishing the complicated tip pocket of the tool.
Step (1) to determine the model number, size and target tool diameter DT of the grindstone,
Step (2) to establish the chip pocket mathematical model r si ,
Step (3) to establish the grindstone radius constraint equation f con1 and
Step (4) to establish the solution objective function of the position and orientation of the grindstone at time t, and
From the objective function of step (4) and the grindstone radius constraint equation f con1 of step (3), the step (5) of solving the position and orientation of the grindstone at time t and
It is characterized by including a step (6) of solving a grindstone locus of a complicated chip pocket by repeating steps (3) to (5) by changing the value of time t.
A method for determining the grindstone trajectory by polishing a complicated tip pocket of a tool.
ｒｓｉ＝［ｘｓｉ，ｙｓｉ，ｚｓｉ］＝［ｘｓｉ（θｉ），ｙｓｉ（θｉ），ｚｓｉ（θｉ）］
ｉ＝１、２、３、４は、それぞれ、複雑なチップポケットを表現するためのエッジ曲線、すくい角線、コア径線、背面線を示し、ｘｓｉ、ｙｓｉ、ｚｓｉは、それぞれ、エッジ曲線、すくい角線、コア径線、背面線の工具座標系における座標値であり、θｉは、エッジ曲線、すくい角線、コア径線、背面線のパラメータ方程式を表現する変数、であることを特徴とする、
請求項１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 In the step (2),
r si = [x si , y si , z si ] = [x si (θ i ), y si (θ i ), z si (θ i )]
i = 1, 2, 3, 4 indicate an edge curve, a rake angle line, a core diameter line, and a back line for expressing a complicated chip pocket, respectively, and x si , y si , and z si are, respectively. It is a coordinate value in the tool coordinate system of the edge curve, the rake angle line, the core diameter line, and the back line, and θ i is a variable expressing the parameter equation of the edge curve, the rake angle line, the core diameter line, and the back line. Characterized by that,
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 1.
請求項２に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 The distance between r s2 and r s1 in step (2) is less than 0.05 DT, and the distance from r s3 to the tool axis is smaller than the distance from r s1 , r s2 or r s4 to the tool axis. Characterized by that,
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 2.
（ａ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心座標ｒｏｗを解く、
ｒｏｗ＝［ｘｏｗ，ｙｏｗ，ｚｏｗ］＝［ｘｏｗ（θ１＿ｔ，θ２，θ３），ｙｏｗ（θ１＿ｔ，θ２，θ３），zｏｗ（θ１＿ｔ，θ２，θ３）］
ｘｏｗ、ｙｏｗ、ｚｏｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の円心の工具座標系における座標値であり、θ１＿ｔは、時刻ｔにおける研磨加工砥石のエッジ曲線上の一点のパラメータ値であり、θ２、θ３は、それぞれ、すくい角線、コア径線パラメータ方程式の変数、
（ｂ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径を解く、
Ｒｗｃ=Ｒｗｃ（θ１＿ｔ，θ２，θ３）
Ｒｗｃは、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の半径、
（ｃ）任意の時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルｎｗを解く、
ｎｗ＝［ｘｎｗ，ｙｎｗ，ｚｎｗ］＝［ｘｎｗ（θ１＿ｔ，θ２，θ３），ｙｎｗ（θ１＿ｔ，θ２，θ３），ｚｎｗ（θ１＿ｔ，θ２，θ３）］
ｘｎｗ、ｙｎｗ、ｚｎｗは、それぞれ、時刻ｔでエッジ曲線、すくい角線、コア径線と同時に交わる円の軸線ベクトルの工具座標系における座標値、
（ｄ）砥石大端円半径拘束方程式を確立する、
ｆｃｏｎ１＝Ｒｃｗ（θ１＿ｔ，θ２，θ３）－Ｒｗ＝０
Ｒｗは、砥石大端円半径、であることを特徴とする、
請求項１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 The step of establishing the grindstone radius constraint equation f con1 in step (3) is
(A) Solve the center coordinates row of the circles that intersect at the same time as the edge curve, rake angle line, and core diameter line at any time t.
r ow = [x ow , y ow , z ow ] = [x ow (θ 1_t , θ 2 , θ 3 ), y ow (θ 1_t , θ 2 , θ 3 ), z ow (θ 1_t , θ 2 ), θ 3 )]
x ow , you ow , and z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively, and θ 1_t is the polishing at time t. It is a parameter value of one point on the edge curve of the machined grindstone, and θ 2 and θ 3 are the rake angle line and the variable of the core diameter line parameter equation, respectively.
(B) Solve the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at any time t.
R wc = R wc (θ 1_t , θ 2 , θ 3 )
R wc is the radius of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at time t.
(C) Solve the axis vector nw of the circle that intersects at the same time as the edge curve, rake angle line, and core diameter line at an arbitrary time t.
n w = [x nw , y nw , z nw ] = [x nw (θ 1_t , θ 2 , θ 3 ), y nw (θ 1_t , θ 2 , θ 3 ), z nw (θ 1_t , θ 2 ), θ 3 )]
x nw , y nw , and z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that intersects at the same time as the edge curve, the rake angle line, and the core diameter line at time t, respectively.
(D) Establish the grindstone large end circle radius constraint equation,
f con1 = R cw (θ 1_t , θ 2 , θ 3 ) -R w = 0
R w is a grindstone large end circular radius.
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 1.
請求項４に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 It is characterized in that R w ≧ 15DT in the step (3).
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 4.
（ａ）背面線と砥石軸線との間の距離方程式を確立する、
ｄａｘｉｓ＝ｄａｘｉｓ（θ１＿ｔ，θ２，θ３，θ４）
（ｂ）背面線と砥石底面との間の距離方程式を確立する、
ｄｐｌａｎｅ＝ｄｐｌａｎｅ（θ１＿ｔ，θ２，θ３，θ４）
（ｃ）背面線と砥石回転面との間の距離方程式を確立する、
ｄＧＷ＝ｄａｘｉｓ－ｄｐｌａｎｅ／ｔａｎ（θｗ）
θｗは、砥石円錐角、
（ｄ）砥石の位置・姿勢の求解目的関数を確立する、
ｆｏｂｊ＝ｍｉｎ（ｄＧＷ（θ１＿ｔ，θ２，θ３，θ４））
請求項１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 In step (4), the step of establishing the solution objective function of the position / orientation of the grindstone at time t is
(A) Establish a distance equation between the back line and the grindstone axis,
d axis = d axis (θ 1_t , θ 2 , θ 3 , θ 4 )
(B) Establish a distance equation between the back line and the bottom of the grindstone,
d plane = d plane (θ 1_t , θ 2 , θ 3 , θ 4 )
(C) Establish a distance equation between the back line and the surface of revolution of the grindstone,
d GW = d axis -d plane / tan (θ w )
θw is the grindstone cone angle,
(D) Establish a solution objective function for the position and orientation of the grindstone,
f obj = min (d GW (θ 1_t , θ 2 , θ 3 , θ 4 ))
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 1.
請求項６に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 It is characterized in that π / 2 ≧ θ w > π / 6 in the step (4).
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 6.
ステップ（３）の方程式ｆｃｏｎ１とステップ（４）の砥石の位置・姿勢の求解目的関数から、時刻ｔに対応するエッジ曲線、すくい角線、コア径線及び背面線パラメータθ１＿ｔ、θ２＿ｔ、θ３＿ｔ、θ４＿ｔを解き、θ１＿ｔ、θ２＿ｔ、θ３＿ｔをステップ（３）の砥石半径方程式ｆｃｏｎ１に代入して時刻ｔにおける砥石の位置・姿勢を解くことを特徴とする、
請求項６に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 In step (5), the step of solving the position / posture of the grindstone at time t is
From the equation f con1 in step (3) and the objective function for solving the position / orientation of the grindstone in step (4), the edge curve, rake angle line, core diameter line and back line parameters θ 1_t , θ 2_t , corresponding to time t, It is characterized in that θ 3_t and θ 4_t are solved, and θ 1_t , θ 2_t and θ 3_t are substituted into the grindstone radius equation f con1 in step (3) to solve the position and posture of the grindstone at time t.
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 6.
請求項８に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 The parameter values of θ 1_t , θ 2_t , θ 3_t , and θ 4_t corresponding to the time t in the step (5) are equal to or greater than the parameter values corresponding to the immediately preceding time.
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 8.
請求項１に記載の工具の複雑なチップポケット研磨による砥石軌跡の決定方法。 A 1A1 or 1V1 type diamond grindstone is adopted as the grindstone in the step (1), and the diameter of the grindstone is 100 mm to 200 mm.
The method for determining a grindstone trajectory by polishing a complicated tip pocket of the tool according to claim 1.
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