WO2021088249A1 - Method for determining trajectory of complex cutter chip pocket grinding wheel - Google Patents

Method for determining trajectory of complex cutter chip pocket grinding wheel Download PDF

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WO2021088249A1
WO2021088249A1 PCT/CN2020/071727 CN2020071727W WO2021088249A1 WO 2021088249 A1 WO2021088249 A1 WO 2021088249A1 CN 2020071727 W CN2020071727 W CN 2020071727W WO 2021088249 A1 WO2021088249 A1 WO 2021088249A1
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grinding wheel
time
core diameter
tool
determining
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PCT/CN2020/071727
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Chinese (zh)
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李国超
戴磊
周宏根
田桂中
刘云龙
赵东豪
艾杼桦
马正宇
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江苏科技大学
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Priority to JP2021504215A priority Critical patent/JP7089134B2/en
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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  • the invention relates to a method for determining the track of a grinding wheel, and more specifically, to a method for determining the track of a grinding wheel for grinding a complex chip flute of a tool.
  • the complex chip flute of the tool means that its rake angle, core diameter, groove width, helix angle and other structural parameters change along the tool axis, which can effectively improve the tool rigidity, strength, and cutting performance. It is widely used in high-end solid end mills. .
  • the grinding of complex chip flutes faces many difficulties: First, the geometric structure of the complex chip flutes is determined by the shape of the grinding wheel and the motion trajectory.
  • the object of the present invention is to provide a method for determining the path of a grinding wheel for grinding a complex chip flute of a tool, which can be applied to the grinding process of a complex chip flute of a tool, and has high accuracy and reliability.
  • the present invention provides a method for determining the path of a grinding wheel for complex chip flutes of a tool, which includes the following steps:
  • step (2) :
  • i 1, 2, 3, 4 respectively represent the cutting edge curve, rake angle, core diameter line and tooth back line used to describe the complex chip flute
  • x si , y si , z si are respectively the knife edge curve and front
  • ⁇ i is the variable describing the parameter equation of the blade curve, the rake angle line, the core diameter line and the tooth back line.
  • the distance between r s2 and r s1 is less than 0.05DT, and the distance between r s3 and the tool axis is less than the distance between r s1 , r s2 or r s4 and the tool axis.
  • step (3) the steps of establishing the wheel radius constraint equation fcon1 in step (3) are:
  • x ow , y ow , z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects with the cutting edge curve, rake angle, and core diameter at time t, and ⁇ 1_t is the grinding wheel blade at time t
  • ⁇ 2 , ⁇ 3 are the variables of the rake angle and core diameter parameter equations respectively;
  • R wc R wc ( ⁇ 1_t , ⁇ 2 , ⁇ 3 )
  • R wc is the radius of the circle that intersects the blade curve, rake angle, and core diameter at the same time at t;
  • x nw , y nw , z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that simultaneously intersects the blade curve, rake angle, and core diameter line at time t;
  • R w is the radius of the large end circle of the grinding wheel, and R w ⁇ 15DT.
  • step (4) the steps of establishing the position of the grinding wheel at time t to solve the objective function are:
  • d axis d axis ( ⁇ 1_t , ⁇ 2 , ⁇ 3 , ⁇ 4 )
  • d plane d plane ( ⁇ 1_t , ⁇ 2 , ⁇ 3 , ⁇ 4 )
  • d GW d axis -d plane /tan( ⁇ w )
  • ⁇ w is the cone angle of the grinding wheel, ⁇ /2 ⁇ w > ⁇ /6;
  • the step (5) to obtain the position of the grinding wheel at time t is: according to the equation f con1 in step (3) and the position of the grinding wheel in step (4) to solve the objective function, the solution to obtain the corresponding blade curve and rake angle at time t
  • the line, core diameter and tooth back line parameters ⁇ 1_t , ⁇ 2_t , ⁇ 3_t , ⁇ 4_t , and ⁇ 1_t , ⁇ 2_t , ⁇ 3_t are brought into step (3) in the wheel radius constraint equation f con1 , and the time t is obtained by solving
  • the parameter values ⁇ 1_t , ⁇ 2_t , ⁇ 3_t , ⁇ 4_t corresponding to time t are greater than or equal to the parameter values corresponding to the previous time.
  • the grinding wheel selects 1A1 type or 1V1 type diamond grinding wheel, the diameter of the grinding wheel is 100mm ⁇ 200mm.
  • FIG. 1 is a flowchart of this method
  • Figure 2 is a schematic diagram of the shape of the grinding wheel
  • Figure 3 is a schematic diagram of the posture of the grinding wheel
  • Figure 4 is a three-dimensional schematic diagram of the grinding results of complex chip flutes with gradual core diameter, equal rake angle, equal groove width, and equal helix angle;
  • Fig. 5 is a projection view of the grinding result of complex chip flutes with constant rake angle, equal groove width and equal helix angle of gradual core diameter on the X T -Y T coordinate plane.
  • x ow , y ow , z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects with the cutting edge curve, rake angle, and core diameter at time t, and ⁇ 1_t is the grinding wheel blade at time t The parameter value of a point on the curve;
  • R wc R wc ( ⁇ 1_t , ⁇ 2 , ⁇ 3 )
  • R wc is the radius of the circle that intersects the blade curve, rake angle, and core diameter at the same time at t;
  • x nw , y nw , z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that simultaneously intersects the blade curve, rake angle, and core diameter line at time t;
  • R w is the radius of the large end circle of the grinding wheel
  • d axis d axis ( ⁇ 1_t , ⁇ 2 , ⁇ 3 , ⁇ 4 )
  • d plane d plane ( ⁇ 1_t , ⁇ 2 , ⁇ 3 , ⁇ 4 )
  • d GW d axis -d plane /tan( ⁇ w )
  • ⁇ w is the cone angle of the grinding wheel
  • the parameters ⁇ 1_t , ⁇ 2_t , ⁇ 3_t , ⁇ corresponding to time t are solved by solving 4_t , take ⁇ 1_t , ⁇ 2_t , ⁇ 3_t into the formulas r ow and n w in step (3), and solve to obtain the position of the grinding wheel at time t.
  • the position of the grinding wheel is shown in Figure 3;
  • r s1 , r s2 , r s3 , and r s4 are the curves that control the cutting edge, rake angle, core diameter, and groove width of the tool. 4. It can be seen from Figure 5 that the plane perpendicular to the tool axis is used to intercept the shape of the chip flute at 3 positions 5mm, 10mm, and 15mm away from the tool tip, and the rake angle and groove width along the tool axis remain unchanged, while the core Chip flutes with changing diameters.

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Abstract

Disclosed is a method for determining the trajectory of a complex cutter chip pocket grinding wheel. The method comprises the following steps: (1) determining the model and size of a grinding wheel and the diameter DT of a target cutter; (2) establishing a chip pocket mathematical model rsi; (3) establishing a grinding wheel radius constraint equation fcon1; (4) establishing a grinding wheel pose solving objective function at moment t; (5) in combination with the objective function in step (4) and the grinding wheel radius constraint equation fcon1 in step (3), obtaining, by means of solving, a grinding wheel pose at the moment t; and (6) changing the value of the moment t, repeating steps (3) to (5), and obtaining, by means of solving, a motion trajectory of the complex chip pocket grinding wheel. The method is applicable to a complex cutter chip pocket grinding process, provides technical and methodological support for the formulation of the complex cutter chip pocket grinding process, and is high in precision and good in reliability.

Description

一种刀具复杂容屑槽磨制砂轮轨迹确定方法A Method for Determining the Track of Grinding Wheel for Complicated Chip Groove of Tool 技术领域Technical field
本发明涉及一种砂轮轨迹确定方法，更具体地，涉及一种刀具复杂容屑槽磨制砂轮轨迹确定方法。The invention relates to a method for determining the track of a grinding wheel, and more specifically, to a method for determining the track of a grinding wheel for grinding a complex chip flute of a tool.
背景技术Background technique
刀具复杂容屑槽是指其前角、芯径、槽宽、螺旋角等结构参数沿刀具轴线发生改变，可以有效提高刀具刚度、强度、切削性能，在高端整硬立铣刀中得到广泛应用。然而，复杂容屑槽磨制面临诸多难点：其一，复杂容屑槽几何结构由砂轮形状及运动轨迹共同决定，工艺求解涉及变量和约束条件繁多，无法直接建立“容屑槽结构参数”与“砂轮形状+运动轨迹”之间的函数关系；其二，空间单参数曲面族包络理论是传统容屑槽几何成形理论基础，该理论以接触线为桥梁建立砂轮与槽形之间的关系，磨制过程中接触线不变，但复杂容屑槽磨制过程中接触线不断变化，因此该理论无法适应，导致复杂容屑槽磨制成形缺失理论基础。因此，现有基于包络理论或试错方法求解容屑槽磨制砂轮运动轨迹的策略无法适用于复杂形状容屑槽，复杂容屑槽制造过程中面临砂轮轨迹求解困难的瓶颈问题。The complex chip flute of the tool means that its rake angle, core diameter, groove width, helix angle and other structural parameters change along the tool axis, which can effectively improve the tool rigidity, strength, and cutting performance. It is widely used in high-end solid end mills. . However, the grinding of complex chip flutes faces many difficulties: First, the geometric structure of the complex chip flutes is determined by the shape of the grinding wheel and the motion trajectory. The process solution involves many variables and constraints, and it is impossible to directly establish the "chip flute structure parameters" and The functional relationship between "wheel shape + trajectory"; second, the spatial single-parameter surface family envelope theory is the basis of traditional chip flute geometric forming theory, which uses the contact line as a bridge to establish the relationship between the grinding wheel and the groove shape , The contact line does not change during the grinding process, but the contact line is constantly changing during the grinding process of the complex chip flute, so the theory cannot be adapted, resulting in the lack of theoretical basis for the grinding of the complex flute. Therefore, the existing strategies based on envelope theory or trial-and-error method to solve the trajectory of the grinding wheel of the chip flute cannot be applied to the complex shape of the chip flute. The manufacturing process of the complex chip flute faces the bottleneck problem of the difficulty of the trajectory of the grinding wheel.
发明内容Summary of the invention
发明目的：本发明的目的是提供一种刀具复杂容屑槽磨制砂轮轨迹确定方法，该方法能够适用于刀具复杂容屑槽刃磨工艺，同时具有高精度和可靠性。Object of the invention: The object of the present invention is to provide a method for determining the path of a grinding wheel for grinding a complex chip flute of a tool, which can be applied to the grinding process of a complex chip flute of a tool, and has high accuracy and reliability.
技术方案：本发明提供了一种刀具复杂容屑槽磨制砂轮轨迹确定方法，，包括以下步骤：Technical Solution: The present invention provides a method for determining the path of a grinding wheel for complex chip flutes of a tool, which includes the following steps:
(1)确定砂轮型号、尺寸及目标刀具直径DT；(1) Determine the wheel model, size and target tool diameter DT;
(2)建立容屑槽数学模型r si； (2) Establish a mathematical model r si of chip flutes;
(3)建立砂轮半径约束方程f con1； (3) Establish a constraint equation f con1 for the radius of the grinding wheel;
(4)建立t时刻砂轮位姿求解目标函数；(4) Establish the objective function of the position and pose of the grinding wheel at time t;
(5)结合步骤(4)中目标函数、步骤(3)中砂轮半径约束方程f con1求解获得t时刻砂轮位姿； (5) Combine the objective function in step (4) and the constraint equation f con1 for the radius of the grinding wheel in step (3) to obtain the position of the grinding wheel at time t;
(6)变更时刻t的值，重复步骤(3)～步骤(5)，求解获得复杂容屑槽砂轮运动轨迹。(6) Change the value of time t, repeat steps (3) to (5), and obtain the trajectory of the grinding wheel with complex chip flutes.
其中，步骤(2)中：Among them, in step (2):
r si＝[x si,y si,z si]＝[x si(θ i),y si(θ i),z si(θ i)]， r si =[x si ,y si ,z si ]=[x si (θ i ),y si (θ i ),z si (θ i )],
其中，i＝1,2,3,4分别表示用于描述复杂容屑槽的刀刃曲线、前角线、芯径线和齿背线，x si、y si、z si分别为刀刃曲线、前角线、芯径线和齿背线在刀具坐标系 中的坐标值，θ i为描述刀刃曲线、前角线、芯径线和齿背线参数方程的变量。其中r s2与r s1之间的距离小于0.05DT，r s3距离刀具轴线的距离小于r s1、r s2或r s4到刀具轴线之间的距离。 Among them, i = 1, 2, 3, 4 respectively represent the cutting edge curve, rake angle, core diameter line and tooth back line used to describe the complex chip flute, x si , y si , z si are respectively the knife edge curve and front The coordinate values of the angle line, the core diameter line and the tooth back line in the tool coordinate system, θ i is the variable describing the parameter equation of the blade curve, the rake angle line, the core diameter line and the tooth back line. The distance between r s2 and r s1 is less than 0.05DT, and the distance between r s3 and the tool axis is less than the distance between r s1 , r s2 or r s4 and the tool axis.
其中，步骤(3)中建立砂轮半径约束方程fcon1步骤为：Among them, the steps of establishing the wheel radius constraint equation fcon1 in step (3) are:
①求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的圆心坐标r ow： ① Solve the center coordinate r ow of the circle that intersects the blade curve, rake angle, 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)] 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 )]
其中，x ow、y ow、z ow分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的圆心在刀具坐标系中的坐标值，θ 1_t为t时刻磨制加工砂轮刀刃曲线上一点的参数值，θ 2、θ 3分别为前角线、芯径线参数方程的变量； Among them, x ow , y ow , z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects with the cutting edge curve, rake angle, and core diameter at time t, and θ 1_t is the grinding wheel blade at time t The parameter value of a point on the curve, θ 2 , θ 3 are the variables of the rake angle and core diameter parameter equations respectively;
②求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的半径：② Solve for the radius of the circle that intersects the blade curve, rake angle, and core diameter at any time t:
R wc＝R wc(θ 1_t,θ 2,θ 3) R wc ＝R wc (θ 1_t ,θ 2 ,θ 3 )
其中，R wc为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的半径； Among them, R wc is the radius of the circle that intersects the blade curve, rake angle, and core diameter at the same time at t;
③求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量n w： ③ Solve the axis vector n w of the circle that intersects the blade curve, rake angle, and core diameter at any 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)] 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 )]
其中，x nw、y nw、z nw分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量在刀具坐标系中的坐标值； Among them, x nw , y nw , z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that simultaneously intersects the blade curve, rake angle, and core diameter line at time t;
④建立砂轮大端圆半径约束方程：④Establish the constraint equation for the radius of the wheel's big end circle:
f con1＝R CW(θ 1_t,θ 2,θ 3)-R w＝0 f con1 = R CW (θ 1_t ,θ 2 ,θ 3 )-R w =0
其中，R w为砂轮大端圆半径，R w≥15DT。 Among them, R w is the radius of the large end circle of the grinding wheel, and R w ≥ 15DT.
其中，步骤(4)中建立t时刻砂轮位姿求解目标函数步骤为：Among them, in step (4), the steps of establishing the position of the grinding wheel at time t to solve the objective function are:
①建立齿背线与砂轮轴线之间的距离方程：①Establish the distance equation between the tooth back line and the axis of the grinding wheel:
d axis＝d axis(θ 1_t,θ 2,θ 3,θ 4) d axis = d axis (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
②建立齿背线与砂轮底面之间的距离方程：②Establish the distance equation between the tooth back line and the bottom surface of the grinding wheel:
d plane＝d plane(θ 1_t,θ 2,θ 3,θ 4) d plane = d plane (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
③建立齿背线与砂轮回转面之间的距离方程：③Establish the distance equation between the back line of the tooth and the turning surface of the grinding wheel:
d GW＝d axis-d plane/tan(θ w) d GW = d axis -d plane /tan(θ w )
其中，θ w为砂轮锥角，π/2≥θ w＞π/6； Among them, θ w is the cone angle of the grinding wheel, π/2≥θ w ＞π/6;
④建立砂轮位姿求解目标函数：④Establish the objective function for the position and pose of the grinding wheel:
f obj＝min(d GW(θ 1_t,θ 2,θ 3,θ 4)) f obj = min(d GW (θ 1_t ,θ 2 ,θ 3 ,θ 4 ))
其中，among them,
Figure PCTCN2020071727-appb-000001
Figure PCTCN2020071727-appb-000001
其中，步骤(5)求解获得t时刻砂轮位姿步骤为：根据步骤(3)中的方程f con1和步骤(4)中砂轮位姿求解目标函数，求解获得t时刻对应的刀刃曲线、前角线、芯径线和齿背线参数θ 1_t、θ 2_t、θ 3_t、θ 4_t，将θ 1_t、θ 2_t、θ 3_t带入步骤(3)中砂轮半径约束方程f con1中，求解获得t时刻砂轮位姿，t时刻对应的θ 1_t、θ 2_t、θ 3_t、θ 4_t等参数值大于或等于前一时刻对应的参数值。 Among them, the step (5) to obtain the position of the grinding wheel at time t is: according to the equation f con1 in step (3) and the position of the grinding wheel in step (4) to solve the objective function, the solution to obtain the corresponding blade curve and rake angle at time t The line, core diameter and tooth back line parameters θ 1_t , θ 2_t , θ 3_t , θ 4_t , and θ 1_t , θ 2_t , θ 3_t are brought into step (3) in the wheel radius constraint equation f con1 , and the time t is obtained by solving For the position and posture of the grinding wheel, the parameter values θ 1_t , θ 2_t , θ 3_t , θ 4_t corresponding to time t are greater than or equal to the parameter values corresponding to the previous time.
其中，砂轮选用1A1型或1V1型金刚石砂轮，砂轮直径100mm～200mm。Among them, the grinding wheel selects 1A1 type or 1V1 type diamond grinding wheel, the diameter of the grinding wheel is 100mm ~ 200mm.
有益效果：1、能够适用于刀具复杂容屑槽磨制工艺，为刀具复杂容屑槽刃磨工艺的制定提供技术和方法支撑；2、精度高；3、可靠性好。Beneficial effects: 1. It can be applied to the grinding process of the complex chip flute of the tool, and provide technical and method support for the formulation of the grinding process of the complex chip flute of the tool; 2. High precision; 3. Good reliability.
附图说明Description of the drawings
图1是本方法的流程图；Figure 1 is a flowchart of this method;
图2是砂轮形状示意图；Figure 2 is a schematic diagram of the shape of the grinding wheel;
图3是砂轮姿态示意图；Figure 3 is a schematic diagram of the posture of the grinding wheel;
图4是渐变芯径等前角、等槽宽、等螺旋角复杂容屑槽磨制结果三维示意图；Figure 4 is a three-dimensional schematic diagram of the grinding results of complex chip flutes with gradual core diameter, equal rake angle, equal groove width, and equal helix angle;
图5是渐变芯径等前角、等槽宽、等螺旋角复杂容屑槽磨制结果在X T-Y T坐标平面上的投影视图。 Fig. 5 is a projection view of the grinding result of complex chip flutes with constant rake angle, equal groove width and equal helix angle of gradual core diameter on the X T -Y T coordinate plane.
具体实施方式Detailed ways
砂轮运动轨迹总体求解流程如图1所示，包括以下步骤：The overall solution process of the grinding wheel motion trajectory is shown in Figure 1, including the following steps:
(1)选用1V1型标准砂轮，如图2所示，砂轮厚度为B w12mm，砂轮锥角为θ W＝1.2217rad，砂轮大端圆直径D W＝116mm，铣刀导程为PT＝60mm，铣刀直径为DT＝20mm； (1) Choose 1V1 standard grinding wheel, as shown in Figure 2, the thickness of the grinding wheel is B w 12mm, the cone angle of the grinding wheel is θ W ＝1.2217rad, the diameter of the big end circle of the grinding wheel D W ＝116mm, and the milling cutter lead is PT＝60mm , The diameter of the milling cutter is DT=20mm;
(2)建立容屑槽数学模型r si： (2) Establish the mathematical model r si of the chip flute:
Figure PCTCN2020071727-appb-000002
Figure PCTCN2020071727-appb-000002
(3)建立砂轮半径约束方程fcon1，具体包括：(3) Establish the wheel radius constraint equation fcon1, which specifically includes:
①求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的圆心坐标：① Solve the coordinates of the center of the circle that intersects the blade curve, rake angle, and core diameter 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)] 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 )]
其中，x ow、y ow、z ow分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的圆心在刀具坐标系中的坐标值，θ 1_t为t时刻磨制加工砂轮刀刃曲线上一点的参数值； Among them, x ow , y ow , z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects with the cutting edge curve, rake angle, and core diameter at time t, and θ 1_t is the grinding wheel blade at time t The parameter value of a point on the curve;
②求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的半径：② Solve for the radius of the circle that intersects the blade curve, rake angle, and core diameter at any time t:
R wc＝R wc(θ 1_t,θ 2,θ 3) R wc ＝R wc (θ 1_t ,θ 2 ,θ 3 )
其中，R wc为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的半径； Among them, R wc is the radius of the circle that intersects the blade curve, rake angle, and core diameter at the same time at t;
③求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量：③ Solve the axis vector of the circle that intersects the blade curve, rake angle, and core diameter at any 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)] 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 )]
其中，x nw、y nw、z nw分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量在刀具坐标系中的坐标值； Among them, x nw , y nw , z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that simultaneously intersects the blade curve, rake angle, and core diameter line at time t;
④建立砂轮大端圆半径约束方程：④Establish the constraint equation for the radius of the wheel's big end circle:
f con1＝R CW(θ 1_t,θ 2,θ 3)-R w＝0 f con1 = R CW (θ 1_t ,θ 2 ,θ 3 )-R w =0
其中，R w为砂轮大端圆半径 Among them, R w is the radius of the large end circle of the grinding wheel
(4)建立t时刻砂轮位姿求解目标函数：(4) Establish the objective function to solve the position of the grinding wheel at time t:
①建立齿背线与砂轮轴线之间的距离方程：①Establish the distance equation between the tooth back line and the axis of the grinding wheel:
d axis＝d axis(θ 1_t,θ 2,θ 3,θ 4) d axis = d axis (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
②建立齿背线与砂轮底面之间的距离方程：②Establish the distance equation between the tooth back line and the bottom surface of the grinding wheel:
d plane＝d plane(θ 1_t,θ 2,θ 3,θ 4) d plane = d plane (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
③建立齿背线与砂轮回转面之间的距离方程：③Establish the distance equation between the back line of the tooth and the turning surface of the grinding wheel:
d GW＝d axis-d plane/tan(θ w) d GW = d axis -d plane /tan(θ w )
其中，θ w为砂轮锥角 Among them, θ w is the cone angle of the grinding wheel
④建立砂轮位姿求解目标函数：④Establish the objective function for the position and pose of the grinding wheel:
f obj＝min(d GW(θ 1_t,θ 2,θ 3,θ 4)) f obj = min(d GW (θ 1_t ,θ 2 ,θ 3 ,θ 4 ))
其中，among them,
Figure PCTCN2020071727-appb-000003
Figure PCTCN2020071727-appb-000003
(5)根据步骤(3)中的方程f con1和步骤(4)中的方程f obj、f con2、f con3、f con4，求解获得t时刻对应的参数θ 1_t、θ 2_t、θ 3_t、θ 4_t，将θ 1_t、θ 2_t、θ 3_t带入步骤(3)中的公式r ow和n w，求解获得t时刻砂轮位姿，砂轮位姿如图3所示； (5) According to the equation f con1 in step (3) and the equations f obj , f con2 , f con3 , and f con4 in step (4), the parameters θ 1_t , θ 2_t , θ 3_t , θ corresponding to time t are solved by solving 4_t , take θ 1_t , θ 2_t , θ 3_t into the formulas r ow and n w in step (3), and solve to obtain the position of the grinding wheel at time t. The position of the grinding wheel is shown in Figure 3;
(6)变更时刻t的值，重复步骤(3)～步骤(5)，求解获得复杂容屑槽砂轮运动轨迹：(6) Change the value of time t, repeat steps (3) to (5), and obtain the trajectory of complex chip flute grinding wheel:
Figure PCTCN2020071727-appb-000004
Figure PCTCN2020071727-appb-000004
Figure PCTCN2020071727-appb-000005
Figure PCTCN2020071727-appb-000005
Figure PCTCN2020071727-appb-000006
Figure PCTCN2020071727-appb-000006
Figure PCTCN2020071727-appb-000007
Figure PCTCN2020071727-appb-000007
采用上述求解轨迹，获得复杂容屑槽刃磨结果，见图4，其中，r s1、r s2、r s3、r s4分别是控制刀具刀刃、前角、芯径和槽宽的曲线，从凸4、图5可以看出，在距离刀尖5mm、10mm、15mm的3个位置处采用垂直于刀具轴线的平面截取容屑槽形状，获得沿刀具轴线前角和槽宽保持不变，而芯径不断变化的容屑槽。 Using the above solution trajectory, the grinding results of complex chip flutes are obtained, as shown in Fig. 4. Among them, r s1 , r s2 , r s3 , and r s4 are the curves that control the cutting edge, rake angle, core diameter, and groove width of the tool. 4. It can be seen from Figure 5 that the plane perpendicular to the tool axis is used to intercept the shape of the chip flute at 3 positions 5mm, 10mm, and 15mm away from the tool tip, and the rake angle and groove width along the tool axis remain unchanged, while the core Chip flutes with changing diameters.

Claims (10)

  1. 一种刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，包括以下步骤：A method for determining the path of a grinding wheel for complex chip flutes of a tool, which is characterized in that it comprises the following steps:
    (1)确定砂轮型号、尺寸及目标刀具直径DT；(1) Determine the wheel model, size and target tool diameter DT;
    (2)建立容屑槽数学模型r si； (2) Establish a mathematical model r si of chip flutes;
    (3)建立砂轮半径约束方程f con1； (3) Establish a constraint equation f con1 for the radius of the grinding wheel;
    (4)建立t时刻砂轮位姿求解目标函数；(4) Establish the objective function of the position and pose of the grinding wheel at time t;
    (5)结合步骤(4)中目标函数、步骤(3)中砂轮半径约束方程f con1求解获得t时刻砂轮位姿； (5) Combine the objective function in step (4) and the constraint equation f con1 for the radius of the grinding wheel in step (3) to obtain the position of the grinding wheel at time t;
    (6)变更时刻t的值，重复步骤(3)～步骤(5)，求解获得复杂容屑槽砂轮运动轨迹。(6) Change the value of time t, repeat steps (3) to (5), and obtain the trajectory of the grinding wheel with complex chip flutes.
  2. 根据权利要求1所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(2)中：The method for determining the trajectory of a grinding wheel for complex chip flutes of a tool according to claim 1, wherein, in the step (2):
    r si＝[x si,y si,z si]＝[x si(θ i),y si(θ i),z si(θ i)]， r si =[x si ,y si ,z si ]=[x si (θ i ),y si (θ i ),z si (θ i )],
    其中，i＝1,2,3,4分别表示用于描述复杂容屑槽的刀刃曲线、前角线、芯径线和齿背线，x si、y si、z si分别为刀刃曲线、前角线、芯径线和齿背线在刀具坐标系中的坐标值，θ i为描述刀刃曲线、前角线、芯径线和齿背线参数方程的变量。 Among them, i = 1, 2, 3, 4 respectively represent the cutting edge curve, rake angle, core diameter line and tooth back line used to describe the complex chip flute, x si , y si , z si are respectively the knife edge curve and front The coordinate values of the angle line, the core diameter line and the tooth back line in the tool coordinate system, θ i is the variable describing the parameter equation of the blade curve, the rake angle line, the core diameter line and the tooth back line.
  3. 根据权利要求2所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(2)中r s2与r s1之间的距离小于0.05DT，r s3距离刀具轴线的距离小于r s1、r s2或r s4到刀具轴线之间的距离。 The method for determining the trajectory of a grinding wheel for complex chip flutes of a tool according to claim 2, wherein the distance between r s2 and r s1 in the step (2) is less than 0.05DT, and the distance between r s3 and the tool axis is less than 0.05DT. It is less than the distance between r s1 , r s2 or r s4 and the tool axis.
  4. 根据权利要求1所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(3)中建立砂轮半径约束方程f con1步骤为： The method for determining the trajectory of a grinding wheel for grinding a complex chip flute of a tool according to claim 1, wherein the step of establishing the radius constraint equation f con1 of the grinding wheel in the step (3) is:
    ①求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的圆心坐标r ow： ① Solve the center coordinate r ow of the circle that intersects the blade curve, rake angle, 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)] 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 )]
    其中，x ow、y ow、z ow分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的圆心在刀具坐标系中的坐标值，θ 1_t为t时刻磨制加工砂轮刀刃曲线上一点的参数值，θ 2、θ 3分别为前角线、芯径线参数方程的变量； Among them, x ow , y ow , z ow are the coordinate values in the tool coordinate system of the center of the circle that intersects with the cutting edge curve, rake angle, and core diameter at time t, and θ 1_t is the grinding wheel blade at time t The parameter value of a point on the curve, θ 2 , θ 3 are the variables of the rake angle and core diameter parameter equations respectively;
    ②求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的半径：② Solve for the radius of the circle that intersects the blade curve, rake angle, and core diameter at any time t:
    R wc＝R wc(θ 1_t,θ 2,θ 3) R wc ＝R wc (θ 1_t ,θ 2 ,θ 3 )
    其中，R wc为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的半径； Among them, R wc is the radius of the circle that intersects the blade curve, rake angle, and core diameter at the same time at t;
    ③求解任意时刻t，同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量n w： ③ Solve the axis vector n w of the circle that intersects the blade curve, rake angle, and core diameter at any 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)] 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 )]
    其中，x nw、y nw、z nw分别为t时刻同时与刀刃曲线、前角线、芯径线相交的圆的轴线向量在刀具坐标系中的坐标值； Among them, x nw , y nw , z nw are the coordinate values in the tool coordinate system of the axis vector of the circle that simultaneously intersects the blade curve, rake angle, and core diameter line at time t;
    ④建立砂轮大端圆半径约束方程：④Establish the constraint equation for the radius of the wheel's big end circle:
    f con1＝R CW(θ 1_t,θ 2,θ 3)-R w＝0 f con1 = R CW (θ 1_t ,θ 2 ,θ 3 )-R w =0
    其中，R w为砂轮大端圆半径。 Among them, R w is the radius of the large end circle of the grinding wheel.
  5. 根据权利要求4所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(3)中R w≥15DT。 The method for determining the trajectory of a grinding wheel for complex chip flutes of a tool according to claim 4, wherein in the step (3), R w ≥ 15DT.
  6. 根据权利要求1所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(4)中建立t时刻砂轮位姿求解目标函数步骤为：The method for determining the trajectory of a grinding wheel for grinding a complex chip flute of a tool according to claim 1, wherein the step of establishing the position of the grinding wheel at time t in the step (4) to solve the objective function is:
    ①建立齿背线与砂轮轴线之间的距离方程：①Establish the distance equation between the tooth back line and the axis of the grinding wheel:
    d axis＝d axis(θ 1_t,θ 2,θ 3,θ 4) d axis = d axis (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
    ②建立齿背线与砂轮底面之间的距离方程：②Establish the distance equation between the tooth back line and the bottom surface of the grinding wheel:
    d plane＝d plane(θ 1_t,θ 2,θ 3,θ 4) d plane = d plane (θ 1_t ,θ 2 ,θ 3 ,θ 4 )
    ③建立齿背线与砂轮回转面之间的距离方程：③Establish the distance equation between the back line of the tooth and the turning surface of the grinding wheel:
    d GW＝d axis-d plane/tan(θ w) d GW = d axis -d plane /tan(θ w )
    其中，θ w为砂轮锥角； Among them, θ w is the cone angle of the grinding wheel;
    ④建立砂轮位姿求解目标函数：④Establish the objective function for the position and pose of the grinding wheel:
    f obj＝min(d GW(θ 1_t,θ 2,θ 3,θ 4)) f obj = min(d GW (θ 1_t ,θ 2 ,θ 3 ,θ 4 ))
    其中，among them,
    Figure PCTCN2020071727-appb-100001
    Figure PCTCN2020071727-appb-100001
  7. 根据权利要求6所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(4)中π/2≥θ w＞π/6。 Tool according to claim 6 complex flutes grinding wheel track determining method, wherein said step (4) is π / 2≥θ w> π / 6 .
  8. 根据权利要求6所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(5)求解获得t时刻砂轮位姿步骤为：根据步骤(3)中的方程f con1和步骤(4)中砂轮位姿求解目标函数，求解获得t时刻对应的刀刃曲线、前角线、芯径线和齿背线参数θ 1_t、θ 2_t、θ 3_t、θ 4_t，将θ 1_t、θ 2_t、θ 3_t带入步骤(3)中砂轮半径约束方程f con1中，求解获得t时刻砂轮位姿。 The method for determining the trajectory of a grinding wheel for complex chip flutes of a tool according to claim 6, characterized in that the step (5) solves and obtains the position of the grinding wheel at time t: according to the equations f con1 and in step (3) In step (4), the objective function of the position of the grinding wheel is solved to obtain the corresponding tool edge curve, rake angle, core diameter and tooth back line parameters at time t θ 1_t , θ 2_t , θ 3_t , θ 4_t , and θ 1_t , θ 2_t , θ 3_t are brought into step (3) in the wheel radius constraint equation f con1 , and solved to obtain the position of the grinding wheel at time t.
  9. 根据权利要求8所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(5)中t时刻对应的θ 1_t、θ 2_t、θ 3_t、θ 4_t等参数值大于或等于前一时刻对应的参数值。 The method for determining the trajectory of a grinding wheel for complex chip flutes of a tool according to claim 8, wherein the corresponding parameter values of θ 1_t , θ 2_t , θ 3_t , θ 4_t at time t in the step (5) are greater than or Equal to the parameter value corresponding to the previous moment.
  10. 根据权利要求1所述的刀具复杂容屑槽磨制砂轮轨迹确定方法，其特征在于，所述步骤(1)中砂轮选用1A1型或1V1型金刚石砂轮，砂轮直径100mm～200mm。The method for determining the trajectory of a grinding wheel for complex chip flutes grinding of a tool according to claim 1, characterized in that in the step (1), a 1A1 or 1V1 type diamond grinding wheel is selected as the grinding wheel, and the diameter of the grinding wheel is 100mm-200mm.
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