阅读说明：本技术 一种基于刀位文件的刀具与工件瞬时接触轮廓提取方法 (Tool and workpiece instantaneous contact contour extraction method based on tool position file ) 是由 *** 仇云杰 王国连 于 2019-10-29 设计创作，主要内容包括：本发明提供一种基于刀位文件的刀具与工件瞬时接触轮廓提取方法,包括：步骤1：获取刀位文件和加工参数；步骤2：根据刀位文件和加工参数建立各个时刻的刀位点分别对应的在待加工表面上的点的直线方程；步骤3：将刀具沿轴向离散成多个切削微元；步骤5：将目标切削微元所在圆面的圆面方程分别与各个时刻的刀位点对应的直线方程联立解得交点；步骤6：根据预设条件从交点中提取若干特征点,使用二次曲线拟合特征点得到拟合曲线,并求解拟合曲线上与目标切削微元的圆面的中心的距离为刀具半径的轮廓点,步骤7：将所有的轮廓点描绘在同一坐标系下,获得刀具与工件瞬时接触轮廓。本发明的方法可以高精度高效率地提取刀具和工件的瞬时接触轮廓。(The invention provides a method for extracting instantaneous contact contour of a cutter and a workpiece based on a cutter position file, which comprises the following steps: step 1: acquiring a tool position file and processing parameters; step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters; and step 3: axially dispersing the tool into a plurality of cutting microelements; and 5: respectively solving a circular surface equation of a circular surface where the target cutting infinitesimal is located and a linear equation corresponding to the cutter location point at each moment in a simultaneous manner to obtain an intersection point; step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve, solving contour points on the fitting curve, wherein the distance between the contour points and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter, and the step 7: and (4) all the contour points are depicted in the same coordinate system, and the instantaneous contact contour of the tool and the workpiece is obtained. The method can extract the instantaneous contact profile of the cutter and the workpiece with high precision and high efficiency.)

1. A method for extracting instantaneous contact contour of a cutter and a workpiece based on a cutter position file is characterized by comprising the following steps:

step 1: acquiring a tool position file and processing parameters;

step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters;

and step 3: axially dispersing the tool into a plurality of cutting microelements;

and 4, step 4: sequentially selecting target cutting micro-elements from the plurality of cutting micro-elements from the bottom of the cutter until the plurality of cutting micro-elements are selected;

and 5: simultaneously solving a circular surface equation of a circular surface where the target cutting infinitesimal is located and the linear equation corresponding to the cutter location point at each moment respectively to obtain an intersection point;

step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve, and solving contour points of which the distance from the fitting curve to the center of the circular surface of the target cutting infinitesimal is the radius of the cutter;

and 7: and (4) describing all the contour points in the same coordinate system to obtain the instantaneous contact contour of the tool and the workpiece.

2. The tool-to-workpiece instantaneous contact profile extraction method based on the tool position file as set forth in claim 1, wherein the step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters, and comprising the following steps of:

step 21: establishing a workpiece coordinate system O at a workpiece fixing position of a vertical milling center_w-X_wY_wZ_w(ii) a Taking any end point of the bottom surface of the workpiece as a coordinate origin O_wThe three axes of the workpiece coordinate system being X respectively_wAxis, Y_wAxis and Z_wA shaft;

step 22: calculating coordinates of points on the surface to be machined of the workpiece corresponding to the tool location points according to the tool location file and the machining parameters;

step 23: calculating the coordinate of the bottom surface central point Q (t) of the cutter at the current moment in a workpiece coordinate system according to the cutter position file

Step 24: and establishing the linear equation according to the coordinates of the points on the surface to be processed and the vector coordinates of the cutter shaft.

3. The tool-to-workpiece instantaneous contact profile extraction method based on the tool location file as set forth in claim 2, wherein the coordinates of the point on the surface to be machined of the workpiece corresponding to the tool location point are calculated from the tool location file and the machining parameters as:

calculating the point T (t) from the tool position Q (t) at the time t to the surface to be machined at the time X according to the cutting depth, the radius of the tool, the tool position Q (t + delta t) at the time t-delta t and the tool position Q (t-delta t) at the time t + delta t_w，Y_wAnd Z_wThe difference of the directions is calculated as follows;

wherein d is the depth of cut, R is the tool radius, Δ X (t), Δ y (t) and Δ z (t) represent the tool location Q (t) and the point T (t) at X, respectively_w，Y_wAnd Z_wA difference in direction;

calculating the coordinate of the point T (t) according to the coordinate of the tool location point Q (t) and the difference value, wherein the calculation formula is as follows:

wherein the content of the first and second substances,

4. The tool-to-workpiece instantaneous contact profile extraction method based on the tool position file as set forth in claim 2, wherein the linear equation is established based on the coordinates of the point on the surface to be machined and the arbor vector as:

wherein the content of the first and second substances,

5. The tool-to-workpiece instantaneous contact profile extraction method based on the tool position file as claimed in claim 1, wherein the step 5: and simultaneously solving the circular surface equation of the circular surface where the target cutting infinitesimal is positioned and the linear equation corresponding to the cutter location point at each moment to obtain an intersection point, wherein the method comprises the following steps of:

step 51: calculating the circular surface equation according to the distance from the target cutting infinitesimal to the bottom surface of the cutter, the cutter vector and the coordinates of a point T (t), wherein the calculation formula is as follows:

wherein D is_hThe offset value of the cutting infinitesimal relative to the cutting infinitesimal of the bottom surface of the cutter is shown, and h is the distance between the cutting infinitesimal and the bottom surface of the cutter;

step 52: respectively combining the circular surface equation with a linear equation corresponding to the cutter position point at each moment to obtain an intersection point T_n(T), the intersection point T_n(t) the coordinates in the object coordinate system are:

wherein the content of the first and second substances,

when n is 1, a first intersection point T is obtained₁(T) coordinates, and so on, to obtain the nth intersection point T_nThe coordinates of (t) obtain the coordinates of the intersection point.

6. The tool-to-workpiece instantaneous contact profile extraction method based on the tool position file as claimed in claim 1, wherein the step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve, and solving contour points on the fitting curve, wherein the distance between the contour points and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter, and the contour points comprise:

step 61: calculating the distance between the intersection point of the current moment and the central point of the circular surface according to the central point Q (t, h) of the circular surface of the target cutting infinitesimal

wherein the content of the first and second substances,

step 62: select to make

And step 63: establishing a tool coordinate system O at the center of the bottom surface of the tool_c-X_cY_cZ_cTaking the end point of the bottom surface of the workpiece as the origin of coordinates O_cThe three axes of the tool coordinate system are respectively X_cAxis, Y_cAxis and Z_cThe shaft is provided with a plurality of axial holes,

step 64: feature points T using coordinate transformation_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) converting the coordinate values in the workpiece coordinate system to coordinate values in the tool coordinate system;

step 65: fitting the characteristic points T under the tool coordinate system by using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t) obtaining a fitted curve;

and step 66: and solving the fitting curve and the circular equation in a simultaneous manner to obtain the coordinates of the contour points, and transforming the coordinates of the contour points from the tool coordinate system to the workpiece coordinate system to obtain the coordinates of the contour points in the workpiece coordinate system.

7. The tool-to-workpiece instantaneous contact profile extraction method based on tool position file as claimed in claim 6, wherein said feature point T is transformed by using coordinate_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) conversion of coordinate values in the workpiece coordinate system to the toolThe transformation process of the coordinate values in the coordinate system is represented as follows:

wherein α and β represent rotation angles around the z-axis and the y-axis, respectively, M (α) and N (β) are rotation matrices around the z-axis and around the y-axis, respectively,

said M (α) and N (β) are:

8. the tool-to-workpiece instantaneous contact profile extraction method based on tool position file as claimed in claim 6, characterized in that the feature point T is fitted under the tool coordinate system using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t) obtaining a fitted curve comprising:

a fitting error function is established, which can be expressed as:

wherein E (a, b, c) is a fitting error function; a, b and c are fitting parameters;

calculating partial derivatives of the fitting error function for each parameter and enabling the partial derivatives to be equal to 0, and then solving a plurality of partial derivative equations in a simultaneous mode to obtain values of each parameter;

the equation for the quadratic function is as follows:

f(x)＝ax²+bx+c；

and substituting the obtained values of a, b and c into the equation of the quadratic curve function to obtain the fitting curve.

Technical Field

The invention relates to the technical field of contour extraction, in particular to a method for extracting instantaneous contact contour of a cutter and a workpiece based on a cutter position file.

Background

At present, five-axis milling has been widely used in the production of complex parts in aerospace, automotive, mold and biomedical industries. The machining process usually needs to maintain the machining precision and improve the machining efficiency. To this end, researchers typically simulate the cutting process to select the best machining parameters. One of the most important steps in this process is to extract the tool/workpiece instantaneous contact profile. Tool/workpiece instantaneous contact profile extraction remains a challenge in five-axis side milling due to complex workpiece profile information and different tool motions. Many surfaces to be machined are difficult to describe with accurate mathematical expressions. This makes many methods limited or computationally quite complex.

Patent 1: the patent with the application number of 201711212327.5 discloses a method for extracting the instantaneous contact contour of a cutter and a workpiece in the process of five-axis side milling, which carries out solid dispersion on the surface to be processed through CAM software and changes a curved surface into a series of scattered points. Then, dispersing the cutter into a plurality of cutter micro-elements along the axial direction, traversing each micro-element by taking the vertical length from the axis of the cutter and the axial range of the cutter micro-elements as limiting conditions, and extracting a coordinate point near the contour line of the cutter; and connecting the coordinate points to obtain the contact contour of the cutter and the workpiece at the designated cutter position point in the layer milling process. The method is very effective for workpieces with complex curved surface information. However, this method requires the use of CAM to discretize the surface into discrete points, which is also time consuming. Moreover, a curved surface model must be used, which makes the method limited.

Document 2: "Li ZL, Wang XZ, Zhu LM, arc-surface interaction method, machining tool, engagement elements for generating tool cutting in five-axism [ J ]. Computer-aid Design,2015,73: 1-10" discloses a camber intersection method for calculating the instantaneous contact area of a tool workpiece. The method is characterized in that the rotating surface of the cutter is represented by a section circle family, and two contact points of each section circle are analyzed according to an envelope condition. The contact point divides the circle into two circles and then extracts a feasible arc of contact to intersect the workpiece surface. By adopting the method based on the intersection and distance fields of the circular arcs/curved surfaces, the contact contour of the closed instantaneous cutter workpiece can be accurately and effectively calculated. This method can achieve high accuracy in calculating the contact area, but for a workpiece to be machined having complex curved surface information, the method requires iterative calculation, which increases the calculation time. Because the method depends on the mathematical expression of the curved surface, when the surface to be processed is difficult to describe by an accurate mathematical expression, the method cannot calculate the instantaneous contact profile of the cutter/workpiece.

Disclosure of Invention

In order to accurately and quickly extract the instantaneous contact contour of a cutter/workpiece, particularly for a workpiece to be machined with complex curved surface information, the invention provides a cutter and workpiece instantaneous contact contour extraction method based on a cutter position file.

The embodiment of the invention provides a method for extracting instantaneous contact contour of a cutter and a workpiece based on a cutter position file, which comprises the following steps:

step 1: acquiring a tool position file and processing parameters;

step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters;

and step 3: axially dispersing the tool into a plurality of cutting microelements;

and 4, step 4: sequentially selecting target cutting micro-elements from the plurality of cutting micro-elements from the bottom of the cutter until all the cutting micro-elements are selected;

and 5: respectively solving a circular surface equation of a circular surface where the target cutting infinitesimal is located and a linear equation corresponding to the cutter location point at each moment in a simultaneous manner to obtain an intersection point;

step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve, and solving contour points on the fitting curve, wherein the distance between the contour points and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter;

and 7: and (4) all the contour points are depicted in the same coordinate system, and the instantaneous contact contour of the tool and the workpiece is obtained.

Optionally, step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters, and comprising the following steps of:

step 21: establishing a workpiece coordinate system O at a workpiece fixing position of a vertical milling center_w-X_wY_wZ_w(ii) a Taking any end point of the bottom surface of the workpiece as a coordinate origin O_wThe three axes of the workpiece coordinate system being X respectively_wAxis, Y_wAxis and Z_wA shaft;

step 22: calculating coordinates of points on the surface to be machined of the workpiece corresponding to the tool location points according to the tool location file and the machining parameters;

step 23: calculating the coordinate of the bottom surface central point Q (t) of the cutter at the current moment in a workpiece coordinate system according to the cutter position file

The axis vector coordinate of the cutter is

Step 24: and establishing the linear equation according to the coordinates of the points on the surface to be processed and the vector coordinates of the cutter shaft.

Optionally, calculating coordinates of points on the surface to be machined of the workpiece corresponding to the tool location point according to the tool location file and the machining parameters is as follows:

calculating the point T (t) from the tool position Q (t) at the time t to the surface to be machined at the time X according to the cutting depth, the radius of the tool, the tool position Q (t + delta t) at the time t-delta t and the tool position Q (t-delta t) at the time t + delta t_w，Y_wAnd Z_wThe difference of the directions is calculated as follows;

wherein d is the depth of cut, R is the tool radius, Δ X (t), Δ y (t) and Δ z (t) represent the tool location Q (t) and the point T (t) at X, respectively_w，Y_wAnd Z_wA difference in direction;

respectively represents the tool location point Q (t + delta t) in the workpiece coordinate system X_wAnd Y_wCoordinate values of the direction;respectively represents the tool location point Q (t-delta t) in the workpiece coordinate system X_wAnd Y_wCoordinate values of the direction;

respectively represents the tool location point Q (t) in the workpiece coordinate system X_wCoordinate values of the direction;

calculating the coordinate of the point T (t) according to the coordinate of the tool location point Q (t) and the difference value, wherein the calculation formula is as follows:

wherein the content of the first and second substances,

and

respectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

respectively represents the tool location point Q (t) in the workpiece coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction; Δ X (t), Δ y (t) and Δ z (t) represent the knife location Q (t) and the point T (t) at X_w，Y_wAnd Z_wThe difference in direction.

Optionally, establishing the linear equation according to the coordinates of the point on the surface to be processed and the arbor vector is as follows:

wherein the content of the first and second substances,

and

respectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

respectively X of the axis vector coordinates of the tool_w，Y_wAnd Z_wCoordinate values of the directions.

Optionally, step 5: and simultaneously solving the circular surface equation of the circular surface where the target cutting infinitesimal is positioned and the linear equation corresponding to the cutter location point at each moment to obtain an intersection point, wherein the method comprises the following steps of:

step 51: calculating the circular surface equation according to the distance from the target cutting infinitesimal to the bottom surface of the cutter, the cutter vector and the coordinates of a point T (t), wherein the calculation formula is as follows:

wherein D is_hThe offset value of the cutting infinitesimal relative to the cutting infinitesimal of the bottom surface of the cutter is shown, and h is the distance between the cutting infinitesimal and the bottom surface of the cutter;

respectively X of the axis vector coordinates of the tool_w，Y_wAnd Z_wCoordinate values of the direction;

and

respectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

step 52: respectively combining the circular surface equation with the linear equation corresponding to the cutter position point at each moment to obtain an intersection point T_n(T), the intersection point T_n(t) the coordinates in the object coordinate system are:

wherein the content of the first and second substances,

the tool location point T (T- (n-1) delta T) at the time T- (n-1) delta T respectively is X under the workpiece coordinate system_w，Y_wAnd Z_wCoordinate values of the direction;

x in the workpiece coordinate system respectively as the intersection point_w，Y_wAnd Z_wCoordinate value of direction, m_nThe intermediate coefficients are the coefficients of the intermediate coefficients,

when n is 1, a first intersection point T is obtained₁(T) coordinates, and so on, to obtain the nth intersection point T_nThe coordinates of (t) obtain the coordinates of the intersection point.

Optionally, step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve, and solving contour points on the fitting curve, wherein the distance between the contour points and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter, and the contour points comprise:

step 61: calculating the distance between the intersection point of the current moment and the central point of the circular surface according to the central point Q (t, h) of the circular surface of the target cutting infinitesimal

The calculation formula is as follows:

wherein the content of the first and second substances,

x of the central point Q (t, h) in the workpiece coordinate system_w，Y_wAnd Z_wCoordinate values of the direction;

x in the workpiece coordinate system respectively as the intersection point_w，Y_wAnd Z_wCoordinate values of the direction;

step 62: select to make

The intersection point at which the value is the minimum is taken as the feature point T_q(T) and selecting the characteristic point T_q(T) is a central left-side near feature point T_q(T) two points and a right side near feature point T_q(T) two points are respectively marked as characteristic points T in the sequence from left to right_q-2(T) characteristic Point T_q-1(T) characteristic Point T_q+1(T) characteristic Point T_q+2(t)；

And step 63: establishing a tool coordinate system O at the center of the bottom surface of the tool_c-X_cY_cZ_cTaking the end point of the bottom surface of the workpiece as the origin of coordinates O_cThe three axes of the tool coordinate system are respectively X_cAxis, Y_cAxis and Z_cThe shaft is provided with a plurality of axial holes,

step 64: feature points T using coordinate transformation_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) converting the coordinate values in the workpiece coordinate system to coordinate values in the tool coordinate system;

step 65: fitting the characteristic points T under the tool coordinate system by using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t) obtaining a fitted curve;

and step 66: and solving the fitting curve and the circular equation in a simultaneous manner to obtain the coordinates of the contour points, and transforming the coordinates of the contour points from the tool coordinate system to the workpiece coordinate system to obtain the coordinates of the contour points in the workpiece coordinate system.

Optionally, the feature point T is transformed using coordinates_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) the transformation process of converting the coordinate values in the workpiece coordinate system to the coordinate values in the tool coordinate system is represented as:

wherein α and β represent rotation angles around the z-axis and the y-axis, respectively, M (α) and N (β) are rotation matrices around the z-axis and around the y-axis, respectively,

respectively represent the characteristic points T_q(t) X in the tool coordinate system_cAxis, Y_cAxis and Z_cCoordinate values in the axial direction;

respectively represent the characteristic points T_q(t) X in the tool coordinate System_wAxis, Y_wAxis and Z_wCoordinate values in the axial direction;

said M (α) and N (β) are:

optionally, fitting the characteristic point T under the tool coordinate system by using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t) obtaining a fitted curve comprising:

a fitting error function is established, which can be expressed as:

wherein E (a, b, c) is a fitting error function; a, b and c are fitting parameters;

calculating partial derivatives of the fitting error function for each parameter and enabling the partial derivatives to be equal to 0, and then solving a plurality of partial derivative equations in a simultaneous mode to obtain values of each parameter;

the equation for the quadratic function is as follows:

f(x)＝ax²+bx+c；

and substituting the obtained values of a, b and c into the equation of the quadratic curve function to obtain a fitting curve.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

FIG. 1 is a schematic diagram of a tool-to-workpiece instantaneous contact profile extraction method based on a tool location file according to an embodiment of the present invention;

FIG. 2 is a flowchart of software for implementing a tool-to-workpiece instantaneous contact profile extraction method based on a tool location file according to an embodiment of the present invention;

FIG. 3 is a schematic view of a tool-to-workpiece instantaneous contact profile in five-axis machining;

FIG. 4 is a schematic illustration of a calculation of points on a surface to be machined according to an embodiment of the present invention;

FIG. 5 is a diagram illustrating the calculation of contour points according to an embodiment of the present invention;

FIG. 6 is a schematic view of a surface to be machined according to an embodiment of the present invention.

In the figure:

1. a cutter axis vector; 2. the surface to be processed is provided with straight lines; 3. forming surface fingerprint lines; 4. a tool path; 5. contour points; 6. and (6) fitting a curve.

Detailed Description

The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.

The embodiment of the invention provides a method for extracting an instantaneous contact contour of a cutter and a workpiece based on a cutter position file, which comprises the following steps of:

step 1: acquiring a tool position file and processing parameters;

step 2: establishing a linear equation of points on the surface to be machined, which correspond to the tool location points at each moment respectively, according to the tool location file and the machining parameters;

and step 3: axially dispersing the tool into a plurality of cutting microelements;

and 4, step 4: sequentially selecting target cutting micro-elements from the plurality of cutting micro-elements from the bottom of the cutter until the plurality of cutting micro-elements are selected;

and 5: respectively solving a circular surface equation of a circular surface where the target cutting infinitesimal is located and a linear equation corresponding to the cutter location point at each moment in a simultaneous manner to obtain an intersection point;

step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitting curve 6, solving a contour point 5 on the fitting curve 6, wherein the distance between the contour point and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter,

and 7: all the contour points 5 are depicted in the same coordinate system, and the instantaneous contact contour of the tool and the workpiece is obtained.

The working principle and the beneficial effects of the technical scheme are as follows:

the method comprises the steps of establishing linear equations of points on a surface to be processed, which correspond to tool location points at various moments respectively, according to a tool location file and processing parameters; axially dispersing the tool into a plurality of cutting microelements; sequentially selecting the cutting micro elements from the bottom of the cutter, and solving a plurality of intersection points according to a circular equation of a circular surface where the selected cutting micro elements are located and the linear equation; and fitting the intersection points by using a quadratic curve to obtain a fitted curve 6, solving contour points 5, the distance between the fitted curve 6 and the center of the circular surface of the cutting infinitesimal is the radius of the cutter, reselecting the cutting infinitesimal to calculate the contour points 5, and drawing all the contour points 5 under the same coordinate system to obtain the instantaneous contact contour of the cutter and the workpiece.

The method solves the instantaneous contact contour of the cutter and the workpiece based on the cutter position file. The existing process for solving the instantaneous contact contour of the cutter workpiece needs not only a cutter position file but also information of a curved surface to be machined. However, many of the mathematical expressions for surfaces to be machined are complex, which makes the computation process of some methods time consuming. In particular, some surfaces to be machined cannot be expressed with an accurate mathematical expression, which renders some existing methods useless. The method can extract instantaneous contact profiles of the cutter and the workpiece with high precision and high efficiency, and provides a theoretical basis for a simulation process of a milling process.

In one embodiment, step 2: according to the tool position file and the machining parameters, linear equations of points on the surface to be machined corresponding to the tool position points at all times are established, and the method comprises the following steps:

step 21: establishing a workpiece coordinate system O at a workpiece fixing position of a vertical milling center_w-X_wY_wZ_w(ii) a Taking any end point of the bottom surface of the workpiece as a coordinate origin O_wThe three axes of the workpiece coordinate system being X respectively_wAxis, Y_wAxis and Z_wA shaft;

step 22: calculating coordinates of points on the surface to be machined of the workpiece corresponding to the tool location points according to the tool location file and the machining parameters;

step 23: calculating the coordinate of the bottom surface central point Q (t) of the cutter at the current moment in a workpiece coordinate system according to the cutter position file

Axis vector of cutterQuantity 1 coordinate is

Step 24: and establishing a linear equation of the surface to be processed according to the coordinates of the points on the surface to be processed and the coordinates of the cutter shaft vector 1.

The working principle and the beneficial effects of the technical scheme are as follows:

the coordinates of points on the surface to be machined of the workpiece are directly calculated according to the tool position file and the machining parameters, the information of the curved surface to be machined is not needed, and the complicated calculation of the information of the curved surface to be machined is omitted; the coordinates of the points of the surface to be machined are determined quickly. And expressing the processing lines of the surface to be processed according to the coordinates of the points of the surface to be processed and the coordinates of the cutter shaft vector 1 (linear equation).

In one embodiment, the coordinates of points on the surface to be machined of the workpiece corresponding to the tool location points are calculated from the tool location file and the machining parameters as:

calculating the point T (t) from the tool position Q (t) at the time t to the surface to be machined at the time X according to the cutting depth, the radius of the tool, the tool position Q (t + delta t) at the time t-delta t and the tool position Q (t-delta t) at the time t + delta t_w，Y_wAnd Z_wThe difference of the directions is calculated as follows;

wherein d is the depth of cut, R is the tool radius, Δ X (t), Δ y (t) and Δ z (t) represent the tool location Q (t) and the point T (t) at X, respectively_w，Y_wAnd Z_wA difference in direction;respectively represents the tool location point Q (t + delta t) in the workpiece coordinate system X_wAnd Y_wCoordinate values of the direction;respectively represents the tool location point Q (t-delta t) in the workpiece coordinate system X_wAnd Y_wCoordinate values of the direction;respectively represents the tool location point Q (t) in the workpiece coordinate system X_wCoordinate values of the direction;

calculating the coordinate of the point T (t) according to the coordinate of the tool location point Q (t) and the difference value, wherein the calculation formula is as follows:

wherein the content of the first and second substances,

andrespectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

respectively represents the tool location point Q (t) in the workpiece coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction; Δ X (t), Δ y (t) and Δ z (t) represent the knife location Q (t) and the point T (t) at X_w，Y_wAnd Z_wThe difference in direction.

The working principle and the beneficial effects of the technical scheme are as follows:

wherein, the time difference between adjacent knife location points is delta t; the current moment is the t moment, so the information of the curved surface to be machined is calculated by replacing the coordinate values of the tool location point at the current moment and the two adjacent tool location points, and the complicated calculation of the information of the curved surface to be machined is omitted; the coordinates of the points of the surface to be machined are determined quickly. The information of the tool location can be directly obtained in the tool location file.

In one embodiment, a linear equation is established according to the coordinates of the point on the surface to be processed and the arbor vector 1 as follows:

wherein the content of the first and second substances,

and

respectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

x of the axis vector 1 coordinate of the tool_w，Y_wAnd Z_wCoordinate values of the directions.

The working principle and the beneficial effects of the technical scheme are as follows:

according to the milling principle, when a constant radial cutting depth parameter is selected, the cutter axis vector 1 of the cutter is equidistantly offset according to the surface to be processed, and then the cutter axis vector 1 of the cutter point at the current moment is the same as the straight line vector of the corresponding surface to be processed, so that a linear equation can be directly determined according to the coordinates of the point on the surface to be processed and the corresponding cutter axis vector 1.

In one embodiment, step 5: and simultaneously solving the circular surface equation of the circular surface where the target cutting infinitesimal is positioned and the linear equation corresponding to the cutter location point at each moment to obtain an intersection point, wherein the method comprises the following steps of:

step 51: calculating the circular surface equation according to the distance from the target cutting infinitesimal to the bottom surface of the cutter, the cutter vector and the coordinates of a point T (t), wherein the calculation formula is as follows:

wherein D is_hThe offset value of the cutting infinitesimal relative to the cutting infinitesimal of the bottom surface of the cutter is shown, and h is the distance between the cutting infinitesimal and the bottom surface of the cutter;

x of the axis vector 1 coordinate of the tool_w，Y_wAnd Z_wCoordinate values of the direction;

and

respectively representing points T (t) in the object coordinate system X_w，Y_wAnd Z_wCoordinate values of the direction;

when the cutter is dispersed into a plurality of cutting micro-elements, each cutting micro-element can be approximately seen as a circle with the height h from the bottom surface of the cutter;

step 52: respectively combining the circular equation with the linear equation corresponding to the cutter position point at each moment to obtain an intersection point T_n(T), the intersection point T_n(t) the coordinates in the object coordinate system are:

wherein the content of the first and second substances,

the tool location point T (T- (n-1) delta T) at the time T- (n-1) delta T respectively is X under the workpiece coordinate system_w，Y_wAnd Z_wCoordinate values of the direction;

x in the workpiece coordinate system respectively as the intersection point_w，Y_wAnd Z_wCoordinate value of direction, m_nThe intermediate coefficients are the coefficients of the intermediate coefficients,

when n is 1, a first intersection point T is obtained₁(T) coordinates, and so on, to obtain the nth intersection point T_nThe coordinates of (t) obtain the coordinates of the intersection point.

The working principle and the beneficial effects of the technical scheme are as follows:

and (3) establishing a circular equation after the cutter is dispersed into a plurality of cutting infinitesimals, establishing a linear equation through points of the surface to be processed, and determining the intersection point of the circular equation and the linear equation. The contour points 5 of the instantaneous contact contour of the tool and the workpiece can be obtained only by further screening the intersection points.

In one embodiment, step 6: extracting a plurality of characteristic points from the intersection points according to preset conditions, fitting the characteristic points by using a quadratic curve to obtain a fitted curve 6, and solving a contour point 5 on the fitted curve 6, wherein the distance between the contour point and the center of the circular surface of the target cutting infinitesimal is the radius of the cutter, and the contour point comprises the following steps:

step 61: calculating the distance L between the intersection point at the current moment and the central point of the circular surface according to the central point Q (t, h) of the circular surface of the target cutting infinitesimal_Q(t,h)-Tn(t)The calculation formula is as follows:

wherein the content of the first and second substances,

x of the central point Q (t, h) in the workpiece coordinate system_w，Y_wAnd Z_wCoordinate values of the direction;x in the workpiece coordinate system respectively as the intersection point_w，Y_wAnd Z_wCoordinate values of the direction;

step 62: select to make

The intersection point at which the value is the minimum is taken as the feature point T_q(T) and selecting the characteristic point T_q(T) is a central left-side near feature point T_q(T) two points and a right side near feature point T_q(T) two points are respectively marked as characteristic points T in the sequence from left to right_q-2(T) characteristic Point T_q-1(t)Characteristic point T_q+1(T) characteristic Point T_q+2(t)；

And step 63: establishing a tool coordinate system O at the center of the bottom surface of the tool_c-X_cY_cZ_cTaking the end point of the bottom surface of the workpiece as the origin of coordinates O_cThe three axes of the tool coordinate system are respectively X_cAxis, Y_cAxis and Z_cThe shaft is provided with a plurality of axial holes,

step 64: feature points T using coordinate transformation_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) converting the coordinate values in the workpiece coordinate system to coordinate values in the tool coordinate system;

step 65: fitting the characteristic points T under the tool coordinate system by using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t), obtaining a fitting curve 6;

and step 66: and solving the fitting curve 6 and the circular equation in a simultaneous manner to obtain the coordinate of the contour point 5, and transforming the coordinate of the contour point 5 from a tool coordinate system to a workpiece coordinate system to obtain the coordinate of the contour point 5 in the workpiece coordinate system.

The working principle and the beneficial effects of the technical scheme are as follows:

the circular equation is in the tool coordinate system, so the fitted curve 6 should be in the tool coordinate system; however, the intersection point is in the workpiece coordinate system, so that after a proper intersection point is selected, the coordinate system of the selected intersection point needs to be converted into the tool coordinate system from the workpiece coordinate system, and then a fitting curve 6 is obtained; solving according to the fitted curve 6 and the circular equation to obtain a contour point 5; finally, converting the contour point 5 into a workpiece coordinate system; the contour points 5 are acquired more accurately through the steps.

In one embodiment, the feature points T are transformed using coordinates_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T) and characteristic Point T_q+2(t) the transformation process of converting the coordinate values in the workpiece coordinate system to the coordinate values in the tool coordinate system is represented as:

wherein α and β represent rotation angles around the z-axis and the y-axis, respectively, M (α) and N (β) are rotation matrices around the z-axis and around the y-axis, respectively,

respectively represent the characteristic points T_q(t) X in the tool coordinate system_cAxis, Y_cAxis and Z_cCoordinate values in the axial direction;

respectively represent the characteristic points T_q(t) X in the tool coordinate System_wAxis, Y_wAxis and Z_wCoordinate values in the axial direction;

said M (α) and N (β) are:

the working principle and the beneficial effects of the technical scheme are as follows:

the fast transformation of the coordinate system is achieved based on the rotation of the rotation matrix.

In one embodiment, the feature points T are fitted to the tool coordinate system using a quadratic curve function_q-2(T), characteristic point T_q-1(T), characteristic point T_q(T), characteristic point T_q+1(T), characteristic point T_q+2(t), obtaining the fitted curve 6 includes:

a fitting error function is established, which can be expressed as:

wherein E (a, b, c) is a fitting error function; a, b and c are fitting parameters;

calculating partial derivatives of the fitting error function for each parameter and enabling the partial derivatives to be equal to 0, and then solving a plurality of partial derivative equations in a simultaneous mode to obtain values of each parameter;

the equation for the quadratic function is as follows:

f(x)＝ax²+bx+c；

substituting the obtained values of a, b and c into the equation of the quadratic curve function to obtain a fitting curve 6;

the working principle and the beneficial effects of the technical scheme are as follows:

the fitting is best when the partial derivative of the fitting error for each parameter is 0, so that the best fitting parameter and thus the best fitting curve 6 are obtained.

FIG. 2 is a flow chart of software for applying the tool-to-workpiece instantaneous contact profile extraction method based on the tool location file of the present invention. FIG. 3 shows the instantaneous contact profile of the tool with the workpiece in five-axis machining. It can be seen that the profile consists of four parts, the most difficult of which is the set of points of entry (profile points 5) (where the arrows are drawn in the figure). The calculation of this portion of the contact profile can be calculated by the method of the present invention. The remainder can be calculated similarly by the methods herein. Fig. 4 shows the contact process of the tool and the workpiece at time t, in fig. 4, the tool path 4 passes through a point Q (t- Δ t), a point Q (t), and a point Q (t + Δ t) in sequence, and the ruled line 2 of the surface to be machined can be represented by a fingerprint equation; the forming surface fingerprint lines 3 are also present on the forming surface after the workpiece has been machined, and the calculation of the points on the surface to be machined can be seen in fig. 4. FIG. 5 illustrates a specific process for calculating the point of entry (contour point 5) herein, and when the intersection point of the found discrete fingerprint line of the surface to be machined and the bottom surface cylinder of the tool is not the point of entry (contour point 5), the closest point T to the radius of the tool can be selected_q(t) and four points in the vicinity thereof. Five points are selected by using quadratic curve fitting, and the intersection point is obtained by combining the quadratic curve and the bottom surface cylinder of the cutter, namely the entry point (contour point 5). And similarly, the contact points of the contact profiles of the rest parts can be calculated, and the instantaneous contact profile of the tool and the workpiece can be obtained by describing all the calculated points in the same coordinate system. The invention directly calculates the instantaneous contact contour of the cutter and the workpiece according to the cutter position file, thereby avoiding the iterative calculation process of using complex curved surface information to be processed in the traditional method. In particularThe method has more obvious advantages when the curved surface to be processed is complicated and cannot be described by a specific mathematical formula. The calculation result of the method keeps higher precision, greatly improves optimization efficiency and has wide application prospect. The method has important significance for parametric design and simulation in the milling process; the method for extracting the instantaneous contact profile between the tool and the workpiece based on the tool position file is described by taking specific numerical values as an example:

to verify the accuracy of the method herein, the 7-entry point (contour point 5) shown in FIG. 5 was calculated and compared to the method in patent 1. The remaining points are found similarly.

The cutter radius R of a common end mill is 6mm, the cutter tooth number N is 2, the cutter helix angle is 30 degrees, the feeding speed is 200mm/min, the main shaft rotation speed is 1000R/min, and the workpiece material is 7075 aluminum alloy. An 'S' type test piece as shown in fig. 6 is selected, which is composed of a cubic B-spline curve whose control point information is as follows:

and generating 1000 machining tool positions according to the information of the curved surface to be machined and computer-aided software. To verify the accuracy of the proposed method, the tool bottom surface infinitesimal at the 230 th tool site was chosen. Experimental the method proposed by the present invention and the method proposed in patent 1 calculate the 7-cut angle shown in fig. 5, respectively. The calculation steps using the methods herein are as follows:

establishing linear equation expressions corresponding to all tool positions (tool positions at all times) according to the tool position file and the machining parameters:

establishing a workpiece coordinate system O at a workpiece fixing position of a vertical milling center_w-X_wY_wZ_w(ii) a Taking the end point of the bottom surface of the workpiece as the origin of coordinates O_wThe three axes of the workpiece coordinate system being X respectively_wAxis, Y_wAxis and Z_wA shaft;

calculating points on the surface to be machined; setting the coordinates of a central point Q (t) of the bottom surface of the cutter at the current moment in a workpiece coordinate system as (280.1437,47.9084,1.0602), setting the coordinate of a cutter axis vector 1 of the cutter as (-0.11574,0.210294,0.970763), wherein the parameters can be obtained from a cutter location file, setting the radial cutting depth as 2mm, setting the radius of the cutter as 6mm, and setting the time difference value between adjacent cutter location points as delta t; and (3) recording the tool location point at the time t-delta t as Q (t-delta t), and the tool location point at the time t + delta t as Q (t + delta t), then recording the point of the surface to be machined, which is obtained by calculating the current tool location point, as T (t), and the coordinates of the point in the workpiece coordinate system can be expressed as:

wherein

Wherein

And

respectively, the coordinate values of the point t (t) in the x, y and z directions in the workpiece coordinate system.

And respectively represent coordinate values of the point Q (t + Δ t) in the x and y directions in the workpiece coordinate system.

And respectively represent the coordinate values of the point Q (t- Δ t) in the x and y directions in the workpiece coordinate system. Δ x (t), Δ y (t) and Δ z (t) respectively represent the difference between the current tool position and the surface point to be machined in the x, y and z directions, and the solutionThe values obtained were 3.7501, -1.1988 and 0.7068, respectively.Values of (d) are obtained directly from the bit file, 279.9155, 47.2059, 280.3675, 48.6161, respectively.

Establishing a linear equation expression according to the calculated points on the surface to be processed and the corresponding cutter axis vector 1;

according to the milling principle, when a constant radial cutting depth parameter is selected, the cutter axis vector 1 of the cutter is equidistantly offset according to the surface to be processed, then the cutter axis vector 1 of the current cutter location point is the same as the ruled line vector of the corresponding surface to be processed, and a ruled line of the surface to be processed obtained according to the current cutter location point can be expressed as:

and similarly, the ruled line equation of the surface to be processed corresponding to all the cutter location points can be obtained according to the cutter location file.

Dispersing a cutter into a plurality of cutting micro-elements along the axial direction, selecting one cutting micro-element, and solving according to a circular surface equation and a linear equation where the micro-element is located to obtain a series of intersection points:

selecting a tool bottom surface infinitesimal, wherein the distance h from the tool bottom surface is 0, and the equation of a circular surface where the infinitesimal is located is as follows:

-0.1154x+0.210294y+0.970763z+D_h＝0

wherein

D_h＝-(-0.11574·274.3936+0.210294·49.1072+0.970763·0.3534)

The equation of the circular surface and the equation of the straight line are combined to obtain a series of intersection points T_n(t) (n ═ 1,2,3 …), and the coordinates of these intersections in the object coordinate system can be expressed as:

wherein

When the value of n is changed, calculating to obtain the intersection point T of the circular surface and the linear equation₁(t)，T₂(t)，T₃(t)，…，T_n(t)；

In this particular embodiment:

T₁(t) is (280.6154,49.2786, 0.8196); t is₂(t) is (280.3815,48.5910, 0.9407);

T₃(t) is (280.1437,47.9084, 1.0602); t is₄(t) is (279.9020,47.2308, 1.1782);

T₅(t) is (279.6562,46.5583, 1.2946).

And fitting the calculated partial intersection points by using a quadratic curve, solving a point on the fitting curve 6, which is away from the center of the corresponding height circular surface by the radius of the cutter, selecting the rest cutting infinitesimals again and executing the same calculation process:

recording the central point of the circular surface of the height h at the time t as Q (t, h), namely the current tool location point Q (t), and calculating the distance L between the intersection point of the current time and the central point of the circular surface of the corresponding height by the coordinates of (280.1437,47.9084,1.0602)_Q(t,h)-Tn(t)It can be expressed as:

when t and h are not changed, the selection is made so that

T at the smallest value_q(t) is (278.6336, 43.9184, 1.7445) (q is more than or equal to 1 and less than or equal to n); t is_q(T) is the point closest to 6 (radius of the tool) from the center point of the current micro-element, and is also the point closest to the required cutting point, and is also one of the intersection points of the micro-element surface and the surface to be processed, and the closest point T_q(t) coordinates are: (278.6336, 43.9184, 1.7445) points around the left and right (because the line equations are one after the other, each intersection with the current surface of the element is unique, these intersections are also one after the other, T_q-1(t) is in the order of processing timeAt T_q(t) previous points) their coordinates are as follows: t is_q-2(t)(279.1530，45.2283，1.5227)；T_q-1(t)(278.8953，44.5709，1.6344)；T_q+1(t)(278.3680，43.2709，1.8531)；T_q+2(t)(278.0981，42.6284，1.9601)。

Establishing a tool coordinate system O at the center of the bottom surface of the tool_c-X_cY_cZ_cTaking the end point of the bottom surface of the workpiece as the origin of coordinates O_cThe three axes of the workpiece coordinate system being X respectively_cAxis, Y_cAxis and Z_cAxis, point T using coordinate transformation_q-2(t)，T_q-1(t)，T_q(t)，T_q+1(T) and T_q+2(t) converting to the tool coordinate system, the coordinate transformation process can be expressed as:

where α and β represent the rotation angles about the z-axis and y-axis, respectively, and have values of-0.5031 rad and 0.2424 rad. M (α) and N (β) are rotation matrices about the z-axis and about the y-axis, respectively, which can be expressed as:

due to T_q-2(t)，T_q-1(t)，T_q(t)，T_q+1(t)，T_q+2(t) lie within the same circle of the tool coordinate system, a quadratic curve fit can be used as follows:

f(x)＝ax²+bx+c

to express the fitting effect, a fitting error function E is established, which can be expressed as:

where E (a, b, c) is the fitting error function for the constants a, b and c to be found. To maximize the fit, according to the formula:

calculating a partial derivative of each parameter to be calculated and enabling the partial derivative to be equal to 0, and then simultaneously solving a plurality of partial derivative equations to obtain parameter values which are respectively as follows: 0.01256, 0.8505 and-5.34

Solving the fitted quadratic curve and the equation of the circle where the blade is located in a simultaneous manner to obtain the coordinate of the entry point (the contour point 5), and transforming the coordinate of the entry point (the contour point 5) into a workpiece coordinate system to obtain the coordinate of the entry point (the contour point 5) in the workpiece coordinate system; the cut angle is easily found to be 2.3310, whereas the cut angle calculated using the method described in patent 1 is 2.3311. Thereby proving the correctness of the method in calculating the instantaneous contact profile.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.