CN112147893B - Five-axis milling cutter shaft vector optimization method based on ruled surface space - Google Patents

Five-axis milling cutter shaft vector optimization method based on ruled surface space Download PDF

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CN112147893B
CN112147893B CN202011003079.5A CN202011003079A CN112147893B CN 112147893 B CN112147893 B CN 112147893B CN 202011003079 A CN202011003079 A CN 202011003079A CN 112147893 B CN112147893 B CN 112147893B
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宫政
李炳燃
张辉
叶佩青
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Tsinghua University
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Abstract

The invention provides a five-axis milling cutter shaft vector optimization method based on ruled surface space, which uses the ruled surface space to carry out cutter shaft vector optimization, generates the ruled surface space according to the original cutter shaft vector, carries out fitting fairing treatment on the ruled surface space, uses curve parameters of a cutter shaft tail end line to represent the ruled surface space for each cutter position point, selects cutter vector tail end line parameters in each ruled surface space, carries out optimization by using an optimization algorithm to obtain a group of optimized cutter shaft tail end line curve parameters, and maps the values of the curve parameter space to the coordinate space of a machine tool rotation driving shaft by carrying out kinematic solution on the optimized curve parameters, thereby realizing the cutter shaft vector optimization. The method for optimizing the cutter shaft vector based on the ruled surface space limits the feasible range of the cutter shaft vector in a one-dimensional space, and has the advantages of high operation efficiency, improvement of the dynamic performance of a machine tool and small change on the original cutter shaft vector.

Description

Five-axis milling cutter shaft vector optimization method based on ruled surface space
Technical Field
The invention belongs to the field of milling, and particularly relates to a five-axis milling cutter shaft vector optimization method based on ruled surface space.
Background
Cutter shaft vector optimization is one of core problems in five-axis milling, improper cutter direction can affect the surface appearance and contour accuracy of a workpiece, and drastic change of the cutter direction can cause the kinematic error of a driving shaft to be out of tolerance, so that the processing effect is affected. In addition, the numerical control system can perform a series of optimization after the numerical control program is input, the optimization can change the cutter location point and the cutter axis vector in the original program, and if the cutter axis vector optimization is not performed, the processing effect can be influenced.
In the process of arbor vector optimization, many factors need to be considered. Firstly, the optimized cutter shaft vector can not cause new collision and interference; secondly, the stability of the angle change of the rotary driving shaft of the machine tool needs to be considered; thirdly, the extreme values of the angular speed and the angular acceleration of the motion of the rotary driving shaft of the machine tool cannot exceed the limit values of the machine tool and should be reduced as much as possible; in addition, the optimized arbor vector cannot cause vibrations during machine tool machining.
In the existing method for optimizing the cutter shaft vector, a plurality of methods optimize cutter collision, interference or cutter track smoothness, but the dynamic characteristic of a rotary driving shaft of a machine tool is not considered, or the optimization efficiency is extremely low due to overlarge calculation amount of the method. For example, a cutter axis vector optimization method based on a covariant field functional (application No. 201710748234.8) disclosed in the chinese patent, which utilizes a discretization method to avoid cutter collision and interference, but cannot ensure the stability of cutter axis vector change and good kinematic characteristics of a machine tool rotation driving shaft; the cutter shaft vector optimization method and system based on multi-objective constraint disclosed in Chinese patent (application No. 201810745901.1) ensure that collision and interference cannot occur in the cutter movement process and the smoothness of cutter movement is also ensured, but the optimization method does not have the dynamic characteristic of a machine tool rotation driving shaft, so that the acceleration of the machine tool rotation driving shaft is possibly caused to exceed the limit, and even the machine tool is caused to vibrate; the knife axis vector fairing method (application No. 201810100426.2) based on the kinematic characteristics of the machine tool rotation feed axis disclosed in the chinese patent considers the dynamic characteristics of the machine tool rotation drive axis, but only takes the smooth motion of the rotation drive axis as the optimization target, and does not consider the acceleration variation trend and the jerk magnitude of the rotation drive axis, so that the vibration of the machine tool may be caused.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a five-axis milling cutter axis vector optimization method based on ruled surface space. The method uses the ruled surface space to carry out cutter shaft vector optimization, generates the ruled surface space according to the original cutter shaft vector, carries out fitting fairing treatment on the ruled surface space, can represent the ruled surface space by utilizing curve parameters of a cutter shaft tail end line for each cutter position point, selects a cutter vector tail end line parameter in each ruled surface space, carries out optimization by utilizing an optimization algorithm, inputs of the optimization algorithm are the curve parameters selected at each cutter position point, and maps values of the curve parameter space into a coordinate space of a machine tool rotating driving shaft by carrying out kinematic solution on the optimized curve parameters, thereby realizing the cutter shaft vector optimization. The cutter shaft vector optimization method based on the ruled surface space has the advantages of high operation efficiency, improvement of the dynamic performance of a machine tool and small change on the original cutter shaft vector.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a five-axis milling cutter shaft vector optimization method based on ruled surface space, which is characterized by comprising the following steps of:
1) building cutter shaft vector optimization model based on ruled surface space
Setting N cutter location points involved in the machining process, calculating cutter shaft vectors at the cutter location points through the coordinates of a rotary driving shaft and the structural characteristics of a five-axis machine tool input in a numerical control program, and calculating the position of each cutter shaft terminal point in space by using a fixed cutter length, wherein the calculation process is as follows:
Figure BDA0002694986890000021
Figure BDA0002694986890000022
wherein, PX，i，PY，i，PZ，iRespectively is the position vector P of the ith tool location point in the numerical control programiThe components along the X, Y, Z axes in the machine coordinate system, i ═ 1,2, …, N; TL is the fixed cutter length; qX，i，QY，i，QZ，iRespectively is the position vector Q of the end point of the cutter shaft at the ith cutter positioniComponents along the X, Y, Z axes in the machine coordinate system;
Figure BDA0002694986890000023
respectively the coordinates of the rotating driving shafts A and C corresponding to the ith cutter position point in the input numerical control program,
Figure BDA0002694986890000024
respectively is the ith cutter shaft vector input in the numerical control program
Figure BDA0002694986890000025
The component on each coordinate axis in the machine tool coordinate system;
sequentially connecting the tail end points of the cutter shaft of each cutter position point by straight lines to form a space broken line, and defining the space broken line as an initial cutter shaftEnd line
Figure BDA0002694986890000026
If xi is the broken line parameter of the end line of the initial cutter shaft, the end line of the initial cutter shaft
Figure BDA0002694986890000027
The broken line equation of (a) is expressed as follows:
Figure BDA0002694986890000028
wherein ξiIs the broken line parameter at the ith knife location, and xii＜ξ＜ξi+1；
To the tail end line of the initial cutter shaft
Figure BDA0002694986890000029
Carrying out fairing treatment to obtain a curve-shaped cutter shaft end line C (xi);
connecting line segments from any one cutter position point to all points on a cutter shaft end line C (xi) to form a ruled surface space S (xi, i), namely limiting connecting lines between the points on the cutter shaft end line C (xi) and the corresponding cutter position points in the ruled surface space S (xi, i), and establishing a cutter shaft vector optimization model based on the ruled surface space as follows:
Figure BDA0002694986890000031
wherein, alpha Pi+βQiThe epsilon S (xi, i) represents that any point on the cutter shaft end line C (xi) and a point on a connecting line between the corresponding cutter position points are all positioned in the ruled surface space, alpha and beta are coefficients respectively, and the larger the value is, the closer the point on the connecting line is to the cutter position point or the cutter shaft end point is indicated; t isiIs the cutter axis vector at the ith cutter position;
2) setting optimization target and optimization constraint condition
Setting an optimization target of a cutter axis vector optimization model based on the dynamic characteristics of the five-axis machine tool;
the movement of the rotary driving shaft of the five-axis machine tool is set to meet the following constraint conditions:
Figure BDA0002694986890000032
wherein, thetaaxis，i，ωaxis，i，εaxis，i，Jaxis，iRespectively the angle, the angular velocity, the angular acceleration and the angular jerk of a machine tool rotating driving shaft at the ith cutter position,
Figure BDA0002694986890000033
angular velocity limit, angular acceleration limit and angular jerk limit, f, of the rotating drive shaft of the machine tool, respectivelyiThe feed speed of a machine tool rotating driving shaft at the ith cutter position point;
setting an optimized selectable interval of the cutter shaft vector in the ruled surface space as a straight line near the original cutter shaft vector on the ruled surface space;
3) cutter axis vector optimization model based on ruled surface space
Solving the arbor vector optimization model based on ruled surface space by using an optimization algorithm to obtain a group of optimized arbor tail end line curve parameters
Figure BDA0002694986890000034
The curve parameters at the end point of the ith cutter shaft are optimized;
4) mapping optimization results to a driveshaft coordinate space
According to the obtained optimized curve parameter of the tail end line of the cutter shaft
Figure BDA0002694986890000035
Calculating optimized position vectors of cutter shaft tail end points corresponding to the cutter position points
Figure BDA0002694986890000036
Calculating the corresponding cutter axis vector by using the following formula:
Figure BDA0002694986890000037
wherein the content of the first and second substances,
Figure BDA0002694986890000041
respectively are the components of the optimized cutter shaft vector along the X, Y and Z axes in the machine tool coordinate system,
Figure BDA0002694986890000042
respectively is the component P of the position vector of the cutter shaft terminal point at the ith optimized cutter position on each coordinate axis in the machine tool coordinate systemX，i，PY，i，PZ，iThe components of the position vector of the ith tool location point input into the numerical control program along the X, Y and Z axes in the machine tool coordinate system are respectively, | | | |, is a vector two-norm;
and mapping the cutter shaft vector to a coordinate space of the rotary driving shaft to obtain a corresponding coordinate of the rotary driving shaft, wherein a calculation formula is as follows:
Figure BDA0002694986890000043
wherein the content of the first and second substances,
Figure BDA0002694986890000044
the coordinates of the rotating driving shafts A and C corresponding to the optimized ith cutter position point are respectively, and n is any integer.
The beneficial effects achieved by the scheme are as follows:
1. the change of the cutter shaft vector is limited in the straight grain surface near the original cutter shaft vector, the space position of the optimized cutter shaft vector is close to the track surface of the cutter before optimization in the space, so that the method of the invention has small change to the original cutter shaft vector, the change is in the feeding direction, if the optimized parameter is properly selected, the cutter collision and interference can not be caused, and the material removal rate is not influenced.
2. The invention takes the dynamic characteristics of the machine tool as an optimization target, the optimized acceleration curve of the rotary driving shaft is more stable, and the extreme value of the acceleration curve is reduced, thereby ensuring that the motion of the machine tool is more stable and the vibration is reduced in the processing process than before the optimization,
3. compared with a common cutter shaft vector optimization method, the method limits the feasible range of the cutter shaft vector in a one-dimensional space, and the common cutter shaft vector optimization method selects a feasible solution of the cutter shaft vector in a two-dimensional space.
Drawings
FIG. 1 is a block flow diagram of the present invention.
Fig. 2 is a schematic view of an optimized front arbor vector in an embodiment of the present invention.
Fig. 3 is a schematic diagram of a ruled surface generation process in the embodiment of the present invention.
Fig. 4 is a schematic diagram of an optimized arbor vector in an embodiment of the present invention.
Fig. 5 is a genetic algorithm convergence process in an embodiment of the present invention.
FIG. 6 shows the dynamic characteristics of the rotary driving shafts of the machine tool before and after the optimization of the cutter axis vector in the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
In order to better understand the present invention, an application example of the five-axis milling cutter axis vector optimization method based on ruled surface space proposed by the present invention is described in detail below by taking an AC cradle type five-axis milling process as an example.
Referring to fig. 1, a five-axis milling cutter axis vector optimization method based on ruled surface space in the embodiment of the present invention includes the following steps:
1) building cutter shaft vector optimization model based on ruled surface space
The method comprises the following steps of setting N cutter points (taking cutter points as cutter points) involved in the machining process, calculating a cutter shaft vector at each cutter point through the coordinates of a rotary driving shaft and the structural characteristics of an AC cradle type five-axis machine tool input into a numerical control program, and calculating the position of a cutter shaft terminal point in space according to the fixed cutter length, wherein the calculation process is as follows:
Figure BDA0002694986890000051
Figure BDA0002694986890000052
wherein, PX，i，PY，i，PZ，iRespectively is the position vector P of the ith tool location point in the numerical control programiThe components along the X, Y, Z axes in the machine coordinate system, i ═ 1,2, …, N; TL is the length of the fixed cutter, namely the distance from the cutter location point to the tail end of the cutter shaft; qX，i，QY，i，QZ，iRespectively is the position vector Q of the end point of the cutter shaft at the ith cutter positioniComponents along the X, Y, Z axes in the machine coordinate system;
Figure BDA0002694986890000053
respectively the coordinates of the rotating driving shafts A and C corresponding to the ith cutter position point in the input numerical control program,
Figure BDA0002694986890000054
respectively is the ith cutter shaft vector input in the numerical control program
Figure BDA0002694986890000055
The components on each coordinate axis in the machine coordinate system.
Sequentially connecting the cutter shaft tail end points of each cutter position point by straight lines to form a space broken line, and defining the space broken line as an initial cutter shaft tail end line
Figure BDA0002694986890000056
Let xi be the broken line parameter of the cutter shaft end line, then the cutter shaft end line is initialized
Figure BDA0002694986890000057
The broken line equation of (a) is expressed as follows:
Figure BDA0002694986890000058
wherein Q isiIs the position vector of the end point of the cutter shaft at the ith cutter position in the coordinate system of the machine tool, xiiIs the broken line parameter at the ith knife location, and xii＜ξ＜ξi+1，ξi，ξi+1Respectively, the polyline parameters at the ith and (i + 1) th knife sites. The arbor vector and the initial arbor tip line are shown in FIG. 2.
To the tail end line of the initial cutter shaft
Figure BDA0002694986890000059
And performing fairing processing to obtain a curve-form cutter shaft end line C (xi) so as to avoid the situation that a subsequently established ruled surface space has unsmooth curved surface due to factors such as sudden change of original cutter shaft vectors or too few selected cutter shaft end points and the like. In this embodiment, a pseudo interpolation is performed on the tool spindle end line by three times of NURBS curve interpolation using the tool spindle end point of each tool location point as a control point, and the tool spindle end point corresponding to each tool location point and the front and rear 2 tool spindle end points thereof are selected as an interpolation range, where the formula is as follows:
Figure BDA0002694986890000061
wherein N isi，3(xi) is the cubic spline basis function, QiIs the position vector of the end point of the cutter shaft at the ith cutter position in the coordinate system of the machine tool, RiIs a weighting factor. The specific interpolation process refers to interpolation study of Korean Qingyao, Dongyun wind, teacher's red, cubic NURBS space curve [ J]Coal mining machinery, 2007,28(001):44-46.
Connecting line segments from any one cutter location point to all points on a cutter shaft end line C (xi) to form a ruled surface space S (xi, i), and establishing an cutter shaft vector optimization model based on the ruled surface space as follows:
Figure BDA0002694986890000062
wherein, alpha Pi+βQiE.g. S (xi, i) represents that a point on a connecting line between any point on a cutter shaft end line C (xi) and a corresponding cutter position point is positioned in a ruled surface space, alpha and beta are coefficients respectively, and the larger the value is, the closer the point on the connecting line is to the cutter position point or the cutter shaft end point is indicated; the connecting line between any point on the cutter shaft end line C (xi) and the corresponding cutter position point is limited in the ruled surface space S (xi, i) through the model, and all straight lines passing through the cutter position points in the ruled surface space are the feasible cutter shaft vectors T at the corresponding cutter position pointsiAnd the straight line of the cutter shaft vector is intersected with the cutter shaft tail end line C (xi).
For a certain knife position point, the corresponding ruled surface space is uniquely determined by the knife shaft end line, so the ruled surface space formed by the knife shaft end line after the fairing treatment is uniquely changed and smoothed, and the ruled surface space is as shown in fig. 3.
2) Setting optimization target and optimization constraint condition
Firstly, selecting an objective function of an optimization process, wherein the objective function needs to consider the dynamic characteristics of a machine tool, such as speed, acceleration, jerk and the like; in the present embodiment, the optimization target is the minimum of the square average of the jerks of the respective rotational drive shafts.
And secondly, setting constraint conditions of the optimization process, wherein the constraint conditions need to consider the kinematic limit of the machine tool, the cutter axis vector selection interval and the like. In order to ensure the feasibility and the high efficiency of the cutter shaft vector optimization process, optimization constraint conditions in the following aspects are required to be set, wherein the constraint conditions are set in the aspect of the dynamics of a rotary driving shaft of a machine tool, and the selection interval of the cutter shaft vector on a ruled surface space is set.
Firstly, inputting the maximum values of the speed, the acceleration and the jerk of the rotating driving shaft allowed by the machine tool into an optimization process, and setting the motion of the rotating driving shaft of the machine tool to meet the following constraint conditions:
Figure BDA0002694986890000071
wherein, thetaaxis，i，ωaxis，i，εaxis，i，Jaxis，iRespectively the angle, the angular velocity, the angular acceleration and the angular jerk of a machine tool rotating driving shaft at the ith cutter position,
Figure BDA0002694986890000072
angular velocity limit, angular acceleration limit and angular jerk limit, f, of the rotating drive shaft of the machine tool, respectivelyiFor the feed speed, P, of the rotary drive shaft of the machine tool at the ith tool positioniIs the position vector of the ith tool location point in the machine tool coordinate system.
Secondly, selecting an optimized selectable interval of the cutter axis vector in the ruled surface space, wherein the selectable interval is generally a straight line near the original cutter axis vector on the ruled surface space, and the selectable interval of the cutter axis vector is as follows:
Figure BDA0002694986890000073
wherein, TiIs the axis vector, Q, at the ith tool locationiIs the position vector of the end point of the cutter shaft at the ith cutter position, xiLB、ξUBCurve parameters corresponding to the boundary points of the desirable sections of the cutter shaft vector on the tail end line of the cutter shaft are respectively obtained, for example, the curve parameters corresponding to the front cutter position point and the rear cutter position point are obtained.
3) Cutter axis vector optimization model based on ruled surface space
The cutter shaft vector optimization problem is converted into mathematics through the establishment of a cutter shaft vector optimization model and the establishment of an optimization target and an optimization constraint conditionOptimizing the problem, wherein the optimized variable is the curve parameter of the tail end point of the cutter shaft, and the optimal solution search can be carried out by utilizing the existing optimization method to obtain a group of optimized curve parameters of the tail end line of the cutter shaft
Figure BDA0002694986890000074
The curve parameter at the end point of the ith cutter shaft after optimization.
Specifically, the genetic algorithm can be used to perform arbor vector optimization to first generate the decision variable { ξ1，ξ2，…，ξi，…，ξNTaking a parameter value of a cutter shaft tail end line corresponding to a desirable cutter shaft vector of each cutter position point as a decision variable, namely an input value of a genetic algorithm, wherein the value of each decision variable is limited in the cutter shaft vector selection interval; in addition, parameters such as population size, convergence judgment condition, cross probability, mutation probability and the like of the genetic algorithm are required to be set, and the genetic algorithm optimization process is shown in Whitley D.A genetic algorithm tutoreial [ J]Statistics and computing,1994,4(2): 65-85. The convergence process of the genetic algorithm in this embodiment is shown in fig. 5.
4) Mapping optimization results to a driveshaft coordinate space
Obtaining a set of optimized cutter shaft end line curve parameters
Figure BDA0002694986890000075
Optimized position vector of cutter shaft end point corresponding to each cutter position point
Figure BDA0002694986890000076
For the optimized position vector of the cutter shaft terminal point corresponding to the ith cutter position point, the corresponding cutter shaft vector can be calculated through the coordinates of the cutter shaft terminal point by using the following formula:
Figure BDA0002694986890000081
wherein the content of the first and second substances,
Figure BDA0002694986890000082
respectively are the components of the optimized cutter shaft vector along the X, Y and Z axes in the machine tool coordinate system,
Figure BDA0002694986890000083
respectively is the component P of the position vector of the end point of the cutter shaft at the ith optimized cutter position on each coordinate axis in the machine tool coordinate systemX，i，PY，i，PZ，iThe components of the position vector of the ith tool location point input into the numerical control program along the X, Y and Z axes in the machine tool coordinate system are respectively, | | | |, is a vector two-norm.
Then according to the structural characteristics of the machine tool, the cutter axis vector can be mapped to the coordinate space of the rotary driving shaft, so that the corresponding coordinate of the rotary driving shaft is calculated, and the calculation process is as follows:
Figure BDA0002694986890000084
wherein the content of the first and second substances,
Figure BDA0002694986890000085
the coordinates of the rotating driving shafts A and C corresponding to the optimized ith cutter position point are respectively, and n is any integer.
By calculating the kinematic characteristics of the machine tool before and after the optimization of the cutter shaft vector in the embodiment, as shown in fig. 6, it can be seen that the optimization method proposed by the present invention has small changes to the original cutter shaft vector (fig. 6(a) and 6(b)), so that the original processing surface appearance and surface quality can be ensured, and the smoothness of the angular velocity (fig. 6(c) and 6(d)) and the angular acceleration (fig. 6(e) and 6(f)) of the machine tool rotating drive shaft is improved, which shows that the motion of the machine tool is more stable, the absolute value extreme value of the angular jerk (fig. 6(g) and 6(h)) of the rotating drive shaft is reduced, and the vibration of the machine tool is reduced.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (3)

1. A five-axis milling cutter axis vector optimization method based on ruled surface space is characterized by comprising the following steps:
1) building cutter shaft vector optimization model based on ruled surface space
Setting N cutter location points involved in the machining process, calculating cutter shaft vectors at the cutter location points through the coordinates of a rotary driving shaft and the structural characteristics of a five-axis machine tool input in a numerical control program, and calculating the position of each cutter shaft terminal point in space by using a fixed cutter length, wherein the calculation process is as follows:
Figure FDA0003114445720000011
Figure FDA0003114445720000012
wherein, PX,i,PY,i,PZ,iRespectively is the position vector P of the ith tool location point in the numerical control programiThe components along the X, Y, Z axes in the machine coordinate system, i ═ 1,2, …, N; TL is the fixed cutter length; qX,i,QY,i,QZ,iRespectively is the position vector Q of the end point of the cutter shaft at the ith cutter positioniComponents along the X, Y, Z axes in the machine coordinate system;
Figure FDA0003114445720000013
respectively the coordinates of the rotating driving shafts A and C corresponding to the ith cutter position point in the input numerical control program,
Figure FDA0003114445720000014
respectively the ith one of the input numerical control programsCutter axis vector
Figure FDA0003114445720000015
The component on each coordinate axis in the machine tool coordinate system;
sequentially connecting the cutter shaft tail end points of each cutter position point by straight lines to form a space broken line, and defining the space broken line as an initial cutter shaft tail end line
Figure FDA0003114445720000016
If xi is the broken line parameter of the end line of the initial cutter shaft, the end line of the initial cutter shaft
Figure FDA0003114445720000017
The broken line equation of (a) is expressed as follows:
Figure FDA0003114445720000018
wherein ξiIs the broken line parameter at the ith knife location, and xii<ξ<ξi+1；
To the tail end line of the initial cutter shaft
Figure FDA0003114445720000019
Carrying out fairing treatment to obtain a curve-shaped cutter shaft end line C (xi);
connecting line segments from any one cutter position point to all points on a cutter shaft end line C (xi) to form a ruled surface space S (xi, i), namely limiting connecting lines between the points on the cutter shaft end line C (xi) and the corresponding cutter position points in the ruled surface space S (xi, i), and establishing a cutter shaft vector optimization model based on the ruled surface space as follows:
Figure FDA00031144457200000110
wherein, alpha Pi+βQiE.S (ζ, i) represents the axis C (ζ) at the end of the knife shaftThe point on the connecting line between any point and the corresponding tool location point is positioned in the ruled surface space, alpha and beta are coefficients respectively, and the larger the value is, the closer the point on the connecting line is to the tool location point or the end point of the cutter shaft; t isiIs the cutter axis vector at the ith cutter position;
2) setting optimization target and optimization constraint condition
Setting an optimization target of a cutter axis vector optimization model based on the dynamic characteristics of the five-axis machine tool;
the movement of the rotary driving shaft of the five-axis machine tool is set to meet the following constraint conditions:
Figure FDA0003114445720000021
wherein, thetaaxis,i,ωaxis,i,εaxis,i,Jaxis,iRespectively the angle, the angular velocity, the angular acceleration and the angular jerk of a machine tool rotating driving shaft at the ith cutter position,
Figure FDA0003114445720000022
angular velocity limit, angular acceleration limit and angular jerk limit, f, of the rotating drive shaft of the machine tool, respectivelyiThe feed speed of a machine tool rotating driving shaft at the ith cutter position point; piThe position vector of the ith tool location point in the machine tool coordinate system is shown;
setting an optimized selectable interval of the cutter shaft vector in the ruled surface space as a straight line near the original cutter shaft vector on the ruled surface space;
3) cutter axis vector optimization model based on ruled surface space
Solving the arbor vector optimization model based on ruled surface space by using an optimization algorithm to obtain a group of optimized arbor tail end line curve parameters
Figure FDA0003114445720000023
Figure FDA0003114445720000024
The curve parameters at the end point of the ith cutter shaft are optimized;
4) mapping optimization results to a driveshaft coordinate space
According to the obtained optimized curve parameter of the tail end line of the cutter shaft
Figure FDA0003114445720000025
Calculating optimized position vectors of cutter shaft tail end points corresponding to the cutter position points
Figure FDA0003114445720000026
Calculating the corresponding cutter axis vector by using the following formula:
Figure FDA0003114445720000027
wherein the content of the first and second substances,
Figure FDA0003114445720000028
respectively are the components of the optimized cutter shaft vector along the X, Y and Z axes in the machine tool coordinate system,
Figure FDA0003114445720000029
respectively is the component P of the position vector of the cutter shaft terminal point at the ith optimized cutter position on each coordinate axis in the machine tool coordinate systemX,i,PY,i,PZ,iThe components of the position vector of the ith tool location point input into the numerical control program along the X, Y and Z axes in the machine tool coordinate system are respectively, | | | |, is a vector two-norm;
and mapping the cutter shaft vector to a coordinate space of the rotary driving shaft to obtain a corresponding coordinate of the rotary driving shaft, wherein a calculation formula is as follows:
Figure FDA0003114445720000031
wherein the content of the first and second substances,
Figure FDA0003114445720000032
the coordinates of the rotating driving shafts A and C corresponding to the optimized ith cutter position point are respectively, and n is any integer.
2. The five-axis milling cutter axis vector optimization method according to claim 1, wherein in the step 1), the initial cutter axis end line is subjected to
Figure FDA0003114445720000033
Three-fold NURBS curve interpolation was used for fairing.
3. The five-axis milling cutter axis vector optimization method according to claim 1, characterized in that in step 3), a genetic algorithm is used to solve the ruled surface space-based cutter axis vector optimization model.
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