CN115857429A - Method for generating smooth path of cutter of five-axis machine tool - Google Patents
Method for generating smooth path of cutter of five-axis machine tool Download PDFInfo
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Abstract
The invention provides a method for generating a smooth path of a five-axis machine tool cutter, belonging to the technical field of multi-axis numerical control machines, and the method comprises the following steps: determining the number n of initial key tool positions and collecting n key tool position positions; calculating the feasible region of the cutter axis vector of each key cutter position, and obtaining the cutter axis vector sequence S of the key cutter position based on the greedy strategy i (ii) a Interpolation cutter shaft vector sequence S i Obtaining the tool postures of all tool contacts of the corresponding whole tool path; judging whether collision interference exists in the tool posture; if yes, abandoning the corresponding cutter shaft vector sequence S i (ii) a If not, the cutter axis vector sequence S is processed i Put into set H; selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H; and interpolating the optimal key tool position set and the cutter axis vector sequence to obtain the tool postures of all the contacts of the tool path. The method can realize high-speed processing of the five-axis machine tool and ensure stable movement of the machine tool shaft, thereby improving the surface processing quality of the complex curved surface part.
Description
Technical Field
The invention relates to the technical field of multi-axis numerical control machine tools, in particular to a method for generating a cutter fairing path of a five-axis machine tool.
Background
The multi-axis linkage numerical control machining technology is widely applied to machining of high-precision complex curved surface thin-wall parts. Compared with the traditional three-axis machine tool, the five-axis machine tool has obvious advantages in the aspect of machining flexibility. These advantages result from the two axes of rotation of the machine tool. In five-axis numerical control high-speed machining, the acceleration and deceleration required by cutter shaft vector sudden change may exceed the driving limit of a machine tool rotating shaft, damage of a cutter and instability of a machining process are caused, the surface machining quality of a part is directly affected, cutter marks are left on a workpiece, and the workpiece is even cut excessively. Therefore, how to realize the smooth path machining of the five-axis cutter is a research hotspot and difficulty at home and abroad.
In the prior art, a quaternion interpolation method and a spline interpolation method are generally adopted to generate smooth cutter-axis vectors, and the procedures of the methods are to set a cutter-axis vector sequence of an initial key cutter position set, then interpolate the cutter-axis vectors of the key cutter position set, and obtain the cutter-axis vectors at each cutter contact point of a cutter path. And then collision detection is carried out, if collision interference is found, a non-collision interference tool position is selected as a new key tool position in a collision interference area and added to the key tool position set, and then the steps are repeated until the tool positions at the tool contacts of the tool path are free of collision interference. The key cutter position sets have different cutter shaft vector sequences and different interpolation results. The sequence of the cutter axis vectors of the initial key cutter location set influences the cutter axis vectors at the contact points of the cutters of the cutter path.
However, in the prior art, the cutter-axis vector sequence of the initial key tool position set is usually directly specified, and how to select the cutter-axis vector sequence of the initial key tool position set is rarely studied; the existing method selects the cutter axis vector of a new key cutter position according to the cutter axis vector sequence of the existing key cutter position set, limits the freedom degree of selecting the cutter axis vector of the new key cutter position, and may influence the integral smoothness of the whole cutter axis vector sequence. Thus, the five-axis tool fairing path still has room for improvement.
Disclosure of Invention
In order to overcome the problems in the related art, the invention aims to provide a method for generating a cutter fairing path of a five-axis machine tool, which can realize high-speed machining of the five-axis machine tool and ensure stable movement of a machine tool shaft, thereby improving the surface machining quality of a complex curved surface part.
A method for generating a smooth path of a five-axis machine tool cutter comprises the following steps:
determining the number n of initial key tool positions and collecting n key tool position positions;
calculating the feasible region of the cutter axis vector of each key cutter position, and obtaining the cutter axis vector sequence S of the key cutter position based on the greedy strategy i Wherein i =0,1, \8230, m-1, m is the number of feasible cutter shaft vectors at the position of the first key cutter position;
for each cutter axis vector sequence S i Interpolation is carried out to obtain the tool postures of all tool contacts of the corresponding whole tool path; judging whether collision interference exists in the tool posture; if yes, abandoning the corresponding cutter shaft vector sequence S i (ii) a If not, the cutter axis vector sequence S is processed i Put into set H;
judging whether the set H is an empty set, if so, increasing the number of the initial key tool positions, and repeating the operation; if not, selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H through a fairing evaluation index;
and interpolating the optimal key tool position set and the cutter axis vector sequence to obtain the tool postures of all the contacts of the tool path.
In a preferred technical scheme of the invention, the cutter shaft vector sequence S of the key cutter position is obtained based on a greedy strategy i Before, still include:
calculating the feasible range of the attitude angle of each key tool position through collision detection among the tool, the tool handle and the surface of the workpiece; and the attitude angle feasible domain element is the position of a rotating shaft of the machine tool.
In a preferred technical solution of the present invention, the calculating the feasible attitude angle domain of each key tool position includes:
within a specified range of a tool rake angle alpha, a roll angle beta, and a machine tool rotation axis theta 4 、θ 5 And sampling the travel range, and calculating the feasible range of the attitude angle of each key tool position.
In a preferred embodiment of the present invention, the greedy strategy-based method obtains the arbor vector sequence S of the key tool position i The method comprises the following steps:
selecting an attitude angle in the attitude angle feasible domain of the 0 th key tool position
Selecting one attitude angle in the attitude angle feasible domain of the 1 st key tool position
So that the posture angle->
And the posture angle->
The distance between them is minimal;
selecting one attitude angle in the attitude angle feasible domain of the 2 nd key tool position
So that->
And &>
The distance between the key cutter positions is the minimum, and the attitude angles of all the key cutter positions are determined by analogy;
obtaining a key cutter position cutter shaft vector sequence S through attitude angles of all key cutter positions i Wherein
In a preferred technical solution of the present invention, after determining the attitude angles of all the key tool positions, the method further includes:
judging whether i is equal to m, if so, setting H = { S = 0 ，S 1 ，S 2 …S m-1 }; if not, executing i = i +1, and continuously acquiring attitude angles of all key tool positions until i = m.
In a preferred technical solution of the present invention, the determining the initial key tool position number n and acquiring n key tool position includes:
selecting a tool path;
determining the number n of initial key tool positions;
and collecting the tool path at equal intervals, and determining n key tool position positions.
In a preferred technical solution of the present invention, the smoothness evaluation index is a square weighted sum of first, second, and third derivatives of a motion trajectory of a machine tool rotation axis, and an expression thereof is as follows:
wherein w 1 ,w 2 ,w 3 Weights, w, of the sum of squares of the first, second and third derivatives of the curve, respectively 4 ,w 5 Weight F 'representing smooth corresponding motion tracks of fourth rotation axis and fifth rotation axis of five-axis machine tool' 4,i ，F′ 5,i ，F″ 4,i ，F″ 5,i ，F″′ 4,i ，F″′ 5,i Is a key cutter position cutter shaft vector sequence S i And the square sum of the first derivative, the second derivative and the third derivative of the motion trail of the corresponding machine tool rotating shaft.
In a preferred embodiment of the present invention, the first, second and third derivative square sum expressions of the curve are as follows:
wherein
Is the control point of the motion track of the machine tool rotating shaft, l represents the number of the control points, H 1 、H 2 、H 3 Represents a stiffness matrix whose elements are represented as follows
Wherein i is more than or equal to 0, j is more than or equal to l-1, p represents the times of B spline curve, B i,p (u) is the basis function of the B-spline, [ u ] u p ,u l ]Is the definition domain of the motion trail of the machine tool rotating shaft.
In a preferred embodiment of the present invention, the vector sequence S for each cutter axis i Performing interpolation, including:
interpolating by using B spline curve to make the B spline curve pass through the cutter shaft vector sequence S i Each element of (1).
The invention has the beneficial effects that:
the invention provides a method for generating a smooth path of a five-axis machine tool cutter i (ii) a And all S are i Combining into a set H; by S i Obtaining the tool postures of all tool contacts of the whole tool path; judging whether collision interference exists in the tool posture; finally, selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H; and interpolating the optimal key tool position set and the cutter axis vector sequence to obtain the tool postures of all the contacts of the tool path. The method can reasonably set the cutter shaft vector sequence of the initial key cutter position, and also determine the cutter shaft vector sequence of the key cutter position set through a greedy strategy, thereby ensuring that the movement track of the machine tool rotating shaft has no mutation phenomenon, ensuring the smoothness of the cutter shaft vector sequence of each cutter contact of a cutter rail, ensuring the stable movement of the machine tool shaft and further improving the surface processing quality of the complex curved surface part.
Drawings
FIG. 1 is a flow chart of a method for generating a smooth path of a tool of a five-axis machine tool provided by the invention;
FIG. 2 is a logic diagram of a method for generating a smooth path of a tool of a five-axis machine tool provided by the invention;
FIG. 3 is a graph of the arc length of a tool nose point trajectory of the A axis of the machine tool provided during AC machining provided in the embodiments of the present invention;
fig. 4 is a diagram showing an arc length of a C-axis tool nose point trajectory provided in the AC machine tool provided in the embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention have been illustrated in the accompanying drawings, it is to be understood that the invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
It is to be understood that, although the terms first, second, third, etc. may be used herein to describe various information, such information should not be limited by these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of the present invention. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
Examples
The existing method adopts a quaternion interpolation method and a spline interpolation method to generate smooth cutter shaft vectors, the procedures of the methods are firstly to set a cutter shaft vector sequence of an initial key cutter position set, then to interpolate the cutter shaft vectors of the key cutter position set to obtain the cutter shaft vectors at each cutter contact point of a cutter rail, then to carry out collision detection, if collision interference is found, to select a non-collision interference cutter position as a new key cutter position in a collision interference area to be added to the key cutter position set, and then to repeat the steps until the cutter positions at each cutter contact point of the cutter rail are non-collision interference. The key cutter position sets have different cutter shaft vector sequences and different interpolation results. The sequence of the cutter axis vectors of the initial key cutter location set influences the cutter axis vectors at the contact points of the cutters of the cutter path. However, the prior art has studied less how to select the sequence of arbor vectors of the key tool location set, which is usually the sequence of arbor vectors directly specifying the initial key tool location set. In addition, the existing method selects the cutter axis vector of the new key cutter position according to the cutter axis vector sequence of the existing key cutter position set, limits the freedom degree of the selection of the cutter axis vector of the new key cutter position, and may influence the integral smoothness of the cutter axis vector sequence of the whole cutter path.
Based on this, the present application proposes a method for generating a tool fairing path of a five-axis machine tool, as shown in fig. 1 to 4, the method comprising:
s100, determining the number n of initial key tool positions, and collecting n key tool position positions; more specifically, the process comprises the steps of:
s110, selecting a tool path;
s120, determining the number n of the initial key tool positions;
s130, collecting the tool path at equal intervals, and determining n key tool position positions. In practical application, n key tool position positions can be acquired at unequal intervals on a tool path.
S200, calculating a cutter axis vector feasible region of each key cutter position, and then calculating the position of each key cutter position through collision detection among the cutter, the cutter handle and the surface of the workpieceAn attitude angle feasible region; wherein, calculate the feasible domain of attitude angle of every key sword position, include: within a specified range of a tool rake angle alpha, a roll angle beta, and a machine tool rotation axis theta 4 、θ 5 And sampling the travel range, and calculating the feasible range of the attitude angle of each key tool position. In practical applications, the roll angle β is typically the local coordinate system of the workpiece. And the attitude angle feasible domain element is the position of a rotating shaft of the machine tool. Finally, obtaining a cutter shaft vector sequence S of the key cutter position based on a greedy strategy i Wherein i =0,1, \8230, m-1,m is the number of feasible cutter shaft vectors at the first key cutter position.
Wherein n and m are natural numbers larger than zero, and can be formulated according to actual requirements.
S300, using B spline curve to perform S on each cutter axis vector sequence i Interpolation is carried out to obtain the tool postures of all tool contacts of the whole tool path; judging whether collision interference exists in the tool posture; if yes, abandoning the corresponding cutter shaft vector sequence S i (ii) a If not, the cutter axis vector sequence S is processed i Put into set H;
s400, judging whether the set H is an empty set, if so, increasing the number of initial key tool positions, and repeating the operation; if not, selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H through a fairing evaluation index;
s500, interpolating the optimal key cutter position set and the cutter axis vector sequence to obtain the cutter postures of all the contacts of the cutter path.
In the method for generating the fairing path of the five-axis machine tool cutter, after the cutter axis vector feasible region of each key cutter position, the cutter axis vector sequence S of the key cutter position is obtained based on the greedy strategy i (ii) a And all S are i Combining into a set H; by S i Obtaining the tool postures of all tool contacts of the whole tool path; judging whether collision interference exists in the tool posture; finally, selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H; and interpolating the optimal key tool position set and the cutter axis vector sequence to obtain the tool postures of all the contacts of the tool path. The method can reasonably set the cutter axis vector sequence of the initial key cutter positionAnd the cutter shaft vector sequence of the key cutter position set is determined through a greedy strategy, so that the movement track of the machine tool rotating shaft is ensured to have no mutation phenomenon, the cutter shaft vector sequence of each cutter contact of the cutter rail is ensured to be smooth, the machine tool shaft moves stably, and the surface processing quality of the complex curved surface part is improved.
More specifically, the greedy strategy-based method obtains an arbor vector sequence S of key tool position i The method comprises the following steps:
selecting an attitude angle in the attitude angle feasible domain of the 0 th key tool position
Selecting one attitude angle in the attitude angle feasible domain of the 1 st key tool position
So that the posture angle->
And attitude angle>
The distance between them is minimal;
selecting one attitude angle in the attitude angle feasible domain of the 2 nd key tool position
So that->
And &>
The distance between the key cutter positions is the minimum, and the attitude angles of all the key cutter positions are determined by analogy;
obtaining a key cutter position cutter axis vector sequence S through attitude angles of all key cutter positions i Wherein
Ensuring any attitude angle
And/or>
The minimum distance between the cutter and the cutter can improve the smoothness of the cutter path.
Furthermore, after determining the attitude angles of all the key tool positions, the method further includes:
judging whether i is equal to m, if so, setting H = { S = 0 ，S 1 ，S 2 …S m }; if not, executing i = i +1, and continuously acquiring attitude angles of all key tool positions until i = m.
Further, the fairing evaluation index claimed by the present application is:
the first, second and third derivative square weighted sum of the motion trail of the machine tool rotating shaft has the following expression:
wherein w 1 ,w 2 ,w 3 Weights, w, of the sum of squares of the first, second and third derivatives of the curve, respectively 4 ,w 5 Weight F 'representing smooth correspondence of motion tracks of fourth rotating shaft and fifth rotating shaft of five-axis machine tool' 4,i ，F′ 5,i ，F″ 4,i ，F″ 5,i ，F″′ 4,i ，F″′ 5,i Is a key cutter position cutter shaft vector sequence S i And the square sum of the first derivative, the second derivative and the third derivative of the motion trail of the corresponding machine tool rotating shaft.
Further, the first, second and third derivative of the curve sum of squares expression is as follows:
wherein
Is the control point of the motion track of the machine tool rotating shaft, l represents the number of the control points, H 1 、H 2 、H 3 Represents a stiffness matrix whose elements are represented as follows
Wherein i is more than or equal to 0, j is more than or equal to l-1, p represents the times of B spline curve, B i,p (u) is the basis function of the B-spline, [ u ] u p ,u l ]Is the definition domain of the motion trail of the machine tool rotating shaft.
In a more specific embodiment, the pair of each cutter-axis vector sequence S i Performing interpolation, including:
using large 3-5 times B spline curve interpolation to make B spline curve pass through cutter shaft vector sequence S i Each element of (1).
Performing S using a multiple B-spline curve i Interpolation can ensure the smoothness of the tool path. The B-spline curve (B-spline curve) refers to a special representation form in mathematical sub-discipline numerical analysis. It is a linear combination of B-spline base curves. Created by Isaac Jacob Schoenberg. The B-spline curve surface has many excellent properties of geometric invariance, convex hull property, convex protection property, variation reduction property, local support property and the like, and is a common geometric property of a CAD systemThe method is expressed, and therefore parameterization and B-spline surface reconstruction based on measurement data are one of research hotspots and key technologies of reverse engineering.
In order to make the aforementioned objects, features and advantages of the present patent more comprehensible, embodiments of the present patent are described in detail below with reference to fig. 3 to 4. The parameters of the ball end mill used in this embodiment are: the diameter is 8mm, the edge length is 16mm, and the overhanging length of the cutter is 39mm. The five-axis machine tool used was a double-turret AC type machine tool, and the stroke ranges of the rotary shafts were [ -10 °,100 ° ], [0 °,360 ° ], respectively. In the embodiment, the collision detection of the tool, the tool holder and the workpiece is performed based on a distance method. In the implementation, the maximum residual height is used for restraining and generating the knife contact point track of the curved surface of the blade disc, and the maximum value of the residual height is set to be 0.002. The number of knife contacts of each knife contact track is designated as 120, and the knife contacts are obtained on the tracks in an equal parameter mode. The initial number of the key cutter positions is 10. The variation ranges of the front rake angle and the side rake angle of the cutter are respectively [0 degrees, 90 degrees ], [ -180 degrees ] and 180 degrees ], the cutter shaft vectors are sampled and calculated in the range and the stroke range of the machine tool rotating shaft (the sampling intervals of the front rake angle and the side rake angle are both set to be 4 degrees, the sampling interval of the machine tool rotating shaft is set to be 2 degrees), then collision detection is carried out, and whether the cutter attitude angle is feasible or not is judged.
After the tool fairing path generation method is executed, the arc length of the obtained machine tool A axis tool nose point track is shown in fig. 3, and the arc length of the machine tool C axis tool nose point track is shown in fig. 4. Practice proves that the processing tool path controlled by the tool smooth path generation method claimed by the application has good smooth degree.
The application also provides a machine tool for implementing the cutter smooth path generation method, the machine tool is high in machining quality, and the machining requirements of high-precision curved surface parts can be met.
The relative arrangement of the components and steps, the numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present application unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures. In the description of the present application, it is to be understood that the orientation or positional relationship indicated by the directional terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal" and "top, bottom", etc., are generally based on the orientation or positional relationship shown in the drawings, and are used for convenience of description and simplicity of description only, and in the case of not making a reverse description, these directional terms do not indicate and imply that the device or element being referred to must have a particular orientation or be constructed and operated in a particular orientation, and therefore, should not be considered as limiting the scope of the present application; the terms "inner and outer" refer to the inner and outer relative to the profile of the respective component itself.
For ease of description, spatially relative terms such as "over 8230 \ 8230;,"' over 8230;, \8230; upper surface "," above ", etc. may be used herein to describe the spatial relationship of one device or feature to another device or feature as shown in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary terms "at 8230; \8230; above" may include both orientations "at 8230; \8230; above" and "at 8230; \8230; below". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of protection of the present application is not to be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A method for generating a smooth path of a five-axis machine tool cutter is characterized by comprising the following steps:
determining the number n of initial key tool positions and collecting n key tool position positions;
calculating the feasible region of the cutter axis vector of each key cutter position, and obtaining the cutter axis vector sequence S of the key cutter position based on the greedy strategy i (ii) a Wherein i =0,1, \8230, m-1,m is the number of feasible cutter shaft vectors at the first key cutter position;
for each cutter axis vector sequence S i Interpolation is carried out to obtain the tool postures of all tool contacts of the corresponding whole tool path; judging whether collision interference exists in the tool posture; if yes, abandoning the corresponding cutter shaft vector sequence S i (ii) a If not, the cutter axis vector sequence S is processed i Put into set H;
judging whether the set H is an empty set, if so, increasing the number of the initial key tool positions, and repeating the operation; if not, selecting an optimal key cutter position set and an optimal cutter axis vector sequence from the set H through a fairing evaluation index;
and interpolating the optimal key tool position set and the cutter axis vector sequence to obtain the tool postures of all the contacts of the tool path.
2. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 1, wherein:
obtaining a cutter shaft vector sequence S of a key cutter position based on a greedy strategy i Before, still include:
calculating the feasible region of the attitude angle of each key tool position through collision detection among the tool, the tool holder and the surface of the workpiece; and the attitude angle feasible domain element is the position of a rotating shaft of the machine tool.
3. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 2, wherein:
the calculating the feasible range of the attitude angle of each key tool position comprises the following steps:
within a specified range of a tool rake angle alpha, a roll angle beta, and a machine tool rotation axis theta 4 、θ 5 And sampling the travel range, and calculating the feasible range of the attitude angle of each key tool position.
4. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 2, wherein:
obtaining a cutter shaft vector sequence S of a key cutter position based on a greedy strategy i The method comprises the following steps:
selecting an attitude angle in the attitude angle feasible domain of the 0 th key tool position
Selecting one attitude angle in attitude angle feasible domain of 1 st key tool position
So that the attitude angle>
And the posture angle->
The distance between them is minimal;
attitude at 2 nd key tool positionSelecting an attitude angle in the angular feasible region
So that->
And/or>
The distance between the key cutter positions is the minimum, and the attitude angles of all the key cutter positions are determined by analogy;
obtaining a key cutter position cutter shaft vector sequence S through attitude angles of all key cutter positions i Wherein
5. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 4, wherein:
after the attitude angles of all key tool positions are determined, the method further comprises the following steps:
judging whether i is equal to m, if so, setting H = { S = 0 ，S 1 ，S 2 …S m-1 }; if not, executing i = i +1, and continuously acquiring attitude angles of all key tool positions until i = m.
6. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 1, wherein:
the determining the number n of the initial key cutter positions and collecting the n key cutter positions comprises the following steps:
selecting a tool path;
determining the number n of initial key tool positions;
and collecting the tool path at equal intervals, and determining n key tool position positions.
7. The five-axis machine tool smooth path generation method according to any one of claims 1 to 6, characterized in that:
the fairing evaluation index is the square weighted sum of first, second and third derivatives of the motion trail of the rotating shaft of the machine tool, and the expression is as follows:
wherein w 1 ,w 2 ,w 3 Weights, w, of the sum of squares of the first, second and third derivatives of the curve, respectively 4 ,w 5 Weight F 'representing smooth corresponding motion tracks of fourth rotation axis and fifth rotation axis of five-axis machine tool' 4,i ，F′ 5,i ，F″ 4,i ，F″ 5,i ，F″′ 4,i ，F″′ 5,i Is a key cutter position cutter shaft vector sequence S i And the square sum of the first derivative, the second derivative and the third derivative of the motion trail of the corresponding machine tool rotating shaft.
8. The method for generating the smooth path of the tool of the five-axis machine tool according to claim 6, wherein:
the first, second and third derivative square sum expression of the curve is as follows:
wherein
Is the control point of the motion track of the machine tool rotating shaft, l represents the number of the control points, H 1 、H 2 、H 3 Represents a stiffness matrix whose elements are represented as follows
Wherein i is more than or equal to 0, j is more than or equal to l-1, p represents the times of B spline curve, B i,p (u) is the basis function of the B-spline, [ u ] u p ,u l ]Is the definition domain of the motion trail of the machine tool rotating shaft.
9. The method for generating the fairing path of the tool of the five-axis machine tool according to claim 8, wherein:
the vector sequence S of each cutter shaft i Performing interpolation, including:
interpolating by using a B spline curve so that the B spline curve passes through the cutter shaft vector sequence S i Each element of (1).
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117371222A (en) * | 2023-10-23 | 2024-01-09 | 内蒙古工业大学 | Curve fairing optimization method based on discrete curvature and multistage optimization points |
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| CN117371222A (en) * | 2023-10-23 | 2024-01-09 | 内蒙古工业大学 | Curve fairing optimization method based on discrete curvature and multistage optimization points |
| CN117371222B (en) * | 2023-10-23 | 2024-04-26 | 内蒙古工业大学 | Curve fairing optimization method based on discrete curvature and multistage optimization points |
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