CN106903555A - A kind of decision method in tool-workpiece contact region - Google Patents
A kind of decision method in tool-workpiece contact region Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
- B23Q17/22—Arrangements for observing, indicating or measuring on machine tools for indicating or measuring existing or desired position of tool or work
- B23Q17/2233—Arrangements for observing, indicating or measuring on machine tools for indicating or measuring existing or desired position of tool or work for adjusting the tool relative to the workpiece
- B23Q17/2241—Detection of contact between tool and workpiece
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Abstract
The invention discloses a kind of decision method in tool work piece contact region, it is mainly included the following steps that：Tool coordinate system and workpiece coordinate system are set up respectively, determine description of the cutting edge infinitesimal synchronization in two coordinate systems；Determine cutting edge infinitesimal whether outside workpiece machining surface；Determine cutting edge infinitesimal whether under preceding cutting edge cycle minimum point；Determine cutting edge infinitesimal whether in preceding cutter tooth enveloping surface；According to abovementioned steps, determine cutting edge infinitesimal whether in effective contact region.The algorithm of technical solution of the present invention, overcome the deficiency that prior art efficiency is low, process is complicated, with calculate the time it is short, precision of prediction is high the characteristics of, especially in terms of five axle complex surface machinings, efficiency and precision can be preferably taken into account, the calculating process of Tool in Cutting power is greatly optimized.
Description
Technical Field
The invention belongs to the field of cutting machining, and particularly relates to a method for judging a cutter-workpiece contact area based on cutting edge infinitesimal classification.
Background
In the cutting process, in order to ensure the machining precision of the workpiece, the states of the tool and the workpiece in the cutting process need to be closely monitored. The cutting force is the force required by the cutter to cut into a workpiece and cut off chips, is one of important physical phenomena in the cutting process, is a direct factor for promoting the deformation of the cutter, the workpiece and the like, and is an important basis for monitoring the states of the cutter and the workpiece in the cutting process, so that the accurate prediction of the cutting force has important significance for better researching a cutting mechanism and planning a cutter track.
In order to determine whether the Cutting edge of the tool is involved in Cutting to obtain the total Cutting force, a Cutting edge region (Cutting edge region) of the tool and the workpiece needs to be determined, and the determination of the Cutting edge region is one of the key points of research in the prediction of the Cutting force. The determination of the contact area is a dynamic process, and the curved surfaces of the tool and the workpiece need to be updated as the cutting progresses. With the increasingly wide application and the advantages of the five-axis milling of the free-form surface in the machining, accurate and efficient cutting force modeling is carried out on the five-axis milling, and related theories such as contact area judgment and the like need to be further promoted and improved. The current calculation methods for determining the contact area are roughly classified into two types: boolean operation method and Z-map method.
The boolean operation method has a large calculation amount, and particularly for five-axis complex curved surface machining, a large amount of time is consumed in the calculation process. The Z-map can set discrete grid points according to the precision requirement, and the smaller the grid point is, the longer the calculation time is, and the higher the prediction precision is; conversely, the larger the grid point, the shorter the calculation time. In practical application, the Boolean operation method has certain advantages in processing some low-axis simple curved surface processing problems, but in the aspect of five-axis complex curved surface processing, time and labor are consumed, and the precision is difficult to guarantee; although the Z-map operation method can meet the precision requirement of five-axis complex surface machining, the method cannot give consideration to both efficiency and precision.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a method for judging the contact cutting area of the cutter-workpiece, which divides cutting edge micro elements into different categories, so that whether the cutting edge micro elements participate in contact cutting can be quickly judged, accurate and efficient judgment of the contact cutting area is realized, the method has the characteristics of short calculation time and high prediction accuracy, and especially in the aspect of five-axis complex curved surface machining, the method can better give consideration to both efficiency and accuracy compared with the prior art.
To achieve the above object, according to one aspect of the present invention, there is provided a method for determining a tool-workpiece contact area, comprising the steps of:
step one, establishing a tool coordinate system and a workpiece coordinate system by respectively taking a tool and a workpiece as reference systems, determining mathematical description of cutting edge infinitesimal in the tool coordinate system and the workpiece coordinate system at any moment, and determining mathematical description of a workpiece processing surface in the workpiece coordinate system at any moment;
determining mathematical description of the cutting edge micro element and the current workpiece processing surface in the same coordinate system at the current moment, determining the position relation of the cutting edge micro element and the current workpiece processing surface through the mathematical description of the cutting edge micro element and the current workpiece processing surface in the same coordinate system, and judging whether the cutting edge micro element is positioned in a possible contact space;
step three, acquiring mathematical descriptions of the lowest point of the cutting cycle finished at the previous moment in a tool coordinate system and a workpiece coordinate system, determining the position relation between the cutting edge infinitesimal and the lowest point at the current moment through the mathematical descriptions of the cutting edge infinitesimal and the lowest point of the cutting cycle in the same coordinate system, and judging whether the cutting edge infinitesimal is positioned below the lowest point;
step four, comparing the cutting radius of the cutting edge infinitesimal with the cutter radius of the discrete layer at the same axial height of the position where the cutting edge infinitesimal is located at the same moment, wherein if the cutting radius is larger than the cutter radius, the cutting edge infinitesimal is not in the front cutter tooth envelope, and if the cutting radius is not larger than the cutter radius, the cutting edge infinitesimal is in the front cutter tooth envelope, namely determining whether the cutting edge infinitesimal is in the front cutter tooth envelope;
step five, the micro element meeting one of the following conditions is positioned in the effective contact cutting area:
the condition one, the cutting edge infinitesimal is not in the impossible contact space, and the cutting edge infinitesimal is positioned below the lowest point of the front cutting edge period;
and secondly, the cutting edge infinitesimal is not in the impossible contact space, and is not below the lowest point of the front cutting edge period, and the cutting edge infinitesimal is positioned in the envelope surface of the front cutter teeth.
The algorithm of the technical scheme of the invention is based on the principle that a tool coordinate system and a workpiece coordinate system are respectively establishedThe cutting edge is expressed in a infinitesimal form in a tool coordinate system and a workpiece coordinate system. And comparing the position relation of the cutting edge micro-elements in the workpiece coordinate system through different boundary conditions to determine whether the current region is the effective contact region. In particular, it is necessary to establish a tool coordinate system and an object coordinate system with the tool and the object as references, respectively, wherein the tool coordinate system is moved relative to the object coordinate system, which is not random. For the cutting edge element, both in the tool coordinate system and in the workpiece coordinate system, the cutting edge element will therefore have two descriptions at the same time, namely its description in the tool coordinate systemAnd description in the object coordinate SystemWPH,t. Similarly, the current workpiece cutting surface may also be described using mathematical expressions. Through the above description, in combination with a mathematical geometry calculation method, the positional relationship between the cutting edge infinitesimal and the workpiece processing surface, whether the cutting edge infinitesimal is below the lowest point of the front cutting edge period, and whether the cutting edge infinitesimal is within the envelope of the front cutter tooth can be determined, the three conditions jointly determine whether the cutting edge infinitesimal is within the effective contact area of the workpiece, and the determination conditions need to be completed respectively.
In the coordinate system description method, the position relation between the cutting edge infinitesimal and the workpiece processing surface is specifically the position relation between the midpoint and the surface of the coordinate system in the coordinate system. The workpiece machining surface is a definite surface in the workpiece coordinate system, the expression of which in the workpiece coordinate system can be determined, and the cutting edge element is a point, and the positional relation with the workpiece machining surface can be determined through the expression of which in the workpiece coordinate system. The cutting edge infinitesimal element can be positioned on the workpiece processing surface or any one of two sides of the workpiece processing surface, wherein one side of the cutting edge infinitesimal element does not contain an effective contact area, and when the cutting edge infinitesimal element is positioned on one side not containing the effective contact area, namely in the space which cannot be contacted, the cutting edge infinitesimal element cannot be positioned in the effective contact area; when a cutting edge element is not located on the side that does not include an effective contact area, the cutting edge element may be within the effective contact area. In a coordinate system space, a workpiece processing surface divides the space into three parts, wherein one side is a side which does not contain an effective contact area of the workpiece, namely the space cannot be contacted; the side containing the effective contact area of the workpiece and the processing surface of the workpiece are possible contact spaces.
Similarly, the front edge cycle nadir is the lowest point of the removed area during the completed cutting cycle, i.e., the lowest point of all cutting edge elements in the previous cutting edge cycle in the cutting cycle. The expression of the lowest point can be determined, and the position relation between the cutting edge infinitesimal and the lowest point can be determined by comparing the expression sizes of the cutting edge infinitesimal and the lowest point by a mathematical calculation method. In particular, if a cutting edge element is below the position of the aforesaid lowest point and the cutting edge element is simultaneously satisfied not being in the impossible contact space, the cutting edge element must be within the effective contact area; if the cutting edge element is not below the location of the aforementioned lowest point and the cutting edge element is not in a space where contact with the cutting edge is impossible, the cutting edge element is not necessarily in the effective contact area.
After the previous cutting cycle is completed, the cutting area in the envelope surface of the front cutter tooth completes the cutting work and does not contain an effective contact area. Thus, the cutting edge microelements located in the effective contact area are not necessarily within the front tooth envelope. And comparing the cutting radius of the cutting edge infinitesimal with the cutter radius of the discrete layer at the same axial height of the position of the cutting edge infinitesimal at the same moment, and determining whether the cutting edge infinitesimal is in the envelope surface of the front cutter tooth or not so as to determine whether the current contact area is effective or not. Specifically, if the cutting radius is greater than the tool radius, the cutting edge infinitesimal is not within the leading tooth envelope, and if the cutting radius is not greater than the tool radius, the cutting edge infinitesimal is within the leading tooth envelope. This condition does not work alone, it also needs to be combined with other conditions to determine the specific location of the infinitesimal.
And step five, defining the conditions which need to be met by the cutting edge micro element in the effective contact area, wherein the cutting edge micro element belongs to the effective contact area only if the cutting edge micro element is not in the impossible contact space and is positioned below the lowest point of the front cutting edge period, or the cutting edge micro element is not in the impossible contact space and is not positioned below the lowest point of the front cutting edge period and is positioned in the envelope surface of the front cutter teeth.
The judging method of the technology of the invention actually divides the coordinate system of the workpiece into different areas by using linear programming theory of higher mathematics through different boundary conditions, and the effective contact area is one part of the different areas. And comparing the cutting edge infinitesimal with each boundary condition one by one to determine the area of the cutting edge infinitesimal, and finishing the cutting action only in the effective contact area. In other words, the cutting edge infinitesimal needs to be subjected to the above-mentioned boundary condition determination to determine whether it is located in the effective contact area.
As a preferred technical scheme of the invention, in the step one, the mathematical description of the cutting edge infinitesimal in the tool coordinate system and the workpiece coordinate systemAndWPH,tthere exists the following mapping relationship between
Wherein,is a composite transformation matrix from the tool coordinate system to the workpiece coordinate system at any time t,
in the formula,WPL,tis the position of the tool location point at the time t in the workpiece coordinate systemThe position of the vector is set, and the position of the vector,WxL,t，WyL,tandWzL,tis a description of the tool coordinate system in the object coordinate system, wherein,
in the formula, atAs the feed vector of the tool at time t, vtIs the axis vector of the tool at time t.
In the formula,WPL,tandWPL,t-△tand a tool location point position vector under the workpiece coordinate system at the t moment and the t-delta t moment, wherein the description is determined by the following formula:
v istThe arbor vector for the tool at time t is described by:
wherein i is the number of the knife position point, FiFor the tool at two cutting positions PL,iAnd PL,i+1V of the feed speed betweeniThe axis vector, t, of the tool point with index iiThe moment corresponding to the ith knife location point.
During cutting, the tool is moved relative to the workpiece, as is the tool coordinate system with the tool and workpiece as a reference basis, but this motion is not random, unpredictable, and quantifiable. The inventionIn the technical scheme, at a certain time t, from a tool coordinate system to a workpiece coordinate system, a composite transformation matrix existsAnd after the matrix is utilized to carry out compound transformation on the points in the tool coordinate system, the description of the points in the workpiece coordinate system at the moment t is obtained. Although the tool is moving relative to the workpiece, the tool itself is also located in the workpiece coordinate system, and the position vector of the tool location point in the workpiece coordinate system at time t is represented asWPL,t(ii) a Similarly, the tool coordinate system at time t also has a corresponding positional description in the workpiece coordinate system, i.e. the tool coordinate system at time t has a corresponding positional descriptionWxL,t，WyL,tAndWzL,t. The position vector of the tool location point and the description of the tool coordinate system in the workpiece coordinate system are both determined by a formula which is determined according to the actual cutting scheme of the tool. The determination method provided by the technical scheme of the invention is only used as a preferred scheme of the technical scheme of the invention, and does not limit the technical scheme of the invention.
The feed vector a of the tool during the actual cutting processtAnd also over time, the magnitude of which is related to the specific position of the tool in the workpiece coordinate system and the specific position of the tool coordinate system in the workpiece coordinate system, i.e., the feed vector atIs given a value ofWPL,t，WxL,t，WyL,tAndWzL,tare determined jointly.
As a preferred technical scheme of the invention, the radius of the cutter in the step four is described as R (z),
when the cutter is an arc-shaped cutter,
when the cutter is a ball-head cutter,
when the cutter is a flat-bottom cutter,
R(z)＝D/2；
d is the diameter of the cylindrical surface part of the cutter, and r is the arc radius of the arc surface part of the cutter.
In the process of cutting a workpiece, different tools are required to be used according to different cutting requirements, and the different tools have different descriptions in a coordinate system. Specifically, the tool types include a circular arc tool, a ball nose tool, a flat bed tool, and the like, and each tool has a corresponding expression. The cutter includes the arc surface part of cylinder face part and bottom, and the cylinder face part is the cylinder, and the arc surface part is different according to the cutter difference. The diameter of the cylindrical surface portion is constant for a particular tool, i.e., D is constant for a particular tool, but the arcuate surface portions are slightly different. The values of D and r are different corresponding to different properties. In the technical scheme of the invention, expressions of a circular arc knife, a ball head knife and a flat bottom knife are preferably listed, but the list belongs to common knives, and is not meant to exclude expressions of other knives which are not listed, and should not be regarded as limiting the technical scheme of the invention.
In a preferred embodiment of the present invention, Δ t is a time bin. The position of the cutting edge element, i.e. the spatial element, in the coordinate system is not fixed, and it generally moves with time. Representing spatial infinitesimal by time element is a commonly used research technique in disciplines such as mathematics and physics, and is most common in representing the problem of motion in the temporal-spatial relationship.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
1) according to the algorithm of the technical scheme, the cutting edge micro elements are divided into different categories, so that whether the cutting edge micro elements participate in contact can be quickly judged, and accurate and efficient contact area judgment is realized;
2) the algorithm of the technical scheme of the invention can change the type of the coordinate system according to the cutting tool and the cutting object, is applied to various cutting machining working types, and has wide application range.
Drawings
FIG. 1 is a flow chart illustrating a touch area determination method according to an embodiment of the invention;
FIG. 2 is a chart of contact relation of the method of the embodiment of the present invention applied to five-axis machining of a free-form surface.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention will be described in further detail with reference to specific embodiments.
Fig. 1 is a schematic flow chart of a touch area determination method according to an embodiment of the present invention. In the present embodiment, the determination of the contact area is preferably performed by taking five-axis machining as an example, but the present invention is not limited thereto, and is also applicable to other multi-axis machining.
In the actual calculation process, for convenience of description, a method for determining a five-axis machining cutting edge infinitesimal is given, and the method can be specifically confirmed according to the following steps:
determining description of unit vectors of coordinate axes of tool coordinate system at any time t in workpiece coordinate system
In the formula, atFor the feed vector of the tool at time t, this is determined by
In the formula,WPL,ta tool location vector for time t in the workpiece coordinate system, the description of which is determined by:
v istThe arbor vector for the tool at time t is described by:
wherein, FiFor the tool at two cutting positions PL,iAnd PL,i+1A feed speed of; Δ t is a time bin.
From the definition of the tool coordinate system by the formula (1), the description of each coordinate axis of the tool coordinate system in the workpiece coordinate system can be written in the form of a matrix (WxL,t，WyL,t，WzL,t) (ii) a Writing the description of the tool coordinate system under the coordinate system into a matrix form, and making the description into a matrix E3I.e. by
E3Is an identity matrix.
The rotation transformation matrix from the tool coordinate system to the workpiece coordinate system is recorded asThen there is
Simultaneous equations (5) and (6) can obtain the rotation transformation matrix from the tool coordinate system to the workpiece coordinate system at time t
In the formula,WxL,t，WyL,tandWzL,tcan be obtained from equation (1).
Further, a composite transformation matrix from the tool coordinate system to the workpiece coordinate system at the time t can be obtained
In the above-mentioned formulas, the first and second substrates,WxL,t，WyL,tandWzL,tcan be obtained from the formula (1),WPL,tcan be obtained from equation (3).
Similarly, a composite transformation matrix from the tool coordinate system to the workpiece coordinate system at time t- Δ t may be obtained
In the formula,WxL,t-Δt，WyL,t-ΔtandWzL,t-Δtcan be obtained from the formula (1),WPL,t-Δtcan be obtained from formula (3); Δ t is a time bin.
Cutting edge infinitesimal PH,tDescription in the tool coordinate system and the workpiece coordinate system at time tAndWPH,thaving the following mapping relationship
In the formula, a composite transformation matrixDetermined by equation (6).
The cutting edge infinitesimal points can be divided into the different types shown in fig. 2 according to the spatial relationship of the cutting edge infinitesimal to the workpiece and the front cutting edge period. In the figure, SE,t-ΔtRepresenting the front cutting edge periodic tool envelope surface, SE,tRepresenting the current cutting edge period tool envelope, SDRepresenting the design curve of the workpiece, SWRepresenting the machined surface of the workpiece, and the broken line in the figure is the path line of the contact point of the cutter. In the embodiment of the invention, whether a cutting edge element participates in cutting is determined, namely whether the element is positioned in an effective contact area of a workpiece is judged. As shown in fig. 2, here, "within the effective contact area" includes two conditions: one is to process the front surface S of the workpieceWThe following; the other is not in the cut workpiece body, or in other words, in the tool envelope of the front cutting edge period.
Five points denoted by 1, 2, 3, 4, and 5 in fig. 2 represent five types of contact-cut relationships, respectively, as shown in table 1, in which none of the first three types of infinitesimal elements participate in cutting in the current cutting edge cycle. In particular, the type 1, 2 infinitesimal elements are located on the working surface SWOtherwise, it does not contact the workpiece. Type 3 microelements are in the surface of the workpiece, but are cut aheadIn the envelope surface of the cutting edge periodical cutter, the workpiece is not contacted. The 4 th and 5 th infinitesimal participate in cutting, but the 4 th infinitesimal is positioned below the lowest point of the front cutting edge periodic tool envelope surface, and the infinitesimal is directly positioned outside the front cutting edge periodic tool envelope surface without distance calculation and judgment. The category 5 point needs further calculations to determine that it lies outside the front cutting edge cycle tool envelope.
As shown in fig. 1, after inputting relevant data of tool geometry, workpiece curved surface information, machining parameters, and the like, first judging whether a cutting edge infinitesimal is outside the workpiece machining surface to distinguish between the 1 st and 2 nd and the 3 rd, 4 th and 5 th categories, if the cutting edge infinitesimal is outside the workpiece machining surface, continuing to judge whether the cutting edge is below the lowest point of the front cutting edge period, further distinguishing between the 3 rd, 5 th and 4 th categories, if the cutting edge is the 4 th category, directly determining to participate in cutting without further judgment, and if the cutting edge is the 3 rd and 5 th categories, further judging whether the cutting edge is in the front cutter tooth envelope surface to finally determine. Table 1 is a free-form surface five-axis machining contact condition type determination table.
Table 1 table for judging types of contact conditions in five-axis machining of free-form surfaces
In the cutting edge infinitesimal, only the 4 th and 5 th points participate in contact, specifically:
the mathematical description of the 4 th point is
The mathematical description of the point of category 5 is
Wherein R (z) is the radius of the tool in the discrete layer where the cutting micro-element with the axial height z of the tool is located, specifically, when the tool is a circular arc tool,
when the cutter is a ball-head cutter,
when the cutter is a flat-bottom cutter,
R(z)＝D/2 (15)
it should be noted that the above boundary conditions do not cover all boundary conditions used in the technical solution of the present invention, and other means that are easily understood by those skilled in the art or are commonly used in the calculation process, such as workpiece edge constraint, are not listed. It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. A method of determining a tool-workpiece contact area, comprising the steps of:
step one, respectively establishing a tool coordinate system and a workpiece coordinate system by taking a tool and a workpiece as reference systems, determining mathematical description of cutting edge infinitesimal in the tool coordinate system and the workpiece coordinate system at any moment, and simultaneously determining mathematical description of a workpiece processing surface in the workpiece coordinate system at any moment;
determining mathematical description of the cutting edge micro element and the current workpiece processing surface in the same coordinate system at the current moment, and accordingly determining the position relation of the cutting edge micro element and the current workpiece processing surface, so as to judge whether the cutting edge micro element is positioned in a possible contact space on one side of the processing surface or in an impossible contact space on the other side;
step three, acquiring mathematical descriptions of the cutting lowest point in the cutter coordinate system and the workpiece coordinate system at the previous moment, determining the position relation between the cutting edge micro element and the cutting lowest point at the current moment through the cutting edge micro element and the mathematical description of the cutting lowest point in the same coordinate system, and judging whether the cutting edge micro element is positioned below the cutting lowest point;
step four, comparing the cutting radius of the cutting edge infinitesimal with the cutter radius of the discrete layer at the same axial height of the position where the cutting edge infinitesimal is located at the same moment, and determining whether the cutting edge infinitesimal is in the front cutter tooth envelope surface or not, wherein if the cutting radius is larger than the cutter radius, the cutting edge infinitesimal is not in the front cutter tooth envelope surface, and if the cutting radius is not larger than the cutter radius, the cutting edge infinitesimal is in the front cutter tooth envelope surface;
step five, the cutting edge infinitesimal meeting any one of the following conditions is positioned in the effective contact area:
the cutting edge infinitesimal is not in the impossible contact space, and the cutting edge infinitesimal is positioned below the lowest point of the front cutting edge period;
and (II) the cutting edge infinitesimal is not in the impossible contact space, and the cutting edge infinitesimal is not below the lowest point of the front cutting edge period, but is positioned in the envelope surface of the front cutter teeth.
2. The method for determining the tool-workpiece contact area according to claim 1, wherein the mathematical description of the cutting edge infinitesimal in the tool coordinate system and the workpiece coordinate system in the first stepAndWPH,tthere exists the following mapping relationship between
Wherein,is a composite transformation matrix from the tool coordinate system to the workpiece coordinate system at any time t,
in the formula,WPL,tis the position vector of the tool location point under the workpiece coordinate system at the time t,WxL,t，WyL,tandWzL,tis a description of the tool coordinate system in the object coordinate system, wherein,
in the formula, atAs the feed vector of the tool at time t, vtIs the axis vector of the tool at time t.
In the formula,WPL,t-△tand the position vector of the tool location point under the workpiece coordinate system at the moment of t-delta t.
3. The method for determining a tool-workpiece contact area according to claim 1, wherein the radius of the tool in the fourth step is R (z),
when the cutter is an arc-shaped cutter,
when the cutter is a ball-head cutter,
when the cutter is a flat-bottom cutter,
R(z)＝D/2；
d is the diameter of the cylindrical surface part of the cutter, and r is the arc radius of the arc surface part of the cutter.
4. An algorithm for determining a tool-workpiece contact area as claimed in claim 2, wherein Δ t is a time bin.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107728576A (en) * | 2017-09-21 | 2018-02-23 | 武汉科技大学 | Multi-shaft numerical control machining knife axial vector optimization method based on cutter stress deformation |
| CN109765841A (en) * | 2019-01-09 | 2019-05-17 | 西北工业大学 | The space-time mapping method of online monitoring data and part Working position |
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