CN106903555B - A kind of determination method in tool-workpiece contact region - Google Patents
A kind of determination method in tool-workpiece contact region Download PDFInfo
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- CN106903555B CN106903555B CN201710224722.9A CN201710224722A CN106903555B CN 106903555 B CN106903555 B CN 106903555B CN 201710224722 A CN201710224722 A CN 201710224722A CN 106903555 B CN106903555 B CN 106903555B
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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 determination methods in tool-workpiece contact region, mainly comprise the steps that and establish tool coordinate system and workpiece coordinate system 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 period 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, the deficiency for overcoming prior art low efficiency, process complexity has the characteristics that the calculating time is short, precision of prediction is high, especially in terms of five axis 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 machining fields, and in particular to a kind of tool-workpiece contact based on the classification of cutting edge infinitesimal
The determination method in region.
Background technique
In cutting process, in order to guarantee the machining accuracy of workpiece, need closely to monitor cutting process cutter and work
Part state.Cutting force is power required for cutter incision workpiece and excision chip, is that the important physical in cutting process is existing
As one of, since cutting force is the direct factor for promoting cutter and workpiece etc. to be deformed, and monitoring cutting process cutter with
The important evidence of work status, Accurate Prediction cutting force is for preferably studying cutting scheme and planning cutter path with important
Meaning.
In order to judge whether tool in cutting sword participates in cutting to obtain total cutting force, it is thus necessary to determine that the contact of cutter and workpiece
Region (Cutting engagement region), the determination in contact region are one of the research key points in prediction of Turning Force with Artificial.
The determination in contact region is a dynamic process, needs the curved surface for being updated cutter and workpiece with cutting.With free song
Face five-axis milling work in-process increasingly extensive application and the advantage that shows, accurately efficiently cut for five-axis milling processing
Cut force modeling, the correlation theories such as contact region decision need to be pushed further into and perfect.The meter of the determination in contact region at present
Calculation method generally has two classes: boolean operation method (Boolean operation method) and Z-map method.
Wherein, boolean operation method calculation amount is larger, for five axis complex surface machinings, calculating process
It needs to take a substantial amount of time.Z-map can need that discrete grid block point is arranged according to precision, and mesh point is smaller, and the calculating time is longer,
Precision of prediction is higher；Conversely, mesh point is bigger, it is shorter to calculate the time.In actual application, boolean operation method is in processing one
There is certain advantage in a little low axis simple surface processing problems, but in terms of five axis complex surface machinings, take time and effort, essence
Degree is difficult to ensure；Although Z-map operation method can satisfy the required precision of five axis complex surface machinings, but this method without
Method takes into account efficiency and precision.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of tool-workpiece contact regions
Determination method, this method cutting edge infinitesimal is divided into it is different classes of, so as to quickly determine whether cutting edge infinitesimal participates in
Accurate efficient contact region decision is realized in contact, has the characteristics that the calculating time is short, precision of prediction is high, especially multiple in five axis
In terms of miscellaneous Machining of Curved Surface, compared to the prior art, efficiency and precision can be preferably taken into account.
To achieve the above object, according to one aspect of the present invention, a kind of judgement in tool-workpiece contact region is provided
Method, which comprises the following steps:
Step 1 establishes tool coordinate system and workpiece coordinate system using cutter and workpiece as reference system respectively, when determining any
Mathematical description of the cutting edge infinitesimal in tool coordinate system and workpiece coordinate system is carved, determines any time workpiece machining surface in work
Mathematical description in part coordinate system；
Step 2 determines that current time cutting edge infinitesimal is retouched with mathematics of the current workpiece machining surface in the same coordinate system
It states, by the mathematical description of cutting edge infinitesimal and current workpiece machining surface in the same coordinate system, determines cutting edge infinitesimal and work as
The positional relationship of preceding workpiece machining surface, judges whether cutting edge infinitesimal is located in possible contact space；
Step 3 obtains number of the cutting period minimum point of previous moment completion in tool coordinate system and workpiece coordinate system
Description is learned, by the mathematical description of cutting edge infinitesimal in the same coordinate system and cutting period minimum point, determines that current time cuts
The positional relationship of sword infinitesimal and the minimum point, judges whether the cutting edge infinitesimal is located under the minimum point；
Step 4 compares radius of clean-up and the same axial direction in cutting edge infinitesimal position in synchronization cutting edge infinitesimal
The tool radius size of the discrete layer of height, wherein if radius of clean-up is greater than tool radius, the cutting edge infinitesimal is not in preceding knife
In tooth enveloping surface, if radius of clean-up is not more than tool radius, which determines cutting in preceding cutter tooth enveloping surface
Whether sword infinitesimal is in preceding cutter tooth enveloping surface；
Step 5, the infinitesimal for meeting one of following condition are located in effective contact region:
Condition one, cutting edge infinitesimal not can not contact space, and to be located at the preceding cutting edge period minimum for cutting edge infinitesimal
Under point；
Condition two, cutting edge infinitesimal is not or not impossible contact space, and cutting edge infinitesimal is not minimum in the preceding cutting edge period
Under point, and cutting edge infinitesimal is located in preceding cutter tooth enveloping surface.
The algorithm of technical solution of the present invention, principle are, establish tool coordinate system and workpiece coordinate system respectively, in cutter
Cutting edge is expressed in the form of infinitesimal in coordinate system and workpiece coordinate system.By different boundary conditions, compare cutting edge infinitesimal
Positional relationship in workpiece coordinate system, to determine whether current region is effective contact region.Specifically, need respectively with
Cutter and workpiece are used as referring to establishing tool coordinate system and workpiece coordinate system, wherein tool coordinate system opposite piece coordinate system is
Movement, this movement is not random.For cutting edge infinitesimal, both in tool coordinate system, also in workpiece coordinate
In system, therefore synchronization lower cutting edge infinitesimal can have there are two types of description form, i.e. its description in tool coordinate system
With the description in workpiece coordinate systemWPH,t.Similar, current workpiece cutting surface can also be retouched using mathematic(al) representation
It states.By foregoing description, in conjunction with mathematics geometry calculation method, it can be determined that close the position of cutting edge infinitesimal and workpiece machining surface
Whether system judges cutting edge infinitesimal under preceding cutting edge period minimum point and whether cutting edge infinitesimal is in preceding cutter tooth enveloping surface
It is interior, above three condition jointly determine cutting edge infinitesimal whether in effective contact region of workpiece, and above-mentioned Rule of judgment need
It is respectively completed.
It is described in method in this coordinate system, the positional relationship of cutting edge infinitesimal and workpiece machining surface, specific to coordinate
It is coordinate system midpoint and face positional relationship in system.Workpiece machining surface is a specific face in workpiece coordinate system,
Expression formula in workpiece coordinate system passes through its expression formula in workpiece coordinate system it was determined that cutting edge infinitesimal is a point
It can determine the positional relationship of itself and workpiece machining surface.Cutting edge infinitesimal can be located on workpiece machining surface or workpiece adds
Any side in the two sides of work surface, wherein side does not include effective contact region centainly, does not include when cutting edge infinitesimal is located at
When effective contact region side, that is, it is located at it is not possible that the cutting edge infinitesimal centainly can not be in effective contact when in contact space
In region；When cutting edge infinitesimal is not located at not comprising effective contact region side, which may be in effective contact
In region.In coordinate system space, workpiece machining surface divides the space into three parts, and wherein side is effective not comprising workpiece
The side in contact region, being exactly can not contact space；Finished surface comprising workpiece effective contact region side and workpiece
All being possible contact space.
Similar, preceding cutting edge period minimum point belongs in the cutting periodic process completed, and cut-away area is minimum
Point is cutting a point minimum in the period in other words for all cutting edge infinitesimals in the previous cutting edge period.The minimum point
Expression formula be it is believed that comparing the expression formula size of cutting edge infinitesimal Yu the minimum point using mathematic calculation, i.e.,
It can determine positional relationship between the two.Specifically, if cutting edge infinitesimal is under the position of above-mentioned minimum point, and this is cut
It cuts sword infinitesimal while meeting not in impossible contact space, then the cutting edge infinitesimal one is scheduled in effective contact region；Such as
Fruit cutting edge infinitesimal is not under the position of above-mentioned minimum point, and the cutting edge infinitesimal is not it is not possible that contact space, the cutting
Sword infinitesimal is not necessarily in effective contact region.
After the completion of the previous cutting period, the cutting zone in preceding cutter tooth enveloping surface has completed cutwork, no longer contains
There is effective contact region.Therefore, the cutting edge infinitesimal in effective contact region is not centainly in preceding cutter tooth enveloping surface.Than
Compared with the knife of the discrete layer of radius of clean-up and the same axial height in cutting edge infinitesimal position in synchronization cutting edge infinitesimal
Have radius size, can determine cutting edge infinitesimal whether in preceding cutter tooth enveloping surface, it is whether effective with the current contact region of determination.
Specifically, if radius of clean-up is greater than tool radius, the cutting edge infinitesimal is not in preceding cutter tooth enveloping surface, if radius of clean-up is not
Greater than tool radius, then the cutting edge infinitesimal is in preceding cutter tooth enveloping surface.The condition does not work individually, also need with
Other conditions combine the specific location that could be judged where infinitesimal.
The condition that the cutting edge infinitesimal in effective contact region needs to meet is specified in step 5, only cutting edge is micro-
Member is not in the case where impossible contact space and cutting edge infinitesimal are located at preceding cutting edge period minimum point or cutting edge infinitesimal is not
Possible contact space and cutting edge infinitesimal is not under preceding cutting edge period minimum point and cutting edge infinitesimal is located at preceding cutter tooth envelope
In face, just belong to effective contact region.
The judgment method of the technology of the present invention utilizes the linear gauge of higher mathematics indeed through different boundary conditions
Theory is drawn, workpiece coordinate system is divided into different regions, effective contact region is a portion.By cutting edge infinitesimal with
Each boundary condition is compared one by one, determines cutting edge infinitesimal region, could be complete only in effective contact region
At stock removal action.In other words, cutting edge infinitesimal needs the judgement by above-mentioned boundary condition, is just capable of determining whether to be located at effective
In contact region.
As an optimal technical scheme of the invention, cutting edge infinitesimal described in step 1 is in tool coordinate system and workpiece
Mathematical description in coordinate systemWithWPH,tBetween there are following mapping relations
Wherein,It is complex transformation matrix of any t moment tool coordinate system to workpiece coordinate system,
In formula,WPL,tIt is position vector of the t moment cutter location under workpiece coordinate system,WxL,t,WyL,tWithWzL,tIt is that cutter is sat
Mark ties up to the description in workpiece coordinate system, wherein
In formula, atFeeding vector for cutter in moment t, vtFor cutter moment t generating tool axis vector.
In formula,WPL,tWithWPL,t-△tT moment and t- time Δt cutter location position vector under workpiece coordinate system, description by
Following formula determines:
The vtIt is cutter in the generating tool axis vector of moment t, describes to be determined by following formula:
Wherein, i is cutter location serial number, FiIt is cutter in two cutter location PL,iWith PL,i+1Between feed speed, viFor serial number
For the generating tool axis vector of the cutter location of i, tiAt the time of correspondence for i-th of cutter location.
During the cutting process, cutter is movement relative to workpiece, is sat using cutter and workpiece as the cutter of reference basis
Mark system relative to workpiece coordinate system be also movement, but it is this movement be not it is random, unpredictable, can not quantitative expression.This
In inventive technique scheme, at a time t, from tool coordinate system to workpiece coordinate system, there is complex transformation matrixesBenefit
With the matrix by after the point complex transformation in tool coordinate system, as description of this of t moment in workpiece coordinate system.Although knife
Tool is movement relative to workpiece, but cutter itself also is located in workpiece coordinate system, and t moment cutter location is in workpiece coordinate system
Position vector be expressed asWPL,t；Similar, t moment tool coordinate, which ties up in workpiece coordinate system, also there is corresponding position to retouch
It states, that is,WxL,t,WyL,tWithWzL,t.The position vector and tool coordinate of cutter location tie up to the description in workpiece coordinate system, by public affairs
Formula determines that the formula is determined according to the actual cutting scheme of cutter.The method of determination that technical solution of the present invention provides, only makees
For a preferred embodiment of technical solution of the present invention, the limitation to technical solution of the present invention is not constituted.
Cutter feeds vector a in actual cutting processtAlso with the time variation and change, size and knife
Having the specific location that specific location in workpiece coordinate system and tool coordinate tie up in workpiece coordinate system has relationship, also that is,
Feed vector atValue be byWPL,t,WxL,t,WyL,tWithWzL,tIt determines jointly.
As an optimal technical scheme of the invention, tool radius described in step 4 is described as R (z),
When the cutter is circular arc knife,
When the cutter is ball head knife,
When the cutter is flat-bottomed cutter,
R (z)=D/2；
The D is the diameter of cutter cylindrical surface portion, and r is the arc radius of knife tool arc face part.
In workpiece cutting process, according to different cutting demands, need using different cutters, different cutters is in coordinate
There is different descriptions in system.Specifically, tool category has circular arc knife, ball head knife, flat-bottomed cutter etc. a variety of, each cutter
With corresponding expression formula.Cutter includes the arc surface part of cylindrical surface portion and bottom, and cylindrical surface portion is cylindrical body, circular arc
Face part is according to cutter difference difference.For a specific cutter, the diameter of cylindrical surface portion be it is constant,
That is D is constant, but arc surface part then slightly has difference for a specific cutter.Corresponding different stage property,
D with r value taken is different.In technical solution of the present invention, it is preferably listed the expression of circular arc knife, ball head knife, flat-bottomed cutter, but this
Kind, which is enumerated, belongs to common cutter, is not meant to exclude other unlisted cutters expression, be not construed as to the technology of the present invention side
The limitation of case.
As an optimal technical scheme of the invention, Δ t is time infinitesimal.Cutting edge infinitesimal, i.e. space infinitesimal, are sitting
Position in mark system is not fixed and invariable, generally as the time moves.Carry out representation space infinitesimal with tempon, is mathematics
Commonly study gimmick with subjects such as physics, performance when, void relation motion problems in it is most commonly seen.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect
Fruit:
1) algorithm of technical solution of the present invention, it is different classes of by the way that cutting edge infinitesimal to be divided into, so as to quickly sentence
Determine whether cutting edge infinitesimal participates in contact, realizes accurate efficient contact region decision；
2) algorithm of technical solution of the present invention can change coordinate set type according to cutting element and cutting object, and answer
For a variety of machining job categories, have wide range of applications.
Detailed description of the invention
Fig. 1 is the flow diagram of the contact regional determination method of one embodiment of the invention；
Fig. 2 is the contact relationship matters figure that present invention method is applied on free form surface five-axis robot.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.The present invention is described in more detail With reference to embodiment.
It is the flow diagram of the contact regional determination method of one embodiment of the invention as shown in Figure 1.In the present embodiment
It is preferred that carrying out contact regional determination by taking five-axis robot as an example, but this is not construed as limiting in the present invention, it is same in other Multi-axis Machinings
It is applicable in.
In practical calculating process, for ease of description, the determination method of five-axis robot cutting edge infinitesimal is provided, it is specific
It can be confirmed in accordance with the following steps:
Determine description of the unit vector of any time t each reference axis of tool coordinate system under workpiece coordinate system
In formula, atIt is cutter in the feeding vector of moment t, is determined by following formula
In formula,WPL,tFor the cutter location position vector of workpiece coordinate system lower moment t, description is determined by following formula:
The vtIt is cutter in the generating tool axis vector of moment t, describes to be determined by following formula:
Wherein, FiIt is cutter in two cutter location PL,iWith PL,i+1Between feed speed；Δ t is time infinitesimal.
Definition by formula (1) to tool coordinate system, can be by each reference axis of tool coordinate system under workpiece coordinate system
Description write as matrix form be (WxL,t,WyL,t,WzL,t)；Description tool coordinate tied up under local Coordinate System is write as matrix
Form enables it for matrix E3, i.e.,
E3For unit matrix.
The rotational transformation matrix of tool coordinate system to workpiece coordinate system is denoted asThen have
Simultaneous formula (5) and (6) can obtain the tool coordinate system of moment t to the rotational transformation matrix of workpiece coordinate system
In formula,WxL,t,WyL,tWithWzL,tIt can be obtained by formula (1).
And then the tool coordinate system of moment t can be obtained to the complex transformation matrix of workpiece coordinate system
In the above formulas,WxL,t,WyL,tWithWzL,tIt can be obtained by formula (1),WPL,tIt can be obtained by formula (3).
Similarly, the tool coordinate system of moment t- Δ t can be obtained to the complex transformation matrix of workpiece coordinate system
In formula,WxL,t-Δt,WyL,t-ΔtWithWzL,t-ΔtIt can be obtained by formula (1),WPL,t-ΔtIt can be obtained by formula (3)；Δ t is
Time infinitesimal.
Cutting edge infinitesimal PH,tDescription in the tool coordinate system and workpiece coordinate system of moment tWithWPH,tWith with
Lower mapping relations
In formula, complex transformation matrixIt is determined by formula (6).
According to cutting edge infinitesimal and workpiece and the spatial relationship in preceding cutting edge period, cutting edge infinitesimal point can be divided into
Different type shown in Fig. 2.In figure, SE,t-ΔtCutting edge period cutter enveloping surface, S before representingE,tRepresent the current cutting edge period
Cutter enveloping surface, SDRepresent workpiece design curved surface, SWWork pieces process curved surface is represented, dotted line is cutter-contact point trace line in figure.In this hair
It in bright embodiment, determines whether certain cutting edge infinitesimal participates in cutting, that is, judges whether the infinitesimal is located at workpiece " effective contact region
It is interior ".As shown in Fig. 2, herein including two conditions " in effective contact region ": one is in work pieces process front surface SWBelow；
The other is not cutting off in workpiece body, or it is sayed, not in the cutter enveloping surface in preceding cutting edge period.
In Fig. 21,2,3,4,5 mark five points respectively represent five kinds of contact relationship types, as shown in table 1, wherein first three
Class infinitesimal is not involved in the cutting in current cutting edge period.Specifically, the 1st, 2 class infinitesimals are located at finished surface SWIn addition, it does not connect
Touch workpiece.Though the 3rd class infinitesimal is in workpiece surface, in preceding cutting edge period cutter enveloping surface, also not contact workpiece.4th,
5 class infinitesimals both participate in cutting, but the 4th class infinitesimal is located at preceding cutting edge period cutter enveloping surface minimum point hereinafter, can directly obtain
It is located at other than preceding cutting edge period cutter enveloping surface, and need not carry out distance and calculate judgement.5th class point then needs further to count
It calculates to determine that it is located at other than preceding cutting edge period cutter enveloping surface.
It is related to machined parameters etc. in input cutter geometry, curve surface of workpiece information such as the determination flow that Fig. 1 is contact region
After data, first determine whether that cutting edge infinitesimal is the 1st, 2 classes and the 3rd, 4,5 to distinguish whether other than workpiece machining surface
Class, if it is the latter, then continue to determine whether in preceding cutting edge period minimum point hereinafter, further distinguish the 3rd, 5 classes and
4th class then directly determines participation cutting if it is the 4th class, no longer needs to make a decision, and if it is the 3rd, 5 classes, then further judgement is
It is no in preceding cutter tooth enveloping surface, finally to determine.Table 1 is free form surface five-axis robot contact situation classification judgement table.
1 free form surface five-axis robot contact situation classification of table judges table
In above-mentioned cutting edge infinitesimal, only the 4th class and the 5th class point participate in contact, specific:
The mathematical description of 4th class point is
The mathematical description of 5th class point is
In formula, R (z) is the tool radius of discrete layer where the cutting infinitesimal that cutter axial height is z, specifically, cutter
When for circular arc knife,
When cutter is ball head knife,
When cutter is flat-bottomed cutter,
R (z)=D/2 (15)
It is important to note that above-mentioned boundary condition does not cover all boundary used in technical solution of the present invention
Condition, other those skilled in that art are readily comprehensible or calculating process in common means, such as edge of work constrains
Etc. common means, there is no list one by one.As it will be easily appreciated by one skilled in the art that the foregoing is merely of the invention preferable
Embodiment is not intended to limit the invention, it is done within the spirit and principles of the present invention it is any modification, equally replace
It changes and improves, should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of determination method in tool-workpiece contact region, which comprises the following steps:
Step 1 establishes tool coordinate system and workpiece coordinate system using cutter and workpiece as reference system respectively, determines that any time cuts
Mathematical description of the sword infinitesimal in tool coordinate system and workpiece coordinate system is cut, while determining any time workpiece machining surface in work
Mathematical description in part coordinate system；
Step 2 determines current time cutting edge infinitesimal and mathematical description of the current workpiece machining surface in the same coordinate system,
The positional relationship of cutting edge infinitesimal Yu current workpiece machining surface is determined therefrom that, so that it is described to judge whether cutting edge infinitesimal is located at
In impossible contact space in possibility contact space on finished surface side or finished surface or positioned at the other side；
Step 3 obtains mathematical description of the previous moment cutting minimum point in tool coordinate system and workpiece coordinate system, by same
The mathematical description of cutting edge infinitesimal and the cutting minimum point in one coordinate system determines current time cutting edge infinitesimal and the cutting
The positional relationship of minimum point, judges whether the cutting edge infinitesimal is located under the cutting minimum point；
Step 4 compares radius of clean-up and the same axial height in cutting edge infinitesimal position in synchronization cutting edge infinitesimal
Discrete layer tool radius size, determine cutting edge infinitesimal whether in preceding cutter tooth enveloping surface with this, wherein if radius of clean-up
Greater than tool radius, then the cutting edge infinitesimal is not in preceding cutter tooth enveloping surface, if radius of clean-up is not more than tool radius, this is cut
Sword infinitesimal is cut in preceding cutter tooth enveloping surface；
Step 5, the cutting edge infinitesimal for meeting following either condition are located in effective contact region:
(1) cutting edge infinitesimal is not or not impossible contact space, and cutting edge infinitesimal is located under preceding cutting edge period minimum point；
(2) cutting edge infinitesimal not can not contact space, and cutting edge infinitesimal is under preceding cutting edge period minimum point, but
Cutting edge infinitesimal is not in preceding cutter tooth enveloping surface；
Mathematical description of cutting edge infinitesimal described in step 1 in tool coordinate system and workpiece coordinate systemWithWPH,tBetween
There are following mapping relations
Wherein,It is complex transformation matrix of any t moment tool coordinate system to workpiece coordinate system,
In formula,WPL,tIt is position vector of the t moment cutter location under workpiece coordinate system,WxL,t,WyL,tWithWzL,tIt is tool coordinate system
Description in workpiece coordinate system, wherein
In formula, atFeeding vector for cutter in moment t, vtFor cutter moment t generating tool axis vector；
In formula,WPL,t-△tIt is position vector of the t- time Δt cutter location under workpiece coordinate system.
2. a kind of determination method in tool-workpiece contact region according to claim 1, wherein knife described in step 4
Tool radius is R (z),
When the cutter is circular arc knife,
When the cutter is ball head knife,
When the cutter is flat-bottomed cutter,
R (z)=D/2；
The D is the diameter of cutter cylindrical surface portion, and r is the arc radius of knife tool arc face part.
3. a kind of determination method in tool-workpiece contact region according to claim 1, wherein the Δ t is that the time is micro-
Member.
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| CN102622489B (en) * | 2012-03-26 | 2014-01-15 | 上海交通大学 | Five-axis side milling cutting force predicting method based on ACIS platform |
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