CN108255134A - A kind of difficult-to-machine material high-speed turning prediction of Turning Force with Artificial method for considering chamfered edge geometry - Google Patents
A kind of difficult-to-machine material high-speed turning prediction of Turning Force with Artificial method for considering chamfered edge geometry Download PDFInfo
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Abstract
Prediction of Turning Force with Artificial method when the present invention provides a kind of difficult-to-machine material high-speed turning of consideration chamfered edge geometry, it obtains first and using turnery processing parameter and material constitutive parameter as input quantity, establish orthogonal coordinate system, calculate the corresponding undeformed chip thickness of cutting infinitesimal, the cutting force of cutting infinitesimal is calculated using the obtained momentary cutting thick of cutting infinitesimal, the cutting force of infinitesimal will be cut, it is transformed by space coordinates matrixing in the orthogonal coordinate system, it is integrated after addition along cutting edge, obtain whole cutting force, the present invention considers the influence of chamfered edge land length and chamfered edge angle counter blade mouth force coefficient, further perfect cutting edge force coefficient calibration equation, so as to efficient, calculate to a nicety chamfered edge circular bit turnery processing when cutting force.
Description
Technical field
The invention belongs to the efficiently high-precision Machining Technology for Cutting fields of metal, and in particular to a kind of difficulty for considering chamfered edge geometry adds
Work material high-speed turning prediction of Turning Force with Artificial method.
Background technology
The machining property assessment of the prediction of cutting force this conventional machining mode to turning has extremely important finger
Meaning is led, especially when processing Inconel 718 when difficult processing metals, the variation of cutting force and distribution are to the longevity of cutter
Life and the quality of machined surface all have significant effect.At present, domestic and international experts and scholars are in conventional diamond shape lathe tool and three
The research in angular lathe tool cutting force field is highly developed, but circular bit because its machining region geometry complexity,
It is thus relatively fewer to studying in this respect.
Meanwhile circular bit cutting edge has important role, especially chamfered edge to improving cutting ability and extending cutter life
Cutting edge improves characteristic, in difficult processing metal high-speed cutting processing field by its good antiwear property and intensity
In be widely used, it is common as ceramic circular lathe tool, CBN cutters etc., but due to this chamfered edge circular knives cutting geometry
Complexity and the cost of charp tool are higher, the research of its prediction of Turning Force with Artificial method are also needed to further deeply and perfect.
At present, scholar does correlative study for the prediction of the cutting force under this Complicated Turning environment, such as
Ren H and Altintas Y (" Machanics of machining with chamfered tools " J Manuf Sci
Eng Trans ASME 2000； 122(4)：It 650-659) proposes a kind of based on sliding field model and least energy principle
Chamfering tool cuts force analysis model, can export the cutting force and cutting heat of three deformed regions.Weng J, Zhuang K
(“An analytical force prediction model for turning operation by round insert
considering edge effect”In J Mech Sci 2017；128:168-180) have studied chamfered edge circular bit turning
When the small influence for cutting thick region cutting edge power to cutting force, and derived cutting edge force coefficient calibration equation with reference to finite element analysis, but
It is the influence that chamfered edge circular bit chamfered edge angle counter blade mouth force coefficient is not accounted in this method, thus today for circular bit
Prediction of Turning Force with Artificial it is comprehensive not enough, in addition, the needs of cutting force and chamfered edge geometric parameter more go to explore and verify by experiment.
Invention content
The technical problem to be solved by the present invention is to：It is cut during the difficult-to-machine material high-speed turning that a kind of consideration chamfered edge geometry is provided
Force prediction method is cut, can accurately and accurately predict the cutting force of difficult-to-machine material high-speed turning.
The technical solution taken by the invention to solve the above technical problem is：A kind of difficult processing material for considering chamfered edge geometry
Expect prediction of Turning Force with Artificial method during high-speed turning, it is characterised in that：It includes the following steps：
S1, acquisition and using turnery processing parameter and material constitutive parameter as input quantity：
Turnery processing parameter includes tool radius R, cutting depth ap, cutting speed V and feed engagement f；Material constitutive
Parameter includes yield strength A, strength factor B, strain rate sensitivity coefficient C, thermal softening Coefficient m and strain hardening exponent n；
S2, orthogonal coordinate system is established：
The Z axis that cutter is axially orthogonal coordinate system is defined, cutting feed direction is the X-axis of orthogonal coordinate system, with X-axis, Z axis
Vertical direction is Y-axis, and chamfered edge circular knives include rake face, chamfered edge face and rear knife face, using the center of circle of rake face as orthogonal seat
The space origins of system are marked, chamfered edge circular knives cutting edge is separated into a series of cutting infinitesimals in X/Y plane, obtain each ginseng
With the infinitesimal of machining；
S3, the corresponding undeformed chip thickness of cutting infinitesimal is calculated：
According to angle is immersed, it is two parts that machining region division will be participated on rake face, every in given area respectively
A infinitesimal corresponds to the calculation expression of undeformed chip thickness, specific as follows：
Wherein
In above-mentioned expression,For the corresponding undeformed chip thickness of j-th of infinitesimal, φsFor the corresponding immersion of j-th of infinitesimal
Angle, fcIt is feed engagement in the projection of rake face, φstIt is the immersion angle of machining region starting point, φmidIt is machining region subregion point
Immersion angle, φexIt is the immersion angle of machining region terminating point；
S4, the momentary-cutting-thick of cutting infinitesimal obtained using S3 calculate the cutting force of cutting infinitesimal：
It is each to cut the corresponding cutting speed direction of infinitesimal, cutting force tangentially and radiallyWithRespectively：
Wherein
In above-mentioned statement, Ktc、KfcAnd KrcRepresent cutting infinitesimal in cutting speed direction, shearing tangentially and radially respectively
Force coefficient, Kte、KfeAnd KreCutting edge force coefficient of the cutting infinitesimal on these three directions, d are represented respectivelyjRepresent the width of infinitesimal,
dφsAngle infinitesimal during for cutting edge discretization,Representing the cutting edge inclination of infinitesimal, R represents cutter radius of corner,Represent micro-
The method anterior angle of member, hjRepresent the undeformed chip thickness on the plane of reference；
S5, the cutting force that will cut infinitesimal are transformed by space coordinates matrixing in the orthogonal coordinate system,
It is integrated after addition along cutting edge, obtains whole cutting force：
WithRepresent cutting infinitesimal in the cutting force of the X-axis of orthogonal coordinate system, Y-axis and Z-direction, F respectivelyx、
FyAnd FzThe whole cutting force of X-axis, Y-axis and Z-direction is represented respectively,The projected angle for being tool cutting edge angle on the plane of reference.
As stated above, the Ktc、KfcAnd KrcIt calculates and obtains by the following method：
Wherein,It is the flowing shear stress on infinitesimal,And ηj cBe respectively infinitesimal normal rake,
Angle of friction, the angle of shear, cutting edge inclination and chip flow angle.
As stated above, the Kte、KfeAnd KreIt calculates and obtains by the following method：
If cutting edge force coefficient and the sine of shear stress, chamfered edge length and chamfer angle are linear：
θ is chamfer angle, and l is chamfered edge length,It is the flowing shear stress on infinitesimal, d φsDuring for cutting edge discretization
Angle infinitesimal, pt、pf、prIt is the linear constant item in cutting speed direction, radial direction, tangential cutting edge force coefficient respectively,It is
The tool cutting edge angle of j cutting edge infinitesimal, C1To C6For intermediate parameter.
As stated above, the chamfered edge circular knives are sintex.
Beneficial effects of the present invention are：
1st, the present invention considers the influence of chamfered edge land length and chamfered edge angle counter blade mouth force coefficient, further perfect sword
Mouth force coefficient calibration equation, so as to accurately and accurately predict cutting force during chamfered edge circular bit turnery processing.
2nd, cutting edge force coefficient and shearing force coefficient are solved using analytical model algorithm, establish the cutting Force Model of cutting infinitesimal,
Avoid a large amount of cutting experiments.
Description of the drawings
Fig. 1 is the method flow diagram of one embodiment of the invention.
Fig. 2 is the schematic diagram of the tool work piece cutting geometrical analysis in circular bit cutting process.
Fig. 3 is machining region in the division at rake face visual angle and infinitesimal discrete case.
Fig. 4 is the schematic three dimensional views of cutting edge infinitesimal local angle parameter.
Fig. 5 is the schematic diagram of 3-D graphic lower cutting edge infinitesimal local angle parameter.
Fig. 6 when using thickness of cutting as independent variable predicts that cutting force moves by correction model with Jason-Cook constitutive models
State change curve.
Fig. 7 is the schematic diagram of chamfer angle on chamfered edge cutting edge circular shear blade.
Fig. 8 a and Fig. 8 b are the emulation experiment that is carried out using finite element software Advantedge to verify cutting edge power model
As a result.
Fig. 9 a, the comparison diagram that b, c and Figure 10 a, b, c are theoretical prediction result and measured result.
In figure：1- rake faces, 2- chamfered edges face, knife face after 3-.
Specific embodiment
With reference to specific example and attached drawing, the present invention will be further described.
Prediction of Turning Force with Artificial method, such as Fig. 1 when the present invention provides a kind of difficult-to-machine material high-speed turning of consideration chamfered edge geometry
Shown, it includes the following steps：
S1, acquisition and using turnery processing parameter and material constitutive parameter as input quantity：
Turnery processing parameter includes tool radius R, cutting depth ap, cutting speed V and feed engagement f；Material constitutive
Parameter includes yield strength A, strength factor B, strain rate sensitivity coefficient C, thermal softening Coefficient m and strain hardening exponent n.
S2, orthogonal coordinate system is established：
The Z axis that cutter is axially orthogonal coordinate system is defined, cutting feed direction is the X-axis of orthogonal coordinate system, with X-axis, Z axis
Vertical direction is Y-axis, as shown in fig. 7, chamfered edge circular knives include rake face 1, chamfered edge face 2 and rear knife face 3, with rake face
The center of circle be orthogonal coordinate system space origins, in X/Y plane by chamfered edge circular knives cutting edge be separated into it is a series of cutting it is micro-
Member obtains each infinitesimal for participating in machining.As shown in Fig. 2, workpiece tool space relative position is shown when (a) is turnery processing
It is intended to, X-axis negative direction is tool feeding direction, and Y-axis is cutter radial, and Z axis is cutter axial direction and cutting speed direction；
(b) it is classical inclined cutting theory schematic diagram；(c) be circular knife turnery processing when and workpiece contact zone schematic diagram, therefrom
It is irregular for can see its thickness of cutting, is separated into a large amount of cutting infinitesimals in the present invention, then to each infinitesimal
Its cutting force is solved with classical inclined cutting theory；(d) it show circular knives schematic diagram；(e) it is chamfered edge cutting edge cutter shown in
Cut schematic diagram.
S3, the corresponding undeformed chip thickness of cutting infinitesimal is calculated：
As shown in figure 3, irregular area (color is deeper) i.e. machining region folded by two adjacent tool positions, in order to make calculating more
To be accurate, machining region is divided into machining region 1 and machining region 2, A is the starting point of workpiece and tool contact.According to immerse angle,
It is two parts that machining region division will be participated on rake face, and each infinitesimal corresponds to not deformed chip in given area respectively
The calculation expression of thickness, it is specific as follows：
Wherein
In above-mentioned expression,For the corresponding undeformed chip thickness of j-th of infinitesimal, φsFor the corresponding immersion of j-th of infinitesimal
Angle, fcIt is feed engagement in the projection of rake face, φstIt is the immersion angle of machining region starting point, φmidIt is machining region subregion point
Immersion angle, φexIt is the immersion angle of machining region terminating point, d φsWhat is represented is the angle step for dividing infinitesimal,It represents j-th
The width of infinitesimal.
S4, the momentary-cutting-thick of cutting infinitesimal obtained using S3 calculate the cutting force of cutting infinitesimal：
Schematic three dimensional views of the Fig. 4 for cutting edge infinitesimal local angle parameter, wherein PrFor the plane of reference, CproExist for rake face
Projection in the plane of reference.
1) the corresponding cutting edge inclination of each cutting edge infinitesimals ofNormal rakeIt can be calculated by coordinate transform:
Wherein
In statement,WithIt is corresponding normal rake and cutting edge inclination at A points；
2) the corresponding normal shear angle of each infinitesimals ofWith normal direction angle of frictionThe equation of least energy rule can be passed through
Iteration acquires:
3) overall situations chip flow direction is by assuming that the sum of interaction force between infinitesimal is acquired for 0:
Fig. 6 describes in the present invention correction model used with Jason-Cook constitutive models using thickness of cutting as independent variable
When predict cutting force dynamic changing curve figure, it can be seen from the figure that cutting thick region small, correction model is due to considering down
The influence of rib geometry, prediction is more accurate, so revised flowing shear stressCalculation formula is：
Wherein,The flowing shear stress on each infinitesimal solved for Jason-Cook constitutive models.
According to classical cutting Force Model it is found that each corresponding cutting speed direction of cutting infinitesimal, cutting tangentially and radially
Cut power WithRespectively：
Wherein
In above-mentioned statement, Ktc、KfcAnd KrcRepresent cutting infinitesimal in cutting speed direction, shearing tangentially and radially respectively
Force coefficient, Kte、KfeAnd KreCutting edge force coefficient of the cutting infinitesimal on these three directions, d are represented respectivelyjRepresent the width of infinitesimal,
dφsAngle infinitesimal during for cutting edge discretization,Representing the cutting edge inclination of infinitesimal, R represents cutter radius of corner,Represent micro-
The method anterior angle of member, hjRepresent the undeformed chip thickness of the plane of reference；.
The Ktc、KfcAnd KrcIt calculates and obtains by the following method：
Wherein,It is the flowing shear stress on infinitesimal,And ηj cBe respectively infinitesimal normal rake,
Angle of friction, the angle of shear, cutting edge inclination and chip flow angle.
Fig. 8 a and Fig. 8 b are the emulation experiment that is carried out using finite element software Advantedge to verify cutting edge power model
As a result.As shown in FIG., respectively using chamfered edge length and chamfer angle as variable.Cutting edge power is with it can be seen from the curve in figure
Positive correlation characteristic is presented in rib length and chamfer angle sine, it can be considered that assuming cutting edge power and chamfered edge length and chamfer angle
Sine is directly proportional to be reasonable.Therefore the expression formula of cutting edge force coefficient proposed in the present invention can be provided.The Kte、Kfe
And KreIt calculates and obtains by the following method：
If cutting edge force coefficient and the sine of shear stress, chamfered edge length and chamfer angle are linear：
With reference to the formula derived in Fig. 5 and Fig. 6, it can be deduced that the calibration equation of constant term in cutting edge force coefficient：
θ is chamfer angle, as shown in fig. 7, chamfer angle, that is, chamfered edge face 2 and the angle of rake face 1；L is chamfered edge length,It is micro-
Flowing shear stress in member, d φsAngle infinitesimal during for cutting edge discretization, pt、pf、prBe respectively cutting speed direction,
Radially, the linear constant item in tangential cutting edge force coefficient,It is the tool cutting edge angle of j-th of cutting edge infinitesimal, C1To C6For centre
Parameter.
S5, the cutting force that will cut infinitesimal are transformed by space coordinates matrixing in the orthogonal coordinate system,
It is integrated after addition along cutting edge, obtains whole cutting force：
WithRepresent cutting infinitesimal in the cutting force of the X-axis of orthogonal coordinate system, Y-axis and Z-direction, F respectivelyx、
FyAnd FzThe whole cutting force of X-axis, Y-axis and Z-direction is represented respectively,For tool cutting edge angle the plane of reference projected angle.
Heretofore described round chamfered edge lathe tool be sintex, the workpiece material processed for Inconel 718 this
The typical difficult-to-cut alloy of kind, sintex is more extensively used and cuts because its is wear-resisting, high temperature resistant, is not easy the features such as adhesion
Cut the higher difficult-to-machine material of manufacture field, especially workhardness.Inconel 718 is as a kind of than more typical difficult processing
Material is using very extensive in aircraft industry and nuclear industry, and advantage is apparent, but has the disadvantage that and is difficult to, to knife
The loss of tool is very big, it is difficult to obtain preferable piece surface integrality.The present invention is directed to the processing operating mode of this kind of difficult-to-machine material,
The prediction of Turning Force with Artificial method of proposition can predict the cutting force of difficult-to-machine material in process well, can be efficient high
Being realized to cutting force in finishing monitors in real time, therefore process can be controlled and to Optimization of cutting etc. offer
More perfect technical research guidance.
Clearly to illustrate in the present invention comprehensively with reference to specific round ceramic lathe tool machining example
Modeling process.
It is installed in the present embodiment using diameter 12.7mm round ceramics blade (concrete model is RNGN120400)
During lathe tool, rake face minimum point is the front end along workpiece axial feed, i.e. B points in Fig. 3, anterior angle is -6 °.The material of workpiece
Material is Inconel 718, and the model of lathe is CAK5085nzj, and the model of dynamometer is Kistler9257B, and sample frequency is
40kHz, specific cutting force numerical value are obtained by calculating the average value in certain section of section among sampled value.First by a large amount of
Experimental data in the present invention give cutting edge force coefficient in constant term demarcate, calibration result is as shown in table 1：
Table 1
By more than derivation and given Cutting Parameters, can predict to obtain not using MATLAB numerical simulations
With the cutting force numerical value in tri- directions of X, Y, Z under Cutting Parameters.Corresponding Cutting Parameters, theoretical prediction result and reality
It surveys result and prediction error is as shown in table 2.
Table 2
When Fig. 9 a, Fig. 9 b and Fig. 9 c describe cutting speed 150mm/min, cutting-in 0.5mm, feed speed 0.1mm/r, no
In the case of chamfered edge length, the theoretical prediction result of cutting force in tri- directions of X, Y, Z and the comparing result of measured result.
Figure 10 a, Figure 10 b and Figure 10 c describe cutting speed 150mm/min, feed speed 0.1mm/r, and cutting-in is
0.5mm, in the case of different chamfer angles, the theoretical prediction result of the cutting force in tri- directions of X, Y, Z and the comparison knot of measured result
Fruit.
Invention further contemplates cutting force and cutting edge parameter and the relationship of Cutting Parameters, and it is directed to
This typical difficult processing metal of Inconel 718 carries out multigroup above-mentioned experiment, from prediction with can be in experimental data comparison
It was found that the difficult-to-machine material high-speed turning Predictive Model of Cutting Force of this consideration chamfered edge geometry proposed in the present invention can be well
It is practical to meet the cutting of chamfered edge circular bit, there is very high accuracy, compared with the modeling method proposed in other technologies, more entirely
Face, the Tutrning Process for systematically having reacted chamfered edge cutting edge circular bit, while can meet to turnery processing cutting force essence
The demand really controlled.
It is appreciated that embodiment as described herein can be by hardware, software, firmware, middleware, microcode or its arbitrary combination
To realize.For hardware implementation mode, processing unit can be at one or more application-specific integrated circuits (ASIC), digital signal
Manage device (DSP), digital signal processing device (DSPD), programmable logic device (PLD), field programmable gate array (FPGA),
Processor, microprocessor, microcontroller, is designed other electronic units or its group to perform function described herein at controller
It is realized in closing.When with software, firmware, middleware or microcode, program code or code segment come when realizing embodiment, can be by it
Be stored in the machine readable media of such as storage assembly.
Above example is merely to illustrate the design philosophy and feature of the present invention, and its object is to make technology in the art
Personnel can understand present disclosure and implement according to this, and protection scope of the present invention is not limited to the above embodiments.So it is all according to
The equivalent variations made according to disclosed principle, mentality of designing or modification, within protection scope of the present invention.
Claims (4)
1. prediction of Turning Force with Artificial method during a kind of difficult-to-machine material high-speed turning of consideration chamfered edge geometry, it is characterised in that：It includes
Following steps：
S1, acquisition and using turnery processing parameter and material constitutive parameter as input quantity：
Turnery processing parameter includes tool radius R, cutting depth ap, cutting speed V and feed engagement f；Material constitutive parameter packet
Include yield strength A, strength factor B, strain rate sensitivity coefficient C, thermal softening Coefficient m and strain hardening exponent n；
S2, orthogonal coordinate system is established：
The Z axis that cutter is axially orthogonal coordinate system is defined, cutting feed direction is the X-axis of orthogonal coordinate system, vertical with X-axis, Z axis
Direction for Y-axis, chamfered edge circular knives include rake face, chamfered edge face and rear knife face, using the center of circle of rake face as orthogonal coordinate system
Space origins, chamfered edge circular knives cutting edge is separated into a series of cutting infinitesimals in X/Y plane, obtains and each participates in cutting
Cut the infinitesimal of processing；
S3, the corresponding undeformed chip thickness of cutting infinitesimal is calculated：
According to angle is immersed, it is two parts that machining region division will be participated on rake face, each micro- in given area respectively
The calculation expression of the corresponding undeformed chip thickness of member, it is specific as follows：
Wherein
In above-mentioned expression,For the corresponding undeformed chip thickness of j-th of infinitesimal, φ on rake facesIt is corresponding for j-th of infinitesimal
Immerse angle, fcIt is feed engagement in the projection of rake face, φstIt is the immersion angle of machining region starting point, φmidIt is machining region point
The immersion angle of area's point, φexIt is the immersion angle of machining region terminating point；
S4, the momentary-cutting-thick of cutting infinitesimal obtained using S3 calculate the cutting force of cutting infinitesimal：
It is each to cut the corresponding cutting speed direction of infinitesimal, cutting force F tangentially and radiallyt j、WithRespectively：
Wherein
In above-mentioned statement, Ktc、KfcAnd KrcShearing force system of the cutting infinitesimal in cutting speed direction, tangentially and radially is represented respectively
Number, Kte、KfeAnd KreCutting edge force coefficient of the cutting infinitesimal on these three directions, d are represented respectivelyjRepresent the width of infinitesimal, d φs
Angle infinitesimal during for cutting edge discretization,Representing the cutting edge inclination of infinitesimal, R represents cutter radius of corner,Represent infinitesimal
Method anterior angle, hjRepresent the undeformed chip thickness of the plane of reference；
S5, the cutting force that will cut infinitesimal are transformed by space coordinates matrixing in the orthogonal coordinate system, are added
It is integrated afterwards along cutting edge, obtains whole cutting force：
WithRepresent cutting infinitesimal in the cutting force of the X-axis of orthogonal coordinate system, Y-axis and Z-direction, F respectivelyx、FyAnd Fz
The whole cutting force of X-axis, Y-axis and Z-direction is represented respectively,The projected angle for being tool cutting edge angle on the plane of reference.
2. prediction of Turning Force with Artificial method during the difficult-to-machine material high-speed turning of consideration chamfered edge geometry according to claim 1,
It is characterized in that：The Ktc、KfcAnd KrcIt calculates and obtains by the following method：
Wherein,It is the flowing shear stress on infinitesimal,And ηj cIt is normal rake, the friction of infinitesimal respectively
Angle, the angle of shear, cutting edge inclination and chip flow angle.
3. prediction of Turning Force with Artificial method during the difficult-to-machine material high-speed turning of consideration chamfered edge geometry according to claim 1,
It is characterized in that：The Kte、KfeAnd KreIt calculates and obtains by the following method：
If cutting edge force coefficient and the sine of shear stress, chamfered edge length and chamfer angle are linear：
θ is chamfer angle, and l is chamfered edge length,It is the flowing shear stress on infinitesimal, d φsAngle during for cutting edge discretization
Infinitesimal, pt、pf、prIt is the linear constant item in cutting speed direction, radial direction, tangential cutting edge force coefficient respectively,It is j-th
The tool cutting edge angle of cutting edge infinitesimal, C1To C6For intermediate parameter.
4. prediction of Turning Force with Artificial method during the difficult-to-machine material high-speed turning of consideration chamfered edge geometry according to claim 1,
It is characterized in that：The chamfered edge circular knives are sintex.
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| CN111061218A (en) * | 2019-12-31 | 2020-04-24 | 华中科技大学 | Complex curved surface machining cutting force prediction method and device based on ACIS |
| CN111590393A (en) * | 2020-06-18 | 2020-08-28 | 天津大学 | Interference checking method for ultra-precise turning tool |
| CN112720070A (en) * | 2020-12-21 | 2021-04-30 | 江苏集萃华科智能装备科技有限公司 | Cutting force modeling method for chamfering cutting edge cutter |
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| CN109657307A (en) * | 2018-12-05 | 2019-04-19 | 武汉理工大学 | A kind of hot modeling method of three-dimensional inclined cutting suitable for circular hard alloy lathe tool |
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| CN111061218B (en) * | 2019-12-31 | 2021-07-27 | 华中科技大学 | Complex curved surface machining cutting force prediction method and device based on ACIS |
| CN111590393A (en) * | 2020-06-18 | 2020-08-28 | 天津大学 | Interference checking method for ultra-precise turning tool |
| CN111590393B (en) * | 2020-06-18 | 2021-08-06 | 天津大学 | Interference checking method for ultra-precise turning tool |
| CN112720070A (en) * | 2020-12-21 | 2021-04-30 | 江苏集萃华科智能装备科技有限公司 | Cutting force modeling method for chamfering cutting edge cutter |
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