CN108595806A - A kind of three-dimension lathe power Analytic modeling method - Google Patents
A kind of three-dimension lathe power Analytic modeling method Download PDFInfo
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Abstract
The invention discloses a kind of three-dimension lathe power Analytic modeling methods, include the following steps：The cutting edge of lathe tool is along the circumferential direction separated into a series of cutting infinitesimals on rake face；The shear flow stress of each cutting infinitesimal is calculated by material JC constitutive models；According to the geometrical relationship of lathe tool and coordinate transform, obtain the radial position angle of cutting infinitesimal, infinitesimal drift angle, cutting width, cutting depth, thickness of cutting and chip-load expression formula；According to the dynamic balance in the constraint dynamic balance of adjacent chip and all chip units, the chip flow angle of overall situation and partial situation is calculated；The cutting force that each cutting infinitesimal is subject to is calculated using modified inclined cutting prediction model；The cutting force of all cutting infinitesimals is overlapped, the value of entire lathe tool D cutting operations power is obtained.The present invention, which need to only input workpiece material parameter, lathe tool geometric parameter and cutting parameter, can soon predict Cutting Force, have higher accuracy and rapidity.
Description
Technical field
The present invention relates to a kind of Technology for Turning Machining more particularly to a kind of three-dimension lathe power Analytic modeling methods.
Background technology
During three-dimension lathe, lathe tool has complicated geometry, participates in the cutting edge of cutting to work pieces process
Surface quality has important influence.Therefore, it is necessary to establish accurate cutting Force Model to ensure the precision of prediction of cutting force.By
It is only applicable to specific tool-workpiece combination of materials in the mechanical model and empirical equation of prediction of Turning Force with Artificial, and needs to carry out big
The cutting experiment of amount, therefore, the shortcomings that of high cost, poor universality largely constrain the prediction to cutting force.And
Although the analytic modell analytical model of cutting prediction avoids the problem of carrying out high experimental cost and triviality, but do not consider to deposit in turning process
Chip effect of contraction.
Invention content
In order to overcome the problems, such as existing modeling method there are uncertain more than experiment number and to chip-flowing, the present invention provides
A kind of three-dimension lathe power Analytic modeling method, it establishes a kind of analytical Prediction model of three-dimension lathe power, only need to input workpiece
Material parameter, lathe tool geometric parameter and cutting parameter can soon predict Cutting Force, with higher accuracy and quickly
Property, it can solve the problems, such as existing machinery and numerical method calibration cost height and intricate operation.
The technical solution adopted by the present invention to solve the technical problems is：
A kind of three-dimension lathe power Analytic modeling method, includes the following steps：
The geometric parameter of S1, the geometric parameter for determining lathe tool and selected cutting parameter, lathe tool includes normal rake αn, sword inclines
Angle λs, normal relief angle γn, tool cutting edge angle krWith corner radius re；Cutting parameter includes cutting depth ap, amount of feeding ftAnd cutting
Speed V；
S2, by the cutting edge of lathe tool in rake face AγOn be along the circumferential direction separated into (K+2) a cutting infinitesimal, it is each to cut
The cutting characteristic of infinitesimal regards the Oblique Cutting Process constrained containing chip flow outgoing direction as, i.e., due to the phase interaction between adjacent chip
It is flowed out in the same direction with all chip units are made；
S3, due to rake face AγUpper all chip infinitesimals chip flow direction all having the same, therefore obtain k-th of chip
The local chip flow angle of infinitesimalExpression formulaWherein,For global flow angle,For cutting infinitesimal deflection
Angle；
S4, due to all chip infinitesimal flow directions having the same, k-th of chip infinitesimal is constrained by adjacent chip
Dynamic balance and the dynamic balance that is applied on all chip units be combined, obtain the equilibrium equation of chip infinitesimal It is resultant force caused by the adjacent chip unit by k-th of chip infinitesimal, thus calculates
It arrivesAnd then it calculates
S5, according to modified oblique cutting model, calculate k-th of cutting infinitesimal and produced by the shearing effect of main shear zone
Raw shearing forceAnd normal force
Wherein, τshFor the shear flow stress of main shear zone, AkThe chip-load for cutting infinitesimal for k-th,It is k-th
The cutting edge inclination of infinitesimal is cut,The normal shear angle for cutting infinitesimal for k-th,The anterior angle for cutting infinitesimal for k-th,For
The normal direction angle of friction of k-th of cutting infinitesimal,The local chip flow angle for cutting infinitesimal for k-th,It is micro- for k-th of cutting
The shear flow angle of member；
S6, pass through coordinate transform, k-th of cutting infinitesimal tangential component dF caused by shear actiont,j, radial component
dFr,j, axial thrust load dFa,jExpression formula be
S7, by coordinate transform, the cutting force that all cutting infinitesimals generate are overlapped, the expression of total cutting force is obtained
Formula is
Wherein, Fx、Fy、FzComponent of respectively total cutting force in three axis direction of x, y, z.
According to the above technical scheme, entrance angle is calculated according to lathe tool geometric parameter and cutting parameterCut out angleIt is discrete
AngleInitial position angle
Then the radial position angle of each cutting infinitesimal is calculated according to thisInfinitesimal drift angleCutting width wk, cutting depthThickness of cutting tk, chip-load Ak, cutting edge inclinationNormal rakeAnd cutting drift angle
Wherein,
According to the above technical scheme, in step S4, since k-th of chip infinitesimal is constrained by adjacent chip infinitesimal, therefore kth
The equilibrium equation of a chip infinitesimal is
Wherein, XcWith rake face AγVertically, ZcIt is chip-flowing, ycWith AγMiddle chip-flowing is vertical,For shear flow
Direction,For shear surface normal orientation,WithRespectively rake face AγInterior normal force and frictional force,It is to be cut by adjacent
Consider resultant force caused by infinitesimal to be worth doing,WithIt is the shearing force and normal force of main shear surface respectively；
It is cancelled out each other according to internal force between chip infinitesimal, the equilibrium equation for obtaining being applied to all chip infinitesimals is
According to the above technical scheme, in step S5, according to coordinate transform and geometrical relationship, cutting for k-th chip infinitesimal is determined
Cut flow angleWith normal direction angle of friction
Wherein, P0It is the normal pressure at point of a knife,ξ is pressure profile exponent,
μsIt is the coefficient of sliding friction between knife is considered to be worth doing, τs=τsh, normal shear angleIt is determined as by correcting Merchant formulaC1、C2Depending on workpiece and cutter material,
Main shear flow stress is determined according to material JC constitutive models
Wherein, the performance characteristic of material is by yield strength A, strength factor B, strain hardening exponent n, strain hardening and strain-rate sensitivity system
Number C and thermal softening Coefficient m determine that γ is shear strain,For shear strain rate,To refer to strain rate, T is material temperature, Tr
It is relative temperature, TmIt is the melting temperature of material.
According to the above technical scheme, ξ=3, μs=0.5, Tr=25 DEG C.
The beneficial effect comprise that：The present invention is based on the oblique cutting model constrained containing chip flow outgoing direction,
Using workpiece material parameter, lathe tool geometric parameter and cutting parameter as mode input parameter, the cutting edge of lathe tool is resolved into one
Series cutting infinitesimal calculates the cutting force component being applied on each cutting infinitesimal by modified oblique cutting model, and
It obtains total cutting force, three-dimension lathe power can be gone out with fast prediction.
Description of the drawings
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing：
Fig. 1 a are the discretization schematic diagrames of lathe tool cutting edge in the embodiment of the present invention；
Fig. 1 b are perspective views of Fig. 1 a in reference planes；
Fig. 2 a are the oblique cutting model graphics that infinitesimal is cut in the embodiment of the present invention；
Fig. 2 b are the oblique cutting model plan views that infinitesimal is cut in the embodiment of the present invention；
Fig. 3 a are the comparison diagrams of the Cutting Force prediction result of the 1st group of chip parameter in the embodiment of the present invention；
Fig. 3 b are the comparison diagrams of the Cutting Force prediction result of the 2nd group of chip parameter in the embodiment of the present invention；
Fig. 3 c are the comparison diagrams of the Cutting Force prediction result of the 3rd group of chip parameter in the embodiment of the present invention.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention.
A kind of three-dimension lathe power Analytic modeling method, includes the following steps：
The geometric parameter of S1, the geometric parameter for determining lathe tool and selected cutting parameter, lathe tool includes normal rake αn, sword inclines
Angle λs, normal relief angle γn, tool cutting edge angle krWith corner radius re；Cutting parameter includes cutting depth ap, amount of feeding ftAnd cutting
Speed V；
S2, as shown in Figure 1 a, 1 b, by the cutting edge of lathe tool in rake face AγOn along the circumferential direction decile be separated into (K+
2) a cutting infinitesimal, each cutting characteristic for cutting infinitesimal regard the Oblique Cutting Process constrained containing chip flow outgoing direction as, i.e.,
Since the interaction between adjacent chip makes all chip units flow out in the same direction；
S3, due to rake face AγUpper all chip infinitesimals chip flow direction all having the same, therefore obtain k-th of chip
The local chip flow angle of infinitesimalExpression formulaWherein,For global flow angle,For cutting infinitesimal deflection
Angle；
S4, due to all chip infinitesimal flow directions having the same, k-th of chip infinitesimal is constrained by adjacent chip
Dynamic balance and the dynamic balance that is applied on all chip units be combined, obtain the equilibrium equation of chip infinitesimal It is resultant force caused by the adjacent chip unit by k-th of chip infinitesimal, thus calculates
It arrivesAnd then it calculates
S5, as shown in Fig. 2 a, Fig. 2 b, according to modified oblique cutting model, calculate k-th of cutting infinitesimal by main shearing
Shearing force caused by the shearing effect in areaAnd normal force
Wherein, τshFor the shear flow stress of main shear zone, AkThe chip-load for cutting infinitesimal for k-th,It is k-th
The cutting edge inclination of infinitesimal is cut,The normal shear angle for cutting infinitesimal for k-th,The anterior angle for cutting infinitesimal for k-th,For
The normal direction angle of friction of k-th of cutting infinitesimal,The local chip flow angle for cutting infinitesimal for k-th,It is micro- for k-th of cutting
The shear flow angle of member；
S6, pass through coordinate transform, k-th of cutting infinitesimal tangential component dF caused by shear actiont,j, radial component
dFr,j, axial thrust load dFa,jExpression formula be
S7, by coordinate transform, the cutting force that all cutting infinitesimals generate are overlapped, the expression of total cutting force is obtained
Formula is
Wherein, Fx、Fy、FzComponent of respectively total cutting force in three axis direction of x, y, z.
In a preferred embodiment of the invention, entrance angle is calculated according to lathe tool geometric parameter and cutting parameterCut out angleWalk-off angleInitial position angle
Then the radial position angle of each cutting infinitesimal is calculated according to thisInfinitesimal drift angleCutting width wk, cutting depthThickness of cutting tk, chip-load Ak, cutting edge inclinationNormal rakeAnd cutting drift angle
Wherein,
In a preferred embodiment of the invention, in step S4, since k-th of chip infinitesimal is by the pact of adjacent chip infinitesimal
Beam, therefore the equilibrium equation of k-th of chip infinitesimal is
Wherein, XcWith rake face AγVertically, ZcIt is chip-flowing, ycWith AγMiddle chip-flowing is vertical,For shear flow
Direction,For shear surface normal orientation,WithRespectively rake face AγInterior normal force and frictional force,It is to be cut by adjacent
Consider resultant force caused by infinitesimal to be worth doing,WithIt is the shearing force and normal force of main shear surface respectively；
It is cancelled out each other according to internal force between chip infinitesimal, the equilibrium equation for obtaining being applied to all chip infinitesimals is
In a preferred embodiment of the invention, in step S5, according to coordinate transform and geometrical relationship, k-th of chip is determined
The shear flow angle of infinitesimalWith normal direction angle of friction
Wherein, P0It is the normal pressure at point of a knife,ξ is pressure profile exponent,
μsIt is the coefficient of sliding friction between knife is considered to be worth doing, τs=τsh, normal shear angleIt is determined as by correcting Merchant formulaC1、C2Depending on workpiece and cutter material,
Main shear flow stress is determined according to material JC constitutive models
Wherein, the performance characteristic of material is by yield strength A, strength factor B, strain hardening exponent n, strain hardening and strain-rate sensitivity system
Number C and thermal softening Coefficient m determine that γ is shear strain,For shear strain rate,To refer to strain rate, T is material temperature, Tr
It is relative temperature, TmIt is the melting temperature of material.
In a preferred embodiment of the invention, ξ=3, μs=0.5, Tr=25 DEG C.
Core of the invention includes mainly following three step：
1, as shown in Figure 1 a, 1 b, the cutting edge of lathe tool is along the circumferential direction divided into K+2 cutting infinitesimal, and determined
Entrance angleCut out angleWalk-off angleInitial position angleThen the radial position angle of each cutting infinitesimal is calculatedInfinitesimal drift angleCutting width wk, cutting depthThickness of cutting tk, chip-load Ak, cutting edge inclinationNormal rake
And cutting drift angle
2, the shear force that cutting infinitesimal is subject to is calculated, as shown in Fig. 2 a, Fig. 2 b, according to the dynamic balance side of chip unit
Journey calculates global chip flow angleWith local chip flow angleThen it according to lathe tool geometry and coordinate conversion relation, calculates
Shear flow angleWith the shear stress τ of main shear zones, then can obtain the shear force (dF that cutting infinitesimal is subject tos,
dNs)；
3, total cutting force that lathe tool is subject to is calculated, shear force (dF is passed throughs,dNs), it calculates micro- for k-th of cutting
Three component dF that member is subject tot,j,dFr,j,dFa,j(it is tangential, it is radial, axial), the cutting force phase that all cutting infinitesimals are generated
Add, calculates the total cutting force acted on lathe tool.
The Analytic modeling process of the present invention is more clearly visible explained below in conjunction with a specific embodiment.
The present embodiment select lathe tool several parameters be：Hard alloy, -6 ° of cutting edge inclination, 6 ° of anterior angle, knife tool arc radius
0.8mm, 75 ° of tool cutting edge angle；Cutting parameter is divided into 3 groups, as shown in table 1；The workpiece material of selection is nickel-aluminum bronze.In numerically controlled lathe
Upper progress bar work machining experiment verifies above-mentioned cutting force Analytic modeling method.
1 cutting parameter of table
| Group number | The amount of feeding (mm/r) | Cutting speed (rpm) |
| 1 | 0.1 | 90 |
| 2 | 0.2 | 90 |
| 3 | 0.2 | 150 |
Fig. 3 a, Fig. 3 b, Fig. 3 c give the comparison of each group Predictive Model of Cutting Force and experimental result.It can be found that according to
The cutting force result that analytical Prediction model obtains has preferable consistency with experimental result.With propose in the prior art it is all kinds of
Modeling method is compared, and what this method need to only input that machining condition and characteristic parameter can be quickly predicts Cutting Force, has
Higher accuracy and rapidity.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (5)
1. a kind of three-dimension lathe power Analytic modeling method, which is characterized in that include the following steps：
The geometric parameter of S1, the geometric parameter for determining lathe tool and selected cutting parameter, lathe tool includes normal rake αn, cutting edge inclination λs、
Normal relief angle γn, tool cutting edge angle krWith corner radius re；Cutting parameter includes cutting depth ap, amount of feeding ftAnd cutting speed
V；
S2, by the cutting edge of lathe tool in rake face AγOn be along the circumferential direction separated into (K+2) a cutting infinitesimal, each cut infinitesimal
Cutting characteristic regard the Oblique Cutting Process constrained containing chip flow outgoing direction as, i.e., since the interaction between adjacent chip makes
All chip units flow out in the same direction；
S3, due to rake face AγUpper all chip infinitesimals chip flow direction all having the same, therefore obtain k-th of chip infinitesimal
Local chip flow angleExpression formulaWherein,For global flow angle,To cut infinitesimal deflection angle；
S4, due to all chip infinitesimal flow directions having the same, the power that k-th of chip infinitesimal is constrained by adjacent chip
It balances and is applied to the dynamic balance on all chip units to be combined, obtain the equilibrium equation of chip infinitesimal It is resultant force caused by the adjacent chip unit by k-th of chip infinitesimal, thus calculates
It obtainsAnd then it calculates
S5, according to modified oblique cutting model, calculate caused by shearing effect of k-th of cutting infinitesimal by main shear zone
Shearing forceAnd normal force
Wherein, τshFor the shear flow stress of main shear zone, AkThe chip-load for cutting infinitesimal for k-th,It is cut for k-th
The cutting edge inclination of infinitesimal,The normal shear angle for cutting infinitesimal for k-th,The anterior angle for cutting infinitesimal for k-th,It is k-th
The normal direction angle of friction of infinitesimal is cut,The local chip flow angle for cutting infinitesimal for k-th,Cutting for infinitesimal is cut for k-th
Cut flow angle；
S6, pass through coordinate transform, k-th of cutting infinitesimal tangential component dF caused by shear actiont,j, radial component dFr,j, axis
To component dFa,jExpression formula be
S7, by coordinate transform, the cutting force that all cutting infinitesimals generate are overlapped, the expression formula for obtaining total cutting force is
Wherein, Fx、Fy、FzComponent of respectively total cutting force in three axis direction of x, y, z.
2. three-dimension lathe power Analytic modeling method according to claim 1, which is characterized in that according to lathe tool geometric parameter and
Cutting parameter calculates entrance angleCut out angleWalk-off angleInitial position angle
Then the radial position angle of each cutting infinitesimal is calculated according to thisInfinitesimal drift angleCutting width wk, cutting depth
Thickness of cutting tk, chip-load Ak, cutting edge inclinationNormal rakeAnd cutting drift angle
Wherein,
3. three-dimension lathe power Analytic modeling method according to claim 2, which is characterized in that in step S4, due to k-th
Chip infinitesimal is constrained by adjacent chip infinitesimal, therefore the equilibrium equation of k-th of chip infinitesimal is
Wherein, XcWith rake face AγVertically, ZcIt is chip-flowing, ycWith AγMiddle chip-flowing is vertical,For shear flow direction,For shear surface normal orientation,WithRespectively rake face AγInterior normal force and frictional force,It is by adjacent chip infinitesimal
Generated resultant force,WithIt is the shearing force and normal force of main shear surface respectively；
It is cancelled out each other according to internal force between chip infinitesimal, the equilibrium equation for obtaining being applied to all chip infinitesimals is
4. three-dimension lathe power Analytic modeling method according to claim 3, which is characterized in that in step S5, according to coordinate
Transformation and geometrical relationship, determine the shear flow angle of k-th of chip infinitesimalWith normal direction angle of friction
Wherein, P0It is the normal pressure at point of a knife,ξ is pressure profile exponent, μsIt is
The coefficient of sliding friction between knife bits, τs=τsh, normal shear angleIt is determined as by correcting Merchant formulaC1、C2Depending on workpiece and cutter material,
Main shear flow stress is determined according to material JC constitutive models
Wherein, the performance characteristic of material is by yield strength A, strength factor B, strain hardening exponent n, strain hardening and strain-rate sensitivity coefficient C
Determine that γ is shear strain with thermal softening Coefficient m,For shear strain rate,To refer to strain rate, T is material temperature, TrIt is
Relative temperature, TmIt is the melting temperature of material.
5. three-dimension lathe power Analytic modeling method according to claim 4, which is characterized in that ξ=3, μs=0.5, Tr=25
℃。
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111198061A (en) * | 2018-10-30 | 2020-05-26 | 中车株洲电力机车研究所有限公司 | Decoupling method of three-dimensional turning force, force measuring structure design method and force measuring structure |
| CN111651867A (en) * | 2020-05-15 | 2020-09-11 | 西北工业大学 | Method for determining ultimate shear stress of chip formation in cutting machining |
| CN111759488A (en) * | 2020-07-09 | 2020-10-13 | 山东大学 | Design method and system and preparation of variable cross-section nickel-titanium root canal file applied to root canal preparation |
| CN112446153A (en) * | 2020-12-02 | 2021-03-05 | 山东大学 | Calculation method and system for storage energy field of first deformation region in steady-state cutting |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111198061A (en) * | 2018-10-30 | 2020-05-26 | 中车株洲电力机车研究所有限公司 | Decoupling method of three-dimensional turning force, force measuring structure design method and force measuring structure |
| CN111651867A (en) * | 2020-05-15 | 2020-09-11 | 西北工业大学 | Method for determining ultimate shear stress of chip formation in cutting machining |
| CN111651867B (en) * | 2020-05-15 | 2022-03-08 | 西北工业大学 | Method for determining ultimate shear stress of chip formation in cutting machining |
| CN111759488A (en) * | 2020-07-09 | 2020-10-13 | 山东大学 | Design method and system and preparation of variable cross-section nickel-titanium root canal file applied to root canal preparation |
| CN111759488B (en) * | 2020-07-09 | 2021-08-24 | 山东大学 | Design method and system and preparation of variable cross-section nickel-titanium root canal file applied to root canal preparation |
| CN112446153A (en) * | 2020-12-02 | 2021-03-05 | 山东大学 | Calculation method and system for storage energy field of first deformation region in steady-state cutting |
| WO2022116381A1 (en) * | 2020-12-02 | 2022-06-09 | 山东大学 | Method and system for calculating storage energy field in steady-state cutting first deformation zone |
| CN112446153B (en) * | 2020-12-02 | 2023-01-06 | 山东大学 | Calculation method and system for storage energy field of first deformation region in steady-state cutting |
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