CN113400092B - Metal cutting force prediction method considering material accumulation - Google Patents

Metal cutting force prediction method considering material accumulation Download PDF

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CN113400092B
CN113400092B CN202110743438.9A CN202110743438A CN113400092B CN 113400092 B CN113400092 B CN 113400092B CN 202110743438 A CN202110743438 A CN 202110743438A CN 113400092 B CN113400092 B CN 113400092B
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CN113400092A (en
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万敏
温丹阳
张卫红
杨昀
任圆圆
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Northwestern Polytechnical University
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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
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    • B23Q17/09—Arrangements for observing, indicating or measuring on machine tools for indicating or measuring cutting pressure or for determining cutting-tool condition, e.g. cutting ability, load on tool

Abstract

The invention relates to a metal cutting force prediction method considering material accumulation, which comprises the steps of firstly determining the radius of a tool nose blunt circle of a used tool through measurement; then, calculating the theoretical instantaneous undeformed chip thickness in the cutting process and calculating the cutting force; obtaining the size of the plastic deformation area in the workpiece material by using the cutting force obtained by calculation and the Hertz contact theory; calculating the deformation of the workpiece in the width cutting direction before and after the cutting process; according to the principle of volume invariance, in combination with the cutting speed, the material accumulation volume is equal to the difference between the volume of the material flowing to the tool tip in unit time and the volume of the material flowing out of the tool tip after the material is subjected to broadening deformation; simplifying the shape of the stacked material into a triangle, calculating to obtain a stacked height, taking the stacked height at the moment as a cutting depth compensation value at the next moment, compensating the theoretical instantaneous undeformed chip thickness at the next moment, then calculating a cutting force, a plastic deformation area and the like at the next moment, and performing the calculation process at the next moment until the cutting process is finished.

Description

Metal cutting force prediction method considering material accumulation
Technical Field
The invention belongs to the technical field of machining, relates to a prediction method for cutting force in a metal cutting process, and particularly relates to a prediction method for the cutting force when material accumulation is formed under the condition that a tool nose is considered to be rounded.
Background
In modeling metal cutting, the tool tip is generally considered to be completely sharp. However, in practice, the cutting tip always has a blunt circle, and particularly for micro-cutting processes or when using a dull tool, the cutting amount of the cutting teeth is small compared with the blunt radius of the cutting tip, and the blunt circle effect is not negligible. When the undeformed cutting thickness is small, no chips are generated in the cutting process, and workpiece materials are accumulated in front of the blunt tip, so that the actual undeformed cutting thickness in the cutting process is changed, and the cutting force is further influenced. Therefore, to ensure the accuracy of the cutting force modeling, the influence of the material accumulation on the cutting force needs to be accurately predicted.
Document 1 "X.Lai, H.Li, C.Li, Z.Lin, J.Ni, modeling and analysis of micro scale milling size effect, micro cutter edge radius and minimum chip thickness, International Journal of Machine Tools and manufacturing 48(1) (2008) 1-14" discloses a cutting process finite element simulation modeling method, the results of which clearly show the formation of material build-up. However, this article does not give any theoretical explanation of the nature, cause, influence, etc. associated with the material accumulation.
Document 2 "m.wan, d. -y.wen, y. -c.ma, w. -h.zhang, On material separation and cutting for prediction in micro milling machining of the effect of the blade metal zone, International Journal of Machine Tools and manual 146(2019) 103452" discloses a cutting force prediction method that takes into account the nose rounding and its influence. In the method, the height of the accumulated material before the blunt circle of the cutter tip is approximately calculated by the included angle between the tangent line of the blunt circle of the cutter tip and the feeding direction at the height corresponding to the theoretical thickness of undeformed cuttings. However, in this method, there is no theoretical basis for this approximate calculation method.
Typical features of the above documents are: when modeling the cutting process, the material accumulation phenomenon can not be theoretically predicted through analytic modeling, and the influence on the aspects of cutting force and the like can not be theoretically explained.
Disclosure of Invention
Technical problem to be solved
In order to solve the problem that the material accumulation and the influence on the cutting force cannot be theoretically predicted when the cutting force is modeled by the conventional method, the invention provides a method for realizing material accumulation amount calculation and cutting force prediction through theoretical modeling.
Technical scheme
The invention provides a method for realizing material accumulation amount calculation and cutting force prediction through theoretical modeling, which firstly needs to determine the radius of a tool nose obtuse circle of a used tool through measurement. It is then necessary to calculate the theoretical instantaneous undeformed chip thickness of the cutting process and to calculate the cutting force. And obtaining the size of the plastic deformation area in the workpiece material by using the cutting force obtained by calculation and the Hertz contact theory. And calculating the deformation of the workpiece in the width cutting direction before and after the cutting process by means of a Caulikov rolling and widening formula. According to the principle of constant volume, in combination with the cutting speed, the material accumulation volume is equal to the difference between the volume of the material flowing to the blade tip in a unit time and the volume of the material flowing out of the blade tip after the material is subjected to the broadening deformation. Simplifying the shape of the stacked material into a triangle, calculating to obtain a stacking height, taking the stacking height at the moment as a cutting depth compensation value at the next moment, compensating the theoretical instantaneous undeformed chip thickness at the next moment, then calculating the cutting force, the plastic deformation area and the like at the next moment, and performing the calculation process at the next moment. And circulating the calculation process until the cutting process is finished, so that the material accumulation condition in the cutting process can be theoretically predicted and the cutting force of the material accumulation is considered.
The expected technical effect is as follows: the metal cutting force prediction method considering the accumulation of the material before the blunt rounding of the tool tip can calculate the accumulation amount of the material before the blunt rounding of the tool tip and the influence of the accumulation amount on the cutting force through theoretical analysis.
The technical scheme adopted by the invention for solving the technical problems is as follows: a metal cutting force prediction method considering material accumulation before a tool nose is blunt and round is characterized by comprising the following steps:
step one, microscopically observing the radius R of a blunt circle of a cutting edge tool tip of a used tool in millimeters and the rake angle alpha of the tool in degrees.
Step two, making the theoretical undeformed chip thickness of the cutting process at the moment t be h0In millimeters. The compensation value h of the thickness of the undeformed chip is set to 0 at the initial time t ad00 in mm, bulk volume of material V p00 in cubic millimeters.
And step three, the thickness of the undeformed cuttings at the current moment t is h, and the unit is millimeter.
Figure BDA0003143506960000031
In the formula h1Distance of lower vertex of the metal dead zone from the blunt round bottom part of the tool nose is in millimeter, and refer to the literature "M.Wan, D. -Y.Wen, Y. -C.Ma., W. -H.Zhang, On material separation and cutting forceprediction in micro-milling threading the effect of dead metal zone, International Journal of Machine Tools and manufacturing 146(2019)103452.
Step four, judging the thickness h of the plough cutting action at the momenteAnd shear thickness hcIn units of millimeters:
Figure BDA0003143506960000032
Figure BDA0003143506960000033
step five, calculating the tangential shear force F at the momenttcShear force F in the normal directionrcIn newtons:
Figure BDA0003143506960000034
Figure BDA0003143506960000035
wherein B is the cutting width in mm, Ktc、Krc、ptc、prc、qtcAnd q isrcFor the shear force coefficient, it is determined by referring to the method disclosed in "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro fine threading in the effect of dead metal zone, International Journal of Machine Tools and production 146 (2019)" 103452.
Step six, calculating the tangential plowing and shearing force F at the momenttcNormal plough force FrcIn newtons:
Figure BDA0003143506960000036
Figure BDA0003143506960000037
wherein B is the cutting width in mm, Kte、Kre、pte、pre、qteAnd q isreFor the plow index, it is determined by referring to the method disclosed in "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for prediction in micro milling through winding of the effect of the dead metal zone, International Journal of Machine Tools and Manual 146(2019) 103452".
Step seven, calculating the shearing angle
Figure BDA0003143506960000041
The unit is degree:
Figure BDA0003143506960000042
in the formula betaeIs the angle of friction, αeFor equivalent rake angles, the units are degrees, all determined according to the methods disclosed in the documents "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro milling of the effect of the dead metal zone, International Journal of Machine Tools and manufacturing 146(2019) 103452".
Step eight, calculating the length l of the shearing surfacecIn units of millimeters:
Figure BDA0003143506960000043
step nine, calculating the positive stress p on the shearing surfacecAnd shear stress qcThe unit is megapascal:
Figure BDA0003143506960000044
Figure BDA0003143506960000045
step ten, calculating a stress state caused by shearing in a shearing plane coordinate system:
Figure BDA0003143506960000046
Figure BDA0003143506960000047
Figure BDA0003143506960000048
in the formula sigmaxxcIs a positive stress in the abscissa direction, σzzcIs a positive stress in the ordinate direction, τxzcThe shear stress is in MPa. Where s represents the abscissa at the calculated position and z represents the ordinate at the calculated position, in millimeters.
Step eleven, calculating the length l of the section of the plougheIn units of millimeters:
Figure BDA0003143506960000051
step twelve, calculating the cutting angle of the plough
Figure BDA0003143506960000052
The unit is degree:
Figure BDA0003143506960000053
step thirteen, calculating the positive stress p on the plough cutting surfaceeAnd shear stress qeThe unit is megapascal:
Figure BDA0003143506960000054
Figure BDA0003143506960000055
step fourteen, calculating the stress state caused by plough cutting in a plough cutting plane coordinate system:
Figure BDA0003143506960000056
Figure BDA0003143506960000057
Figure BDA0003143506960000058
in the formula sigmaxxePositive stress, σ, in the abscissa directionzzeNormal stress in the ordinate direction, τxzeFor shear stress, the units are in MPa. Where s represents the abscissa at the calculated position and z represents the ordinate at the calculated position, in millimeters.
Fifteenth, referring to the method disclosed in the literature "Wan M, Ye Xiang-Yu, Yang Yun, Zhang WH. the theoretical prediction of machining-induced stress in the three-dimensional biological adjacent processes [ J ], International Journal of Mechanical Sciences,2017,133: 426-437", the stress caused by plowing and the stress caused by shearing are converted into the coordinate system of the workpiece to obtain the cutting stress distribution, and the boundary of the plastic deformation zone is judged according to the Missess yield criterion.
Sixthly, setting the cutting direction of the tool nose as front, measuring the horizontal distance from the foremost end of the plastic deformation area to the origin of the workpiece coordinate system, and recording the horizontal distance as LzIn millimeters. Measuring the distance from the lowest end of the plastic deformation region to the newly generated surface, and recording the distance as hzIn millimeters.
Seventhly, calculating the deformation increment delta b of the material in the width cutting direction by using a Caulff formula, wherein the unit is millimeter:
Figure BDA0003143506960000061
wherein the value of parameter C is determined by:
Figure BDA0003143506960000062
where e is the natural logarithm.
Eighteen, calculating the stacking length L of the materialspIn units of millimeters:
Figure BDA0003143506960000063
nineteen steps of calculating the material accumulation volume V at the current time t by using the volume invariance principlep：
Vp＝vcB(h0+hz)dt+Vp0-vc(B+Δb)hzdt
In the formula vcThe cutting speed is given in units of millimeters per second. dt is the time in units of seconds.
Twenty step, calculating the material stacking height hadIn units of millimeters:
Figure BDA0003143506960000071
twenty-one step of ordering had0＝had，Vp0＝VpAnd t is t + dt, and repeating the steps from the third step to the twenty-one step circularly until the cutting process is finished.
Advantageous effects
According to the metal cutting force prediction method considering material accumulation, the deformation in the width cutting direction can be obtained through complete theoretical calculation according to input machining parameters and tool geometric parameters, the material accumulation volume and the accumulation height under the blunt circle of a tool nose are further obtained, the accumulation height is superposed on the theoretical undeformed chip thickness, and the cutting force can be obtained through calculation. Compared with the literature 1, the method can theoretically calculate the material stacking volume and height, and the theoretical calculation process is complete. Compared with the document 2, the method can provide a theoretical calculation process of the material accumulation height, and considers the influence of material accumulation in the cutting force calculation process, so that the theoretical explanation of the material accumulation is more reasonable, and the cutting force calculation result is more accurate.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 shows the invention when the undeformed chip thickness h is greater than h1Time contact model geometry schematic.
FIG. 2 shows the invention when the undeformed chip thickness h is less than h1Time contact model geometry schematic.
Fig. 3 is a schematic of the material stacking geometry of the present invention.
FIG. 4 shows a 2-tooth milling cutter with a diameter of 1 mm, a blunt nose radius of 0.009 mm, a rake angle of 10 degrees, and a helix angle of 30 degrees; the cutting material is aluminum alloy 7050-T7451; the rotation speed of the milling cutter is 5000 revolutions per minute in the cutting process, and the feed per tooth is fzThe predicted cutting force results at 0.0005 mm axial cut depth and 0.2 mm radial cut depth were compared to predicted cutting force and experimental results without considering material accumulation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. 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 experiment is designed as down milling, a 2-tooth milling cutter with the diameter of 1 mm is used, the radius of a blunt circle of a tool nose is 0.009 mm, the front angle of the tool is 10 degrees, and the helix angle is 30 degrees; the cutting material is aluminum alloy 7050-T7451; the rotation speed of the milling cutter is 5000 revolutions per minute in the cutting process, and the feed per tooth is fz0.0005 mm, an axial cut of 0.2 mm and a radial cut of 0.5 mm.
Step one, microscopic observation confirms that the radius R of a tool tip blunt circle of a cutting edge of the used tool is 0.009 mm, the tool rake angle alpha is 10 degrees (used for determining the equivalent rake angle in the step seven), and the milling cutter is equally divided into a plurality of infinitesimals with the length of 0.01 mm along the axial direction.
And step two, setting the initial time t to be 0 as the time when the milling cutter just contacts the workpiece. The undeformed chip thickness compensation value h of all cutting units on all cutter teeth of the milling cutter ad0,i,j0 in mm, bulk volume of material V p0,i,j0 in cubic millimeters.
Step three, aiming at the time t. Theoretical instantaneous undeformed chip thickness h of the ith cutting tooth and jth cutting unit of a milling cutter during milling0,i,jCalculated in millimeters from the following formula:
Figure BDA0003143506960000081
in the formula
Figure BDA0003143506960000082
The instantaneous tooth position angle of the jth cutting unit of the ith cutter tooth of the milling cutter at the current moment is measured in degrees.
And step four, the thickness of the undeformed cuttings at the current time t is h, and the unit is millimeter.
Figure BDA0003143506960000083
In the formula h1The distance between the lower vertex of the dead metal area and the blunt round bottom of the tool tip is in millimeters, and the reference is made to the literature "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for prediction in micro-milling of the effect of dead metal zone, International Journal of Machine Tools and Manufacture 146(2019)103452 "", as determined by the method disclosed10.0021 mm.
Step five, judging the thickness h of the plough cutting action at the momenteAnd shear thickness hcIn units of millimeters:
Figure BDA0003143506960000091
Figure BDA0003143506960000092
step six, calculating the tangential shear force F at the momenttcShear force F in the normal directionrcIn newtons:
Figure BDA0003143506960000093
Figure BDA0003143506960000094
wherein B is the cutting width in mm, Ktc、Krc、ptc、prc、qtcAnd q isrcFor the shear force coefficient, it is determined by the method disclosed in "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro milling through winding of the effect of the dead metal zone, International Journal of Machine Tools and Manual 146(2019) 103452", K.tc＝851.3、Krc＝402.3、ptc＝0.6382、prc＝0.9781、qtc＝0.1023、qrc＝-0.08319。
Step seven, calculating the tangential plowing and shearing force F at the momenttcNormal plough shearing force FrcIn newtons:
Figure BDA0003143506960000095
Figure BDA0003143506960000096
wherein B is the cutting width in mm, Kte、Kre、pte、pre、qteAnd q isreFor the shear factor, it is determined by the method disclosed in "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for prediction in micro milling through winding of the effect of the dead metal zone, International Journal of Machine Tools and Manual 146(2019) 103452", Kte＝1182、Kre＝1584、pte＝0.8532、pre＝0.6071、qte＝0.01174、qre＝0.2832。
Step eight, calculating a shearing angle
Figure BDA0003143506960000097
The unit is degree:
Figure BDA0003143506960000098
in the formula betaeIs the angle of friction, αeFor equivalent rake angles, the units are degrees, all determined according to the methods disclosed in the documents "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro milling of the effect of the dead metal zone, International Journal of Machine Tools and manufacturing 146(2019) 103452".
Step nine, calculating the length l of the shearing surfacecIn units of millimeters:
Figure BDA0003143506960000101
step ten, calculating the normal stress p on the shearing surfacecAnd shear stress qcIn units of mpa:
Figure BDA0003143506960000102
Figure BDA0003143506960000103
step eleven, calculating a stress state caused by shearing in a shearing plane coordinate system:
Figure BDA0003143506960000104
Figure BDA0003143506960000105
Figure BDA0003143506960000106
in the formula sigmaxxcIs a positive stress in the abscissa direction, σzzcIs a positive stress in the ordinate direction, τxzcFor shear stress, the units are in MPa. Where s represents the abscissa at the calculated position and z represents the ordinate at the calculated position, in millimeters.
Step twelve, calculating the length l of the section of the plougheIn units of millimeters:
Figure BDA0003143506960000111
thirteen step, calculating the cutting angle of the plough
Figure BDA0003143506960000112
The unit is degree:
Figure BDA0003143506960000113
step fourteen, calculating the normal stress p on the plough cutting surfaceeAnd shear stress qeThe unit is megapascal:
Figure BDA0003143506960000114
Figure BDA0003143506960000115
step fifteen, calculating the stress state caused by plough cutting in the coordinate system of the plough cutting surface:
Figure BDA0003143506960000116
Figure BDA0003143506960000117
Figure BDA0003143506960000118
in the formula sigmaxxePositive stress, σ, in the abscissa directionzzeIs a positive stress in the ordinate direction, τxzeThe shear stress is in MPa. Where s represents the abscissa at the calculated position and z represents the ordinate at the calculated position, in millimeters.
Sixthly, referring to the method disclosed in the literature of "Wan M, Ye Xiang-Yu, Yang Yun, Zhang WH. the theoretical prediction of machining-induced stress in three-dimensional biological adjacent processes [ J ], International Journal of Mechanical Sciences,2017,133: 426-437", converting the stress caused by plowing and the stress caused by shearing into a workpiece coordinate system to obtain cutting stress distribution, and judging the boundary of the plastic deformation zone through the Missess yield criterion.
Seventhly, setting the cutting direction of the tool nose as front, measuring the horizontal distance from the foremost end of the plastic deformation area to the origin of the coordinate system of the workpiece, and recording the horizontal distance as LzIn millimeters. Measuring the distance from the lowest end of the plastic deformation area to the newly generated surface, and recording the distance as hzIn millimeters.
Eighteen, calculating the deformation increment delta b of the material in the width cutting direction by using a Caulff formula, wherein the unit is millimeter:
Figure BDA0003143506960000121
wherein the value of parameter C is determined by the following formula:
Figure BDA0003143506960000122
where e is the natural logarithm.
Nineteen steps of calculating the stacking length L of the materialspIn units of millimeters:
Figure BDA0003143506960000123
twenty, calculating the material accumulation volume V at the current time t by using the volume invariance principlep：
Vp＝vcB(h0+hz)dt+Vp0-vc(B+Δb)hzdt
In the formula vcThe cutting speed is given in millimeters per second. dt is a time element in seconds.
Twenty one step, calculating the material stacking height hadIn units of millimeters:
Figure BDA0003143506960000124
and twenty-two steps, namely circulating the steps from three to twenty-two, and calculating the material accumulation and the cutting force of all the cutting units of all the cutter teeth of the current milling cutter.
Twenty-third, referring to the literature "m.wan, d. -y.wen, y. -c.ma, w. -h.zhang, On-material separation and cutting for prediction in micro fine threading through threading of the effect of the dead metal zone, International Journal of Machine Tools and manufacturing 146(2019) 103452.", the x-direction cutting force F received by the milling cutter at the current time t is calculated under the Machine coordinate systemxAnd a cutting force F in the y directionyIn newtons.
Twenty five steps, order had0,i,j＝had，Vp0,i,j＝VpAnd t is t + dt, and the step three to the step twenty three are repeated in a circulating mode until the cutting process is finished.
Twenty-six step, drawing the cutting force F in the x direction of the milling cutterxAnd a cutting force F in the y directionyThe curve varies with time t, resulting in figure 4.
The 2-tooth milling cutter with the diameter of 1 mm can be obtained through the steps, the radius of the blunt circle of the cutter point is 0.009 mm, the front angle of the cutter is 10 degrees, and the helix angle is 30 degrees; the cutting material is aluminum alloy 7050-T7451; the rotation speed of the milling cutter is 5000 revolutions per minute in the cutting process, and the feed per tooth is fzTheoretical prediction of cutting force for a 0.0005 mm axial cut depth of 0.2 mm and a 0.5 mm radial cut depth is shown in fig. 4. As can be seen from the attached figure 4, the cutting force result obtained by calculation of the method can be well matched with the experimental actual measurement result, and the difference between the prediction result without considering the material accumulation and the actual measurement result is large, so that the effectiveness of the cutting force prediction method considering the material accumulation is proved.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.

Claims (1)

1. A metal cutting force prediction method considering material accumulation is characterized by comprising the following steps:
step 1: microscopically observing the radius R of a tool tip blunt circle of a cutting edge of the used tool and the rake angle alpha of the tool;
and 2, step: let the theoretical undeformed chip thickness of the cutting process at time t be h0(ii) a The compensation value h of the undeformed chip thickness is set to 0 at the initial time tad0Bulk volume of material V ═ 0p0＝0；
And 3, step 3: the undeformed chip thickness at the current time t is h:
Figure FDA0003143506950000011
in the formula h1The distance between the lower vertex of the metal dead zone and the bottom of the blunt circle of the tool nose is;
and 4, step 4: judging the thickness h of the plowing action at the momenteAnd shear thickness hc：
Figure FDA0003143506950000012
Figure FDA0003143506950000013
And 5: the tangential shear force F at this time was calculatedtcShear force F in the normal directionrc：
Figure FDA0003143506950000014
Figure FDA0003143506950000015
Wherein B is the cutting width, Ktc、Krc、ptc、prc、qtcAnd q isrcIs the shear force coefficient;
and 6: calculating the tangential plowing and shearing force F at the momenttcNormal plough shearing force Frc：
Figure FDA0003143506950000016
Figure FDA0003143506950000017
Wherein B is the cutting width, Kte、Kre、pte、pre、qteAnd q isreIs the plough shear coefficient;
and 7: calculating the shear angle
Figure FDA0003143506950000018
Figure FDA0003143506950000019
In the formula betaeIs the angle of friction, αeIs an equivalent rake angle;
and step 8: calculating the shear plane length lc：
Figure FDA0003143506950000021
And step 9: calculating the positive stress p on the shear planecAnd shear stress qc：
Figure FDA0003143506950000022
Figure FDA0003143506950000023
Step 10: calculating the stress state caused by shearing in a coordinate system of a shearing surface:
Figure FDA0003143506950000024
Figure FDA0003143506950000025
Figure FDA0003143506950000026
in the formula sigmaxxcIs a positive stress in the abscissa direction, σzzcIs a positive stress in the ordinate direction, τxzcFor shear stress, s represents the abscissa at the calculated position, and z represents the ordinate at the calculated position;
step 11: calculating the length l of the cross section of the ploughe：
Figure FDA0003143506950000027
Step 12: calculating plough cutting angle
Figure FDA0003143506950000028
Figure FDA0003143506950000031
Step 13: calculating the normal stress p on the cutting surface of the plougheAnd shear stress qe：
Figure FDA0003143506950000032
Figure FDA0003143506950000033
Step 14: calculating the stress state caused by the cutting in the cutting plane coordinate system:
Figure FDA0003143506950000034
Figure FDA0003143506950000035
Figure FDA0003143506950000036
in the formula sigmaxxeIs a positive stress in the abscissa direction, σzzeIs a positive stress in the ordinate direction, τxzeFor shear stress, s represents the abscissa at the calculated position, and z represents the ordinate at the calculated position;
step 15: converting the stress caused by plough cutting and the stress caused by shearing into a workpiece coordinate system to obtain cutting stress distribution, and judging the boundary of a plastic deformation area according to a Misses yield criterion;
step 16: setting the cutting direction of the tool nose as front, measuring the horizontal distance from the most front end of the plastic deformation area to the origin of the workpiece coordinate system, and recording as LzMeasuring the distance from the lowest end of the plastic deformation area to the newly generated surface, and recording the distance as hz；
And step 17: and (3) calculating the deformation increment delta b of the material in the width cutting direction by utilizing a Caulff formula:
Figure FDA0003143506950000037
wherein the value of parameter C is determined by:
Figure FDA0003143506950000041
wherein e is a natural logarithm;
step 18: calculating the material stacking length Lp：
Figure FDA0003143506950000042
Step 19: calculating the material accumulation volume V at the current time t by using the volume invariance principlep：
Vp＝vcB(h0+hz)dt+Vp0-vc(B+Δb)hzdt
In the formula vcDt is the cutting speed, dt is the time infinitesimal;
step 20: calculating the material stacking height had：
Figure FDA0003143506950000043
Step 21: let had0＝had，Vp0＝VpAnd when t is t + dt, repeating the steps 3-21 circularly until the cutting process is finished.
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