CN113400092A - Metal cutting force prediction method considering material accumulation - Google Patents
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Abstract
本发明涉及一种考虑材料堆积的金属切削力预测方法，首先需要通过测量确定所用刀具的刀尖钝圆的半径；然后需要计算切削过程的理论瞬时未变形切屑厚度并计算切削力；利用计算得到的切削力与赫兹接触理论得到工件材料内部塑性变形区尺寸；计算切削过程前后工件在切宽方向变形量；依据体积不变原理，结合切削速度，材料堆积体积等于单位时间内流向刀尖的材料体积与宽展变形后流出刀尖的材料体积之差；将堆积材料形状简化为三角形，计算得到堆积高度，并将此刻的堆积高度作为下一时刻的切削深度补偿值，对下一时刻的理论瞬时未变形切屑厚度进行补偿，随后计算下一时刻的切削力、塑性变形区等，进行下一时刻的计算过程，直至切削过程结束。
The invention relates to a metal cutting force prediction method considering material accumulation. First, the radius of the blunt circle of the tool tip of the used tool needs to be determined by measurement; then the theoretical instantaneous undeformed chip thickness of the cutting process needs to be calculated and the cutting force is calculated; According to the cutting force and Hertz contact theory, the size of the plastic deformation zone inside the workpiece material is obtained; the deformation of the workpiece in the cutting width direction before and after the cutting process is calculated; according to the principle of constant volume, combined with the cutting speed, the material accumulation volume is equal to the material flowing to the tool tip per unit time. The difference between the volume and the volume of the material flowing out of the tool tip after widening and deformation; simplify the shape of the accumulated material into a triangle, calculate the stacking height, and use the current stacking height as the cutting depth compensation value at the next moment. The instantaneous undeformed chip thickness is compensated, and then the cutting force, plastic deformation zone, etc. at the next moment are calculated, and the calculation process at the next moment is carried out until the end of the cutting process.
Description
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.
Typical features of the above documents are: when modeling the cutting process, the material accumulation phenomenon can not be theoretically predicted through analytical 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 calculation and cutting force prediction through theoretical modeling, which firstly needs to determine the radius of a tool nose blunt 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 material accumulation before the blunt edge of the cutter can calculate the material accumulation amount before the blunt edge of the cutter and the influence of the material 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 cutting process theory at the moment t notThe deformed chip thickness is 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 time t is h, and the unit is millimeter.
In the formula h1The distance of the lower vertex of the metal dead zone from the blunt rounded bottom of the tool tip is measured in millimeters and is determined by the method disclosed in the literature "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for prediction of the effect of dead zone by micro milling and cutting method, 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:
step five, calculating the tangential shear force F at the momenttcShear force F in the normal directionrcIn newtons:
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:
wherein B is the cutting width in mm, Kte、Kre、pte、pre、qteAnd q isreFor the shear coefficient, it is determined by referring to the method disclosed in the document "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro fine threading of the effect of the dead metal zone, International Journal of Machine Tools and Manufacture 146 (2019)" 103452 ".
Step seven, calculating the shearing angle
The unit is degree:
in the formula betaeIs the angle of friction, αeFor equivalent rake angles, units are degrees, all referred to the literature "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro milling threading of the effect of the dead metal zoneInternational Journal of Machine Tools and Manual 146(2019)103452.
Step eight, calculating the length l of the shearing surfacecIn units of millimeters:
step nine, calculating the positive stress p on the shearing surfacecAnd shear stress qcThe unit is megapascal:
step ten, calculating the stress state caused by shearing in the shearing surface coordinate system:
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:
step twelve, calculating the cutting angle of the plough
The unit is degree:
step thirteen, calculating the positive stress p on the plough cutting surfaceeAnd shear stress qeThe unit is megapascal:
step fourteen, calculating the stress state caused by the plough cutting in the coordinate system of the plough cutting surface:
in the formula sigmaxxeIs a positive stress in the abscissa direction, σzzeIs 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.
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 area 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:
wherein the value of parameter C is determined by the following formula:
where e is the natural logarithm.
Eighteen, calculating the stacking length L of the materialspIn units of millimeters:
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 vcAs cutting speed, in units of mm per unitAnd second. dt is the time in units of seconds.
Twenty step, calculating the material stacking height hadIn units of millimeters:
twenty-one step, order 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 of 1 mm diameter with a blunt nose radius of 0.009 mm, a rake angle of 10 degrees and a helix angle of 30 degrees; the cutting material being aluminiumAlloy 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, 0.2 mm axial cut and 0.5 mm radial cut.
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:
in the formula
The unit is the instantaneous tooth position angle of the jth cutting unit of the ith cutter tooth of the milling cutter at the current moment.
And step four, the thickness of the undeformed cuttings at the current time t is h, and the unit is millimeter.
In the formula h1The distance between the lower vertex of the metal dead zone and the blunt round bottom part of the tool nose is in millimeters, and is determined by the method disclosed in the documents "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On-material separation and cutting for prediction of the effect of dead zone by using micro milling and cutting, International Journal of Machine Tools and manufacturing 146 (2019)" 10345210.0021 mm.
Step five, judging the thickness h of the plough cutting action at the momenteAnd shear thickness hcIn units of millimeters:
step six, calculating the tangential shear force F at the momenttcShear force F in the normal directionrcIn newtons:
wherein B is the cutting width in mm, Ktc、Krc、ptc、prc、qtcAnd q isrcFor shear force coefficients, it is determined by the method disclosed in the document "M.Wan, D. -Y.Wen, Y. -C.Ma, W. -H.Zhang, On material separation and cutting for compression in micro fine threading of the effect of the dead metal zone, International Journal of Machine Tools and production 146(2019)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 force FrcIn newtons:
wherein B is the cutting width in mm, Kte、Kre、pte、pre、qteAnd q isreFor the determination of the shear 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 of the effect of the dead metal zone, International Journal of Machine Tools and Manual 146(2019)te＝1182、Kre＝1584、pte＝0.8532、pre＝0.6071、qte＝0.01174、qre＝0.2832。
Step eight, calculating a shearing angle
The unit is degree:
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:
step ten, calculating the positive stress p on the shearing surfacecAnd shear stress qcThe unit is megapascal:
step eleven, calculating a stress state caused by shearing in a shearing plane coordinate system:
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 twelve, calculating the length l of the section of the plougheIn units of millimeters:
thirteen step, calculating the cutting angle of the plough
The unit is degree:
step fourteen, calculating the normal stress p on the plough cutting surfaceeAnd shear stress qeThe unit is megapascal:
step fifteen, calculating the stress state caused by the plough cutting in the plough cutting plane coordinate system:
in the formula sigmaxxeIs a positive stress in the abscissa direction, σzzeIs 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:
wherein the value of parameter C is determined by the following formula:
where e is the natural logarithm.
Nineteen steps of calculating the stacking length L of the materialspIn units of millimeters:
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 the time in units of seconds.
Twenty one step, calculating the material stacking height hadIn units of millimeters:
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 repeating the steps from three to twenty-three 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 fig. 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 in the cutting process is 5000 revolutions per minuteTooth feed amount of fzThe theoretical prediction results of cutting force when the axial cutting depth is 0.0005 mm, the axial cutting depth is 0.2 mm, and the radial cutting depth is 0.5 mm, refer to 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;
step 2: let the theoretical undeformed chip thickness of the cutting process at time t be h0(ii) a The compensation value h of the thickness of the undeformed chip is set to 0 at the initial time tad0Bulk volume of material V ═ 0p0＝0；
And step 3: the undeformed chip thickness at the current time t is h:
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：
And 5: the tangential shear force F at this time was calculatedtcShear force F in the normal directionrc：
Wherein B is the cutting width, Ktc、Krc、ptc、prc、qtcAnd q isrcIs the shear force coefficient;
step 6: calculating the tangential plowing and shearing force F at the momenttcNormal plough force Frc：
Wherein B is the cutting width, Kte、Kre、pte、pre、qteAnd q isreIs the plough shear coefficient;
and 7: calculating the shear angle
In the formula betaeIs the angle of friction, αeIs an equivalent rake angle;
and 8: calculating the shear plane length lc：
And step 9: calculating the positive stress p on the shear planecAnd shear stress qc：
Step 10: calculating the stress state caused by shearing in a shearing plane coordinate system:
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 plough sectione：
Step 12: calculating plough cutting angle
Step 13: calculating the normal stress p on the cutting surface of the plougheAnd shear stress qe：
Step 14: calculating the stress state caused by the cutting in the cutting plane coordinate system:
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 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 area according to the 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:
wherein the value of parameter C is determined by the following formula:
wherein e is a natural logarithm;
step 18: calculating the material stacking length Lp：
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：
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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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114429065A (en) * | 2022-01-07 | 2022-05-03 | 西北工业大学 | Springback calibration method of flank contact material in micro-milling process based on finite element |
| CN114492013A (en) * | 2022-01-07 | 2022-05-13 | 西北工业大学 | A damping modeling method for micro-milling process considering metal dead space and material springback |
| CN115730399A (en) * | 2022-11-05 | 2023-03-03 | 西北工业大学 | Micro-milling cutting force modeling method considering cutter deformation influence |
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| CN114492013A (en) * | 2022-01-07 | 2022-05-13 | 西北工业大学 | A damping modeling method for micro-milling process considering metal dead space and material springback |
| CN114429065B (en) * | 2022-01-07 | 2024-02-23 | 西北工业大学 | Method for calibrating rebound of contact material of rear tool face in micro-milling process based on finite element |
| CN115730399A (en) * | 2022-11-05 | 2023-03-03 | 西北工业大学 | Micro-milling cutting force modeling method considering cutter deformation influence |
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