CN110472308B - Metal cutting tool nose dead zone shape prediction method considering metal slippage - Google Patents

Metal cutting tool nose dead zone shape prediction method considering metal slippage Download PDF

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CN110472308B
CN110472308B CN201910686604.9A CN201910686604A CN110472308B CN 110472308 B CN110472308 B CN 110472308B CN 201910686604 A CN201910686604 A CN 201910686604A CN 110472308 B CN110472308 B CN 110472308B
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dead zone
angle
tool
tool nose
blunt circle
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CN110472308A (en
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万敏
温丹阳
张卫红
杨昀
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Northwestern Polytechnical University
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Abstract

The invention relates to a method for completely theoretically calculating dead zone morphology by utilizing a metal slip line theory. Then, the front angle and the friction angle of each position on the blunt circle of the tool nose need to be calculated, and then the front angle and the friction angle are obtainedThe shear angle at each location is the shear direction of the metal. And then, obtaining the friction coefficient of each position by using the friction angle, and further solving the included angle between the metal slip line and the plastic boundary, namely the included angle between the boundary line of the dead zone and the cutter point obtuse circle. The boundary line of the metal shearing direction and the dead zone is collinear, and then the dead zone vertex S on the blunt circle of the tool nose can be solved1And S2The position of (a). Determine the vertex S1And S2Whether or not there is a post, using vertex S1And S2The included angle between the boundary line of the two dead regions and the obtuse circle of the tool nose, and the vertex S is obtained through the derivation of the geometrical relationship3The shape of the dead area of the tool nose can be completely determined. The complete shape of the dead zone of the tool nose can be predicted through complete theoretical calculation without any factor needing to be given manually.

Description

Metal cutting tool nose dead zone shape prediction method considering metal slippage
Technical Field
The invention relates to a method for predicting the flowing condition of metal at a tool nose in a cutting process, in particular to a dead zone shape prediction method for forming a dead zone by metal staying at the tool nose under the condition of considering the obtuse circle of the tool nose.
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 equivalent to the blunt circle radius of the cutting tip, and the blunt circle influence is not negligible. At this time, the metal is retained near the blade to form a dead zone. The metal has different flowing speeds inside and outside the dead zone, namely, the flowing speed is discontinuous in the normal direction of the dead zone boundary, which indicates that the dead zone boundary line is a slip line. The existence of the dead zone causes the metal flow to be more complicated, so the appearance of the dead zone of the metal tool nose needs to be accurately predicted to ensure the accuracy of modeling in the cutting process.
Document 1 "D.J.Waldorf, R.E.DeVor, S.G.Kapor, A slip-line field for relating to dead zone of the nose, Journal of Manufacturing Science and Engineering 120(4) (1998) 693-699" discloses a simple slip line model taking into account the dead zone of the nose, which theoretically predicts the apex S of the dead zone of the nose using the theory of metal plasticity1And S3(see figure 1). But inThe unpredicted vertex S in the model2And the boundary S of the dead zone1S3And S2S3Is considered to be the boundary of the metal plastic deformation region, not the slip line.
Document 2 "s.ozturn, e.altan, a slip-line approach to The machining with rounded-edge tool, The International Journal of Advanced Manufacturing Technology 63(5-8) (2012) 513-. But in its model, the vertex S of the dead zone1And S2Are selected manually.
Typical features of the above documents are: when the dead zone of the tool tip is modeled, the dead zone boundary is not considered as a slip line, or the model contains components needing to be selected manually, so that theoretical explanation cannot be achieved.
Disclosure of Invention
Technical problem to be solved
In order to solve the problem that partial content needs to be manually selected when the dead zone of the tool tip is modeled by the conventional method, the invention provides a method for completely theoretically calculating the dead zone morphology by using a metal slip line theory.
Technical scheme
A metal cutting tool nose dead zone morphology prediction method considering metal slippage is characterized by comprising the following steps:
step 1: let the distance from an unknown point on the blunt circle of the tool tip to the lowest point of the blunt circle be hsThe rake angle alpha at the unknown point on the blunt circle of the tool nose is determinedsExpressed as:
Figure BDA0002146551310000021
wherein r iseThe radius of a tool point blunt circle of a cutting edge of a tool used for microscopic observation;
will shear angle phisExpressed as:
φs＝45°-(βs-αs)
wherein, betasIs the rubbing angle at the unknown point;
step 2: solving the following formula to obtain the included angle omega between the slip line at the unknown point and the obtuse tangent of the tool nosesAbout hsExpression (c):
Figure BDA0002146551310000022
and step 3: under the following conditions:
-90°<αs<90°
solving the following equation:
cot(φs)+cot(180°-φs-ωs)＝∞
two are obtainedsValue, where the smaller is denoted as h1Larger is denoted as h2Respectively represent dead zone vertices S1And S2Distance to the lowest point of the blunt circle;
and 4, step 4: calculating S according to step 11And S2Front angle of (a)1And alpha2(ii) a If the following conditions are satisfied:
α<α1
no dead zone exists; wherein α is the tool rake angle; if the following conditions are satisfied:
α1<α<α2
then h is2The substitution is calculated from the following formula:
Figure BDA0002146551310000031
in the formula, h is the current instantaneous unmodified chip thickness, beta is the friction angle of the cutting process, phi is the shearing angle of the cutting process, and alpha is replaced by the formula given in the step 1sIs alpha, betasIs calculated as beta;
and 5: calculating the distance h from the separation position of the chip and the rake face to the lowest point of the blunt circle of the tool nose by adopting the following formulac：
Figure BDA0002146551310000032
In the formula, alphaeTo an equivalent rake angle, hlimCritical unmodified chip thickness;
step 6: if the following conditions are satisfied:
hc<h1
no dead zone exists; if the following conditions are satisfied:
h1<hc<h2
then h is2The substitution is calculated from the following formula:
h2＝hc
and 7: in the presence of a dead zone, the dead zone vertex S3Distance h to the lowest point of the blunt circle of the tool nose3The calculation process of (2) is as follows:
∠S1OS2＝-α2+α1
Figure BDA0002146551310000033
∠S1S3S2＝360°-∠S1OS2-(ω1+90°)-(ω2+90°)
Figure BDA0002146551310000041
Figure BDA0002146551310000042
Figure BDA0002146551310000043
Figure BDA0002146551310000044
in the formula, angle S1OS2、
Figure BDA0002146551310000045
∠S1S3S2、
Figure BDA0002146551310000046
And < S1OS3Is a geometric parameter.
Advantageous effects
The invention provides a method for completely theoretically calculating dead zone morphology by using a metal slip line theory. The method firstly needs to determine the radius of the blunt tip circle of the used tool through measurement. Then, the front angle and the friction angle of each position on the tool nose blunt circle need to be calculated, and then the shearing angle of each position, namely the metal shearing direction, is obtained. And then, obtaining the friction coefficient of each position by using the friction angle, and further solving the included angle between the metal slip line and the plastic boundary, namely the included angle between the boundary line of the dead zone and the cutter point obtuse circle. The boundary line of the metal shearing direction and the dead zone is collinear, and then the dead zone vertex S on the blunt circle of the tool nose can be solved1And S2The position of (a). Determine the vertex S1And S2Whether or not there is a post, using vertex S1And S2The included angle between the boundary line of the two dead regions and the obtuse circle of the tool nose, and the vertex S is obtained through the derivation of the geometrical relationship3The shape of the dead area of the tool nose can be completely determined.
According to the method, the direction of a slip line and the material shearing direction of each point on the blunt circle of the tool tip can be obtained through complete theoretical calculation through input machining parameters and geometrical parameters of the tool, the vertex of a dead zone on the arc of the tool tip can be obtained through solving the point which meets the coincidence of the two directions and judging the existence relation of the two points, and then the complete morphology of the dead zone is obtained through the geometrical relation. Compared with the literature 1, the dead zone boundary is regarded as the slip line, the theoretical explanation is more reasonable, and the vertex S can be predicted2. Compared with the document 2, the method can avoid the interference of human factors, and the calculation result is more accurate.
Drawings
Figure 1 is a geometric schematic view of the nose dead zone of the present invention.
FIG. 2 is a comparison of the predicted tool tip dead zone vertex position and the finite element simulation position when the tool with the tool tip blunt circle of 0.02mm and the rake angle of 5 degrees is used in the invention.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the tool nose dead zone shape prediction method provided by the invention can predict the complete shape of the tool nose dead zone through complete theoretical calculation without any factor needing to be given manually.
The method specifically comprises the following steps:
step one, microscopically observing the radius r of a blunt circle of a cutting edge and a tool tip of a used tooleIn millimeters, and a tool rake angle α in degrees.
Setting the distance from an unknown point on the blunt circle of the tool nose to the lowest point of the blunt circle as hsIn millimeters.
Step three, the rake angle alpha of the unknown point on the tool nose blunt circle is obtainedsExpressed as:
Figure BDA0002146551310000051
step four, adopting the following formula to calculate the shearing angle phi at the unknown pointsAbout hsExpression (c):
φs＝45°-(βs-αs)
φsthe unit is degree. Beta is asThe friction angle at this unknown point was determined by reference to the cutting database disclosed in the references "M.Kaymakci, Z.M.Kilic, Y.Altingtas, Unified cutting for model for turning, ringing, drilling and milling operations, International Journal of Machine Tools and manufacturing 54-55(2012) 34-45".
Fifthly, solving the following formula to obtain an included angle omega between the slip line at the unknown point and the obtuse tangent of the tool nosesAbout hsExpression (c):
Figure BDA0002146551310000052
ωsthe unit is degree.
And a sixth step, combining the fourth step and the fifth step, under the following conditions:
-90°<αs<90°
solving the following equation:
cot(φs)+cot(180°-φs-ωs)＝∞
two are obtainedsValue, where the smaller is denoted as h1Larger is denoted as h2Respectively represent dead zone vertices S1And S2Distance to the lowest point of the blunt circle.
The seventh step, combining the third step to calculate S1And S2Front angle of (a)1And alpha2. If the following conditions are satisfied:
α<α1
there is no dead zone. If the following conditions are satisfied:
α1<α<α2
then h is2The substitution is calculated from the following formula:
Figure BDA0002146551310000061
where h is the current instantaneous unmodified chip thickness. Beta is the friction angle of the cutting process and is determined by reference to the cutting database disclosed in the references "M.Kaymakci, Z.M.Kilic, Y.Altinas, united cutting for model for turning, ringing, drilling and milling operations, International Journal of Machine Tools and manufacturing 54-55(2012) 34-45". Phi is the shear angle of the cutting process, and alpha is replaced by the formula given in the fourth stepsIs alpha, betasCalculated as β.
Eighthly, calculating the distance h from the separation position of the chips and the rake face to the lowest point of the blunt circle of the tool nose by adopting the following formulac：
Figure BDA0002146551310000062
Intermediate effective rake angle alphaeAnd critical unmodified chip thickness hlimThis is determined by reference to the method disclosed in "G.Bissacco, H.N.Handen, J.Slunsky, modeling the cutting edge size effect for the purpose of prediction in micro milling, CIRP Annals-Manufacturing Technology 57(1) (2008)113 and 116".
Ninth, if the following conditions are satisfied:
hc<h1
there is no dead zone. If the following conditions are satisfied:
h1<hc<h2
then h is2The substitution is calculated from the following formula:
h2＝hc
tenth step, in the case of dead zone, dead zone vertex S3Distance h to the lowest point of the blunt circle of the tool nose3The calculation process of (2) is as follows:
∠S1OS2＝-α2+α1
Figure BDA0002146551310000071
∠S1S3S2＝360°-∠S1OS2-(ω1+90°)-(ω2+90°)
Figure BDA0002146551310000072
Figure BDA0002146551310000073
Figure BDA0002146551310000074
Figure BDA0002146551310000075
formula medium angle S1OS2、
Figure BDA0002146551310000076
∠S1S3S2、
Figure BDA0002146551310000077
And < S1OS3Is a geometric parameter.
Example 1:
the finite element simulation is set as a two-dimensional right-angle cutting simulation model of aluminum alloy 7050-T7451, and the cutter is set as a cutter point obtuse circle radius re0.02mm, and a rake angle α of 5 degrees. The friction coefficient of the blunt circle of the tool point and the rake face part of the tool is determined by cutting data disclosed in a right-angle cutting parameter library. The modeling method of the model is described in "X.jin, Y.Altatis, Prediction of micro-milling tools with fine element method," Journal of Materials Processing Technology 212(3), (2012)542 and 552 ".
Step one, setting the distance from an unknown point on a blunt circle of the tool nose to the lowest point of the blunt circle as hs. The rake angle alpha at the unknown point on the blunt circle of the tool nose is determinedsExpressed as:
Figure BDA0002146551310000081
will shear angle phisExpressed as:
φs＝45°-(βs-αs)
angle of friction beta at the unknown pointsAnd determining by referring to a cutting database disclosing a right-angle cutting parameter library.
Second step, under the solutionObtaining the included angle omega between the slip line at the unknown point and the tangent line of the blunt circle of the tool nosesAbout hsExpression (c):
Figure BDA0002146551310000082
thirdly, under the following conditions:
-90°<αs<90°
solving the following equation:
cot(φs)+cot(180°-φs-ωs)＝∞
get the vertex S1Position h10.0023 mm, S2Position h2The thickness of the alloy is 0.0060 mm,
fourthly, calculating to obtain S1And S2Front angle of (a)1-50.29 ° and α2-23.60 °. The following conditions are not satisfied:
α<α1
and the following conditions are not satisfied:
α1<α<α2
fifthly, calculating the distance h from the separation position of the chips and the rake face to the lowest point of the blunt circle of the tool nose by adopting the following formulac：
Figure BDA0002146551310000083
Where h is the current instantaneous unmodified chip thickness. Beta is the friction angle of the cutting process and is determined by reference to the published cutting database. Phi is the shear angle of the cutting process. Intermediate effective rake angle alphaeAnd critical unmodified chip thickness are determined with reference to the cutting database disclosed in the G.Bissacco, H.N.Handen, J.Slunsky, modeling the cutting edge size effect for the purpose of compression in micro milling, CIRP Annals-Manufacturing Technology 57(1 (2008) 113-.
And sixthly, if the following conditions are met:
hc<h1
there is no dead zone. If the following conditions are satisfied:
h1<hc<h2
then h is2The substitution is calculated from the following formula:
h2＝hc
seventh step, in the case of dead zone, dead zone vertex S3Distance h to the lowest point of the blunt circle of the tool nose3The calculation process of (2) is as follows:
∠S1OS2＝-α2+α1
Figure BDA0002146551310000091
∠S1S3S2＝360°-∠S1OS2-(ω1+90°)-(ω2+90°)
Figure BDA0002146551310000092
Figure BDA0002146551310000093
Figure BDA0002146551310000094
Figure BDA0002146551310000095
formula medium angle S1OS2、
Figure BDA0002146551310000096
∠S1S3S2、
Figure BDA0002146551310000097
And < S1OS3A geometric parameter.
The appearance of the dead zone under different instantaneous unmodified chip thicknesses can be obtained by the steps when a cutter with a cutter point blunt circle of 0.02mm and a rake angle of 5 degrees is used, as shown in the attached figure 2. As can be seen from the attached figure 2, the dead zone morphology obtained by calculation of the method can be well matched with the finite element simulation result, and the effect of the method for predicting the dead zone morphology of the extracted cutter tip is proved.

Claims (1)

1. A metal cutting tool nose dead zone morphology prediction method considering metal slippage is characterized by comprising the following steps:
step 1: let the distance from an unknown point on the blunt circle of the tool tip to the lowest point of the blunt circle be hsThe rake angle alpha at the unknown point on the blunt circle of the tool nose is determinedsExpressed as:
Figure FDA0002146551300000011
wherein r iseThe radius of a tool point blunt circle of a cutting edge of a tool used for microscopic observation;
will shear angle phisExpressed as:
φs＝45°-(βs-αs)
wherein, betasIs the rubbing angle at the unknown point;
step 2: solving the following formula to obtain the included angle omega between the slip line at the unknown point and the obtuse tangent of the tool nosesAbout hsExpression (c):
Figure FDA0002146551300000012
and step 3: under the following conditions:
-90°<αs<90°
solving the following equation:
cot(φs)+cot(180°-φs-ωs)＝∞
two are obtainedsValue, where the smaller is denoted as h1Larger is denoted as h2Respectively represent dead zone vertices S1And S2Distance to the lowest point of the blunt circle;
and 4, step 4: calculating S according to step 11And S2Front angle of (a)1And alpha2(ii) a If the following conditions are satisfied:
α<α1
no dead zone exists; wherein α is the tool rake angle; if the following conditions are satisfied:
α1<α<α2
then h is2The substitution is calculated from the following formula:
Figure FDA0002146551300000021
in the formula, h is the current instantaneous unmodified chip thickness, beta is the friction angle of the cutting process, phi is the shearing angle of the cutting process, and alpha is replaced by the formula given in the step 1sIs alpha, betasIs calculated as beta;
and 5: calculating the distance h from the separation position of the chip and the rake face to the lowest point of the blunt circle of the tool nose by adopting the following formulac：
Figure FDA0002146551300000022
In the formula, alphaeTo an equivalent rake angle, hlimCritical unmodified chip thickness;
step 6: if the following conditions are satisfied:
hc<h1
no dead zone exists; if the following conditions are satisfied:
h1<hc<h2
then h is2The substitution is calculated from the following formula:
h2＝hc
and 7: in the presence of a dead zone, the dead zone vertex S3Distance h to the lowest point of the blunt circle of the tool nose3The calculation process of (2) is as follows:
∠S1OS2＝-α2+α1
Figure FDA0002146551300000023
∠S1S3S2＝360°-∠S1OS2-(ω1+90°)-(ω2+90°)
Figure FDA0002146551300000024
Figure FDA0002146551300000025
Figure FDA0002146551300000031
Figure FDA0002146551300000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002146551300000033
∠S1S3S2、
Figure FDA0002146551300000034
and < S1OS3Is a geometric parameter.
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