CN112059723B - Method suitable for rapidly identifying cutting force coefficient of ultrasonic machining - Google Patents

Method suitable for rapidly identifying cutting force coefficient of ultrasonic machining Download PDF

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CN112059723B
CN112059723B CN202010851412.1A CN202010851412A CN112059723B CN 112059723 B CN112059723 B CN 112059723B CN 202010851412 A CN202010851412 A CN 202010851412A CN 112059723 B CN112059723 B CN 112059723B
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陈雪林
丁撼
何道广
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Central South University
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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
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Abstract

The invention discloses a method suitable for rapidly identifying a cutting force coefficient of ultrasonic machining, which comprises the following steps: s1, obtaining actual processing parameters under the ultrasonic vibration auxiliary processing condition according to the ultrasonic vibration auxiliary processing condition; s2, obtaining the shearing stress of the material according to the material shearing stress intensity correction model and the actual processing parameters obtained in the step S1; s3, obtaining the cutting force in the ultrasonic vibration auxiliary processing according to the shearing stress parameter; and S4, obtaining the cutting force coefficient in the ultrasonic vibration auxiliary machining according to the cutting force. According to the invention, the actual processing parameters under the ultrasonic vibration auxiliary processing condition are obtained according to the influence of the ultrasonic vibration on the processing parameters by the ultrasonic vibration auxiliary processing, and the corresponding cutting force and cutting force coefficient are obtained according to the actual processing parameters and the stress correction model, so that the accurate acquisition of the cutting force coefficient in the ultrasonic vibration auxiliary processing is realized, and a powerful basis is provided for the processing analysis under the ultrasonic vibration auxiliary processing condition.

Description

Method suitable for rapidly identifying cutting force coefficient of ultrasonic machining
Technical Field
The invention relates to the field of machining, in particular to a method suitable for rapidly identifying a cutting force coefficient of ultrasonic machining.
Background
The ultrasonic vibration assisted machining can obviously reduce the cutting force and the cutting temperature, improve the stability in machining, prolong the service life of a cutter and improve the machining efficiency, and is widely used for machining various high-strength and high-hardness materials. In order to accurately evaluate the cutting heat in the ultrasonic vibration-assisted machining, it is necessary to accurately obtain the cutting force coefficient in the ultrasonic vibration-assisted machining. The existing cutting force coefficient is obtained through a cutting experiment, and the cutting force and the cutting heat are calculated according to the cutting force coefficient. The cutting force coefficients of different ultrasonic vibration parameters are different, and the cutting parameters under the influence of the ultrasonic vibration also have obvious difference on the cutting force and the heat. The existing cutting force coefficient test cannot realize accurate prediction of cutting force and heat, and therefore the cutting force coefficient in ultrasonic vibration auxiliary machining needs to be accurately obtained.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a method suitable for rapidly identifying the cutting force coefficient of ultrasonic machining, which can accurately acquire the cutting force coefficient under the condition of ultrasonic vibration auxiliary machining.
According to an embodiment of the first aspect of the invention, the method for rapidly identifying the ultrasonic machining cutting force coefficient comprises the following steps:
s1, obtaining actual processing parameters under the ultrasonic vibration auxiliary processing condition according to the ultrasonic vibration auxiliary processing condition;
s2, obtaining the shearing stress of the material according to the material shearing stress intensity correction model and the actual processing parameters obtained in the step S1;
s3, obtaining the cutting force in the ultrasonic vibration auxiliary processing according to the shearing stress parameter;
and S4, obtaining the cutting force coefficient in the ultrasonic vibration auxiliary machining according to the cutting force.
The method for quickly identifying the cutting force coefficient of ultrasonic machining, provided by the embodiment of the invention, at least has the following technical effects: according to the influence of ultrasonic vibration to the processing parameters in the ultrasonic vibration-assisted processing, the actual processing parameters under the ultrasonic vibration-assisted processing conditions are obtained, and the corresponding cutting force and cutting force coefficient are obtained according to the actual processing parameters and the stress correction model, so that the cutting force coefficient in the ultrasonic vibration-assisted processing is accurately obtained, and a powerful basis is provided for the processing analysis under the ultrasonic vibration-assisted processing conditions.
According to some embodiments of the present invention, in step S1, the actual machining parameters include the true cutting speed v and the effective rake angle α of the toolvEffective cutting angle phi of the toolv(ii) a Parameters v, alphavAnd phivThe relationship is as follows:
v＝vt+vv cos(2πfvt+θ)；
vv＝2πfvhv；
vt＝2πnDr；
αv＝α+θ1；
φv＝φ+θ1；
Figure BDA0002644854840000021
wherein h isvAmplitude of ultrasonic vibration, fvThe ultrasonic vibration frequency is alpha, the front angle of the cutter under the condition of no ultrasonic vibration auxiliary processing is alpha, phi is the shear angle under the condition of no ultrasonic vibration auxiliary processing, theta is the phase angle of ultrasonic vibration, and theta is1Is the angle between the cutting speed under the ultrasonic vibration assisted machining and the cutting speed under the ultrasonic vibration-free assisted machining, n is the rotating speed of the workpiece, DrIs the radius of the workpiece.
According to some embodiments of the present invention, the original shear angle of the tool may be obtained by the following formula:
Figure BDA0002644854840000031
where χ is the propagation velocity of sound in the medium, τsIs the shear strength of the material, h is the undeformed chip thickness, vcC is the moving speed of the cutting chip relative to the cutter, c is the specific heat melting of the material, rho is the density of the material, and k is the thermal conductivity coefficient of the material; xi1And xi2Is the influence coefficient of the shear angle.
According to some embodiments of the invention, the chip moves at a speed V relative to the toolcThe relationship of (A) is as follows:
Figure BDA0002644854840000032
according to some embodiments of the invention, the shear stress modification model in step S2 is:
Figure BDA0002644854840000033
wherein
Figure BDA0002644854840000034
Figure BDA0002644854840000035
Figure BDA0002644854840000036
Figure BDA0002644854840000037
Figure BDA0002644854840000038
Tm，Tr，Eu，
Figure BDA0002644854840000039
εvRespectively the melting point, room temperature, ultrasonic vibration energy density, strain rate and strain of the material;
Figure BDA00026448548400000310
is a reference strain rate; a is the yield strength of the material, B is the hardening modulus of the material, C is the strain rate coefficient of the material, n is the hardening coefficient of the material, m is the thermal softening coefficient of the material, and d and e are the influence coefficients of ultrasonic vibration on the stress of the material; t isvIs the temperature of the shear band under ultrasonic vibration; lambda [ alpha ]s，vIs the heat ratio value transferred to a workpiece material under the condition of ultrasonic vibration auxiliary processing, eta is the thermal coefficient of converting strain energy into heat, tau is the shear flow stress of the material in a shear zone, psi is the thermal softening coefficient of the material,
Figure BDA0002644854840000041
is the specific heat capacity of the material; ρ is the density of the material, ctIs the heat transfer coefficient of the material, csIs the specific heat system of the material, h1The cutting depth under ultrasonic vibration-assisted machining.
According to some embodiments of the invention, in step S3, a cutting force in the direction of the ultrasonically-vibrationally-combined cutting velocity may be obtained
Ftc，v＝Fc，v cos(βv-αv)；
Cutting force along ultrasonic vibration composite feeding direction
Ffc，v＝Fc，v sin(βv-αv)；
Cutting force in cutting speed direction
Ftc＝Ffc，v cos(θ1)；
Cutting force in the feed direction
Ffc＝Ffc，v sin(θ1)；
Wherein Fc，vThe resultant of the cutting forces.
According to some embodiments of the invention, the cutting force resultant Fc，vCan be obtained by the following formula:
Figure BDA0002644854840000042
Figure BDA0002644854840000043
Figure BDA0002644854840000044
Figure BDA0002644854840000045
b is the cutting width;
Fs，vis the shear force of the main shear plane.
According to some embodiments of the present invention, in step S4, based on the obtained cutting force parameter, a cutting force coefficient may be obtained according to the following formula:
Figure BDA0002644854840000051
Figure BDA0002644854840000052
Figure BDA0002644854840000053
Figure BDA0002644854840000054
h is the set depth of cut.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic view of a feed direction ultrasonic vibration assisted machining;
FIG. 2 is a schematic view of a feed direction ultrasonic vibration assisted machining cutting;
FIG. 3 is a schematic view of the ultrasonic vibration assisted turning at various cutting speeds;
FIG. 4 is a schematic diagram of cutting speeds in ultrasonic vibration assisted rectangular cutting;
fig. 5 is a schematic view of cutting speed in ultrasonic vibration assisted cutting.
Detailed Description
The method for quickly identifying the cutting force coefficient in ultrasonic machining provided by the embodiment of the invention comprises the following steps:
s1, obtaining actual processing parameters under the ultrasonic vibration auxiliary processing condition according to the ultrasonic vibration auxiliary processing condition;
s2, obtaining the shearing stress of the material according to the material shearing stress intensity correction model and the actual processing parameters obtained in the step S1;
s3, obtaining the cutting force in the ultrasonic vibration auxiliary processing according to the shearing stress parameter;
and S4, obtaining the cutting force coefficient in the ultrasonic vibration auxiliary machining according to the cutting force.
Referring to fig. 1 to 5, in ultrasonic vibration assisted right-angle turning, ultrasonic vibration vibrates in the feed direction of a tool, and the tool machining schematic and the right-angle cutting principle thereof are shown in fig. 1 and 2. The set cutting depth is h, and the ultrasonic vibration amplitude in the feeding direction is hvThe frequency of the ultrasonic vibration in the feed direction is fvThe cutting tool is set to a cutting speed vt. The depth of cut is substantially the same as the feed per tooth for the same tool.
The real cutting speed after the ultrasonic vibration assisted machining is v, the cutting depth is h, and the feed amount is fz。
And f isz＝h+hv sin(2πfvt+θ)。
In ultrasonic vibration-assisted cutting, the undeformed chip thickness is LuThe method comprises the following steps: l isu＝fzDepth of cut (i.e., undeformed chip thickness) h, depending on the relationship between turning and right-angle cutting1Comprises the following steps: h is1＝Lu。
That is, in the ultrasonic vibration assisted cutting, the cutting depth:
h1＝h+hv sin(2πfvt+θ)。
in turning with ultrasonic vibration, the cutting speed v of the tooltUltrasonic vibration velocity vvThe relationship between the cutting speed v of the ultrasonic vibration-assisted lower cutter is shown in fig. 3.
vv＝2πfvhv；
vt＝2πn Dr；
n is the rotation speed of the workpiece, DrIs the radius of the workpiece.
v＝vt+vv cos(2πfvt+θ)；
Theta is a phase angle of the ultrasonic vibration;
the angle between the cutting speed in ultrasonic vibration-assisted machining and the cutting speed in conventional machining (without ultrasonic vibration assistance) is:
Figure BDA0002644854840000071
in ultrasonic vibration right angle cutting, the original rake angle of the cutter is alpha, and the cutting speed v set by the cuttertUltrasonic vibration velocity vvThe relationship between the cutting speed v of the ultrasonic vibration-assisted lower cutter is shown in fig. 4. Effective rake angle alpha of the toolvI.e. the chip flow angle along the tool rake face, is:
αv＝α+θ1
the effective shearing angle of the cutter under the ultrasonic vibration auxiliary processing is as follows:
φv＝φ+θ1。
the shearing angle is determined by cutting parameters, namely material attributes, and according to an analytic model of the shearing angle, the shearing angle under the conventional processing is as follows:
Figure BDA0002644854840000072
where χ is the propagation velocity of sound in the medium, τsH is the undeformed chip thickness (i.e., depth of cut), v is the shear strength of the materialcC is the specific heat melting of the material, rho is the density of the material, and k is the thermal conductivity of the material. Xi1And xi2The material is determined by the thermodynamic properties of the material, can be respectively defined as the influence coefficient of the shear strength on the shear angle, and the influence coefficient of the shear area on the shear angle is determined by the properties of the material and can be obtained through experimental tests.
During ultrasonic vibration assisted machining, there are the following associated speeds: cutting speed V and shear plane moving speed V in ultrasonic vibration auxiliary machinings2. Shear rate (movement of chip relative to workpiece)Velocity) VSSpeed V of movement of the chip relative to the toolcAs shown in fig. 4.
Figure BDA0002644854840000081
Figure BDA0002644854840000082
At an instant of the ultrasonic vibration assisted machining, it can be considered that a conventional cutting process of the tool along a composite speed of the ultrasonic vibration speed and the cutting speed, that is, a material strength change of the sheared area is caused due to a change of the composite speed in the cutting process.
The corrected model of the material shear stress strength is as follows:
Figure BDA0002644854840000083
wherein A, B, C, n and m are parameters in the model respectively and are known quantities, and Tm，Tr，Eu，
Figure BDA0002644854840000084
εvRespectively the melting point, room temperature, ultrasonic vibration energy density, strain rate and strain of the material.
Figure BDA0002644854840000085
For reference to the strain rate, it is constant and is generally taken to be 1. A is the yield strength of the material, B is the hardening modulus of the material, C is the strain rate coefficient of the material, n is the hardening coefficient of the material, and m is the thermal softening coefficient of the material; d and e are influence coefficients of the ultrasonic vibration on the material stress, and can be obtained by an ultrasonic vibration stretching experiment.
Eu＝ρc(VS)2；
Where ρ is the density of the material to be processed, and c is the propagation velocity of sound in the material to be processed.
Strain epsilon and strain rate of shear zone in conventional processing
Figure BDA0002644854840000089
Can be expressed as:
Figure BDA0002644854840000086
Figure BDA0002644854840000087
the thickness of the shear zone under the ultrasonic vibration auxiliary processing is as follows:
Figure BDA0002644854840000088
the strain and strain rate in the ultrasonic vibration assisted machining are respectively as follows:
Figure BDA0002644854840000091
Figure BDA0002644854840000092
in conventional processing:
the temperature of the shear band can be expressed approximately as
Figure BDA0002644854840000093
Where eta is the thermal coefficient of the transformation of strain energy into heat, tau is the shear flow stress of the material in the shear zone, psi is the thermal softening coefficient of the material,
Figure BDA0002644854840000094
is the specific heat capacity of the material. Lambda [ alpha ]sIs the thermal ratio of the workpiece material.
Heat ratio lambda transferred to the workpiece materialsComprises the following steps:
Figure BDA0002644854840000095
wherein R istIs a dimensionless coefficient of heat
Figure BDA0002644854840000096
Where ρ is the density of the material, ctIs the heat transfer coefficient of the material, csIs the specific heat system of the material.
The heat ratio lambda transmitted to the workpiece material under ultrasonic vibration-assisted machining conditions at a certain moment in the ultrasonic vibration-assisted machinings，vIs composed of
Figure BDA0002644854840000097
Wherein the thermal coefficient R is dimensionless under the ultrasonic vibration-assisted processing conditionst，v：
Figure BDA0002644854840000098
The temperature of the shear band under ultrasonic vibration assisted machining conditions can be expressed approximately as
Figure BDA0002644854840000101
According to the relationship among the strain, strain rate, ultrasonic vibration energy density and temperature of the material, cutting parameters and shearing angles, the correction model can be expressed as:
Figure BDA0002644854840000102
finally, the tau is solved according to the relational expressionvThe flow stress in the shear band (shear band) in the ultrasonic vibration assisted machining was determined.
The friction angles under conventional machining were:
Figure BDA0002644854840000103
the friction angle at a certain moment under the ultrasonic vibration-assisted machining is:
Figure BDA0002644854840000104
defining symbolic functions
Figure BDA0002644854840000105
Shear force F along the main shear planes，vComprises the following steps:
Figure BDA0002644854840000111
and b is the cutting width.
Resultant force F of cutting forcec，vComprises the following steps:
Figure BDA0002644854840000112
the cutting force F in the direction of the ultrasonic vibration composite cutting speed istc，vCutting force F in the direction of feed synthesized by ultrasonic vibrationfc，vComprises the following steps:
Ftc，v＝Fc，v cos(βv-αv)
Ffc，v＝Fc，v sin(βv-αv)
coefficient of cutting force k in direction of ultrasonic vibration composite cutting speedtc，vCoefficient of cutting force k in the ultrasonic vibration composite feed directionfc，vIs composed of
Figure BDA0002644854840000113
h is the depth of cut
Figure BDA0002644854840000114
Cutting force F in the direction of cutting speedtcCutting force F in the feed directionfcAre respectively as
Ftc＝Ffc，v cos(θ1)
Ffc＝Ffc，v sin(θ1)
Coefficient of cutting force k in the direction of cutting speed of the tooltcCoefficient of tangential force k in the feed directionfcComprises the following steps:
Figure BDA0002644854840000115
Figure BDA0002644854840000116
in the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example" or "some examples" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (7)

1. A method for rapidly identifying the coefficient of cutting force of ultrasonic machining is characterized by comprising the following steps:
s1, obtaining actual processing parameters under the ultrasonic vibration auxiliary processing condition according to the ultrasonic vibration auxiliary processing condition;
s2, obtaining the shearing stress of the material according to the material shearing stress intensity correction model and the actual processing parameters obtained in the step S1;
s3, obtaining the cutting force in the ultrasonic vibration auxiliary processing according to the shearing stress parameter;
s4, obtaining a cutting force coefficient in the ultrasonic vibration auxiliary machining according to the cutting force;
the shear stress correction model in step S2 is:
Figure FDA0003099330860000011
wherein
Figure FDA0003099330860000012
Figure FDA0003099330860000013
Figure FDA0003099330860000014
Figure FDA0003099330860000015
Figure FDA0003099330860000016
Tm，Tr，Eu，
Figure FDA0003099330860000017
εvRespectively the melting point, room temperature, ultrasonic vibration energy density, strain rate and strain of the material;
Figure FDA0003099330860000018
is a reference strain rate; a is the yield strength of the material, B is the hardening modulus of the material, C is the strain rate coefficient of the material, n is the hardening coefficient of the material, m is the thermal softening coefficient of the material, and d and e are the influence coefficients of ultrasonic vibration on the stress of the material; t isvIs the temperature of the shear band under ultrasonic vibration; lambda [ alpha ]s，vIs the heat ratio value transferred to a workpiece material under the condition of ultrasonic vibration auxiliary processing, eta is the thermal coefficient of converting strain energy into heat, tau is the shear flow stress of the material in a shear zone, psi is the thermal softening coefficient of the material,
Figure FDA0003099330860000021
is the specific heat capacity of the material; rho is the density of the material, ct is the heat transfer coefficient of the material, csIs the specific heat system of the material, h1The cutting depth under ultrasonic vibration-assisted machining.
2. The method for rapidly identifying ultrasonic machining cutting force coefficient according to claim 1, wherein in step S1, the actual machining parameters comprise the real cutting speed v and the effective rake angle α of the toolvEffective cutting angle phi of the toolv(ii) a Parameters v, alphavAnd phivThe relationship is as follows:
v＝vt+vvcos(2πfvt+θ)；
vv＝2πfvhv；
vt＝2πnDr；
αv＝α+θ1；
φv＝φ+θ1；
Figure FDA0003099330860000022
wherein h isvAmplitude of ultrasonic vibration, fvThe ultrasonic vibration frequency is alpha, the front angle of the cutter under the condition of no ultrasonic vibration auxiliary processing is alpha, phi is the shear angle under the condition of no ultrasonic vibration auxiliary processing, theta is the phase angle of ultrasonic vibration, and theta is1Is the angle between the cutting speed under the ultrasonic vibration assisted machining and the cutting speed under the ultrasonic vibration-free assisted machining, n is the rotating speed of the workpiece, DrIs the radius of the workpiece; cutting speed v set by tooltUltrasonic vibration velocity vvAnd the ultrasonic vibration assists the cutting speed v of the lower cutter.
3. The method for rapidly identifying ultrasonic machining cutting force coefficient according to claim 2, characterized in that the original shearing angle of the cutter can be obtained by the following formula:
Figure FDA0003099330860000031
where χ is the propagation velocity of sound in the medium, τsIs the shear strength of the material, h is the undeformed chip thickness, vcC is the moving speed of the cutting chip relative to the cutter, c is the specific heat melting of the material, rho is the density of the material, and k is the thermal conductivity coefficient of the material; xi1And xi2Is the influence coefficient of the shear angle.
4. Method for the rapid identification of the coefficient of cutting force for ultrasonic machining according to claim 3, characterized in that the speed V of the movement of the chip with respect to the toolcThe relationship of (A) is as follows:
Figure FDA0003099330860000032
5. the method for rapidly identifying a coefficient of ultrasonic machining cutting force of claim 1, wherein: in step S3, a
Cutting force along ultrasonic vibration composite cutting speed direction
Ftc，v＝Fc，vcos(βv-αv)；
Cutting force along ultrasonic vibration composite feeding direction
Ffc，v＝Fc，vsin(βv-αv)；
Cutting force in cutting speed direction
Ftc＝Ffc，vcos(θ1)；
Cutting force in the feed direction
Ffc＝Ffc，vsin(θ1)；
Fc，vThe resultant of the cutting forces.
6. The method for rapidly identifying the ultrasonic machining cutting force coefficient according to claim 5, wherein the method comprises the following steps: resultant force of cutting force Fc，vCan be obtained by the following formula:
Figure FDA0003099330860000033
Figure FDA0003099330860000041
Figure FDA0003099330860000042
Figure FDA0003099330860000043
b is the cutting width;
Fs，vis the shear force of the main shear plane.
7. The method for rapidly identifying a cutting force coefficient of ultrasonic machining according to claim 6, wherein in step S4, the cutting force coefficient is obtained according to the following formula according to the obtained cutting force parameter:
Figure FDA0003099330860000044
Figure FDA0003099330860000045
Figure FDA0003099330860000046
Figure FDA0003099330860000047
h is the set depth of cut.
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