CN111651867A - Method for determining ultimate shear stress of chip formation in cutting machining - Google Patents

Method for determining ultimate shear stress of chip formation in cutting machining Download PDF

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CN111651867A
CN111651867A CN202010412092.XA CN202010412092A CN111651867A CN 111651867 A CN111651867 A CN 111651867A CN 202010412092 A CN202010412092 A CN 202010412092A CN 111651867 A CN111651867 A CN 111651867A
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项俊锋
李晨
易万军
刘道新
张晓化
林钰
刘涛
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Northwestern Polytechnical University
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Abstract

The invention discloses a method for determining ultimate shear stress formed by cutting chips in cutting machining, which is characterized by comprising the steps of defining an action area of a cutter-chip contact interface according to the chip shear stress, calculating an upper boundary of yield shear stress in the chips through a von Mises criterion, establishing a cutter-chip contact simplified model according to a Hertz contact theory, and calculating chip stress distribution with a small friction coefficient or no friction action under the action of normal load according to a contact mechanics theory. A chip stress model based on a plane strain state is established by applying a Hertz contact theory, a scientific basis is provided for defining the ultimate shear stress in the chip forming process, the shear stress of a contact surface of a cutter and a chip is defined as the ultimate shear stress of a material according to the distribution of the maximum shear stress of the chip, and the chip formation in the cutting machining simulation is accurately predicted.

Description

Method for determining ultimate shear stress of chip formation in cutting machining
Technical Field
The invention belongs to the technical field of cutting machining simulation, and particularly relates to a method for determining ultimate shear stress formed by cutting in cutting machining.
Background
The cutting simulation technology plays an irreplaceable role in researching a cutting mechanism, optimizing a cutting machining process and improving the structure design of a cutter, and is an important means for deducing an advanced machining theory and technical development.
A reasonably determined ultimate shear stress is important for the cutting model, which has a great influence on the chip form and the simulation quality in different friction states, and when the friction coefficient is relatively small, the maximum shear stress is below the contact surface, and if the ultimate shear stress is defined by the maximum shear stress, the material below the contact surface fails before the surface material reaches the limit value, so that the accurate definition of the ultimate shear stress is very important, while in the prior art, the chip formation is always the most difficult part of the cutting process simulation because: the ultimate shear stress of the chip and the contact part of the cutter is difficult to be scientifically defined, and the prior art lacks suitable criteria and determination methods for the ultimate shear stress in the chip forming process.
Disclosure of Invention
The invention aims to provide a method for determining ultimate shear stress in chip formation in cutting machining, which aims to solve the problem that the ultimate shear stress in the chip formation process in the prior art lacks of a proper criterion and determination method.
In order to achieve the purpose, the invention provides the following technical scheme: a method of determining ultimate shear stress for chip formation in cutting machining, comprising the steps of:
step one, defining an action area of a tool-chip contact interface according to chip shear stress;
in the cutting area, the position near the tool tip is the adhesion area, and the shear stress taufEqual to the yield shear stress tau of the materialcritAnd in the sliding region away from the nose, the frictional stress is lower than the yield shear stress, and different contact areas between the tool and the chip are determined according to equation (1);
Figure BDA0002493649330000011
where μ is the coefficient of friction, p is the positive pressure, σ is the flow stress, and m is the shear coefficient;
step two, calculating an upper boundary of yield shear stress in the chip through a von Mises criterion;
calculating the upper bound of yield shear stress by von Mises criterion
Figure BDA0002493649330000021
Wherein σ1、σ2、σ3Is the principal stress of the material, σY、τYRespectively representing the yield stress of the material in a tension-compression mode and a shearing mode;
step three, establishing a tool-chip contact simplified model according to a Hertz contact theory;
fourthly, calculating the stress distribution of the chips with small friction coefficient or without friction under the action of normal load according to the contact mechanics theory;
according to the contact mechanics theory, under normal load PcUnder the action, the stress distribution in the chip when the friction coefficient is small or no friction action can be calculated according to the formula (3)
Figure BDA0002493649330000022
Wherein σx、σy、σzFlow stresses in the x, y, z directions, τ, respectivelyxzIs a shear stress, x, y, z are severalWhich coordinates, a is the physical coefficient associated with the state of the contact surface, m1、n1As an intermediate variable, ν is the poisson's ratio, subscript p is the stress component due to positive pressure;
the principal stress of the chip contact zone in the in-plane strain state can be expressed as in equation (4)
Figure BDA0002493649330000023
Step five, calculating the stress distribution of the chips under the friction condition under the action of a tangential load according to a Hertz contact theory;
under frictional conditions, tangential force QcThe stress field distribution in the acting chip can be expressed according to equation (5) as
Figure BDA0002493649330000031
Wherein q is0As tangential friction, q0＝μp0Subscripts p and q denote stress components caused by positive pressure and tangential friction, respectively;
according to the theoretical assumption of Hertz that the tangential friction does not influence the normal stress, the stress field distribution in the XZ plane in the presence of friction can be expressed as
Figure BDA0002493649330000032
Step six, defining the ultimate shear stress for the friction state with the maximum stress not at the contact surface of the cutter and the chip;
preferably, the specific implementation method of the shear stress in the step two is as follows:
step 2.1: determining yield stress, strain hardening index and strain hardening coefficient in the constitutive model by a Hopkinson pressure bar test at normal temperature and a regression analysis method;
step 2.2: determining the strain rate sensitivity coefficient in the constitutive model by combining a regression analysis method under Hopkinson torsion bar tests at different high strain rates at normal temperature;
step 2.3: and obtaining the thermal softening coefficient in the constitutive model through weighted minimum fitting under different strain rates at different temperatures.
Preferably, the specific implementation method of step 2.3 is as follows:
step 2.3.1: on the basis of different high strain rates in the step 2.2, determining test temperatures under different strain rates by adopting a cross replacement mode according to the equal division temperature of the material melting point N, and then performing a Hopkinson torsion bar test;
step 2.3.2: filtering the high strain rate test data, and carrying out data point N on each test working conditioniMaking statistics, and dividing each group of working condition curves by Ni 2Minimization, multiple local minima are compared to determine the coefficient of thermal softening in the constitutive model.
Preferably, the specific implementation method of the step three is as follows:
step 3.1: modeling the relative movement of the chip and the tool, with the workpiece fixed and the tool at a cutting speed VcA cutting movement from right to left;
step 3.2: and establishing a contact mechanical model of the cutting chips and the cutter according to the Hertz contact theory.
Preferably, the specific implementation method of step 3.1 is as follows:
step 3.1.1: a infinitesimal part of a tool-chip contact interface is selected for research, and the relative sliding speed is VchipNormal force per unit length of Pc；
Step 3.1.2: a reasonable simplification is made to the tool-chip contact model, which contains a flat slide with constant chip flow velocity V along a curved profilechipMoving from left to right.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a method for determining ultimate shear stress for chip formation in cutting machining, which has general universality by considering the condition that the ultimate shear stress is matched with a tool and a cutting contact friction state, is suitable for but not limited to the field of cutting machining, and can also be applied to the field of material forming.
The invention provides a method for determining the ultimate shear stress of chip formation in cutting machining, which differentiates chips along a contact interface of a cutter and the chips, establishes a chip stress model based on a plane strain state by applying a Hertz contact theory, provides a scientific basis for defining the ultimate shear stress in the chip formation process, can define the shear stress of a cutter-chip contact surface as the ultimate shear stress of a material according to the distribution of the maximum shear stress of the chips, accurately predicts the chip formation in cutting machining simulation, provides the precision of simulation, and solves the problem that the ultimate shear stress in the chip formation process lacks a proper criterion and a determination method.
Drawings
FIG. 1 is a schematic diagram of the cutting area division of the present invention;
FIG. 2 is a schematic illustration of the sliding and sticking area division at the chip and tool contact interface of the present invention;
FIG. 3 is a schematic view of the tool-chip planar contact of the present invention;
FIG. 4 is a schematic view of the tool-chip two cylinder contact of the present invention;
FIG. 5 is a general flow diagram of the present invention;
FIG. 6 is a schematic diagram of the distribution of shear stress in the chip contact zone at coefficients of friction of 0, 0.15, 0.3, 0.45, 0.56, 0.7, respectively, in accordance with the present invention;
FIG. 7 is a schematic diagram of the predicted chip morphology of the orthogonal free turning model of the present invention;
FIG. 8 is a schematic of the experimental chip morphology of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
A method for determining ultimate shear stress for chip formation in cutting machining, with reference to fig. 1, 2, 3, 4 and 5, comprising the steps of:
step one, defining an action area of a cutter-chip contact interface according to the chip shear stress of the silicon carbide aluminum-based composite material.
In the cutting area, the position near the tool tip is the adhesion area, and the shear stress taufEqual to the yield shear stress tau of the silicon carbide aluminium-based composite materialcritWhereas in the sliding region away from the nose, the frictional stress is lower than the yield shear stress, the different contact areas between tool and chip are determined according to equation (1)
Figure BDA0002493649330000051
And step two, calculating the upper boundary of the yield shear stress in the silicon carbide aluminum-based composite material chip through the von Mises criterion.
Calculating the upper bound of yield shear stress by von Mises criterion
Figure BDA0002493649330000052
Wherein σ1、σ2、σ3Is the principal stress of the material, σY、τYThe yield stress of the material under the tension-compression and shear modes is respectively due to sigmaYTemperature, strain rate line dependent, and therefore the chip shear stress τYAlso with temperature, strain rate.
In cutting processing, the strain rate and temperature change of the silicon carbide aluminum-based composite material are large, and the shear stress at different positions of the silicon carbide aluminum-based composite material is obtained by uniaxial mechanical tests under different temperatures and strain rates of the silicon carbide aluminum-based composite material.
The concrete implementation method of the shear stress in the second step comprises the following steps:
step 2.1: and determining the yield stress, the strain hardening index and the strain hardening coefficient in the silicon carbide aluminum-based composite material constitutive model by a Hopkinson pressure bar test at normal temperature and a regression analysis method.
Step 2.2: and determining the strain rate sensitivity coefficient in the silicon carbide aluminum-based composite material constitutive model by combining a regression analysis method under Hopkinson torsion bar tests at different high strain rates at normal temperature.
Step 2.3: and obtaining the thermal softening coefficient in the silicon carbide aluminum-based composite material constitutive model through weighted minimum fitting under different strain rates at different temperatures.
The specific implementation method of the step 2.3 is as follows:
step 2.3.1: and 2.2, on the basis of different high strain rates in the step 2.2, determining the test temperature under different strain rates by adopting a cross replacement mode according to the equal division temperature of the melting point N of the silicon carbide aluminum-based composite material, and then performing a Hopkinson torsion bar test on the silicon carbide aluminum-based composite material.
Step 2.3.2: for high strain rate (10-10)4s-1) Filtering the test data to obtain data point N of each test conditioniMaking statistics, and dividing each group of working condition curves by Ni 2Minimization, a comparison is made of a number of possible local minima to determine the coefficient of thermal softening in the constitutive model.
And step three, differentiating the chips along the contact interface of the cutter and the chips, and establishing a cutter-chip contact simplified model according to the Hertz contact theory.
The specific implementation method of the step 3 is as follows:
step 3.1: and establishing a relative motion model of the chip and the cutter, fixing the workpiece, and performing cutting motion on the cutter from the right to the left at a cutting speed of 200 m/s.
The specific implementation method of the step 3.1 is as follows:
step 3.1.1: analyzing the contact mechanical conditions of the cutter and the chip, namely selecting a infinitesimal of a cutter-chip contact interface for research, wherein the relative sliding speed is from 0 to 172.7m/s according to different positions, and the normal force of the unit length is 27.3N/mm.
Step 3.1.2: a reasonable simplification is made to the tool-chip contact model, which contains a flat slide with constant chip flow velocity V along a curved profilechipMoving from left to right.
Step 3.2: and establishing a contact mechanical model of the cutting chips and the cutter according to the Hertz contact theory.
For frictionless elastic contacts, the contact problem can be solved by hertzian theory when the contact size is small compared to the size of the contact body.
According to the hertzian contact theory, the problem of plane strain corresponds to the contact between two cylinders, the contact pressure is distributed in a semiellipse between [ -1.72, 1.72] along the contact surface, and the maximum pressure at the contact center is 673 MPa.
And step four, calculating the stress distribution of the chips with small friction coefficient or without friction under the action of normal load according to the contact mechanics theory.
According to the contact mechanics theory, under normal load PcUnder the action, the stress distribution in the chip when the friction coefficient is small or no friction action can be calculated according to the formula (3)
Figure BDA0002493649330000071
Wherein α is 0.7, σx、σy、σzFlow stresses in the x, y, z directions, τ, respectivelyxzIs shear stress, x, y, z are geometric coordinates, a is a physical coefficient related to the state of the contact surface, and m1、n1For intermediate variables, v is the poisson ratio, and subscript p is the stress component due to positive pressure;
the principal stress of the chip contact zone in the in-plane strain state can be expressed as in equation (4)
Figure BDA0002493649330000072
And step five, calculating the stress distribution of the chips under the friction condition under the action of the tangential load according to the contact mechanics theory.
The stress field distribution in the chip under the frictional condition, in which a unit tangential force acts, can be expressed as in equation (5)
Figure BDA0002493649330000081
Wherein q is0As tangential friction, q0＝μp0The subscripts p and q indicate the stress components caused by positive pressure and tangential friction, respectively.
According to the theoretical assumption of Hertz that the tangential friction does not influence the normal stress, the stress field distribution in the XZ plane in the presence of friction can be expressed as
Figure BDA0002493649330000082
And step six, calculating the shear stress distribution of the chip-cutter contact area under different friction coefficients according to the step four and the step five, defining the shear stress of the chip-cutter contact surface as the limit shear stress of the maximum shear stress of the friction coefficient which is not positioned at the chip-cutter contact surface of the cutter, and performing cutting simulation analysis after the maximum shear stress is defined.
Referring to FIG. 6, the shear stress distribution at the chip contact zone is such that when the coefficients of friction are 0, 0.2, 0.3, 0.4, 0.5, 0.6, respectively, the maximum shear stress is below the contact surface under frictionless conditions, which is located approximately 0.3877 α p below the contact surface0When the coefficient of friction is 0.2, the maximum shear stress increases and shifts upward, and when the coefficient of friction further increases to 0.56, the maximum shear stress position gradually shifts toward the tool-chip contact surface, and the surface maximum contact stress is 0.577 α p0At which the contact surface shear stress is at a maximum and equal to
Figure BDA0002493649330000083
The maximum shear stress position of the material of (a) is not changed when the coefficient of friction is 0.6, and in summary, it is necessary to define the tool-chip contact surface shear stress as its ultimate shear stress when the chip-tool coefficient of friction is less than 0.5.
Referring to fig. 7 and 8, the accuracy and reliability of the method are verified, and the chip formation and the chip morphology can be successfully and accurately predicted.
During implementation, the chip is differentiated along a contact interface between the cutter and the chip, a chip stress model based on a plane strain state is established by applying a Hertz contact theory, a scientific basis is provided for defining the ultimate shear stress in the chip forming process, the shear stress of the contact surface between the cutter and the chip is defined as the ultimate shear stress of a material according to the distribution of the maximum shear stress of the chip, the chip formation in the cutting process simulation is accurately predicted, and the precision of simulation is provided.

Claims (5)

1. A method for determining ultimate shear stress for chip formation in cutting machining, comprising the steps of:
step one, defining an action area of a tool-chip contact interface according to chip shear stress;
in the cutting area, the position near the tool tip is the adhesion area, and the shear stress taufEqual to the yield shear stress tau of the materialcritWhereas in the sliding region away from the nose, the frictional stress is lower than the yield shear stress, the different contact areas between tool and chip are determined according to equation (1)
Figure FDA0002493649320000011
Where μ is the coefficient of friction, p is the positive pressure, σ is the flow stress, and m is the shear coefficient;
step two, calculating an upper boundary of yield shear stress in the chip through a von Mises criterion;
calculating the upper bound of yield shear stress by von Mises criterion
Figure FDA0002493649320000012
Wherein σ1、σ2、σ3Is the principal stress of the material, σY、τYRespectively representing the yield stress of the material in a tension-compression mode and a shearing mode;
step three, establishing a tool-chip contact simplified model according to a Hertz contact theory;
fourthly, calculating the stress distribution of the chips with small friction coefficient or without friction under the action of normal load according to the contact mechanics theory;
according to the contact mechanics theory, under normal load PcUnder the action, the stress distribution in the chip when the friction coefficient is small or no friction action can be calculated according to the formula (3)
Figure FDA0002493649320000013
Wherein σx、σy、σzFlow stresses in the x, y, z directions, τ, respectivelyxzIs shear stress, x, y, z are geometric coordinates, a is a physical coefficient related to the state of the contact surface, and m1、n1For intermediate variables, v is the poisson ratio, and subscript p is the stress component due to positive pressure;
the principal stress of the chip contact zone in the in-plane strain state can be expressed as in equation (4)
Figure FDA0002493649320000021
Step five, calculating the stress distribution of the chips under the friction condition under the action of a tangential load according to a Hertz contact theory;
under frictional conditions, tangential force QcThe stress field distribution in the acting chip can be expressed according to equation (5) as
Figure FDA0002493649320000022
Wherein q is0As tangential friction, q0＝μp0Subscripts p and q denote stress components caused by positive pressure and tangential friction, respectively;
according to the theoretical assumption of Hertz that the tangential friction does not influence the normal stress, the stress field distribution in the XZ plane in the presence of friction can be expressed as
Figure FDA0002493649320000023
And step six, defining the ultimate shearing stress for the friction state with the maximum stress not positioned at the contact surface of the cutter and the chip.
2. A method of determining ultimate shear stress for chip formation in cutting machining according to claim 1, characterized in that: the concrete implementation method of the shear stress in the second step comprises the following steps:
step 2.1: determining yield stress, strain hardening index and strain hardening coefficient in the constitutive model by a Hopkinson pressure bar test at normal temperature and a regression analysis method;
step 2.2: determining the strain rate sensitivity coefficient in the constitutive model by combining a regression analysis method under Hopkinson torsion bar tests at different high strain rates at normal temperature;
step 2.3: and obtaining the thermal softening coefficient in the constitutive model through weighted minimum fitting under different strain rates at different temperatures.
3. A method for determining the ultimate shear stress for chip formation in machining operations according to claim 2, characterized in that step 2.3 is embodied by:
step 2.3.1: on the basis of different high strain rates in the step 2.2, determining test temperatures under different strain rates by adopting a cross replacement mode according to the equal division temperature of the material melting point N, and then performing a Hopkinson torsion bar test;
step 2.3.2: filtering the high strain rate test data, and carrying out data point N on each test working conditioniMaking statistics, and dividing each group of working condition curves by Ni 2Minimization, multiple local minima are compared to determine the coefficient of thermal softening in the constitutive model.
4. The method for determining the ultimate shear stress for chip formation in cutting machining according to claim 1, wherein the third step is realized by the following specific method:
step 3.1: modeling the relative movement of the chip and the tool, with the workpiece fixed and the tool at a cutting speed VcA cutting movement from right to left;
step 3.2: and establishing a contact mechanical model of the cutting chips and the cutter according to the Hertz contact theory.
5. A method for determining ultimate shear stress for chip formation in machining operations according to claim 4, characterized in that the method embodied in step 3.1 is:
step 3.1.1: a infinitesimal part of a tool-chip contact interface is selected for research, and the relative sliding speed is VchipNormal force per unit length of Pc；
Step 3.1.2: a reasonable simplification is made to the tool-chip contact model, which contains a flat slide with constant chip flow velocity V along a curved profilechipMoving from left to right.
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