CN117034725A - Thermodynamic entropy value resolving method for friction force and heat conduction of milling cutter rear cutter surface under vibration effect - Google Patents
Thermodynamic entropy value resolving method for friction force and heat conduction of milling cutter rear cutter surface under vibration effect Download PDFInfo
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Abstract
The application provides a thermodynamic entropy value resolving method for friction force and heat conduction of a milling cutter rear cutter surface under the action of vibration, and belongs to the technical field of friction thermomechanics in the milling process. The method comprises the following steps: s1, a cutter tooth rear cutter face friction force entropy model under the vibration effect; s2, a resolving method for generating one-dimensional heat conduction entropy of the rear cutter surface in the milling process under the vibration effect; s3, a one-dimensional heat conduction entropy flow solving method for the rear cutter surface in the milling process under the vibration effect. The technical problem that the influence of vibration on friction speed and friction stress in the milling process is not considered in the prior art is solved. The influence of the cutter vibration on the instantaneous milling behavior in the milling process is further considered, and the influence of the cutter vibration on the thermodynamic behavior of a friction system consisting of the rear cutter surface of the cutter tooth and the processing transition surface is further considered by analyzing the instantaneous milling behavior.
Description
Technical Field
The application relates to a thermodynamic entropy value resolving method of milling cutter rear cutter surface friction force and heat conduction, in particular to a thermodynamic entropy value resolving method of milling cutter rear cutter surface friction force and heat conduction under the action of vibration, belonging to the technical field of friction thermomechanics in the milling process.
Background
The efficient milling technology has higher cutting efficiency on the premise of ensuring the processing surface quality of the workpiece, can save the processing cost, and has wide application in the fields of aerospace, automobile manufacturing, die processing and the like at present. However, as the vibration signals of the cutter always change at the moment in the whole milling process, the rear cutter face of the cutter tooth has different instantaneous offset distances along three directions of a workpiece coordinate system, so that the contact relation between the rear cutter face of the cutter tooth and the processing transition surface of the workpiece is changed, the state of a friction system formed by the rear cutter face and the processing transition surface is complex and changeable, and the instantaneous abrasion degree of the rear cutter face is changed in a nonlinear way.
The fundamental reasons for the complex and changeable states of the friction system are that the entropy generation caused by the sub-process of the friction system such as the friction force of the rear tool face and the entropy generation caused by heat conduction can be changed continuously along with the change of the cutting time of the cutter tooth in the whole cutting process. The conventional method generally considers that two modules are subjected to counter grinding, and stable friction variables are adopted to calculate corresponding entropy generation, but in practice, unavoidable milling vibration exists in the milling process, so that the instantaneous contact relation between a rear cutter surface and a processing transition surface can be changed, and friction variables such as friction stress, friction speed and the like are caused to be unstable; and milling is an intermittent cutting process in which teeth are cyclically cut into the workpiece and the entropy of the heat transfer is different for different contact times of individual teeth with the workpiece. Therefore, when the friction force is calculated and entropy caused by heat conduction is generated, the state of the friction system cannot be accurately expressed without considering milling vibration conditions and contact time of the cutter teeth and the workpiece.
However, the prior art does not consider the influence of vibration on friction speed and friction stress in the milling process, and variables in the friction systems not only influence entropy generation caused by friction force, but also further act on a friction interface to influence the heat conduction condition of a clearance surface.
Disclosure of Invention
The following presents a simplified summary of the invention in order to provide a basic understanding of some aspects of the invention. It should be understood that this summary is not an exhaustive overview of the invention. It is not intended to identify key or critical elements of the invention or to delineate the scope of the invention. Its purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later.
In view of the above, in order to solve the technical problem that the influence of vibration on friction speed and friction stress in the milling process is not considered in the prior art, the invention provides a thermodynamic entropy value resolving method of friction force and heat conduction of the rear cutter face of a milling cutter under the vibration effect.
The method for solving the thermodynamic entropy value of the friction force and the heat conduction of the rear cutter surface of the milling cutter under the vibration effect comprises the following steps:
s1, a cutter tooth rear cutter face friction force entropy model under the vibration effect;
s2, a resolving method for generating one-dimensional heat conduction entropy of the rear cutter surface in the milling process under the vibration effect;
s3, a one-dimensional heat conduction entropy flow solving method for the rear cutter surface in the milling process under the vibration effect.
Preferably, the cutter tooth rear cutter face friction force entropy value model under the vibration effect is specifically as follows:
modeling a dynamic cutting process of the high-feed milling cutter under the combined action of cutter tooth errors and vibration, wherein a conversion model of each coordinate system in the simulation is as follows:
any point on the cutter tooth is converted into a conversion relation in a cutting coordinate system under the vibration action by the cutter tooth coordinate system, and the conversion relation is as follows:
[x v y v z v 1] T ＝B 2 B 1 A 1 [x i y i z i 1] T (1)
wherein x is v y v z v For the milling cutter cutting coordinate system under the vibration action, x i y i z i Is a cutter tooth coordinate system;
A 1 for translating the matrix, B 1 B 2 For the rotation matrix:
wherein phi is i Is x i Axis and x c Included angle of axes, ψ i Is y v Axis and y c Included angle of axis omega i Is x i Axis and y c An included angle of the shaft;
the conversion relation of the point from the cutting coordinate system under the vibration action to the workpiece coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 [x v y v z v 1] T (4)
wherein X is g Y g Z g For the object coordinate system, A 2 A 3 Bit shift matrix, B 3 B 4 For the rotation matrix:
Wherein delta 1(t) 、δ 2(t) Respectively the attitude angle delta of the milling cutter (t) In plane x d -o d- y d 、x d -o d- z d Projection angle, a e Milling width for tool, v f For the cutter feed speed, a p Milling depth for tool, r i Radius of gyration of the i-blade point of the blade tooth A x (t)、A y (t)、A z (t) origin of milling cutter cutting coordinate system under vibration along x d 、y d 、z d The offset distances in the direction, W and H, are the width and height of the workpiece respectively;
the conversion relation from any point on the cutter tooth to the workpiece coordinate system through the cutter tooth coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 B 2 B 1 A 1 [x i y i z i 1] T (7)
relative movement velocity v of any point of cutter tooth rear cutter face in workpiece coordinate system r The components are as follows:
wherein H is i Is the trace equation of the rear cutter surface of the cutter tooth, x (t), y (t), and z (t) are the displacements of the rear cutter surface of the cutter tooth in the x, y and z directions at the moment t, v rx (t) is the relative movement speed in the x direction at the moment t, v ry (t) is the relative movement speed in the y direction at the moment t, v rz (t) is the relative movement speed in the z direction at the moment t,representing displacement versus time bias;
wherein v is r For the relative movement speed, v, of any point of the rear cutter surface of the milling cutter in the workpiece coordinate system rx (t) is the relative movement speed in the x direction at the moment t, v ry (t) is time y of tVelocity of relative movement in direction v rz (t) is the relative movement speed in the z direction at time t;
the normal vector components of any point of the rear tool face in the workpiece coordinate system are as follows:
According to the vector angle formula:
the friction speed of any point of the rear cutter surface is as follows:
v m (t)＝-sinε·v r (t) (12)
the friction energy consumption calculation model is constructed by utilizing the energy conversion relation between tool interface atoms and is as follows:
wherein E is the energy absorbed at time t; omega is the atomic forced vibration frequency; a is the lattice constant; h is a Planck constant; k is a Boltzmann constant; t is the temperature rise of an atomic interface;
the work done by the cutter tooth rear cutter face friction force in dt time is as follows:
dW＝μ(x i ,y i ,z i ,t)·F n (x i ,y i ,z i ,t)·v m (x i ,y i ,z i ,t)·dt (14)
wherein F is n (x i ,y i ,z i T) positive pressure applied to one point of the rear cutter surface of the cutter tooth at the moment t:
F n (x i ,y i ,z i ,t)＝σ n (x i ,y i ,z i ,t)·ds(x i ,y i ,z i ) (15)
the three-dimensional space curved surface area is calculated by:
construction of the stress on the flank face of a tooth sigma in the workpiece coordinate system n (x i ,y i ,z i ,t)：
All the work done by the friction force of the cutter face after the cutter teeth are arranged is converted into heat energy, so as to obtain dW=dE v Therefore, the coefficient of friction μ is obtained as:
obtaining friction stress:
the expression of entropy balance per unit volume is:
wherein s is entropy density; t is time; j (J) s Is the entropy flow of the system; sigma (sigma) s Generating entropy in the system;
calculating entropy generation caused by friction force, and representing entropy change of a cutting friction system consisting of a cutter tooth flank face and a machining transition surface;
the expression for entropy generation in thermodynamics is:
wherein J is i Is the ith thermodynamic stream; x is X i Is the ith thermodynamic force;
The expression for the entropy generation caused by the flank friction stress is:
wherein sigma sf Sigma for entropy generation caused by friction stress f T is the thermodynamic force of entropy generation caused by friction stress, E f Is a thermodynamic stream.
Preferably, the resolving method for generating the one-dimensional heat conduction entropy of the rear cutter surface in the milling process under the vibration effect specifically comprises the following steps:
constructing a heat transfer model of a cutter interface formed by a rear cutter surface and a workpiece:
the temperature gradient gradT is:
heat flux density J q The method comprises the following steps:
wherein lambda is the heat conductivity W/m.k;is warmA degree gradient;
assuming that the density of TC4 does not change with temperature, then MATLAB fitting results give the equation for TC4 thermal conductivity with temperature change as:
λ＝-5.934e-9·T 3 +1.272e-5·T 2 +8.023e-3·T+6.069 20≤T≤900 (28)
the equation for the change in TC4 specific heat capacity with temperature is:
c＝-5.343e-8·T 3 +8.661e-5·T 2 +0.1452·T+515.8 20≤T≤900 (29)
the changes of the thermal conductivity, the specific heat capacity and the heat conductivity coefficient along with the temperature are as follows:
the thermal conductivity with temperature equation is:
λ＝99.2+48.78cos(0.005136T)-12.35sin(0.005136T)+7.673cos(2*0.005136T)-22.58sin(2*0.005136T)22≤T≤800-7.616cos(3*0.005136T)-6.303sin(3*0.005136T) (30)
the temperature conductivity coefficient is as follows:
α＝-9.992e-8·T 3 +1.751e-4·T 2 -0.1159·T+48.46 22≤T≤800 (31)
the equation of change of specific heat capacity with temperature is:
c＝0.03255·exp(-((T-831.3)/91.99) 2 )+0.02332·exp(-((T-600.3)/70.43) 2 )-0.01023·exp(-((T-475.7)/138.5) 2 )+0.2759·exp(-((T-626.1)/1051) 2 )22≤T≤800 (32)
the abrasion area and the contact area of the rear cutter surface are equal in value, and according to the abrasion area prediction model:
A＝κ·n a ·v f b ·a p c (33)
wherein the proportionality coefficient κ=2; the index a= -0.3437; b=0.034; c= 0.3462;
total heat on tool contact area q=e f A; heat flux density J into milling cutter and workpiece qt 、J qg Expressed as:
entropy generation caused by heat conduction is expressed as:
let T (z, T) be the temperature function with respect to heat transfer displacement and time, the initial conditions and boundary conditions for the temperature on the cutter tooth and the heat flux density into the cutter tooth are:
the heat transfer equation along the z-direction is:
wherein alpha is the temperature conductivity coefficient m 2 /s，α＝λ/cρ；
Introducing excess temperature deltat=t-T 0 And (3) deforming the one-dimensional heat transfer equation to obtain:
multiplying the two sides of the equation equal sign by-lambda at the same time, deriving z, and changing the derivation order to obtain:
substituting the heat flux density entering the cutter tooth at the time t into the above formula converts the heat transfer equation along the z direction into:
by introducing a variable χ and solving the temperature and the temperature gradient by using a similarity variation method: setting:
changing the heat transfer equation to:
setting:
obtaining:
the general solution to find Z from the above integral is:
and integrating the above steps to obtain:
introducing an error function erf (x) and a residual error function erfc (x), erf (0) =0; erf (≡) =1; the residual error function erfc (x) =1-erf (x); the error function is in the form of:
the form of the error function is taken in equation 48:
substituted erf (0) =0; erf (≡) =1; χ=0, j q ＝J qt ；χ＝∞，J q Solution of =0 to equation 50:
J q ＝J qt [1-erf(χ)] (52)
defined by the heat flux density in fourier heat transfer:
the temperature change is:
The temperature gradient in the z direction is:
entropy generation caused by heat conduction is:
preferably, the method for resolving the one-dimensional heat conduction entropy flow of the rear cutter surface in the milling process under the vibration effect comprises the following steps:
thermodynamically reflecting milling process by entropy production and entropy flow synthesis:
the second scheme is an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor realizes the first scheme of the thermodynamic entropy value resolving method of the friction force and the heat conduction of the rear cutter surface of the milling cutter under the vibration effect when executing the computer program.
A third aspect is a computer readable storage medium, on which a computer program is stored, where the computer program when executed by a processor implements the method for resolving thermodynamic entropy values of friction and heat conduction of a rear face of a milling cutter under the action of vibration as described in the first aspect.
The beneficial effects of the invention are as follows: according to the method, the influence of cutter vibration on the instantaneous milling behavior in the milling process is considered, and the influence of cutter vibration on the thermodynamic behavior of a friction system formed by the rear cutter surface of the cutter tooth and the processing transition surface is further considered by analyzing the instantaneous milling behavior; the patent solves the problem that the prior art does not consider the vibration of the cutter when resolving the entropy value in the milling process. The entropy generation caused by the friction force of the rear tool face on the third deformation area in the milling process under the vibration effect is solved; the method has the advantages that an instantaneous contact relation model of the rear cutter surface of the milling cutter and a workpiece under the vibration action of the cutter is constructed, the instantaneous friction speed of rear cutter surface characteristic points formed by considering the instantaneous vibration speed, the instantaneous milling speed and the feeding speed is solved, the instantaneous friction stress of the rear cutter surface characteristic points is solved, and the problem that the result error caused by entropy generated by the rear cutter surface friction force is larger due to the fact that the friction variable unsteady state change under the vibration is not considered in the prior art is solved. According to the method, an instantaneous heat transfer model of a cutter interface is constructed, the heat transfer process of the heat generated by a third deformation area in milling on the cutter teeth and the workpiece is considered, the characteristic that the physical performance parameters of the cutter teeth and the workpiece change along with the temperature is considered, the heat flow density entering the cutter teeth and the workpiece under the condition of considering the thermophysical properties of the material is solved, the entropy generation and the entropy flow caused by heat conduction in a milling friction system are further solved, and the heat generation and the conduction condition of the third deformation area in the milling friction system are quantitatively expressed through the specific change of the entropy value.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flow chart of a thermodynamic entropy value resolving method of friction force and heat conduction of a milling cutter back face under the action of vibration;
FIG. 2 is a schematic diagram of an open tribo-thermodynamic system in milling;
FIG. 3 is a schematic diagram of a finite element milling simulation and vibration acceleration signal;
FIG. 4 is a schematic diagram of the structure of a milling cutter and the instantaneous cutting behavior under the action of vibration;
FIG. 5 is a schematic view of a milling cutter biasing structure under vibration;
FIG. 6 is a schematic view of the selected relief feature points of the cutter tooth;
FIG. 7 is a schematic view of the instantaneous contact angle of cutter tooth i;
FIG. 8 is a schematic diagram of the instantaneous contact relationship of the flank face of the milling cutter tooth with the workpiece;
FIG. 9 is a schematic diagram of instantaneous friction speeds of three characteristic points of three contact angles of cutter tooth 1;
FIG. 10 is a schematic diagram of stress relationship of any region of the relief surface of a cutter tooth in a workpiece coordinate system;
FIG. 11 is a schematic diagram showing the variation characteristics of the temperature and friction coefficient of the cutter tooth 1;
FIG. 12 is a schematic diagram of entropy generation caused by cutter tooth 1 friction;
FIG. 13 is a schematic diagram of a heat transfer model of a cutter interface;
FIG. 14 is a schematic diagram showing the relationship between the temperature of the flank face of the cutter tooth and the heat flux density;
FIG. 15 is a schematic diagram of entropy generation due to heat conduction at different periods;
FIG. 16 is a schematic diagram of a thermal conduction entropy flow solution flow;
fig. 17 is an entropy flow diagram of heat conduction at point p1 for different cutting periods.
Detailed Description
In order to make the technical solutions and advantages of the embodiments of the present application more apparent, the following detailed description of exemplary embodiments of the present application is provided in conjunction with the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present application and not exhaustive of all embodiments. It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other.
Example 1, the thermodynamic entropy value resolving method of the friction force and heat conduction of the rear tool face of the milling cutter for action is described with reference to fig. 1-17, a mathematical model of entropy generation caused by the friction force of the rear tool face of the cutter tooth of the high-feed milling cutter under the vibration action is constructed, the model resolves the instantaneous friction speed of the rear tool face through the instantaneous contact relation between the cutter tooth of the high-feed milling cutter and a workpiece by combining milling vibration signals, and the resolving method of entropy generation caused by the friction force is provided according to the thermodynamic force and thermodynamic flow of friction thermodynamics; by constructing an instantaneous heat transfer model of a contact interface between a cutter tooth rear cutter face and a workpiece, solving the heat flow density and the temperature gradient entering a hard alloy cutter and the workpiece at different moments, further providing a method for solving entropy generation and entropy flow caused by heat conduction of a cutter friction interface in the milling process, and specifically comprising the following steps:
S1, a cutter tooth rear cutter face friction force entropy model under the vibration effect;
referring to fig. 2, in the efficient milling process, the milling cutter tooth rear cutter surface and the workpiece processing transition surface generate serious extrusion friction phenomena, the phenomena are accompanied with abrasion of the rear cutter surface and plastic deformation of the workpiece, and the processes are irreversible, so that the thermodynamic system formed by the milling cutter rear cutter surface and the processing transition surface can be studied from the aspect of irreversible thermodynamics, and the method is feasible; in a thermodynamic system formed by the rear cutter surface of the milling cutter and the processing transition surface, the composition of entropy in the research system is analyzed, and the entropy generation caused by various thermodynamic forces and the entropy flow caused by material convection and heat conduction in the friction and abrasion process of the rear cutter surface of the milling cutter and a workpiece are analyzed.
Because the rear cutter surface of the cutter tooth generates severe extrusion friction with the processing transition surface in the milling process, the main reason for abrasion of the rear cutter surface is also because the thermal stress and the physical properties of materials are severely changed under the friction force action of the rear cutter surface, and the rear cutter has important influence on the surface quality of a workpiece; since friction generates a large amount of heat, most of the power consumption caused by friction is dissipated in a thermal way, and heat conduction is a main heat transfer way of the solid material, a heat source formed in a third deformation area in milling can transfer heat on the milling cutter and the workpiece in a heat conduction way, and entropy caused by friction force and heat conduction is generated.
Referring to fig. 3, the calculation is performed according to the values of the form finite element simulation. The experimental measurement phi 32 high-feed milling cutter is characterized in that a Ti-6Al-4V vibration signal is subjected to direct milling, the vibration acceleration signal is subjected to twice integration processing through DHDAS (5922_1394) signal test analysis system software to be converted into vibration displacement, a displacement result value is extracted, then the motion of the milling cutter is restrained in the front processing of the form software, a path definition function related to time is selected in transformation, time and displacement are selected in plot type, and the displacement result is imported and applied so that the cutter vibration can be added in the form milling simulation.
In the cutting process, the manufacturing precision of the milling cutter and the machine tool is not absolute and accurate, so that the contact relation between the rear cutter surface of the cutter and a workpiece can be continuously influenced and changed under the influence of cutter tooth errors and vibration of the milling cutter during processing. Friction of flank faceThe force also presents unsteady state change characteristics, so that the friction thermodynamic behavior of the cutter interface is affected, the same presents unsteady state change characteristics, in order to understand the friction thermodynamic behavior of the cutter interface, the dynamic cutting process of the high-feed milling cutter under the combined action of cutter tooth error and vibration is modeled, and a conversion model of each coordinate system in the simulation is shown in fig. 4: in the figure, o c -x c y c z c The milling cutter structure coordinate system; o (o) i -x i y i z i Is a cutter tooth coordinate system; alpha 0 The cutter tooth mounting angle of the milling cutter; Δz i Is the axial error of the cutter teeth; Δr i Is the radial error of the cutter tooth; r is (r) i The radius of gyration of the knife tooth i knife point; r is (r) max The maximum radius of gyration of the cutter tooth; omega i Is x i Axis and y c An included angle of the shaft; phi (phi) i Is x i Axis and x c The included angle of the axes. O (O) g -X g Y g Z g Is a workpiece coordinate system; L/W/H is the length/width/height of the workpiece; a, a e Milling a width for the tool; v f Is the cutter feeding speed; a, a p Milling a depth for the tool; o (o) d -x d y d z d A milling cutter cutting coordinate system without vibration; o (o) v -x v y v z v Cutting a coordinate system for the milling cutter under the action of vibration; delta (t) is the attitude angle of the milling cutter at the moment t; psi phi type i Is y v Axis and y c The included angle of the axes.
Modeling a dynamic cutting process of the high-feed milling cutter under the combined action of cutter tooth errors and vibration, wherein a conversion model of each coordinate system in the simulation is as follows:
any point on the cutter tooth is converted into a conversion relation in a cutting coordinate system under the vibration action by the cutter tooth coordinate system, and the conversion relation is as follows:
[x v y v z v 1] T ＝B 2 B 1 A 1 [x i y i z i 1] T (1)
wherein x is v y v z v For the milling cutter cutting coordinate system under the vibration action, x i y i z i Is a cutter tooth coordinate system;
A 1 for translating the matrix, B 1 B 2 For the rotation matrix:
wherein phi is i Is x i Axis and x c Included angle of axes, ψ i Is y v Axis and y c Included angle of axis omega i Is x i Axis and y c An included angle of the shaft;
referring to fig. 5, a milling cutter offset structure under the vibration action is constructed, wherein l is the overhanging amount of the milling cutter; delta 1(t) 、δ 2(t) Respectively the attitude angle delta of the milling cutter (t) In plane x d -o d- y d 、x d -o d- z d Is a projection angle of (2); a is that x (t)、A y (t)、A z (t) origin of milling cutter cutting coordinate system under vibration along x d 、y d 、z d Offset distance in the direction.
The conversion relation of the point from the cutting coordinate system under the vibration action to the workpiece coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 [x v y v z v 1] T (4)
wherein X is g Y g Z g For the object coordinate system, A 2 A 3 Bit shift matrix, B 3 B 4 For the rotation matrix:
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wherein delta 1(t) 、δ 2(t) Respectively the attitude angle delta of the milling cutter (t) In plane x d -o d- y d 、x d -o d- z d Projection angle, a e Milling width for tool, v f For the cutter feed speed, a p Milling depth for tool, r i Radius of gyration of the i-blade point of the blade tooth A x (t)、A y (t)、A z (t) origin of milling cutter cutting coordinate system under vibration along x d 、y d 、z d The offset distances in the direction, W and H, are the width and height of the workpiece respectively;
referring to fig. 6, a tooth relief feature point is selected, x in the tooth coordinate system i0 To x i1 Is perpendicular to plane x i o i y i Wherein x is i0 Is the plane where the intersection point of the left side of the upper and lower boundaries is located, x i1 Is the plane where the right intersection point of the upper boundary and the lower boundary is located, x ie Is at the lowest point of the cutting edge and is perpendicular to x i o i y i Is a plane of the (c). Characteristic point p 2 Is a plane x ie An intersection point with the cutting edge; p is p 1 、p 3 Respectively are plane x ie-1 And plane x ie+1 The intersection of the plane and the cutting edge. P is p 1 、p 2 、p 3 Along x i The directions are equally spaced, with Δx=1.48 mm.
Referring to fig. 7, the instantaneous contact angle of cutter tooth i, three characteristic points of three cutter teeth throughout the cutting process, the variation characteristics of thermodynamic entropy values under the conditions of cutting in, cutting in and cutting out at different cutting cycles.
In the efficient milling process, the contact relation between the rear cutter surface of the cutter tooth of the high-feed milling cutter and the processing transition surface of the workpiece can be changed at any time due to the structural error of the high-feed milling cutter and the influence of vibration in the processing process. In order to better reveal what influence the friction force between the tool flank and the workpiece processing transition surface has on the friction thermodynamic behavior in the milling process, the friction force born by the tool tooth flank is solved by constructing a tool interface friction pair model.
Referring to FIG. 8, a transient contact relationship of the flank face of the cutter tooth of the milling cutter with the workpiece is constructed, in which v r Representing the relative movement speed of any point of the rear cutter surface of the milling cutter in a workpiece coordinate system; v m Is the relative movement velocity v r Projection on a public tangent plane, v m Is the friction velocity v of the rear cutter face of the cutter tooth m ＝-v m '；Is the normal vector of any point of the rear cutter surface of the cutter tooth; epsilon is the angle between the normal vector and the relative motion speed.
The conversion relation from any point on the cutter tooth to the workpiece coordinate system through the cutter tooth coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 B 2 B 1 A 1 [x i y i z i 1] T (7)
Relative movement velocity v of any point of cutter tooth rear cutter face in workpiece coordinate system r The components are as follows:
wherein H is i Is the trace equation of the rear cutter surface of the cutter tooth, x (t), y (t), and z (t) are the displacements of the rear cutter surface of the cutter tooth in the x, y and z directions at the moment t, v rx (t) is the relative movement speed in the x direction at the moment t, v ry (t) is the relative movement speed in the y direction at the moment t, v rz (t) is the relative movement speed in the z direction at the moment t,representing displacement versus time bias;
wherein v is r For the relative movement speed, v, of any point of the rear cutter surface of the milling cutter in the workpiece coordinate system rx (t) is the relative movement speed in the x direction at the moment t, v ry (t) is the relative movement speed in the y direction at the moment t, v rz (t) is the relative movement speed in the z direction at time t;
the normal vector components of any point of the rear tool face in the workpiece coordinate system are as follows:
according to the vector angle formula:
the friction speed of any point of the rear cutter surface is as follows:
v m (t)＝-sinε·v r (t) (12)
referring to fig. 9, the instantaneous friction speeds of three characteristic points of three contact angles of the cutter tooth 1 can be seen from the figure, the friction speed variation trend of the three characteristic points is the same under the condition of different contact angles on the cutter tooth 1, the friction speed of the three points is stable as a whole, but the fluctuation of the friction speed is obvious in the whole cutting medium period, and the main reason is that the friction speed v of the cutter surface characteristic points of the cutter tooth m Because the vibration acceleration signal is affected, and the projection angle of the relative movement speed on the public tangential plane is affected, the friction speed presents an unsteady change rule, and the friction speed is correspondingly increased in the integral cutting middle section due to the larger vibration speed; under the condition of 15-degree instantaneous contact angle, average friction speeds of p1, p2 and p3 on the cutter tooth in the whole cutting process are 1206.13mm/s, 1351.65mm/s and 1480.12mm/s respectively, and the distances between the p1, p2 and p3 points and the origin of the coordinate system of the milling cutter structure are p1 when the characteristic points are selected<p2<p3, the instantaneous cutting speed p3 at three points is the largest and p1 at the smallest. The maximum friction speed at point p3 can thus be obtained from the instantaneous cutting speed and vibration acceleration signals,p2 times, p1 is the smallest.
The friction energy consumption calculation model is constructed by utilizing the energy conversion relation between tool interface atoms and is as follows:
wherein E is the energy absorbed at time t; omega is the atomic forced vibration frequency; a is the lattice constant (2.9506 ×10) -10 m); h is planck constant (h= 6.62607015 ×10) -34 J·s); k is a boltzmann constant (k= 1.380649 ×10) -23 J/K); t is the temperature rise of an atomic interface;
the work done by the cutter tooth rear cutter face friction force in dt time is as follows:
dW＝μ(x i ,y i ,z i ,t)·F n (x i ,y i ,z i ,t)·v m (x i ,y i ,z i ,t)·dt (14)
Wherein F is n (x i ,y i ,z i T) positive pressure applied to one point of the rear cutter surface of the cutter tooth at the moment t:
F n (x i ,y i ,z i ,t)＝σ n (x i ,y i ,z i ,t)·ds(x i ,y i ,z i ) (15)
the three-dimensional space curved surface area is calculated by:
referring to FIG. 10, the stress relationship of any region of the tooth flank surface in the workpiece coordinate system, σ x Is the compressive stress component of the x-axis, sigma y For the compressive stress component of the y-axis, sigma z A compressive stress component that is the z-axis; ζ is the combined stress and the normal stressAnd an included angle.
Construction of the stresses imposed by the relief surface of the tooth in the workpiece coordinate system sigma n (x i ,y i ,z i ,t)：
All the work done by the friction force of the cutter face after the cutter teeth are arranged is converted into heat energy, so as to obtain dW=dE v Therefore, the coefficient of friction μ is obtained as:
referring to fig. 11, it can be seen from the characteristic of the change of the temperature and the friction coefficient of the cutter tooth 1, that the temperature at the point p1 is mainly between 20 ℃ and 35 ℃ when the contact angle is 15 ℃, and the temperature change is stable mainly because the milling process is an intermittent cutting process, the valance ultra-high feed milling cutter with the model of f2330.z25.025.z03.01 has three cutter teeth, each cutter tooth circularly cuts into a workpiece, and in two adjacent periods when the cutter tooth 1 cuts into the workpiece, the cutter tooth 1 has a certain cooling time without contacting with the workpiece for a certain period, so that the temperature of the rear cutter face is basically stable when the cutter tooth 1 just cuts into the workpiece (the instantaneous contact angle is 15 ℃) in different periods. With the cutting, the temperature of the rear cutter surface of the cutter tooth is slightly increased. The coulomb friction coefficient was set to 0.6 and the shear friction coefficient was set to 0.4 in the form-3D. It can be seen from the graph that the friction coefficient of the characteristic point of the rear cutter surface of the cutter tooth 1 is basically between 0.50 and 0.60, and the friction coefficient is correspondingly increased along with the increase of the temperature, and the change trend of the friction coefficient is the same as the change trend of the temperature of the rear cutter surface. Mainly because along with the continuous cutting-in of the cutter teeth, the contact time between the cutter teeth and the workpiece is increased, and the larger the friction time between the cutter teeth and the workpiece is, the more the generated heat is increased, the adhesion of the metal oxide on the rear surface of the cutter teeth is increased, so that the friction coefficient is correspondingly increased.
Obtaining friction stress:
the expression of entropy balance per unit volume is:
wherein s is entropy density; t is time; j (J) s Is the entropy flow of the system; sigma (sigma) s Generating entropy in the system;
the flank face and the processing transition surface are pressed and rubbed with each other during cutting, when the stress on the flank face reaches the yield strength of the cutter tooth material, the cutter tooth material is subjected to plastic deformation to cause peeling phenomenon, and abrasion is caused. The friction force applied to the cutter tooth rear cutter surface can change the stress distribution condition of the rear cutter surface, and the entropy generation caused by the friction force is calculated to quantitatively represent the entropy change of a cutting friction system consisting of the cutter tooth rear cutter surface and a processing transition surface, so that the thermodynamic characteristics of dissipating part of energy input into the cutting system in the form of acting through the friction force can be further disclosed.
Calculating entropy generation caused by friction force, and representing entropy change of a cutting friction system consisting of a cutter tooth flank face and a machining transition surface;
the expression for entropy generation in thermodynamics is:
wherein J is i Is the ith thermodynamic stream; x is X i Is the ith thermodynamic force.
Referring to fig. 12, it can be seen that, in 24 cutting cycles, entropy generation caused by friction force shows irregular change, mainly because entropy generation caused by friction force is influenced by friction stress, temperature and friction work, when the cutter tooth 1 just cuts into a workpiece, the transient cutting force is larger, so that the vibration of the milling cutter is stronger, the contact condition of a rear cutter surface and a processing transition surface is influenced, and the fluctuation of the interfacial absorbed atomic energy is larger, so that the friction stress and the friction work are unsteady changed at the moment; the average value of entropy generation caused by friction force at points p1, p2 and p3 on the cutter tooth 1 in the whole cutting process at the contact angle of 15 degrees is 4.8E+6N.J/k.s.mm respectively 2 、6.2E+6N·J/k·s·mm 2 、7.1E+6N·J/k·s·mm 2 The main reason is that the friction speed at the point p3 is greater than that at the point p2 and greater than that at the point p 1. The numerical value generated by the entropy of the three characteristic points is continuously increased along with the continuous cutting of the cutter tooth in the same period, and the state of a friction system formed by the rear cutter surface of the cutter tooth and the processing transition surface is increasingly disordered along with the continuous system state of cutting under the condition of only considering friction and vibration.
The expression for the entropy generation caused by the flank friction stress is:
wherein sigma sf Sigma for entropy generation caused by friction stress f T is the thermodynamic force of entropy generation caused by friction stress, E f Is a thermodynamic stream.
S2, a resolving method for generating one-dimensional heat conduction entropy of the rear cutter surface in the milling process under the vibration effect;
the heat generated by the third deformation area in the milling process increases the temperature of a friction pair formed by the rear cutter surface and the processing transition surface under the action of heat conduction, and the thermal physical property of the cutter tooth material can generate certain influence along with the change of the temperature. The higher temperature gradient in the heat conduction process can lead to the easier thermal fatigue of the cutter tooth material, so that the structure of the cutting friction system and the cutter tooth performance can be obviously changed. The reason for this variation is the result of the nonlinear combination of factors, and the entropy can be used to uniformly take into account the different factors between the heat conduction in the third deformation zone. The heat generation and conduction conditions of the cutting friction system are expressed by quantitatively indicating the entropy generation change of the heat conduction process.
The basic way of milling heat transfer is three: heat conduction, heat convection, heat radiation; the three heat transfer modes exist simultaneously in the milling heat transfer process, and the heat conduction refers to heat conduction from a system with high temperature to a system with low temperature; heat transfer in milling is mainly by means of heat conduction. In the initial stage of researching unsteady state heat conduction in the cutter tooth, in order to simplify calculation and not lose the meaning of calculation and analysis, the cutter tooth of the milling cutter is regarded as a semi-infinite object to be analyzed, and the heat transfer mode in the milling process is assumed to be heat conduction to ignore heat radiation and heat convection; the heat being only along z in the cutter tooth coordinate system i Direction transfer; the density of the tool workpiece material does not change with temperature.
Referring to FIG. 13, a heat transfer model of a tool interface consisting of a relief surface and a workpiece is constructed, in which Q t 、Q g The heat entering the cutter tooth and the workpiece respectively; j (J) qt 、J qg The heat flux density entering the cutter tooth and the workpiece is respectively; the initial temperature of the cutter tooth and the workpiece is T 0 The method comprises the steps of carrying out a first treatment on the surface of the S is the area of the friction contact area;
constructing a heat transfer model of a cutter interface formed by a rear cutter surface and a workpiece:
the temperature gradient gradT is:
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heat flux density J q The method comprises the following steps:
wherein lambda is the heat conductivity W/m.k ；Is a temperature gradient;
the change of the thermal conductivity and the specific heat capacity of TC4 with temperature is shown in tables 1 and 2, wherein the change of the density of TC4 with temperature is small, therefore, the density of TC4 is not changed with temperature, and ρ is obtained g ＝4510kg/m 3 。
TABLE 1 thermal conductivity tables of Ti-6Al-4V at different temperatures
TABLE 2 specific heat capacities of Ti-6Al-4V at different temperatures
Assuming that the density of TC4 does not change with temperature, then MATLAB fitting results give the equation for TC4 thermal conductivity with temperature change as:
λ＝-5.934e-9·T 3 +1.272e-5·T 2 +8.023e-3·T+6.069 20≤T≤900 (28)
the equation for the change in TC4 specific heat capacity with temperature is:
c＝-5.343e-8·T 3 +8.661e-5·T 2 +0.1452·T+515.8 20≤T≤900 (29)
the thermal conductivity, specific heat capacity, thermal conductivity coefficient and density of the YG6 of the hard alloy cutter are all changed along with the temperature moment, but the density change is smaller and can be ignored, wherein ρ is t ＝15000kg/m 3 ；
The changes of the thermal conductivity, the specific heat capacity and the heat conductivity coefficient along with the temperature are as follows:
the thermal conductivity of WC hard alloy with YG6 has the following equation:
λ＝99.2+48.78cos(0.005136T)-12.35sin(0.005136T)+7.673cos(2*0.005136T)-22.58sin(2*0.005136T)22≤T≤800-7.616cos(3*0.005136T)-6.303sin(3*0.005136T) (30)
the temperature coefficient of the WC hard alloy with YG6 changes with temperature as follows:
α＝-9.992e-8·T 3 +1.751e-4·T 2 -0.1159·T+48.46 22≤T≤800 (31)
the equation of the specific heat capacity of WC hard alloy with temperature is as follows:
c＝0.03255·exp(-((T-831.3)/91.99) 2 )+0.02332·exp(-((T-600.3)/70.43) 2 )-0.01023·exp(-((T-475.7)/138.5) 2 )+0.2759·exp(-((T-626.1)/1051) 2 )22≤T≤800 (32)
the abrasion area and the contact area of the rear cutter surface are equal in value, and according to the abrasion area prediction model:
A＝κ·n a ·v f b ·a p c (33)
wherein the proportionality coefficient κ=2; the index a= -0.3437; b=0.034; c= 0.3462.
Total heat on tool contact area q=e f A; heat flux density J into milling cutter and workpiece qt 、J qg Expressed as:
entropy generation caused by heat conduction is expressed as:
let T (z, T) be the temperature function with respect to heat transfer displacement and time, the initial conditions and boundary conditions for the temperature on the cutter tooth and the heat flux density into the cutter tooth are:
the heat transfer equation along the z-direction is:
wherein alpha is the temperature conductivity coefficient m 2 /s，α＝λ/cρ。
Introducing excess temperature deltat=t-T 0 And (3) deforming the one-dimensional heat transfer equation to obtain:
multiplying the two sides of the equation equal sign by-lambda at the same time, deriving z, and changing the derivation order to obtain:
substituting the heat flux density entering the cutter tooth at the time t into the above formula converts the heat transfer equation along the z direction into:
by introducing a variable χ and solving the temperature and the temperature gradient by using a similarity variation method: setting:
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changing the heat transfer equation to:
setting:
obtaining:
the general solution to find Z from the above integral is:
and integrating the above steps to obtain:
introducing an error function erf (x) and a residual error function erfc (x), erf (0) =0; erf (≡) =1; the residual error function erfc (x) =1-erf (x); the error function is in the form of:
the form of the error function is taken in equation 48:
substituted erf (0) =0; erf (≡) =1; χ=0, j q ＝J qt ；χ＝∞，J q Solution of =0 to equation 50:
J q ＝J qt [1-erf(χ)] (52)
referring to fig. 14, the corresponding relation between the temperature of the flank face of the cutter tooth and the heat flux density shows that when the instantaneous contact angle of a single characteristic point in the whole cutting process is 15 degrees, the change amplitude of the cutting temperature of the flank face is stable and basically stabilized between 20 ℃ and 35 ℃, and the cutting temperature of the characteristic point of the flank face is continuously increased along with the continuous cutting of the cutter tooth 1. The main reason is that during the cutting of the cutter teeth 1 in two adjacent cutting cycles, the cutter teeth 2 and 3 continue to cut into the workpiece, and the cutter teeth 1 do not participate in cutting and have a corresponding cooling time. As can be seen from the graph, the heat flux density entering the workpiece is far greater than that entering the cutter teeth of the milling cutter, the change trend of the heat flux density is the same as that of the temperature, and in the whole cutting process, the average heat flux density of the point p3 is the largest, the point p2 is the next smallest and the point p1 is the smallest when the contact angles are the same; and as the cutter tooth 1 is continuously cut into, the value of the heat flux density entering the cutter tooth presents an increasing trend, and the heat flux density entering the workpiece tends to be stable when the contact angle is 45 degrees.
Defined by the heat flux density in fourier heat transfer:
the temperature change is:
The temperature gradient in the z direction is:
entropy generation caused by heat conduction is:
referring to FIG. 15, it can be seen that the average value of entropy generation due to heat conduction at points p1, p2, and p3 at an instantaneous contact angle of 15℃is 1.6E+9J/s.k.mm, respectively 3 、2.8E+9J/s·k·mm 3 、2.8E+9J/s·k·mm 3 The combination of the figures with the instantaneous contact angles of the cutter teeth 1 of 45 ° and 75 ° makes it possible to obtain: with the cutting of the cutter tooth 1, entropy generation of 3 characteristic points caused by heat conduction is also increasing, and the entropy generation value of the point p3 is larger than the point p2 and larger than the point p 1. The main reason is that the friction speed at the point p3 on the cutting edge of the cutter tooth 1 is the largest, so that the friction work at the point p3 is also the largest, and in the case of the same friction area, the value of entropy generation at the point p3 due to heat conduction is the largest because the friction work is all converted into friction heat. It can be seen that entropy generated by heat conduction at three characteristic points in the whole cutting process increases in increasing amplitude at contact angles of 15-45 degrees: the p1 point is increased by 0.6E+9J/s.k.mm 3 The p2 and p3 points are increased by 2.8E+9J/s.k.mm 3 Whereas the magnitude of the increase at contact angles of 45 deg. to 75 deg. is small: both p1 and p2 increase by 0.1J/s.k.mm 3 The p3 point is increased by 0.2J/s.k.mm 3 。
S3, a one-dimensional heat conduction entropy flow solving method for the rear cutter surface in the milling process under the vibration effect.
In a friction thermodynamic system consisting of a flank face and a workpiece processing transition surface, if only entropy generation caused by friction force and heat conduction is considered, the cutting process of a high-feed milling cutter cannot be systematically revealed from a thermodynamic perspective, so that the part analyzes entropy flow caused by heat conduction in the cutting process of the milling cutter teeth, and reflects the milling process from the thermodynamic perspective of the system through the combined action of entropy generation and entropy flow.
Thermodynamically reflecting the milling process by entropy generation and entropy flow synthesis is:
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referring to the entropy flow of heat conduction at the point p1 of different cutting periods in fig. 17, as the contact time of the cutter tooth 1 and the workpiece is continuously increased, the entropy flow caused by heat conduction is generally in a decreasing trend, the entropy flow of the contact time is greatly reduced from 0.004s to 0.012s, the entropy flow value of 0.012s to 0.02s is slowly reduced, the main reason is that the heat flow density and the temperature of the entropy flow are greatly influenced, the temperature of a characteristic point is lower when the cutter tooth is just cut, the temperature is continuously increased and tends to be stable along with the deep temperature of the cutter tooth, and the heat flow density entering the cutter tooth is greatly increased from the middle when the cutter tooth is cut into the middle when the cutter tooth is cut out, and the heat flow density entering the cutter tooth is less increased from the middle when the cutter tooth is cut out; from the right figure, it can be seen that the entropy flow J in the whole cutting process is obtained when the contact time is 0.004s, 0.012s, and 0.012s (i.e. the contact angle of the point p1 on the cutter tooth 1 is 15 DEG, 45 DEG and 75 DEG respectively) thc Average values of (2) are 5.09E+8J/s.k.mm, respectively 2 、2.92E+8J/s·k·mm 2 、2.256E+8J/s·k·mm 2 . In the whole cutting process, the large fluctuation of the p1 point entropy flow mainly occurs in the later cutting half, the entropy flow in the earlier cutting half mainly fluctuates up and down on the average value, and the change amplitude is smaller than that in the later cutting half.
In embodiment 2, the computer device of the present invention may be a device including a processor and a memory, for example, a single chip microcomputer including a central processing unit. And the processor is used for realizing the thermodynamic entropy value resolving method of the friction force and the heat conduction of the rear tool face of the milling cutter under the vibration effect when executing the computer program stored in the memory.
The processor may be a central processing unit (Central Processing Unit, CPU), other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program (such as a sound playing function, an image playing function, etc.) required for at least one function, and the like; the storage data area may store data (such as audio data, phonebook, etc.) created according to the use of the handset, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as a hard disk, memory, plug-in hard disk, smart Media Card (SMC), secure Digital (SD) Card, flash Card (Flash Card), at least one disk storage device, flash memory device, or other volatile solid-state storage device.
Embodiment 3, a computer-readable storage medium embodiment.
The computer readable storage medium of the present invention may be any form of storage medium readable by a processor of a computer device, including but not limited to, nonvolatile memory, volatile memory, ferroelectric memory, etc., on which a computer program is stored, and when the processor of the computer device reads and executes the computer program stored in the memory, the above-described steps of the method for resolving thermodynamic entropy values of the back surface friction and heat conduction of a milling cutter under vibration action can be implemented.
The computer program comprises computer program code which may be in source code form, object code form, executable file or in some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of the above description, will appreciate that other embodiments are contemplated within the scope of the invention as described herein. Furthermore, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. The disclosure of the present invention is intended to be illustrative, but not limiting, of the scope of the invention, which is defined by the appended claims.
Claims (6)
1. The thermodynamic entropy value resolving method of the friction force and the heat conduction of the rear cutter surface of the milling cutter under the vibration effect is characterized by comprising the following steps:
s1, a cutter tooth rear cutter face friction force entropy model under the vibration effect;
s2, a resolving method for generating one-dimensional heat conduction entropy of the rear cutter surface in the milling process under the vibration effect;
s3, a one-dimensional heat conduction entropy flow solving method for the rear cutter surface in the milling process under the vibration effect.
2. The method for solving the thermodynamic entropy value of the friction force and the heat conduction of the rear tool face of the milling cutter under the action of vibration according to claim 1, wherein the model of the entropy value of the friction force of the rear tool face of the cutter tooth under the action of vibration is specifically as follows:
modeling a dynamic cutting process of the high-feed milling cutter under the combined action of cutter tooth errors and vibration, wherein a conversion model of each coordinate system in the simulation is as follows:
any point on the cutter tooth is converted into a conversion relation in a cutting coordinate system under the vibration action by the cutter tooth coordinate system, and the conversion relation is as follows:
[x v y v z v 1] T ＝B 2 B 1 A 1 [x i y i z i 1] T (1)
wherein x is v y v z v For the milling cutter cutting coordinate system under the vibration action, x i y i z i Is a cutter tooth coordinate system;
A 1 for translating the matrix, B 1 B 2 For the rotation matrix:
wherein phi is i Is x i Axis and x c Included angle of axes, ψ i Is y v Axis and y c Included angle of axis omega i Is x i Axis and y c An included angle of the shaft;
the conversion relation of the point from the cutting coordinate system under the vibration action to the workpiece coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 [x v y v z v 1] T (4)
Wherein X is g Y g Z g For the object coordinate system, A 2 A 3 Bit shift matrix, B 3 B 4 For the rotation matrix:
wherein delta 1(t) 、δ 2(t) Respectively the attitude angle delta of the milling cutter (t) In plane x d -o d- y d 、x d -o d- z d Projection angle, a e Milling width for tool, v f For the cutter feed speed, a p Milling depth for tool, r i Radius of gyration of the i-blade point of the blade tooth A x (t)、A y (t)、A z (t) origin of milling cutter cutting coordinate system under vibration along x d 、y d 、z d The offset distances in the direction, W and H, are the width and height of the workpiece respectively;
the conversion relation from any point on the cutter tooth to the workpiece coordinate system through the cutter tooth coordinate system is as follows:
[X g Y g Z g 1] T ＝A 3 A 2 B 4 B 3 B 2 B 1 A 1 [x i y i z i 1] T (7)
relative movement velocity v of any point of cutter tooth rear cutter face in workpiece coordinate system r The components are as follows:
wherein H is i Is the trace equation of the rear cutter surface of the cutter tooth, x (t), y (t), and z (t) are the displacements of the rear cutter surface of the cutter tooth in the x, y and z directions at the moment t, v rx (t) is the relative movement speed in the x direction at the moment t, v ry (t) is the relative movement speed in the y direction at the moment t, v rz (t) is the relative movement speed in the z direction at the moment t,representing displacement versus time bias;
wherein v is r For the relative movement speed, v, of any point of the rear cutter surface of the milling cutter in the workpiece coordinate system rx (t) is the relative movement speed in the y direction at the moment t, v ry (t) is the relative movement speed in the z direction at the moment t, v rz (t) is the relative movement speed in the z direction at time t;
The normal vector components of any point of the rear tool face in the workpiece coordinate system are as follows:
according to the vector angle formula:
the friction speed of any point of the rear cutter surface is as follows:
v m (t)＝-sinε·v r (t) (12)
the friction energy consumption calculation model is constructed by utilizing the energy conversion relation between tool interface atoms and is as follows:
wherein E is the energy absorbed at time t; omega is the atomic forced vibration frequency; a is the lattice constant; h is a Planck constant; k is a Boltzmann constant; t is the temperature rise of an atomic interface;
the work done by the cutter tooth rear cutter face friction force in dt time is as follows:
dW＝μ(x i ,y i ,z i ,t)·F n (x i ,y i ,z i ,t)·v m (x i ,y i ,z i ,t)·dt (14)
wherein F is n (x i ,y i ,z i T) positive pressure applied to one point of the rear cutter surface of the cutter tooth at the moment t:
F n (x i ,y i ,z i ,t)＝σ n (x i ,y i ,z i ,t)·ds(x i ,y i ,z i ) (15)
the three-dimensional space curved surface area is calculated by:
construction of the stress on the flank face of a tooth sigma in the workpiece coordinate system n (x i ,y i ,z i ,t)：
All the work done by the friction force of the cutter face after the cutter teeth are arranged is converted into heat energy, so as to obtain dW=dE v Therefore, the coefficient of friction μ is obtained as:
obtaining friction stress:
the expression of entropy balance per unit volume is:
wherein s is entropy density; t is time; j (J) s Is the entropy flow of the system; sigma (sigma) s Generating entropy in the system;
calculating entropy generation caused by friction force, and representing entropy change of a cutting friction system consisting of a cutter tooth flank face and a machining transition surface;
the expression for entropy generation in thermodynamics is:
Wherein J is i Is the ith thermodynamic stream; x is X i Is the ith thermodynamic force;
the expression for the entropy generation caused by the flank friction stress is:
wherein sigma sf Sigma for entropy generation caused by friction stress f T is the thermodynamic force of entropy generation caused by friction stress, E f Is a thermodynamic stream.
3. The method for resolving the thermodynamic entropy of the friction force and the heat conduction of the rear tool face of the milling cutter under the vibration action according to claim 2, wherein the resolving method for the one-dimensional heat conduction entropy of the rear tool face in the milling process under the vibration action is specifically as follows:
constructing a heat transfer model of a cutter interface formed by a rear cutter surface and a workpiece:
the temperature gradient gradT is:
heat flux density J q The method comprises the following steps:
wherein lambda is the heat conductivity W/m.k;is a temperature gradient;
assuming that the density of TC4 does not change with temperature, then MATLAB fitting results give the equation for TC4 thermal conductivity with temperature change as:
λ＝-5.934e-9·T 3 +1.272e-5·T 2 +8.023e-3·T+6.069 20≤T≤900 (28)
the equation for the change in TC4 specific heat capacity with temperature is:
c＝-5.343e-8·T 3 +8.661e-5·T 2 +0.1452·T+515.8 20≤T≤900 (29)
the changes of the thermal conductivity, the specific heat capacity and the heat conductivity coefficient along with the temperature are as follows:
the thermal conductivity with temperature equation is:
λ＝99.2+48.78cos(0.005136T)-12.35sin(0.005136T)+7.673cos(2*0.005136T)-22.58sin(2*0.005136T) 22≤T≤800-7.616cos(3*0.005136T)-6.303sin(3*0.005136T) (30)
the temperature conductivity coefficient is as follows:
α＝-9.992e-8·T 3 +1.751e-4·T 2 -0.1159·T+48.46 22≤T≤800 (31)
the equation of change of specific heat capacity with temperature is:
c＝0.03255·exp(-((T-831.3)/91.99) 2 )+0.02332·exp(-((T-600.3)/70.43) 2 )-0.01023·exp(-((T-475.7)/138.5) 2 )+0.2759·exp(-((T-626.1)/1051) 2 ) 22≤T≤800 (32)
the abrasion area and the contact area of the rear cutter surface are equal in value, and according to the abrasion area prediction model:
A＝κ·n a ·v f b ·a p c (33)
Wherein the proportionality coefficient κ=2; the index a= -0.3437; b=0.034; c= 0.3462;
total heat on tool contact area q=e f A; heat flux density J into milling cutter and workpiece qt 、J qg Expressed as:
entropy generation caused by heat conduction is expressed as:
let T (z, T) be the temperature function with respect to heat transfer displacement and time, the initial conditions and boundary conditions for the temperature on the cutter tooth and the heat flux density into the cutter tooth are:
the heat transfer equation along the z-direction is:
wherein alpha is the temperature conductivity coefficient m 2 /s，α＝λ/cρ；
Introducing excess temperature deltat=t-T 0 And (3) deforming the one-dimensional heat transfer equation to obtain:
multiplying the two sides of the equation equal sign by-lambda at the same time, deriving z, and changing the derivation order to obtain:
substituting the heat flux density entering the cutter tooth at the time t into the above formula converts the heat transfer equation along the z direction into:
by introducing a variable χ and solving the temperature and the temperature gradient by using a similarity variation method:
setting:
changing the heat transfer equation to:
setting:
obtaining:
the general solution to find Z from the above integral is:
and integrating the above steps to obtain:
introducing an error function erf (x) and a residual error function erfc (x), erf (0) =0; erf (≡) =1; the residual error function erfc (x) =1-erf (x); the error function is in the form of:
the form of the error function is taken in equation 48:
Substituted erf (0) =0; erf (≡) =1; χ=0, j q ＝J qt ；χ＝∞，J q Solution of =0 to equation 50:
J q ＝J qt [1-erf(χ)] (52)
defined by the heat flux density in fourier heat transfer:
the temperature change is:
the temperature gradient in the z direction is:
entropy generation caused by heat conduction is:
4. the method for resolving the thermodynamic entropy of the friction force and the heat conduction of the rear tool face of the milling cutter under the vibration action according to claim 3, wherein the method for resolving the one-dimensional heat conduction entropy flow of the rear tool face in the milling process under the vibration action is specifically as follows:
thermodynamically reflecting milling process by entropy production and entropy flow synthesis:
5. an electronic device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of the thermodynamic entropy value calculation method of friction and heat transfer of the flank face of a milling cutter under the action of vibration according to any one of claims 1 to 4 when executing the computer program.
6. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the thermodynamic entropy value solving method of friction and heat conduction of the flank face of a milling cutter under the action of vibration according to any one of claims 1 to 4.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2016005858A (en) * | 2014-06-20 | 2016-01-14 | 株式会社ジェイテクト | Dynamic characteristic calculation device and dynamic characteristic calculation method for machine tool |
| CN114186175A (en) * | 2021-12-02 | 2022-03-15 | 哈尔滨理工大学 | Method for resolving dynamic characteristics of energy consumption of main cutting force of high-energy-efficiency milling cutter under vibration action |
| CN114429064A (en) * | 2022-01-05 | 2022-05-03 | 哈尔滨理工大学 | Identification method for fractal characteristics of friction boundary of rear cutter face of cutter tooth of high-energy-efficiency milling cutter |
| CN114580090A (en) * | 2021-12-28 | 2022-06-03 | 哈尔滨理工大学 | Dynamic characteristic resolving method for friction coefficient of rear cutter face of cutter tooth pair of square shoulder milling cutter |
| CN114896753A (en) * | 2021-12-09 | 2022-08-12 | 哈尔滨理工大学 | Method for identifying instantaneous friction energy consumption distribution characteristics of rear cutter face of high-energy-efficiency milling cutter |
| CN115647440A (en) * | 2022-11-10 | 2023-01-31 | 哈尔滨理工大学 | Method for solving milling infinitesimal energy consumption characteristic parameters of main and auxiliary cutting edges of square shoulder milling cutter |
| CN116306169A (en) * | 2023-05-08 | 2023-06-23 | 哈尔滨理工大学 | High-efficiency identification method for unsteady friction characteristics of rear cutter face of cutter tooth of milling cutter |
-
2023
- 2023-08-07 CN CN202310984486.6A patent/CN117034725B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2016005858A (en) * | 2014-06-20 | 2016-01-14 | 株式会社ジェイテクト | Dynamic characteristic calculation device and dynamic characteristic calculation method for machine tool |
| CN114186175A (en) * | 2021-12-02 | 2022-03-15 | 哈尔滨理工大学 | Method for resolving dynamic characteristics of energy consumption of main cutting force of high-energy-efficiency milling cutter under vibration action |
| CN114896753A (en) * | 2021-12-09 | 2022-08-12 | 哈尔滨理工大学 | Method for identifying instantaneous friction energy consumption distribution characteristics of rear cutter face of high-energy-efficiency milling cutter |
| CN114580090A (en) * | 2021-12-28 | 2022-06-03 | 哈尔滨理工大学 | Dynamic characteristic resolving method for friction coefficient of rear cutter face of cutter tooth pair of square shoulder milling cutter |
| CN114429064A (en) * | 2022-01-05 | 2022-05-03 | 哈尔滨理工大学 | Identification method for fractal characteristics of friction boundary of rear cutter face of cutter tooth of high-energy-efficiency milling cutter |
| CN115647440A (en) * | 2022-11-10 | 2023-01-31 | 哈尔滨理工大学 | Method for solving milling infinitesimal energy consumption characteristic parameters of main and auxiliary cutting edges of square shoulder milling cutter |
| CN116306169A (en) * | 2023-05-08 | 2023-06-23 | 哈尔滨理工大学 | High-efficiency identification method for unsteady friction characteristics of rear cutter face of cutter tooth of milling cutter |
Non-Patent Citations (6)
| Title |
|---|
| Z. PÁLMAI 等: "The transient changing of forces in interrupted milling", THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY, no. 104, 19 July 2017 (2017-07-19), pages 3787 - 3801 * |
| 丁岩 等: "高速铣刀差异化振动磨损形成机制及其控制方法", 工具技术, vol. 55, no. 7, 20 July 2021 (2021-07-20), pages 1 - 6 * |
| 任勇生 等: "考虑刀杆结构非线性的铣削过程颤振稳定性与主共振", 振动与冲击, no. 23, 15 December 2019 (2019-12-15), pages 1 - 7 * |
| 吴石 等: "凸曲面拼接模具球头铣刀的瞬时铣削力预测", 振动测试与诊断, no. 05, 15 October 2020 (2020-10-15), pages 1 - 6 * |
| 李忠群: "数控切削加工过程动力学建模、仿真分析回顾与展望", 航空制造技术, no. 19, 31 October 2022 (2022-10-31), pages 1 - 15 * |
| 肖忠跃 等: "基于最大熵与交叉熵理论的刀具磨损检测技术", 机床与液压, no. 22, 28 November 2018 (2018-11-28), pages 1 - 8 * |
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