CN116306169B

CN116306169B - High-efficiency identification method for unsteady friction characteristics of rear cutter face of cutter tooth of milling cutter

Info

Publication number: CN116306169B
Application number: CN202310509133.0A
Authority: CN
Inventors: 姜彬; 王彬旭; 赵培轶; 范丽丽; 杨帆
Original assignee: Harbin University of Science and Technology
Current assignee: Harbin University of Science and Technology
Priority date: 2023-05-08
Filing date: 2023-05-08
Publication date: 2023-09-19
Anticipated expiration: 2043-05-08
Also published as: CN116306169A

Abstract

An efficient identification method for unsteady friction characteristics of a cutter tooth rear cutter surface of a milling cutter belongs to the field of machining. Comprising the following steps: a method for resolving the instantaneous pose and contact angle of a milling cutter and cutter teeth under the action of vibration; a cutter tooth rear cutter face instantaneous friction variable solving method; the method for identifying the time domain characteristics of the friction variable of the rear cutter face of the cutter tooth; the method for identifying the frequency domain characteristics of the friction variation of the rear cutter face of the cutter tooth; the method for identifying the unsteady friction distribution characteristics of the rear cutter surface of the cutter tooth; the method for identifying the unsteady friction difference of the rear cutter face of the cutter tooth; the milling vibration affects the identification method of the unsteady friction of the rear tool face; the invention discloses a response characteristic and experimental verification method of cutter tooth rear cutter surface friction, which aims to solve the problem that the traditional research method about milling cutter friction speed ignores milling parameters, cutter tooth errors and milling cutter vibration influences, and causes ambiguity of instantaneous contact relation between the cutter tooth rear cutter surface and a processing transition surface.

Description

High-efficiency identification method for unsteady friction characteristics of rear cutter face of cutter tooth of milling cutter

Technical Field

The invention relates to a method for identifying unsteady friction characteristics of a cutter tooth rear cutter surface of a high-efficiency milling cutter, and belongs to the field of machining.

Background

In milling, the high-efficiency milling cutter is subjected to the comprehensive influence of cutter tooth errors and milling vibration, and the milling cutter and the cutter teeth are in an unstable state in the cutting process, so that the positions of the high-efficiency milling cutter and the cutter teeth are continuously changed, the instantaneous contact relation between the rear cutter surface of the cutter teeth and the workpiece processing transition surface is directly influenced, and further, the instantaneous friction speed and friction energy consumption of the rear cutter surface of the cutter teeth are changed, and the service lives of the cutter teeth of the milling cutter are obviously different. The accurate friction characteristic parameter calculation model is established, the unsteady state characteristic of the instantaneous friction of the rear cutter surface is represented, the influence of cutter tooth errors and vibration on the instantaneous friction characteristic variable of the rear cutter surface of the cutter tooth is revealed, and the method has engineering value for controlling the service life of the milling cutter.

In the prior art, the friction speed of the milling cutter is studied, the influence of cutter tooth errors and milling vibration on the transient contact relation of the cutter is ignored, and the calculation result of the friction speed of the rear cutter surface of the cutter has larger errors, so that the transient friction state of the rear cutter surface of the cutter can not be accurately reflected; the existing calculation of friction energy consumption ignores the conversion of tool interface atomic potential energy, and the essence of friction energy consumption cannot be correctly revealed, so that the difference between calculation results is larger. In the aspect of research on the unsteady state characteristics of the instantaneous friction behavior of the rear cutter face of the cutter tooth, the time domain characteristics of the instantaneous friction speed and the friction energy consumption are generally utilized to represent the change characteristics of the instantaneous friction behavior, and the complex and variable unsteady state friction characteristics of the rear cutter face of the cutter tooth cannot be revealed by adopting the method.

Therefore, aiming at the problems existing in the instantaneous friction behavior of the rear cutter face of the cutter tooth of the efficient milling cutter, the influences of milling parameters, cutter tooth errors and vibration are considered, an instantaneous pose resolving model of the efficient milling cutter and the cutter tooth is established, and an instantaneous friction energy consumption resolving model of the rear cutter face of the cutter tooth is established based on the friction work principle and atomic excitation under the action of potential energy fields of a cutter tool friction interface; on the basis, the complex and variable unsteady state change characteristics of the cutter tooth rear tool face are revealed by utilizing the time domain and frequency domain characteristic variables and the power spectrum entropy of the instantaneous friction behaviors at different positions of the cutter tooth rear tool face, and the influence of milling vibration on the cutter tooth rear tool face instantaneous friction behaviors is revealed by utilizing a cross correlation function.

Disclosure of Invention

The present invention has been developed to solve the problem of ambiguity in the instantaneous contact relationship of the relief surface of the cutter tooth with the machining transition surface caused by the prior research methods concerning the friction speed of the milling cutter ignoring the milling parameters, cutter tooth errors and vibration effects of the milling cutter, and a brief overview of the present invention is provided below to provide a basic understanding of some aspects of the present 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.

The technical scheme of the invention is as follows:

the method for identifying the unsteady friction characteristics of the rear cutter surface of the cutter tooth of the efficient milling cutter comprises the following steps:

step 1, calculating the instantaneous pose and the contact angle of a milling cutter and cutter teeth under the action of vibration;

step 2, calculating a cutter tooth rear cutter face instantaneous friction variable;

step 3, a cutter tooth rear cutter face friction variable time domain characteristic identification method;

step 4, a cutter tooth rear cutter face friction variable frequency domain characteristic identification method;

step 5, a cutter tooth rear cutter surface unsteady friction distribution characteristic identification method;

step 6, a cutter tooth rear cutter face unsteady friction difference identification method;

step 7, a method for identifying the unsteady friction influence of milling vibration on the rear tool face;

and 8, response characteristics and experimental verification methods of cutter tooth rear cutter face friction.

The invention has the following beneficial effects:

1. according to the method, the influence of milling parameters, cutter tooth errors and milling vibration on the instantaneous cutting behaviors of the milling cutter and the cutter teeth is utilized, the change characteristics of the instantaneous positions and the postures of the efficient milling cutter and the cutter teeth are disclosed, and the problem of ambiguity of the instantaneous contact relation between the rear cutter surface of the cutter teeth and the processing transition surface caused by the fact that the milling parameters, the cutter tooth errors and the cutter tooth vibration influence are ignored in the existing method is solved;

2. according to the invention, by utilizing the instantaneous friction speed and friction energy consumption resolving method of the cutter tooth rear cutter face, the instantaneous friction behavior change characteristics of different positions of the cutter tooth rear cutter face are solved, and the difference of the instantaneous friction behavior distribution of the cutter tooth rear cutter face is revealed;

3. According to the invention, complex and variable unsteady state change characteristics of the cutter tooth rear cutter face are revealed by utilizing time domain and frequency domain characteristic variables and power spectrum entropy of the cutter tooth rear cutter face instantaneous friction behavior, and the influence of milling vibration on the cutter tooth rear cutter face instantaneous friction behavior is revealed by utilizing a cross correlation function;

4. the model method provided by the invention is used for the design of the efficient milling cutter and the efficient milling process, and can effectively control the friction and abrasion process of the rear cutter surface of the cutter tooth of the efficient milling cutter.

Drawings

FIG. 1 is a flow chart of a method for identifying unsteady friction characteristics of a cutter tooth flank of a high-efficiency milling cutter according to the present invention;

FIG. 2 is a diagram showing a contact relationship between a milling cutter and a workpiece, and a milling cutter structure according to a first embodiment of the present invention;

FIG. 3 is a diagram showing the relationship between the positions of the milling cutter and the cutter tooth coordinate system under the vibration action according to the first embodiment of the present invention;

FIG. 4 is a schematic view of a cutting angle of a cutter tooth under vibration according to a first embodiment of the present invention;

FIG. 5 is a schematic diagram of experimental vibration signals according to a first embodiment of the present invention;

fig. 6 is a schematic diagram of a milling cutter and a trajectory and an attitude angle of a cutter tooth according to a first embodiment of the present invention, wherein (a) is the trajectory of the milling cutter, (b) is the attitude angle of the milling cutter, (c) is the trajectory of the cutter tooth, and (d) is the attitude angle of the cutter tooth;

FIG. 7 is a graph showing instantaneous contact relationship between a flank surface and a machining transition surface in accordance with a first embodiment of the present invention;

FIG. 8 is a 221 th cycle friction speed time domain plot according to one embodiment of the present invention;

FIG. 9 is a 221 th cycle friction energy time domain property graph of a first embodiment of the present invention;

FIG. 10 is a graph showing the equivalent stress distribution of the flank surface of the tooth 1 according to the first embodiment of the present invention;

FIG. 11 is a graph showing the equivalent strain rate distribution of the flank face of the tooth 1 according to the first embodiment of the present invention;

FIG. 12 is a schematic representation of the flank friction boundary and its feature point selection according to a first embodiment of the present invention;

FIG. 13 is a representation of time domain parameters of friction variables according to a first embodiment of the present invention;

FIG. 14 is a graph showing time domain characteristics of a friction speed according to a first embodiment of the present invention, wherein (a) is a maximum value of the friction speed, (b) is a very poor friction speed, (c) is a root mean square value of the friction speed, (d) is kurtosis of the friction speed, and (e) is a skewness of the friction speed;

FIG. 15 is a graph showing characteristic parameters of friction energy time domain according to the first embodiment of the present invention, wherein (a) is a maximum value of friction speed, (b) is an extremely poor friction speed, (c) is a root mean square value of friction speed, (d) is kurtosis of friction speed, and (e) is a skewness of friction speed;

FIG. 16 is a graph showing the frequency spectrum and power spectrum of the 221 th cycle friction speed according to the first embodiment of the present invention, wherein (a) is the frequency spectrum of the friction speed and (b) is the power spectrum of the friction speed;

FIG. 17 is a graph showing the frequency spectrum and power spectrum of the 221 th cycle friction energy consumption according to the first embodiment of the present invention, wherein (a) is the frequency spectrum of the friction speed and (b) is the power spectrum of the friction speed;

FIG. 18 is a graph depicting a characteristic parameter of a friction characteristic variable distribution in accordance with a first embodiment of the present invention;

FIG. 19 is a graph showing the variation of the friction speed time-frequency parameter at different positions of the cutter tooth 1 according to the first embodiment of the present invention, wherein (a) is the friction speed kurtosis and (b) is the friction speed power spectrum entropy;

FIG. 20 is a graph showing the variation of the friction energy and time frequency parameters at different positions of the cutter tooth 1 according to the first embodiment of the present invention, wherein (a) is the friction speed kurtosis and (b) is the friction speed power spectrum entropy;

FIG. 21 is a graph of a variation in frictional characteristic variable characteristic parameter characterization according to a first embodiment of the present invention;

FIG. 22 shows the same position e of the different cutter teeth according to the first embodiment of the present invention ₁ A point friction speed time-frequency parameter change chart, wherein (a) is friction speed kurtosis and (b) is friction speed power spectrum entropy;

FIG. 23 shows the same position e of different cutter teeth according to the first embodiment of the present invention ₁ Point friction energy-consuming time-frequency parameterA digital variation graph, wherein (a) is friction speed kurtosis and (b) is friction speed power spectrum entropy;

FIG. 24 shows a 221 th cycle e of the first embodiment of the present invention ₁ Schematic cross-correlation function of point vibration and friction speed;

FIG. 25 is a 221 th cycle e of the first embodiment of the present invention ₁ Schematic diagram of cross-correlation function of point vibration and friction energy consumption;

FIG. 26 is a schematic diagram of experimental vibration signals according to a first embodiment of the present invention;

FIG. 27 is a schematic view of friction energy consumption at 221 th cycle of embodiment 2 in accordance with embodiment one of the present invention;

FIG. 28 is e of the first embodiment of the present invention ₁ A dot friction energy consumption kurtosis comparison chart;

FIG. 29 is e of the first embodiment of the present invention ₁ A point friction energy consumption power spectrum entropy comparison chart;

FIG. 30 is a schematic view showing accumulated frictional wear of the rear face of the cutter tooth according to embodiment 1 of the present invention;

FIG. 31 is a schematic diagram of the flank friction energy consumption frequency domain parameters and the wear depth of the embodiment 1 in the first embodiment of the present invention;

FIG. 32 is a schematic view showing cumulative frictional wear of the rear face of the cutter tooth according to embodiment 2 of the present invention;

fig. 33 is a schematic diagram of the flank friction energy consumption frequency domain parameter and the wear depth of the embodiment 2 in the first embodiment of the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention is described below by means of specific embodiments shown in the accompanying drawings. It should be understood that the description is only illustrative and is not intended to limit the scope of the invention. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the present invention.

The connection mentioned in the present invention is divided into a fixed connection and a detachable connection, wherein the fixed connection (i.e. the non-detachable connection) includes, but is not limited to, a conventional fixed connection manner such as a hemmed connection, a rivet connection, an adhesive connection, a welded connection, etc., and the detachable connection includes, but is not limited to, a conventional detachable manner such as a threaded connection, a snap connection, a pin connection, a hinge connection, etc., and when the specific connection manner is not specifically limited, at least one connection manner can be found in the existing connection manner by default, so that the function can be realized, and a person skilled in the art can select the connection according to needs. For example: the fixed connection is welded connection, and the detachable connection is hinged connection.

The first embodiment is as follows: 1-33, the method for identifying the unsteady friction characteristics of the rear cutter surface of the cutter tooth of the high-efficiency milling cutter according to the embodiment utilizes the influence of milling parameters, cutter tooth errors and cutter vibration on milling behaviors to establish an actual instantaneous cutting model to reveal the instantaneous pose of the milling cutter and the cutter tooth; constructing a milling cutter tooth-workpiece contact model, and revealing the instantaneous change of the friction characteristic variable of the rear cutter surface; revealing the unsteady state characteristic of the cutter tooth rear cutter face friction characteristic variable by a time domain-frequency domain conversion method; factor identification is performed by using a cross-correlation function, and specifically comprises the following steps:

step 1.1, acquiring workpiece structure parameters, cutting parameters, milling cutter structure parameters, cutter tooth installation angles, cutter tooth errors and cutter tooth structure parameters;

the cutter tooth error, the cutter tooth installation angle and the milling vibration directly affect the instantaneous position and the instantaneous cutting attitude angle of the milling cutter and further change the instantaneous contact relation and the instantaneous friction characteristic of the rear cutter face and the processing transition surface. The milling cutter structure and the contact relation between the milling cutter and the workpiece are shown in fig. 2.

In FIG. 2, o _i -x _i y _i z _i Z is the coordinate system of the cutter teeth of the milling cutter _i The shaft is a connecting line parallel to the lowest point of the cutter point and the cutting edge in the cutter tooth combining plane; y is _i The shaft is a connecting line parallel to the two cutter points in the cutter tooth combining plane. o (o) ₀ ′-x ₀ ′y ₀ ′z ₀ ' is a milling cutter coordinate system without vibration influence, origino ₀ ' is the intersection point of the central axis of the milling cutter and the plane of the lowest point of the cutter teeth, and x ₀ The' axis is the projection of the maximum radial error of the cutter teeth of the high-efficiency milling cutter and the plane of the lowest point of the axial cutter teeth, and z ₀ The' shaft is the central axis of the milling cutter and is directed towards the shank. o (o) ₀ -x ₀ y ₀ z ₀ For milling cutter coordinate system, point o ₀ And x _v 、y _v 、z _v Vibration-free cutting coordinate system origin o of efficient milling cutter with shaft ₀ ' and x ₀ ′、y ₀ ′、z ₀ The bias of the 'axis'. o (o) _v -x _v y _v z _v For milling cutter cutting coordinate system, origin o _v Is the intersection point of the central axis of the efficient milling cutter and the machined surface, x _v Through o of axis _v The point being parallel to x, y _v Through o of axis _v The point being parallel to y, z _v Through o of axis _v The point is parallel to z. o-xyz is a workpiece coordinate system, the x-axis is a milling feeding direction, the y-axis is a milling cutting width direction, the z-axis is a milling cutting depth direction, and o is an intersection point of three axes. X is x _L For the length of the work, y _L Z is the width of the workpiece _L V is the height of the workpiece _f For the feeding speed of the efficient milling cutter, n is the rotating speed of the efficient milling cutter, a _p For depth of cut, a _e For the cutting width, t is the cutting time,y at t _v Axis and y ₀ ' included angle of axis, r _max Is the maximum radius of gyration of the tooth point of the high-efficiency milling cutter, delta z _i Is the axial error delta r of the cutter tooth i and the cutter tooth i+1 of the high-efficiency milling cutter _i Is the radial error of the cutter teeth i and the cutter teeth i+1 of the high-efficiency milling cutter. l (L) ₁ The distance from the lowest point of the cutter tooth to the upper end face of the cutter handle; l (L) _i The distance from the lowest point of the cutter tooth i to the upper end face of the cutter handle is the distance; s is(s) ₀ S is the distance from the cutter tooth mounting plane to the cutter tooth cutter point ₁ S is the distance from the cutter tooth mounting plane to the lowest point of the cutter tooth cutting edge ₂ Is the distance between two cutter points of the cutter teeth. η (eta) _i The included angle is formed by connecting the origin of the cutter tooth coordinate system and the origin of the milling cutter coordinate system with the connecting line of the two cutter point; alpha ₀ Is the coordinate system z of the cutter tooth _i Z of axis-milling coordinate system ₀ Included angle of axes alpha ₁ An included angle is formed between the connecting line of the two tool nose points and the connecting line of the tool tip point and the lowest point of the cutting edge; θ _i Is the coordinate system x of the cutter teeth _i Axis and x being the milling cutter coordinate system ₀ The included angle of the axes.

The milling cutter coordinate system and the cutter tooth coordinate system conversion matrix are as follows:

the cutting coordinate system and the workpiece coordinate system transformation matrix are as follows:

the relation matrix of the milling cutter coordinate system and the cutting coordinate system without vibration influence is as follows:

the milling cutter coordinate system under the vibration effect and the milling cutter coordinate system conversion matrix without the vibration effect are as follows:

from fig. 3, the relationships among a workpiece coordinate system, a cutting coordinate system, a milling cutter coordinate system without vibration influence, a milling cutter coordinate system under vibration effect and a cutter tooth coordinate system are shown in fig. 3;

in FIG. 3, delta (t) is z ₀ Axis and z ₀ Angle of' axis delta ₁ (t) is z ₀ The axis is x ₀ ′o ₀ ′z ₀ Projection onto' plane and with z ₀ ' included angle, delta ₂ (t) is z ₀ The axis is at y ₀ ′o ₀ ′z ₀ Projection onto' plane and with z ₀ ' included angle, A _x (t) is the milling cutter t, x ₀ Vibration displacement in the' direction, A _y (t) is the milling cutter t, y ₀ Vibration displacement in the' direction, A _z (t) z when milling cutter t ₀ The vibration displacement in the' direction, l, is the amount of overhang of the milling cutter.

Step 1.2, calculating the track and the instantaneous attitude angle of a milling cutter and a cutter tooth under milling vibration, wherein under the influence of cutter tooth errors and milling vibration, the instantaneous positions of the milling cutter and the cutter tooth are in unsteady state offset, so that the instantaneous contact relation between a rear cutter surface and a processing transition surface in the process of cutting the cutter tooth into and out of a workpiece is directly changed, the instantaneous contact change directly influences the cutter tool contact state, and further friction characteristic variables have unsteady state characteristics;

In the milling cutter coordinate system, the origin coordinates of the cutter tooth coordinate system are as follows:

the trajectory of the origin of the cutting coordinate system in the workpiece coordinate system is:

in the method, in the process of the invention,time y for initial cutting t=0 for milling cutter ₀ ' axis and y _v An included angle of the shaft; />Is a milling cutter coordinate system y without vibration influence ₀ ' axis and cutting coordinate System y _v The included angle of the axes.

Milling cutter coordinate system z under vibration ₀ Shaft and milling cutter coordinate system z without vibration influence ₀ The included angle of the' axes is:

then the transformation matrix phi of the cutter tooth coordinate system and the workpiece coordinate system _i And the conversion moment of the milling cutter coordinate system and the workpiece coordinate system under the vibration effect

Matrix phi ₀ The method comprises the following steps of:

Φ _i ＝B ₁ ·B ₂ ·A ₃ ·A ₄ ·A ₂ ·B ₀ ·A ₁ ·A ₀ (12)

Φ ₀ ＝B ₁ ·B ₂ ·A ₃ ·A ₄ ·A ₂ (13)

milling cutter coordinate system origin o under vibration effect ₀ The trajectories in the object coordinate system are:

milling cutter coordinate system y under vibration ₀ The included angle between the axis and the y axis of the workpiece coordinate system is as follows:

cutter tooth coordinate system origin o _i The trajectories in the object coordinate system are:

o _i (x(t),y(t),z(t))＝Φ _i ·[0 0 0 1] ^T (16)

the instantaneous position and the posture of the milling cutter under the vibration action can be obtained by the formula (10), the formula (11), the formula (14) and the formula (15). Using alpha ₀ 、θ _i And the instantaneous pose of the cutter teeth under the vibration action can be obtained by the formula (11), the formula (15) and the formula (16).

And 1.3, calculating contact angles of cutting teeth into and out of the workpiece, establishing a conversion matrix from a cutter tooth coordinate system to the workpiece coordinate system by utilizing the instantaneous contact relation between the milling cutter and the workpiece under the vibration action, obtaining the influence characteristics of vibration and cutter tooth errors on the instantaneous cutting pose and the processing transition surface of the milling cutter and the cutter tooth, and constructing the characteristic time and contact angle calculation method of cutting teeth into and out of the workpiece.

The cutting contact angle of the cutter tooth under the vibration action is shown in fig. 4:

in FIG. 4, a ₀ A is the intersection point of the cutter tooth and the workpiece when the cutter tooth is cut in ₁ For the intersection point of the cutter tooth and the workpiece when cutting, y ⁰ (t ₀ ) For the longitudinal coordinate value, x, of the origin of the milling cutter coordinate system in the workpiece coordinate system when the cutter tooth cuts into the workpiece ⁰ (t ₀ ) For the abscissa value, y of the origin of the milling cutter coordinate system in the workpiece coordinate system when the cutter tooth cuts into the workpiece ⁰ (t ₁ ) Ordinate value, x, of origin of milling cutter coordinate system in workpiece coordinate system when cutting workpiece for cutter tooth ⁰ (t ₁ ) And (3) the abscissa value of the origin of the milling cutter coordinate system in the workpiece coordinate system when the cutter tooth cuts out the workpiece.

From FIG. 4, the point a of the cutting edge of the cutter tooth is solved by utilizing the track equation of the cutting edge of the cutter tooth i and the side equation of the workpiece ₀ The point coordinates and the characteristic time of the cutter tooth cutting into the workpiece.

x(t ₀ )＝min(x(t))；t _T ≤t≤t _T +Δt (18)

Wherein: f (F) _i (x (t), y (t), z (t)) is the path equation of the cutting edge of the cutter tooth i, F _i (x _i ，y _i ，z _i ) Is the cutting edge equation.

Solving the position point a of a cutter tooth cutting workpiece by utilizing a track equation of a cutter tooth i cutting edge and a processing transition surface equation formed by the last cutter tooth cutting edge ₁ The point coordinates and the characteristic time of cutting the workpiece by the cutter teeth.

x(t ₁ )＝max(x(t))；t _T ≤t≤t _T +Δt (20)

Wherein: f (F) _i-1 (x _i-1 ，y _i-1 ，z _i-1 ) For cutter tooth i-1 cutting edge equation, G _i-1 (x (t), y (t), z (t)) is the transition surface equation formed by the cutting edge of the cutter tooth i-1 in the workpiece coordinate system. t is t ₀ ^i-1 For the moment of cutting the cutter tooth i-1, t ₁ ^i-1 The cutting time is the cutting time of the cutter tooth i-1.

The contact angle of the cutter tooth i as the cutting edge cuts into can be expressed as:

the contact angle of the cutting edge of tooth i as it cuts out can be expressed as:

selecting a high-feed milling cutter with the diameter of 32mm, and the rotating speed of 1104r/min and v _f 500mm/min, a _p Is 0.5mm, a _e Milling titanium alloy experiments are carried out by adopting a milling mode of down milling and with cutting parameters of 16mm. The error distribution of the cutter teeth of the milling cutter is shown in table 1.

TABLE 1 milling cutter tooth error distribution

When the experimental scheme is adopted to obtain that the cutting stroke is 250mm, the DH5922 transient signal test analysis system is utilized to measure the vibration of the efficient milling cutter, and five periods are selected in the range and are shown in figure 5.

According to vibration characteristics reflected by vibration signals obtained through experiments, a cutting period (t ₁ ) The instantaneous attitude angle and cutting motion trajectory of the milling cutter and its cutter teeth are shown in fig. 6.

By utilizing the instantaneous contact relation between the milling cutter and the workpiece under the vibration action, a conversion matrix from a cutter tooth coordinate system to a workpiece coordinate system is established, the influence characteristics of vibration and cutter tooth errors on the instantaneous cutting pose and the processing transition surface of the milling cutter and the cutter tooth are revealed, and the characteristic time and contact angle resolving method for cutting the cutter tooth into and out of the workpiece are provided.

Under the influence of cutter tooth errors and milling vibration, the instantaneous pose of the milling cutter and the cutter tooth is in unsteady state bias, and the instantaneous contact relation between the rear cutter surface and the processing transition surface in the process of cutting the cutter tooth into and out of the workpiece is directly changed. Whereas a change in instantaneous contact will directly affect the tool contact state and thus result in a friction characteristic variable having non-steady state characteristics.

step 2.1, performing processing transition surface calculation formed by the cutter tooth cutting edge, cutter tooth rear cutter face instantaneous pose calculation and cutter tooth rear cutter face instantaneous thermal coupling field calculation;

step 2.2, obtaining a contact geometric variable, an instantaneous contact relative motion variable and an instantaneous contact stress according to the step 2.1;

step 2.3, establishing an instantaneous contact model of the rear cutter surface of the cutter tooth of the milling cutter and a processing transition surface according to the step 2.2, and calculating an instantaneous friction speed vector of any point of the rear cutter surface of the cutter tooth through a kinematic and geometric relationship; calculating instantaneous friction energy consumption by utilizing an atomic interface theory, and calculating an instantaneous friction coefficient according to the relationship that the assumed friction energy consumption is equal to heat energy conversion; and solving the instantaneous friction stress by utilizing a thermal coupling field of finite element simulation through a change equation of positive stress and tangential stress obtained by a stress conversion model, and obtaining the time-varying characteristic of the friction variable of the rear cutter surface of the cutter tooth under the influence of vibration action and cutter tooth error of the milling cutter.

The method comprises the following steps:

the instantaneous contact relationship between the relief surface of the tooth and the machined transition surface under the influence of vibration and tooth error is shown in fig. 7.

The machining transition surface equation formed by the cutting edge of the cutter tooth i is as follows:

G _i (x(t),y(t),z(t))＝Φ _i ·g _i (x _i ,y _i ,z _i )，t ₀ ≤t≤t ₁ (23)

the instantaneous pose of the rear cutter face of the cutter tooth in the workpiece coordinate system is as follows:

H _i (x(t),y(t),z(t))＝Φ _i ·H _i (x _i ,y _i ,z _i ) (24)

normal vector of any point on rear cutter face of cutter tooth in workpiece coordinate systemThe components are as follows:

then the instantaneous attitude angle of any point on the rear cutter surface of the cutter tooth in the workpiece coordinate system is as follows:

the relative movement velocity components of any point on the rear cutter surface of the cutter tooth in the workpiece coordinate system are as follows:

the instantaneous friction speed of the rear cutter face of the cutter tooth is as follows:

v _m (t)＝sin(π-γ(t))·v(t) (28)

the friction speed is converted into a cutter tooth coordinate system through coordinate transformation to be expressed as follows.

Selecting the abscissa of the lowest point of the cutter tooth structure after the cutter tooth is mounted as a reference, intersecting a perpendicular line passing through the point as a mounting surface in a cutter tooth coordinate system with the upper and lower friction boundaries, and sequentially taking three points between the intersecting points as e respectively ₁ 、e ₂ 、e ₃ . The magnitude of the friction speed at three points in the three cutter teeth is now specifically calculated as shown in fig. 8.

As is apparent from fig. 8, the variation of the maximum value, the extremely poor, the root mean square, the kurtosis and the skewness of the friction speed at the same point of the same cutter tooth in the same period shows randomness, but the variation is not obvious from the numerical value, and the variation is also reflected in different points of different cutter teeth in different periods; the large kurtosis indicates that the milling cutter vibrates more frequently when cutting in, so that the whole curve protrudes upwards; the deviation indicates that the peak value of the time domain characteristic curve deviates leftwards or rightwards, and if the deviation is positive, the curve in the time domain deviates rightwards, which indicates that the variation value of the friction speed of the cutter tooth in an effective cutting is smaller than the average value of the friction speed in most cases; indicating that the friction speed shows unsteady state and non-periodic variation characteristics under the vibration action.

Because a great amount of energy consumption is generated when a cutter contacts instantaneously, the energy consumption is one of main factors causing cutter abrasion, and a friction energy consumption resolving model is constructed by utilizing the energy conversion relation among cutter interface atoms in order to resolve the dynamic characteristic of the instantaneous friction energy consumption of the rear cutter face of the cutter tooth pair, as shown in the following formula.

By utilizing the energy conversion relation between tool interface atoms, a friction energy consumption resolving model is constructed, and the absorption energy obtained by the interface atom theory is as follows:

wherein E is the energy absorption at time t, ω 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 _es1 And t _es2 Respectively the instantaneous initial time and the final time of energy absorption; v _mi (x _i ,y _i ,z _i T) is the friction speed of any point t of the rear cutter surface of the cutter tooth in the cutter tooth coordinate system; t is the temperature rise of an atomic interface.

Wherein: m is the relative atomic mass of the atoms is 4.34 multiplied by 10 ^-26 kg，ω _n Is of atomic natural frequency 4.39X10 ¹¹ rad/s, Q is the interface potential energy field excitation force pair 1×10 ^-9 N。

The magnitude of the friction energy consumption at three points in the three cutter teeth is now specifically calculated as shown in fig. 9.

The uncertainty of the friction boundary of the rear cutter face of the cutter tooth is revealed by establishing a criterion of the friction upper and lower boundaries of the rear cutter face of the cutter tooth; and characterizing the friction variable by utilizing a time domain characteristic parameter through a friction variable calculation model to obtain a time domain maximum value, a range, a root mean square value, kurtosis and skewness of the friction variable, and obtaining the unsteady state characteristic of the friction variable in the time domain.

The upper friction boundary is obtained by comparing the yield strength of the tool material with the equivalent stress. The discrimination method is shown in the following formula.

σ(x _i ,y _i ,z _i ,t)≥σ _s (36)

Wherein: sigma is equivalent stress, sigma _s Is the yield strength.

As shown in FIG. 10, the instantaneous coordinates (x) of the upper friction boundary can be obtained by the formula (36) _i (t)，y _i (t)，z _i (t)) and then reconstruct the instantaneous friction upper boundary equation.

The lower boundary of the cutter tooth instantaneous friction is identified by the strain mutation rate along the normal vector direction of the cutting edge, and the distinguishing method is as follows:

wherein: ε is the equivalent strain, ε' is the equivalent strain rate.

As shown in FIG. 11, the instantaneous coordinate (x) of the friction lower boundary can be obtained by the formula (37) _i (t)，y _i (t)，z _i (t)) and thereby reconstruct the instantaneous friction lower boundary equation.

The friction upper and lower boundaries are calculated by equations (36) and (37) as shown in fig. 12:

the cutter tooth rear cutter surface friction area D is an area formed by surrounding an instantaneous friction left and right boundary formed by intersecting an instantaneous friction upper and lower boundary of an initial cutting edge of the milling cutter with the left and right sides and the instantaneous friction upper and lower boundary, and a rear cutter surface point e is any point in the friction area. The following formula is shown:

In order to obtain the change characteristics of the friction characteristic variable in the time domain more accurately and intuitively. The time domain feature parameters are selected for characterization, as shown in FIG. 13, and the maximum, minimum, root mean square, kurtosis and skewness are used for calculation.

Root mean square:

kurtosis:

degree of deviation:

the maximum value, the extremely poor, the root mean square value, the kurtosis and the variation of the skewness of three points of three cutter teeth in five cycles of the friction speed are changed, and a radar chart is adopted as shown in fig. 14:

as is apparent from fig. 14, the maximum, minimum and root mean square values in the high efficiency milling cutter in-and-out cycles are significantly greater than in-three cycles; the kurtosis of the time domain curve of the friction speed in five periods has some randomness in the cutting-in period and the cutting-out period, but the kurtosis is integrally larger when the friction speed is cut in and cut out can be directly seen. The large kurtosis indicates that the milling cutter vibrates more frequently when cutting in, so that the whole curve protrudes upwards; the deviation indicates that the peak value of the time domain characteristic curve deviates leftwards or rightwards, and if the deviation is positive, the curve in the time domain deviates rightwards, which indicates that the variation value of the friction speed of the cutter tooth in an effective cutting is smaller than the average value of the friction speed in most cases; indicating that the friction speed is greatly affected by vibration.

The maximum value, the extremely poor, the root mean square value, the kurtosis and the variation of the skewness of three points of three cutter teeth in five cycles of friction energy consumption are shown in a radar chart as shown in fig. 15:

as can be directly derived from fig. 15, the time-domain curve skewness of the friction energy in five cycles is negative in all three tooth skewness in the 311 th cycle of the tangent, which means e in this cycle ₁ The friction energy consumption value of the characteristic points has larger fluctuation frequency and the number of points smaller than the average value is larger than the number of points larger than the average value, or the friction energy consumption value is larger than the average value and the number of points smaller than the average value is smaller and is an odd value; the maximum fluctuation value of the friction energy consumption in five periods, namely the deviation is 406.6948; the figure also shows some subtle manifestations of friction energy consumption, when cutting into a workpiece, the friction energy consumption tends to rise with the increase of cutting time, and after a certain time, the friction energy consumption tends to fall.

the uncertainty of the frequency domain characteristics of the cutter tooth rear cutter face friction variable is obtained by establishing a conversion relation of the cutter tooth rear cutter face friction variable from a time domain to a frequency domain; the friction variable is characterized by utilizing frequency domain characteristic parameters, the frequency spectrum of the friction variable is used for revealing the intensity of the friction characteristic variable, namely the amplitude of a main frequency of the frequency spectrum, the main frequency of the frequency spectrum and the frequency of the gravity center, the frequency of the gravity center reveals the stability of the frequency spectrum of the friction characteristic variable, the power spectrum entropy reveals the complexity of the power spectrum of the friction variable, namely the amplitude of the main frequency of the power spectrum, the main frequency of the power spectrum and the power spectrum entropy, and the non-periodic unsteady characteristic of the friction variable in the frequency domain is revealed.

Fourier transforming the time domain continuous signal is transferred to frequency domain analysis. The specific operation is as follows:

e ^-iωt ＝cos(ωt)-i·sin(ωt) (42)

wherein: omega is the angular frequency; f is the frequency; x (t) is a time domain signal.

In practical situations, the obtained signal is discontinuous, but the signal with discrete sampling frequency is adopted, so that the sampling value is subjected to Fourier transform to obtain a frequency spectrum formula:

wherein: k is the index frequency; n is the number of samples; m is the sampling rate; t is the sequence time; x (q) is a time domain discrete sequence.

The power spectrum can be expressed as:

the power spectral entropy is a quantitative description of how complex the information is to be in the energy distribution in the frequency domain. First, the density distribution function of the power spectrum of each frequency band is calculated.

Since the symmetry of the spectrum and the power spectrum is to reduce the amount of computation, only half of the discrete points need to be computed.

The center of gravity frequency is:

the power spectrum entropy is:

the uncertainty of the frequency domain characteristics of the cutter tooth rear cutter face friction variable is revealed by establishing a conversion model of the cutter tooth rear cutter face friction variable from a time domain to a frequency domain; the friction variable is characterized by utilizing the frequency domain characteristic parameters, the intensity of the friction characteristic variable change is revealed by adopting the frequency spectrum, the stability of the friction characteristic variable frequency spectrum is revealed by the gravity center frequency, and the complexity of the power spectrum is revealed by the power spectrum entropy. Non-periodic unsteady state characteristics of friction variation in the frequency domain are disclosed.

Pair e ₁ The calculation of the frequency spectrum and power spectrum of the point friction velocity is shown in fig. 16 and table 2:

TABLE 2e ₁ Numerical value of point friction speed spectrum and power spectrum

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Pair e ₁ The calculation of the spectrum and power spectrum of the point friction energy consumption is shown in fig. 17 and table 3:

TABLE 3e ₁ Numerical value of point friction energy consumption spectrum and power spectrum

selecting the abscissa of the lowest point of the cutter tooth structure after the cutter tooth is mounted as a reference, intersecting a perpendicular line passing through the point as a mounting surface in a cutter tooth coordinate system with the upper and lower friction boundaries, and sequentially taking three points between the intersecting points as e respectively ₁ 、e ₂ 、e ₃ And (3) carrying out distribution characteristic parameter characterization on the time-frequency characteristic parameter curves of the three points and the five periods, and analyzing by using the extremely poor, root mean square value and association degree.

As shown in fig. 18, the extreme differences are:

the specific way of the correlation degree is to make the cutter tooth 1e ₁ Set as reference sequence notation X _1j (j=0, 1 …, N) with a comparison sequence of cutter teeth 1e ₂ And cutter tooth 1e ₃ Record X separately _2j And X _3j 。

X _1j ＝{X _1j (0),X _1j (1),...,X _1j (N)} (54)

X _2j ＝{X _2j (0),X _2j (1),...,X _2j (N)} (55)

X _3j ＝{X _3j (0),X _3j (1),...,X _3j (N)} (56)

The three sequence variation coefficients are calculated as follows:

thus the sequence delta (X _1j ) And delta (X) _2j )、δ(X _1j ) And delta (X) _3j ) The degree of association of (2) is as follows:

the kurtosis in the five-cycle time domain and the power spectrum entropy curves of the frequency domain of the friction speeds at different points of the same cutter tooth are now characterized, as shown in fig. 19.

TABLE 4 characterization values of the frictional velocity kurtosis and the Power spectral entropy curves at different positions of cutter tooth 1

From Table 4, the cutter tooth 1e is shown ₁ The maximum difference of the point friction speed is the largest, the root mean square of the three points is almost the same, and e in the cutter tooth 1 ₂ The point association is minimal. And the association degree of the points of different characteristics in the power spectrum entropy value is not changed greatly.

The kurtosis in the five-cycle time domain and the power spectrum entropy curves of the frequency domain of the friction energy consumption of different points of the same cutter tooth are now characterized, as shown in fig. 20 and table 5.

TABLE 5 characterization values of the frictional energy consumption kurtosis and the Power spectral entropy curves at different positions of cutter tooth 1

and (3) carrying out differential characteristic parameter characterization on kurtosis and power spectrum entropy of the same characteristic points of three cutter teeth in five periods, and analyzing by using the range, root mean square value and correlation, namely obtaining time domain characteristic parameters, frequency domain characteristic parameters, friction variable distribution characteristic parameters and cutter tooth friction differential characteristic parameters through calculation of cutter tooth rear cutter face friction unsteady characteristic parameters.

By e of cutter tooth 1 ₁ And taking the point as a reference, and sequentially taking the same coordinate point of the cutter teeth 2 and 3 in a cutter tooth coordinate system. The kurtosis and the power spectrum entropy of the same characteristic point of three cutter teeth in five periods are subjected to differential characteristic parameter characterization, and the analysis is carried out by using the range, the root mean square value and the association degree, as shown in fig. 21. Wherein e of cutter tooth 1 ₁ The kurtosis and the power spectrum entropy of the five cutting periods are taken as reference sequences to respectively obtain e of the cutter tooth 2 and the cutter tooth 3 ₁ Point and tooth 1 e ₁ Degree of point association.

The kurtosis in the five-cycle time domain and the power spectrum entropy curves of the frequency domain of the same point friction speeds of different cutter teeth are characterized as shown in fig. 22.

TABLE 6 same position e of different cutter teeth ₁ Characterization value of point friction speed kurtosis and power spectrum entropy curve

From table 6, it is known that the difference, root mean square and correlation of the friction speeds at the same point of different cutter teeth are random. And the cutter tooth 3e with the maximum power spectrum entropy value and root mean square value ₁ The point association is small. Therefore, the power spectrum entropy values of the same point in different periods are different, and the difference of the performances is obvious.

The kurtosis in the five-cycle time domain and the power spectrum entropy curves of the frequency domain of the friction energy consumption of the same point of different cutter teeth are characterized, as shown in fig. 23.

TABLE 7 same position e of different cutter teeth ₁ Characterization value of point friction energy consumption kurtosis and power spectrum entropy curve

and obtaining influence factors of milling cutter vibration and cutter tooth rear cutter surface friction variables by establishing a cross-correlation function of the milling cutter vibration and the cutter tooth rear cutter surface friction variables, and revealing influence degree of the milling cutter vibration on the friction variables through the cross-correlation coefficient value.

Since the randomness of vibration has an influence on the characteristics of the friction characteristic parameters, the cross-correlation function calculation is carried out on the five-period vibration acceleration of the characteristic points and the friction characteristic variable:

the cross-correlation function for a continuous signal can be expressed as:

but is typically performed at a limited number of points in the time domain signal, the cross-correlation function of two discrete pieces of information can be expressed as:

wherein: y is ₁ Is a set of discrete sequences; y is ₂ Is another set of discrete sequences; τ is the time shift.

The influence factors of milling cutter vibration and cutter tooth rear cutter surface friction variables are revealed by establishing a cross-correlation function of the milling cutter vibration and the cutter tooth rear cutter surface friction variables; the influence degree of milling cutter vibration on the friction variable is revealed through the cross-correlation coefficient value.

With vibration acceleration y ₁ Friction speed y ₂ The solution to equation (63) is as shown in fig. 24:

TABLE 8e ₁ Cross-correlation coefficient value of point vibration and friction speed

From Table 8, it can be seen that the vibrationInfluence relation of different directions of dynamic acceleration on the same point of different periods and different cutter teeth. The tangential direction of the vibration acceleration affects different periods and different cutter teeth to a greater extent than the feed direction and the tangential direction as a whole. Locally, the tangential width direction of the vibration acceleration is larger than the feed direction than the influence of the tangential depth direction on the friction speed in a single cycle, but a slight run-out occurs in the respective cycle. Cutter teeth 2e as in cycle 1 and 311 ₁ Point and cutter tooth 3e ₁ The cross-correlation coefficient of the points belongs to strong correlation below 0.5, and besides, the cross-correlation values in the x direction are all larger than 0.5, and the cross-correlation values in the y direction are all larger than 0.7, so that the points belong to remarkable correlation; the magnitude order of the influence of the direction of the vibration acceleration on the friction speed is: in the width direction>Direction of feed>And (5) cutting the depth direction.

With vibration acceleration y ₁ Friction energy consumption is y ₂ The solution to equation (63) is shown in fig. 25 and table 9:

TABLE 9e ₁ Cross-correlation coefficient value of point vibration acceleration and friction energy consumption

It can be seen from table 9 that the tangential width direction of the vibration acceleration is larger than the feed direction in the single cycle than the effect of the tangential depth direction on the friction speed, but that some runout occurs in the respective cycle. For example, 136 th cycle tooth 3e ₁ And the tangential width direction of the vibration acceleration is larger than the tangential depth direction and larger than the feeding direction, so that friction energy is more consumed. But the correlation coefficient values in the depth direction and the feed direction are real correlations and the difference is 0.0732. The order of influence of the direction of the vibration acceleration on the friction energy consumption is as follows: in the width direction>Direction of feed>And (5) cutting the depth direction.

The method for obtaining the cutter tooth rear cutter surface friction characteristic identification and process scheme discrimination results comprises the following steps:

Step 8.1, selecting high-efficiency milling cutters with the same diameter, and adopting a down milling mode to carry out a milling titanium alloy experiment;

step 8.2, according to structural parameters of the milling cutter and the cutter teeth, utilizing cutter tooth errors and vibration data obtained by a milling titanium alloy experiment, solving instantaneous friction energy consumption of three cutter teeth at three points in five periods according to a friction energy consumption model, utilizing fast Fourier change to solve frequency domain parameters, selecting kurtosis of time domain parameters and power spectrum entropy of the frequency domain parameters for comparison analysis, and verifying sensitivity of the model;

and 8.3, calculating friction energy consumption by using an experimental parameter of a milling titanium alloy experiment, utilizing a cutter tooth pose resolving model, a cutter tooth cutting-in and cutting-out contact angle model, a cutter instantaneous contact relation model and a friction characteristic variable resolving model, obtaining frequency domain parameter fluctuation ranges of different characteristic points of three cutter teeth by utilizing Fourier transformation, comparing and analyzing a correlation result of a cutter tooth rear cutter face friction wear morphology section curve and a cutter tooth unworn morphology section curve according to the measured milling titanium alloy experiment, and judging the accuracy of the model according to the similarity of the frequency domain characteristic parameter fluctuation ranges and wear distribution nonuniformity.

Selecting high-efficiency milling cutters with the same diameter, wherein the rotating speed is 1305r/min and v _f 500mm/min, a _p Is 0.5mm, a _e And (3) carrying out milling titanium alloy experiments in a milling mode under the condition of 16mm cutting parameters. The error distribution of the cutter teeth of the milling cutter is shown in the table.

Table 10 distribution of cutter tooth error for milling cutter

A transient signal of the vibration of the high efficiency milling cutter at a cutting stroke of 250mm was obtained and five cycles were selected within this range as shown in fig. 26.

The friction speed is obtained according to the friction energy consumption calculation model, and the change characteristics of the friction energy consumption of three characteristic points of three cutter teeth in five periods are shown in fig. 27:

as can be seen from fig. 27, the friction energy consumption exhibits a transient behavior. The vibration of the milling cutter is severe due to the fact that the instantaneous cutting force is large when the milling cutter is in instantaneous cutting, so that the contact relation between the rear cutter surface of the cutter tooth and the processing transition surface becomes unstable, and the fluctuation of energy absorbed by interface atoms is large. The friction energy consumption calculated by the scheme 1 is compared with the friction energy consumption calculated by the scheme 2, and the friction energy consumption shows a decreasing trend along with the increase of the rotating speed.

Scheme 1 and scheme 2, e ₁ And comparing and analyzing the kurtosis in each time domain and the power spectrum entropy value in the frequency domain of the point friction speed and the friction energy consumption. In the following figure, 1 is the first cycle of milling cutter cutting, 2 is the 136 th cycle of milling cutter cutting, 3 is the 221 th cycle of milling cutter cutting, 4 is the 311 th cycle of milling cutter cutting, and 5 is the last cycle of milling cutter cutting.

From fig. 28 and 29, it is apparent that the friction speeds and the friction energy consumption kurtosis of the schemes 1 and 2 have variability, and the kurtosis of the scheme 2 is significantly lower than that of the scheme 1, and the power spectrum entropy values of the friction speeds and the friction energy consumption are much smaller in the scheme 2 than that of the scheme 1. This indicates that the power spectral entropy of friction energy consumption is a tendency to decrease as the rotational speed increases, which also indicates the reliability of the flank unsteady state friction characteristic identification method.

The wear profile section curves obtained with the white light interferometer according to the milling conditions of experiment 1 were compared with the profile section curves of unworn cutter teeth at the same position as follows.

In FIG. 30, the cutter tooth morphology scale origin is 3470 μm and 5880 μm in abscissa relative to the cutter tooth origin.

Table 11 relief surface Friction energy consumption frequency Domain parameters and experimental analysis results (scheme 1)

W1 in Table 11 is the dominant frequency variation range; w2 is the spectrum amplitude variation range; w3 is the center of gravity frequency variation range; w4 is the power spectrum entropy change range; w5 is the maximum value of the power spectrum entropy; gamma is the correlation degree of the cutter tooth wear profile section curve and the cutter tooth unworn profile section curve; 1-gamma is wear distribution non-uniformity.

For more visual representation and analysis, the friction energy consumption frequency domain parameter values in the table are processed by dividing each column data by the maximum value as shown in fig. 31.

In FIG. 31, 1, 2 and 3 are e, respectively, characteristic points of the cutter tooth 1 ₁ 、e ₂ 、e ₃ And 4, 5 and 6 are respectively the e characteristic points of the cutter tooth 2 ₁ 、e ₂ 、e ₃ And 7, 8 and 9 are respectively the e characteristic points of the cutter tooth 3 ₁ 、e ₂ 、e ₃ . As can be seen from the graph, the main frequency variation range, the spectrum amplitude variation range, the center of gravity frequency variation range and the power spectrum entropy variation range have the same variation trend at different points of the same cutter tooth, and the amplitude variation range, the center of gravity frequency variation range and the power spectrum entropy variation range have larger fluctuation.

The wear profile cross-section curve obtained with a white light interferometer according to the milling conditions of experiment 2 was compared with the profile cross-section curve of the unworn cutter tooth at the same position as follows.

In fig. 32, the cutter tooth morphology scale origin of coordinates is 3470 μm and 5880 μm on the abscissa with respect to the cutter tooth origin of coordinates.

Table 12 the rear blade friction energy consumption frequency domain parameters and experimental analysis results (scheme 2)

For more visual representation and analysis, the friction energy consumption frequency domain parameter values in table 12 are processed by dividing each column data by the maximum value as shown in fig. 33.

From the graph, the distribution trend of the friction energy consumption frequency domain parameters at the characteristic points of the tool face of different cutter teeth is gradually reduced, and the distribution trend is similar to the trend of the uneven wear distribution of the tool face of the cutter teeth. The distribution of the spectrum amplitude variation range and the distribution of the power spectrum entropy variation range under different cutter teeth have larger fluctuation.

Comparative analyses of experimental scheme 1 and experimental scheme 2 are shown in table 13:

table 13 correlation degree of the friction energy consumption frequency domain parameter distribution and the abrasion test result of the rear tool face

From table 13, it can be obtained that the correlation coefficient between the wear distribution non-uniformity of the cutter tooth rear cutter surface and the friction energy consumption frequency domain characteristic parameter fluctuation distribution is larger than 0.59, wherein the main frequency fluctuation range distribution and the power spectrum entropy fluctuation range distribution of the experimental scheme 1 have higher similarity with the wear distribution non-uniformity distribution, and the power spectrum entropy fluctuation range distribution and the main frequency fluctuation range distribution and the wear distribution non-uniformity distribution of the experimental scheme 2 have higher similarity; due to the change of cutter tooth errors, milling parameters and milling vibration, fluctuation distribution of characteristic parameters of a friction energy consumption frequency domain and non-uniformity of wear distribution are obviously changed. Experiments show that the friction and wear distribution non-uniformity can be obviously reflected by utilizing the friction and energy consumption frequency domain characteristic parameters.

It should be noted that, in the above embodiments, as long as the technical solutions that are not contradictory can be arranged and combined, those skilled in the art can exhaust all the possibilities according to the mathematical knowledge of the arrangement and combination, so the present invention does not describe the technical solutions after the arrangement and combination one by one, but should be understood that the technical solutions after the arrangement and combination have been disclosed by the present invention.

The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. The method for identifying the unsteady friction characteristics of the rear cutter surface of the cutter tooth of the efficient milling cutter is characterized by comprising the following steps:

the step 1 comprises the following steps:

step 1.3, calculating contact angles of cutting teeth cutting into and cutting out a workpiece, establishing a conversion matrix from a cutter tooth coordinate system to the workpiece coordinate system by utilizing the instantaneous contact relation between a milling cutter and the workpiece under the action of vibration, obtaining the influence characteristics of vibration and cutter tooth errors on the instantaneous cutting pose and the processing transition surface of the milling cutter and the cutter tooth, and constructing a characteristic time and contact angle calculation method of cutting teeth cutting into and cutting out the workpiece;

the step 2 comprises the following steps:

step 2.3, establishing an instantaneous contact model of the rear cutter surface of the cutter tooth of the milling cutter and a processing transition surface according to the step 2.2, and calculating an instantaneous friction speed vector of any point of the rear cutter surface of the cutter tooth through a kinematic and geometric relationship; calculating instantaneous friction energy consumption by utilizing a thermodynamic coupling field and an atomic interface theory of finite element simulation, and obtaining time-varying characteristics of a cutter tooth rear cutter surface friction variable under the influence of vibration action and cutter tooth errors of a milling cutter;

the step 3 comprises the following steps: the uncertainty of the friction boundary of the rear cutter face of the cutter tooth is revealed by establishing a criterion of the friction upper and lower boundaries of the rear cutter face of the cutter tooth; characterizing the friction variable by utilizing time domain characteristic parameters through a friction variable calculation model to obtain a time domain maximum value, a range, a root mean square value, kurtosis and skewness of the friction variable, and obtaining the unsteady state characteristic of the friction variable in the time domain;

the step 4 comprises the following steps: the uncertainty of the frequency domain characteristics of the cutter tooth rear cutter face friction variable is obtained by establishing a conversion model of the cutter tooth rear cutter face friction variable from a time domain to a frequency domain; the friction variable is characterized by utilizing frequency domain characteristic parameters, the frequency spectrum of the friction variable is used for revealing the intensity of the friction characteristic variable, namely the amplitude of a main frequency of the frequency spectrum, the main frequency of the frequency spectrum and the frequency of the gravity center, the frequency of the gravity center reveals the stability of the frequency spectrum of the friction characteristic variable, the power spectrum entropy reveals the complexity of the power spectrum of the friction variable, namely the amplitude of the main frequency of the power spectrum, the main frequency of the power spectrum and the power spectrum entropy, and the non-periodic unsteady characteristic of the friction variable in the frequency domain is revealed;

the step 5 comprises the following steps: selecting the abscissa of the lowest point of the cutter tooth structure after the cutter tooth is mounted as a reference, intersecting a perpendicular line passing through the point as a mounting surface in a cutter tooth coordinate system with the upper and lower friction boundaries, and sequentially taking three points between the intersecting points as e respectively ₁ 、e ₂ 、e ₃ For the time-frequency characteristic parameters of the three points and the five periodsThe curve is characterized by the distribution characteristic parameters, and the extremely poor, root mean square value and association degree are used for analysis;

the step 6 comprises the following steps: carrying out differential characteristic parameter characterization on kurtosis and power spectrum entropy of the same characteristic points of three cutter teeth in five periods, and analyzing by using the range, root mean square value and association degree, namely obtaining time domain characteristic parameters, frequency domain characteristic parameters, friction variable distribution characteristic parameters and cutter tooth friction differential characteristic parameters through calculation of cutter tooth rear cutter face friction unsteady characteristic parameters;

the step 7 comprises the following steps: the influence factors of the milling cutter vibration and the cutter tooth rear cutter surface friction variable are obtained by establishing a cross-correlation function of the milling cutter vibration and the cutter tooth rear cutter surface friction variable, and the influence degree of the milling cutter vibration on the friction variable is revealed through the cross-correlation coefficient value;

step 8, response characteristics and experimental verification methods of cutter tooth rear cutter face friction;

step 8 obtains the cutter tooth rear cutter surface friction characteristic identification and process scheme discrimination results, and comprises the following steps: