CN105608288B - One kind being based on overdamp effect milling parameter stability prediction method - Google Patents
One kind being based on overdamp effect milling parameter stability prediction method Download PDFInfo
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Abstract
The present invention provides a kind of based on overdamp effect milling parameter stability prediction method,This method is in carrying out workpiece milling process,Obtain milling cutter geometrical structure parameter and milling process dynamic parameter,Determine the gross energy that plow power generates in workpiece milling process in a pirouette period,Utilize law of conservation of energy,Obtain equivalent linearity process damped coefficient,The damping of equivalent linearity process is changed into the equivalent processes damping of the directions x and the damping of the directions y equivalent processes,The directions x equivalent processes damped coefficient and the directions y equivalent processes damped coefficient input milling dynamics equation are obtained into the milling dynamics model of Kernel-based methods damping effect,The milling dynamics model of Kernel-based methods damping effect is solved using ZOA methods,Obtain the flutter stability model of Kernel-based methods damping effect,To obtain the relationship between marginal stability cutting-in and cutter rotating speed,And draw the flutter stability flap figure of Kernel-based methods damping effect.
Description
Technical Field
The invention belongs to the field of machining, and particularly relates to a milling chatter stability prediction method based on an over-damping effect.
Background
Milling is widely applied to industries such as aerospace dies, and regenerative flutter is one of main limiting factors for improving production efficiency. The development of the high-speed machining theory avoids the chatter vibration by selecting the rotating speed of the main shaft and synchronizing the cutting frequency and the chatter vibration frequency of the cutter teeth. At high milling speeds with higher material removal rates, classical flutter lobe maps provide accurate stability predictions. However, in the low speed processing stage, the lobe pattern is too dense due to the large number of complete vibration wavelengths in one rotation cycle of the spindle, so that the classical flutter theory often cannot accurately predict the stability. On the other hand, experimental observations indicate that the stable cutting area of the system increases significantly when the cutting speed is much lower than the natural frequency of the machining system. This significant increase in stable cutting area during low speed cutting can be attributed to the change in cutting speed caused by the frictional interaction between the flank of the tool and the surface of the uneven workpiece, i.e., process damping.
The research on the process damping effect is mainly concentrated in foreign expert scholars' literature, and relatively few studies are made in this field at home. The Altintas teaches that the study of the process damping effect on the flutter stability will be the most challenging subject of study; it is mentioned that tool wear will cause the process damping coefficient to increase, thereby increasing the chatter stability critical area. Budak mentions that the process damping effect in low speed processing becomes one of the research points and difficulties with its complexity. The effect is closely related to factors such as cutting amount, cutting temperature, cutter material characteristics, shearing surface variation and the like; cutting difficult-to-machine materials will produce high heat, easily cause tool wear, will change the geometry of the cutting edge and the machined workpiece corrugated surface that the flank face contacts, thereby increasing the process damping effect.
Disclosure of Invention
A milling chatter stability prediction method based on an over-damping effect comprises the following steps:
step 1: in the process of milling a workpiece, acquiring geometric structure parameters of a milling cutter and dynamic parameters of the milling process;
the milling tool geometry parameters include: number of teeth N of toolfA tool relief angle λ and a tool diameter D;
the milling process dynamic parameters comprise: angular frequency omega of tool fluttercAmplitude of tool A0And tool angular velocity omega.
Step 2: determining the total energy generated by the plowing force in the milling process of a workpiece in a cutter tooth rotation period according to the geometric structure parameters of the milling cutter and the dynamic parameters of the milling process, and equating the total energy generated by the plowing force to the energy generated by the damping force in the equivalent linear process in a period by utilizing the law of energy conservation to obtain the damping coefficient of the equivalent linear process;
step 2.1: determining the tangential displacement of the cutter and the radial displacement of the cutter according to the geometric parameters of the milling cutter and the dynamic parameters of the milling process;
step 2.2: the axial cutting depth a of the cutter is equally divided into NzDetermining tangential ploughing infinitesimal force of cutter teeth and radial ploughing infinitesimal force of the cutter teeth;
step 2.3: determining the energy e of the plough force generated in a vibration cycleiThe sum of the work of the radial ploughing micro-element force and the tangential ploughing micro-element force of the cutter tooth at a vibration wavelength is obtained;
step 2.4: according to the angular frequency omega of tool fluttercDetermining the number of vibration ripples left on the surface of the workpiece after the cutter teeth rotate for one circle according to the cutter angular velocity omega;
step 2.5: determining the total energy of the plowing force, namely the plowing force does work after the cutter teeth rotate for one circle;
step 2.6: and (3) by utilizing an energy conservation law, enabling the total energy of the plowing force to be equivalent to the energy generated by the process damping force adopting linear viscous damping in a period, and obtaining an equivalent linear process damping coefficient.
And step 3: converting the equivalent linear process damping into an x-direction equivalent process damping and a y-direction equivalent process damping to obtain an x-direction equivalent process damping coefficient and a y-direction equivalent process damping coefficient;
and 4, step 4: inputting the equivalent process damping coefficient in the x direction and the equivalent process damping coefficient in the y direction into a milling kinetic equation to obtain a milling kinetic model based on a process damping effect;
and 5: and solving the milling dynamic model based on the process damping effect by adopting a ZOA method to obtain a flutter stability model based on the process damping effect, thereby obtaining the relation between the ultimate stability cutting depth and the tool rotating speed, and drawing a flutter stability lobe graph based on the process damping effect.
The flutter stability model based on the process damping effect is as follows:
wherein,a transfer function matrix of the contact area of the cutter and the workpiece, a direct transfer function of the contact area of the cutter and the workpiece in the x direction, a direct transfer function of the contact area of the cutter and the workpiece in the y direction, a cross transfer function, a is the axial cutting depth of the cutter, and k is the axial cutting depth of the cuttertIs a constant of tangential cutting force, NfNumber of teeth of tool, omegacIs the tool chatter angular frequency, T is the tool rotation period, and i is a complex number.
The invention has the beneficial effects that:
the invention provides a milling flutter stability prediction method based on an over-damping effect, wherein in the low-speed processing of difficult-to-process materials and complex curved surfaces, the process damping effect plays a very important role in flutter stability, and particularly when aviation materials are milled and titanium alloys with low heat conductivity are used, the generated heat is relatively large, so that the cutter is abraded; the milling flutter stability prediction method based on the over-damping effect solves the problem that cutting parameters cannot be selected by using a stable region due to compact flutter stability lobes during low-speed processing, and improves the accuracy of flutter stable region prediction. Therefore, in the actual production, the method has important significance for optimizing parameters in the processing process and improving the production efficiency.
Drawings
FIG. 1 is a flow chart of a milling chatter stability prediction method based on an over-damping effect according to an embodiment of the present invention;
FIG. 2 is a process damping based milling dynamics model in an embodiment of the present invention;
wherein, (a) is the tool cutting into the workpiece model, and (b) is a schematic diagram of the vibration wavelength of the tool invading the workpiece;
Kxis the x-direction stiffness coefficient of the tool, CxIs the x-direction damping coefficient of the tool, KyIs the y-direction stiffness coefficient of the tool, CyAs damping coefficient of tool in y-direction, FptIs a tangential ploughing force, FprIs a radial ploughing force, rjIs the radial distance, u, of the cutter tooth jjIs the tangential distance of a cutter tooth j, and lambda is the cutter relief angle, cutterj-1Is the j-1 cutter tooth of the cutterjIs the jth cutter tooth of the cutter, v is the linear speed of the cutter, A0For tool amplitude, L is the wavelength of an oscillation of the tool into the workpiece, phijFor contact of tool tooth j with workpieceAngle, omega is the cutter angular velocity;
FIG. 3 is a flow chart of the equivalent linear process damping coefficient obtained by equating the total energy generated by the plowing force to the energy generated by the equivalent linear process damping force in one cycle in an exemplary embodiment of the present invention;
FIG. 4 is a graph comparing a flutter stability lobe plot without process damping effect considerations and a flutter stability lobe plot based on process damping effect in an embodiment of the present invention;
FIG. 5 is a graph comparing flutter stability lobes based on process damping effect for different tool relief angles in an embodiment of the present invention;
FIG. 6 is a graph comparing flutter stability lobes based on process damping effect for different tool amplitudes in an embodiment of the present invention;
FIG. 7 is a graph comparing flutter stability lobes based on process damping effect for different tool stiffness conditions in an embodiment of the present invention;
FIG. 8 is a graph comparing flutter stability lobes based on process damping effect under different tool structure damping conditions in an embodiment of the present invention;
FIG. 9 is a comparison graph of flutter stability three-dimensional lobe plots based on process damping effect for different cutter tooth counts in the exemplary embodiment of the invention;
FIG. 10 is a comparison of flutter stability three-dimensional lobes based on process damping effect for different radial cut to tool diameter ratios in an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
The invention provides a milling flutter stability prediction method based on an over-damping effect, which is characterized in that the vibration of a cutter is decomposed into radial reciprocating vibration and tangential linear motion, the work done by the intrusion force of a rear cutter face of the cutter invading the machined surface of a workpiece in one vibration period of cutter teeth is calculated, then the work is multiplied by the complete vibration ripple number in one rotation period of the cutter, the nonlinear damping equivalence is used for linear damping by utilizing the energy equivalence principle, a flutter stability lobe graph is solved by adopting a frequency domain method, and the flutter stability cut depth limit can be efficiently and accurately predicted in the low-speed milling process. Therefore, theoretical guidance is provided for optimizing cutting parameters, processing surface quality and processing efficiency.
A milling chatter stability prediction method based on an over-damping effect is disclosed, as shown in FIG. 1, and comprises the following steps:
step 1: and acquiring geometric parameters of a milling cutter and dynamic parameters of the milling process in the process of milling the workpiece.
In this embodiment, as shown in fig. 2, the milling dynamics model based on process damping includes the following geometric parameters: number of teeth N of cutter with helix angle of 0f4, the cutter back angle lambda is 10 degrees, and the cutter diameter D is 10 mm;
the dynamic parameters of the milling process comprise: angular frequency omega of tool fluttercAmplitude of tool A0And tool angular velocity omega.
Step 2: determining the total energy generated by the plowing force in the milling process of the workpiece in a cutter tooth rotation period according to the geometric parameters of the milling cutter and the dynamic parameters of the milling process, and equating the total energy generated by the plowing force to the energy generated by the damping force in the equivalent linear process in a period by utilizing the law of energy conservation to obtain the damping coefficient of the equivalent linear process, as shown in fig. 3.
Step 2.1: and determining the tangential displacement of the cutter and the radial displacement of the cutter according to the geometric parameters of the milling cutter and the dynamic parameters of the milling process.
In the present embodiment, the angular frequency ω is determined by the tool chatter frequency ωcAmplitude of tool A0The tangential displacement u (t) of the tool and the radial displacement r (t) of the tool determined by the tool angular velocity omega and the tool diameter D are as shown in the formula (1) and the formula (2):
r(t)＝A0sin(ωct) (2)
wherein v is the linear speed of the cutter and t is time.
Step 2.2: the axial cutting depth a of the cutter is equally divided into NzAnd determining the tangential ploughing micro-element force of the cutter teeth and the radial ploughing micro-element force of the cutter teeth.
In this embodiment, the axial cutting depth a of the tool is equally divided into NzThe microelements are shown in formula (3):
Nz＝a/Δz (3)
wherein Δ z is a infinitesimal.
Tangential ploughing micro-element force dF of determined cutter teethpr[φj(t)，kz]Radial plough micro-element force dF of prop tool toothpt[φj(t)，kz]As shown in formulas (4) and (5):
dFpr[φj(t)，kz]＝KspdV[φj(t)，kz]g[φj(t)，kz](4)
dFpt[φj(t)，kz]＝μdFpr[φj(t)，kz](5)
wherein phi isj(t)＝Ωt+(j-1)2π/Nf，φj(t) is the contact angle between the cutter tooth j and the workpiece, and the intrusion force constant K is known from literaturesp＝3000N/mm3V volume of tool penetration into workpiece, kz∈NzThe average friction coefficient mu is 0.3 g [ phi ], known from literaturej(t)，kz]Is a unit step function for determining whether a tooth is in cut.
Unit step function g [ phi ]j(t)，kz]As shown in formula (6):
wherein phi isstIs the cutting angle of the toolexTo cut the corners for the cutter.
Step 2.3: determining the energy e of the plough force generated in a vibration cycleiNamely the sum of the work done by the radial ploughing micro-element force and the tangential ploughing micro-element force of the cutter teeth at a vibration wavelength.
In the present embodiment, the energy e of the plowing force generated in one vibration cycleiAs shown in formula (7), formula (8) and formula (9):
ei＝eiu+eir(7)
wherein e isiuWork done by tangential ploughing of the teeth of the tool by a vibration wave length of the teeth, eirThe work of the radial plough micro-element force of the cutter tooth with a vibration wave length is provided for the cutter tooth, and L is (2 pi v)/omegac，
Step 2.4: according to the angular frequency omega of tool fluttercAnd determining the number of the vibration ripples remained on the surface of the workpiece after the cutter teeth rotate for one circle by the cutter angular speed omega.
In the present embodiment, the angular frequency ω is determined by the tool chatter frequency ωcAnd determining the number of the vibration ripples left on the surface of the workpiece after the cutter teeth rotate for one circle according to the cutter angular velocity omega as shown in the formula (10):
(ωc/Ω)＝η+ζ/2π (10)
wherein eta is the integral number of the vibration ripples remained on the surface of the workpiece after the cutter teeth rotate for one circle, and zeta/2 pi is the decimal number for generating the number of the ripples.
Step 2.5: and determining the total energy of the plowing force, namely the work of the plowing force in one circle of rotation of the cutter tooth of the cutter.
In the present embodiment, the total energy E of the plowing forceiAs shown in formula (11):
Ei＝Eiu+Eir＝η(eiu+eir) (11)
wherein E isiuThe work done by tangential ploughing force in one revolution of the cutter teeth, EirThe power is the work of radially ploughing the micro-element force by rotating the cutter teeth for one circle.
Step 2.6: and (3) by utilizing an energy conservation law, enabling the total energy of the plowing force to be equivalent to the energy generated by the process damping force adopting linear viscous damping in a period, and obtaining an equivalent linear process damping coefficient.
In the present embodiment, the energy generated by the damping force in the process of linear viscous damping in one cycle is expressed by the following equations (12) and (13):
wherein E isp irIs equivalent radialWork done by the process damping force during one tooth rotation period, Ep iuThe work done by the damping force within one tooth rotation period is an equivalent tangential process.
The total energy of the plowing force is equivalent to the energy generated by the damping force in the process of linear viscous damping in one period by utilizing the law of conservation of energy, so that Ep ir＝Eir，Ep iu＝EiuObtaining the damping coefficient c of the radial equivalent linear processprAs shown in equation (14):
the same can be obtained, the damping coefficient c of the tangential equivalent linear processpuAs shown in equation (15):
and step 3: and converting the equivalent linear process damping into the x-direction equivalent process damping and the y-direction equivalent process damping to obtain an x-direction equivalent process damping coefficient and a y-direction equivalent process damping coefficient.
In this embodiment, the x-direction equivalent process damping coefficient C is obtainedpxAnd equivalent process damping coefficient C in the y-directionpyAs shown in equation (16):
the equivalent process damping coefficient in the x and y directions is expressed as:
and 4, step 4: and inputting the equivalent process damping coefficient in the x direction and the equivalent process damping coefficient in the y direction into a milling kinetic equation to obtain a milling kinetic model based on the process damping effect.
In this embodiment, the x-direction equivalent process damping coefficient and the y-direction equivalent process damping coefficient are input into a milling dynamics equation to obtain a milling dynamics model based on the process damping effect, as shown in formula (17):
wherein,for milling system mass coefficient, mxxIs the x-axis mass, m, of the toolyyIs the mass of the y-axis of the cutter,for tool stiffness, KxIs the x-direction stiffness coefficient of the tool, KyIs the rigidity coefficient of the cutter in the y direction,for damping of the milling system, CxIs the x-direction damping coefficient of the tool, CyAs the damping coefficient of the tool in the y direction,is a dynamic displacement of the cutter and is,is the difference of the inner and outer cyclic displacement of the cutter, Deltax is the difference of the inner and outer cyclic displacement of the cutter in the x direction, Deltay is the difference of the inner and outer cyclic displacement of the cutter in the y direction, x (T) is the displacement of the outer cycle of the cutter in the x direction at the time T, y (T) is the displacement of the outer cycle of the cutter in the y direction at the time T, x (T-T) is the displacement of the inner cycle of the cutter in the x direction at the time T, y (T-T) is the displacement of the inner cycle of the cutter in the y direction at the time T, T is thet1596.3MPa is the constant of tangential cutting force,is a time-varying directional coefficient.
The time-varying directional coefficient a is as shown in equation (18):
wherein k isr0.25 is the radial cutting force constant and phi is the instantaneous contact angle of the tool with the workpiece.
And 5: and solving the milling dynamic model based on the process damping effect by adopting a ZOA method to obtain a flutter stability model based on the process damping effect, thereby obtaining the relation between the ultimate stability cutting depth and the tool rotating speed, and drawing a flutter stability lobe graph based on the process damping effect.
In the embodiment, a ZOA method is adopted to solve the milling dynamic model based on the process damping effect, and the flutter stability model based on the process damping effect is obtained as shown in a formula (19):
wherein,the matrix is a transfer function matrix of the contact area of the cutter and the workpiece, the matrix is a direct transfer function of the contact area of the cutter and the workpiece in the x direction, the matrix is a direct transfer function of the contact area of the cutter and the workpiece in the y direction, the matrix is a cross transfer function, and i is a complex number.
Obtaining the ultimate stability of the cutting depthAs shown in equation (20):
wherein, DeltaRpThe real part of the characteristic value delta of the process damping milling dynamic equation is considered, and kappa is the proportion of the imaginary part and the real part of the characteristic value delta of the process damping milling dynamic equation.
Wherein, the characteristic value delta of the process damping milling dynamic equation is shown as the formula (21):
wherein, a0＝φp xx(iωc)φp vv(iωc)(axxayy-axyayx)，a1＝φp xx(iωc)φp yy(iωc)(axxayy-axyayx)，ωnxIs the natural frequency, omega, of the main spindle tool system in the x-directionnyIs the natural frequency, ζ, of the main shaft tool system in the y directionxIs the structural damping ratio, zeta, of the main shaft tool system in the x directionyIs the structural damping ratio, zeta, of the main shaft tool system in the y directionpxProcess damping ratio, ζ, for spindle tool system in x-directionpyIs the process damping ratio in the y-direction of the spindle tool system.
Obtaining a tool rotation speed range n as shown in formula (22):
wherein psi ═ arctan κ is a phase shift taking into account a characteristic value Δ of the process damping milling kinetic equation, lrThe number of vibration cycles.
The modal parameters of the spindle tool system are shown in table 1.
TABLE 1 Modal parameters of spindle tool systems
In the embodiment, a comparative graph of the flutter stability lobe graph without considering the process damping effect and the flutter stability lobe graph based on the process damping effect is drawn by adopting Matlab software, as shown in fig. 4, as can be seen from fig. 4, the flutter stability lobe graph based on the process damping effect can more accurately describe the relationship between the ultimate stability cut depth and the tool rotation speed.
In the present embodiment, a comparison graph of flutter stability lobe diagrams based on process damping effect under different tool relief angles is shown in fig. 5, and when the tool relief angle λ is 5 degrees and λ is 10 degrees, respectively, other parameters are unchanged, and the influence of different relief angles on flutter stability based on process damping effect is programmed through MATLAB. As can be seen in fig. 5, the cut stability limit decreases with increasing cutter relief angle.
In the present embodiment, a comparison graph of flutter stability lobe diagrams based on process damping effect under different tool amplitudes is shown in fig. 6, where the tool amplitude a is taken020 μm and A0The effect of tool amplitude on chatter stability based on process damping effect was programmed by MATLAB with other parameters unchanged at 40 μm. As can be seen from fig. 6, the cut-depth stability limit increases with increasing tool amplitude.
In this embodiment, a comparative graph of flutter stability lobe diagrams based on process damping effect under different tool rigidities is shown in fig. 7, the tool rigidities are taken to be 1 time, 1.5 times and 2 times of the rigidities in table 1 respectively, other parameters are unchanged, and the influence of the tool rigidity on the flutter stability based on the process damping effect is drawn through programming by MATLAB. As can be seen from fig. 7, the cut-depth stability limit increases with increasing tool stiffness.
In this embodiment, a comparative graph of flutter stability lobe diagrams based on process damping effect under different tool structure damping conditions is shown in fig. 8, the tool structure damping is taken as 1 time, 1.5 times and 2 times of the structure damping in table 1, and other parameters are unchanged, and the influence of the tool structure damping on the flutter stability based on the process damping effect is drawn by programming MATLAB. As can be seen in fig. 8, the cut stability limit increases with increasing damping of the tool structure.
In this embodiment, a comparative graph of a flutter stability three-dimensional lobe graph based on a process damping effect under different cutter tooth numbers is shown in fig. 9, when the cutter tooth numbers are taken to be 2, 3, 4 and 5 respectively, other parameters are unchanged, and the influence of the cutter tooth numbers on the flutter stability based on the process damping effect is drawn by programming through MATLAB. As can be seen in fig. 9, the cut-depth stability limit decreases with increasing damping of the tool structure.
In this embodiment, a comparison graph of the flutter stability three-dimensional lobe graph based on the process damping effect under the condition of different ratios of the radial cutting depth to the tool diameter is shown in fig. 10, when the ratios of the radial cutting depth to the tool diameter are taken as 0.5, 0.7 and 0.9, other parameters are not changed, and the influence of the ratio of the radial cutting depth to the tool diameter on the flutter stability based on the process damping effect is programmed and drawn through MATLAB. As can be seen in fig. 10, the cut stability limit decreases with increasing ratio of radial cut to tool diameter.
Claims (3)
1. A milling chatter stability prediction method based on an over-damping effect is characterized by comprising the following steps:
step 1: in the process of milling a workpiece, acquiring geometric structure parameters of a milling cutter and dynamic parameters of the milling process;
step 2: determining the total energy generated by the plowing force in the milling process of a workpiece in a cutter tooth rotation period according to the geometric structure parameters of the milling cutter and the dynamic parameters of the milling process, and equating the total energy generated by the plowing force to the energy generated by the damping force in the equivalent linear process in a period by utilizing the law of energy conservation to obtain the damping coefficient of the equivalent linear process, wherein the specific steps are as follows:
step 2.1: determining the tangential displacement of the cutter and the radial displacement of the cutter according to the geometric parameters of the milling cutter and the dynamic parameters of the milling process;
step 2.2: the axial cutting depth a of the cutter is equally divided into NzDetermining tangential ploughing infinitesimal force of cutter teeth and radial ploughing infinitesimal force of the cutter teeth;
step 2.3: determining the energy e of the plough force generated in a vibration cycleiThe sum of the work of the radial ploughing micro-element force and the tangential ploughing micro-element force of the cutter tooth at a vibration wavelength is obtained;
step 2.4: according to the angular frequency omega of tool fluttercDetermining the number of vibration ripples left on the surface of the workpiece after the cutter teeth rotate for one circle according to the cutter angular velocity omega;
step 2.5: determining the total energy of the plowing force, namely the plowing force does work after the cutter teeth rotate for one circle;
step 2.6: the total energy of the plowing force is equivalent to the energy generated by the process damping force adopting linear viscous damping in a period by utilizing the law of conservation of energy, so that the equivalent linear process damping coefficient is obtained;
and step 3: converting the equivalent linear process damping into an x-direction equivalent process damping and a v-direction equivalent process damping to obtain an x-direction equivalent process damping coefficient and a y-direction equivalent process damping coefficient;
and 4, step 4: inputting the equivalent process damping coefficient in the x direction and the equivalent process damping coefficient in the y direction into a milling kinetic equation to obtain a milling kinetic model based on a process damping effect;
and 5: and solving the milling dynamic model based on the process damping effect by adopting a ZOA method to obtain a flutter stability model based on the process damping effect, thereby obtaining the relation between the ultimate stability cutting depth and the tool rotating speed, and drawing a flutter stability lobe graph based on the process damping effect.
2. The milling chatter stability predicting method based on the over-damping effect according to claim 1Method, characterized in that the milling tool geometry parameters comprise: number of teeth N of toolfA tool relief angle λ and a tool diameter D;
the milling process dynamic parameters comprise: angular frequency omega of tool fluttercAmplitude of tool A0And tool angular velocity omega.
3. The milling chatter stability prediction method based on the over-damping effect according to claim 1, wherein the chatter stability model based on the process damping effect is as follows:
wherein,is a transfer function matrix of the contact area of the cutter and the workpiece,is a direct transfer function of the contact area x direction of the cutter and the workpiece,is a direct transfer function of the y direction of the contact area of the cutter and the workpiece,for the cross-transfer function, a is the axial depth of cut of the tool, ktIs a constant of tangential cutting force, NfNumber of teeth of tool, omegacIs the tool chatter angular frequency, T is the tool rotation period, and i is a complex number.
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| CN106843147B (en) * | 2016-12-15 | 2020-03-17 | 太原科技大学 | Method for predicting milling stability based on Hamming formula |
| CN106647625B (en) * | 2016-12-15 | 2018-12-21 | 太原科技大学 | A method of based on Gear formula predictions milling stability |
| CN106940746A (en) * | 2017-03-14 | 2017-07-11 | 东北大学 | The parallel time domain method of milling parameter stability prediction based on thin-wall part |
| CN107423489B (en) * | 2017-06-27 | 2019-05-31 | 西北工业大学 | Thin-wall part milling process stability method for quick predicting |
| CN107914183B (en) * | 2017-12-05 | 2020-04-07 | 上海复合材料科技有限公司 | Chatter stability prediction method for milling carbon fiber laminated plate |
| CN108804749B (en) * | 2018-04-19 | 2019-04-30 | 西北工业大学 | Thin-wall part milling process Damping Modeling method |
| CN108647413B (en) * | 2018-04-27 | 2021-07-06 | 北京理工大学 | Comprehensive prediction method for position error and stability of fine surface |
| CN108746795B (en) * | 2018-06-20 | 2020-02-14 | 哈尔滨理工大学 | Method for predicting flutter in numerical control milling of mold cavity |
| CN109375578B (en) * | 2018-10-31 | 2020-06-16 | 湖南工学院 | Efficient machining control method for deep hole in engine oil pump shell |
| CN111722586B (en) * | 2020-06-22 | 2023-09-15 | 华中科技大学无锡研究院 | Intermittent milling vibration sectional control method |
| CN112621382B (en) * | 2020-12-17 | 2022-05-24 | 北京工业大学 | Online tool wear monitoring method based on cutting vibration damping characteristics |
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