CN109759901A - Milling parameter control method based on the asymmetric rigidity regulation of axis system - Google Patents
Milling parameter control method based on the asymmetric rigidity regulation of axis system Download PDFInfo
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Abstract
The invention discloses a kind of milling parameter control methods based on the asymmetric rigidity regulation of axis system, and the method comprising the steps of: 1) establishing rectangular coordinate system based on cutting direction；2) Cutting Force Coefficient of experimental method identification specified material workpiece；3) asymmetric rigidity main shaft-milling system kinetic model is established；4) system features equation is sought, suitable, upmilling the stability lobes diagram under asymmetric rigidity different adjustment degree are calculated；5) suitable asymmetric stiffness combine is chosen according to suitable, upmilling and target cutting parameter；6) physical regulating of asymmetric rigidity is realized using piezoelectric actuator.The present invention cuts preceding or online asymmetric regulation major axis X, the rigidity of Y-direction for suitable, the two different cutting ways of upmilling, being capable of effective lifting system milling stability, inhibition flutter, raising machining accuracy and efficiency.Meanwhile this method is easy to implement, and is conducive to industrial practical application.
Description
Technical field
The invention belongs to Milling Process control technology fields, and in particular to one kind is based on the asymmetric rigidity regulation of axis system
Milling parameter control method.
Background technique
Milling Process is using a kind of very extensive machining mode, especially in aerospace field, high speed, height
Effect, Milling Process have become the mainstream of machining.In Milling Processes, since main shaft characteristic changing, damping effect subtract
The reasons such as weak, are easy to happen flutter unstability, cause workpiece to scrap, the harm such as decreased tool life, seriously limit machining accuracy
With the raising of efficiency.Therefore, milling parameter is controlled, is had to high speed, the realization of high-efficient milling and the raising of workpiece processing quality
It is of great significance.
Control for milling parameter has carried out a large amount of research both at home and abroad.2013, Monnin of Switzerland et al.
(J.Monnin,F.Kuster,K.Wegener,Optimal control for chatter mitigation in
milling—Part 1:Modeling and control design,Control Engineering Practice,24
(2014) 167-175.) Integrated Accelerometer on main shaft, the active of milling parameter is realized using optimal control policy
Control.2015, Haitao Zhang et al. (H.T.Zhang, Y.Wu, D.He, H.Zhao, Model predictive control to
mitigate chatters in milling processes with input constraints,International
Journal of Machine Tools&Manufacture, 91 (2015) 54-61.) using the method for Model Predictive Control, lead to
It crosses Active Magnetic Bearing and applies active controlling force, the inhibition and stability for realizing milling parameter are promoted.
Application No. is the patents of invention of CN201610260469.8 to disclose a kind of high-speed milling electro spindle flutter intelligently inspection
Survey and active suppression device, it is characterized in that passing through Integrated Accelerometer, displacement sensor, piezoelectric actuator on main shaft
Deng active suppression of the realization to monitoring and the flutter of milling process.Application No. is the patents of invention of CN201610228617.8
A kind of electro spindle milling parameter time delay Active Control Method is disclosed, is controlled it is characterized in that being calculated using discrete method for optimally controlling
Power processed, and then drive the active control of piezoelectric actuator realization flutter.
Summary of the invention
The purpose of the present invention is provide a kind of based on main shaft system for climb cutting, two kinds of upmilling different Milling Process modes
The milling parameter control method of the asymmetric rigidity of uniting regulation, this method be not only easy to realize in industry processes, Er Qieke
It is promoted with obtaining largely milling stability, is conducive to lifting workpieces processing quality and processing efficiency.
The present invention adopts the following technical scheme that realize:
Based on the milling parameter control method of the asymmetric rigidity regulation of axis system, include the following steps:
1) using milling cutter point of a knife as coordinate origin, using milling feed direction as X-axis, perpendicular to direction of feed and milling cutter axis
Direction is that Y-axis establishes rectangular coordinate system；It measures the frequency response function of point of a knife X, Y-direction respectively using power hammer excitation experiment, and recognizes
Modal mass, rigidity and the several parameters of damping；
2) milling experiment is carried out using specified workpiece and cutter, cutting force system is picked out by the Milling Force measured
Number KtWith radial cutting force COEFFICIENT Kr；
3) it according to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) that identification obtains in step 1), builds
Found asymmetric rigidity main shaft-milling system kinetic model；
4) according to the kinetic model established in step 3), its characteristic equation is calculated, and is directed to two kinds of climb cutting, upmilling differences
Milling mode, draw the milling stability flap under asymmetric rigidity different adjustment degree using Nyquist stability criterion
Figure analyzes milling stability；
5) using stability analysis in step 4) as a result, according to different processing operating conditions, when climb cutting is cut, to the main shaft side Y
Suitable amplification factor is chosen to rigidity；When upmilling is cut, suitable amplification factor is chosen to major axis X directional stiffness, realizes master
The asymmetric rigidity regulation of axis X, Y-direction, and then realize that milling stability promotes the Flutter Control with target operating condition.
A further improvement of the present invention lies in that establishing asymmetric rigidity main shaft-milling system dynamics in the step 3)
Model, detailed process is as follows:
According to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) recognized in step 1), it is non-right to establish
Claim main shaft-milling system kinetics equation as follows:
In formula, X (t)=[x (t) y (t)]TIt is point of a knife in X, the vibration displacement vector of Y-direction；mx、my、cx、cy、kxAnd ky
It is major axis X, the modal mass of Y-direction, damping and rigidity respectively；nxAnd nyRespectively axis system X-direction and Y-direction rigidity is put
Big multiple, and nx≠ny, that is, pass through nxAnd nyThe non-equivalent assignment of two constants realizes axis system X, Y both direction rigidity
Asymmetric adjusting；F (t) is dynamic milling force, and expression is as follows:
In formula, H is to orient dynamic cutting force coefficients matrix, expression such as formula (4), wherein hxx、hxy、hyxAnd hyy
Value is different under climb cutting, the two different milling modes of upmilling, expression such as formula (5)；τ is the time lag period, is equal to milling
The cutter tooth of process is cut by the period, i.e. τ=60/N Ω, wherein N is cutter tooth quantity, and Ω is the speed of mainshaft, and unit is r/min；
In formula, Krc=Kr/Kt；φ is the instantaneous tooth position angle of cutter tooth；φenAnd φexIt is cutter tooth entrance angle and to cut out angle respectively, it is suitable
When milling, φen=arccos (2d/D-1), φex=π；φ when upmillingen=0, φex=arccos (1-2d/D), wherein D is cutter
Diameter, d are radial cutting depth.
A further improvement of the present invention lies in that according to the kinetics equation in step 3), calculating and corresponding in the step 4)
Characteristic equation, utilize the milling stability under Nyquist's theorem analysis climb cutting, the different milling modes of two kinds of upmilling, specific mistake
Journey is as follows:
Formula (3), formula (4) in step 3) is substituted into formula (2), and pull-type transformation is carried out simultaneously to equation both sides, is obtained:
Enable Ψ=NaKt(1-e-iωτThe π of)/4, and then know the characteristic equation of asymmetric rigidity main shaft-milling system are as follows:
This feature equation is major axis X, Y-direction rigidity amplification factor nx、nyFunction, while having with suitable, upmilling cutting way
It closes；For climb cutting and upmilling, constantly increase n respectivelyxAnd ny, the stabilization of milling process is judged using Nyquist stability criterion
Property, draw the milling stability flap figure under different milling modes, asymmetric rigidity different adjustment degree.
A further improvement of the present invention lies in that in the step 5), according to the analysis of step 4) as a result, milling to be improved is steady
It is qualitative, in upmilling cutting process, operating condition, including rotating speed of target and axial cutting-in are cut according to target, it is rigid to choose suitable X-direction
Amplification factor is spent, so that target cutting operating condition of the original place in flutter region is realized after asymmetric stiffness tuning and stablizes cutting,
In suitable rigidity amplification factor with the minimum rigidity amplification factor that can effectively control flutter under target cutting operating condition be preferential
Selective value；In climb cutting cutting process, operating condition is cut also according to target, chooses suitable Y-direction rigidity amplification factor, realizes mesh
Mark cutting operating condition is by flutter to the control target for stablizing cutting.
A further improvement of the present invention lies in that in the step 5), by the integrated piezoelectric actuator in main shaft knife handle, and
According to the parameter that the step is chosen, it is used as power using piezoelectric actuator to main shaft application, realizes that the asymmetric rigidity of axis system is closed
The physical regulating of suitable parameter.
A further improvement of the present invention lies in that complete using two pairs of piezoelectric actuators being integrated on the orthogonal direction of knife handle position
At the physics realization that asymmetric rigidity regulates and controls, detailed process is as follows:
It is integrated with the axis system of two pairs of piezoelectric actuators using on the orthogonal direction of knife handle position, passes through experimental method first
Determine axis system X, on Y-direction stiffness variation ratio and corresponding direction piezoelectric actuator power output corresponding relationship, then adopt
With passive and active control two ways, the asymmetric rigidity regulation of axis system is realized, and then control flutter；According to step 4) and
Analysis in step 5) in upmilling cutting, applies X-direction piezoelectric actuator using torque spanner as a result, for passively regulating and controlling
Corresponding torque, by the rigidity regulation of axis system X-direction to selected ratio；In climb cutting cutting, benefit is in the same way to the side Y
To piezoelectric actuator apply torque, realize the regulation of asymmetric rigidity；And the passive control methods can be according to selected cutting
Parameter is completed to adjust before cutting；The power output and input voltage of piezoelectric actuator are directly proportional, determine the ratio according to handbook first
Example；According to the analysis in step 4) and step 5) as a result, in active control, upmilling is cut, signal generator pair is utilized
The piezoelectric actuator application in major axis X direction makes major axis X directional stiffness change to DC voltage value required for target proportion, will lead
The rigidity of axle system X-direction regulates and controls to selected ratio；Climb cutting is cut, benefit is in the same way to axis system Y-direction
Piezoelectric actuator applies corresponding DC voltage value, realizes the asymmetric rigidity regulation of target proportion；The active control method,
It completes to adjust before cutting, or is regulated and controled online according to the variation of cutting operating condition during the cutting process.
The present invention has following beneficial technical effect:
Milling parameter control method provided by the invention based on the asymmetric rigidity regulation of axis system, cuts for climb cutting
It cuts, the rigidity of regulation main shaft Y-direction；For upmilling cut, only regulate and control major axis X direction rigidity, i.e., according to it is suitable, two kinds of upmilling
Different milling mode, in axis system X, the asymmetric regulation rigidity of Y-direction.The control methods can not only obtain bigger milling
It cuts stability region, and compares while to control both direction energy saving.Asymmetric rigidity regulation is carried out based on piezoelectric actuator,
Regulate and control before being able to achieve cutting, and be able to achieve the online regulation according to cutting operating condition, and control methods are simple and easy, is conducive to work
Industry practical application.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the milling parameter control method of the asymmetric rigidity regulation of axis system.
Fig. 2 is main shaft-milling system rectangular coordinate system.
Fig. 3 is the stability lobes diagram explanation of asymmetric rigidity regulation Flutter Control method.
Fig. 4 is the axis system of integrated piezoelectric actuator, and Fig. 4 (a) is full sectional view, the A-A that Fig. 4 (b) is Fig. 4 (a) to
Cross-sectional view.
Fig. 5 is 0.5 to cut wide ratio, nx=1, nyClimb cutting is stablized under=1,1.1,1.2,1.3,1.4 5 group of asymmetric stiffness combine
Property flap figure comparing result.
Fig. 6 is 0.5 to cut wide ratio, nx=1,1.1,1.2,1.3,1.4, nyClimb cutting is stablized under=1 five group of asymmetric stiffness combine
Property flap figure comparing result.
Fig. 7 is 0.5 to cut wide ratio, nx=1, nyUpmilling is stablized under=1,1.1,1.2,1.3,1.4 5 group of asymmetric stiffness combine
Property flap figure comparing result.
Fig. 8 is 0.5 to cut wide ratio, nx=1,1.1,1.2,1.3,1.4, nyUpmilling is stablized under=1 five group of asymmetric stiffness combine
Property flap figure comparing result.
The comparison of target operating condition and asymmetric rigidity regulation fore-and-aft stability flap figure when Fig. 9 is climb cutting cutting.
The comparison of target operating condition and asymmetric rigidity regulation fore-and-aft stability flap figure when Figure 10 is upmilling cutting.
Specific embodiment
The milling parameter control method of the invention regulated and controled based on the asymmetric rigidity of axis system is made into one in conjunction with example
The explanation of step, but the example is not intended to restrict the invention.
As shown in Figure 1, the milling parameter control method provided by the invention based on the asymmetric rigidity regulation of axis system, packet
Include following step:
1) using milling cutter point of a knife as coordinate origin, using milling feed direction as X-axis, perpendicular to direction of feed and milling cutter axis
Direction is that Y-axis establishes rectangular coordinate system.It measures the frequency response function of point of a knife X, Y-direction respectively using power hammer excitation experiment, and recognizes
Modal mass, rigidity and the several parameters of damping.Two-freedom rectangular coordinate system is established, power hammer excitation Experimental Identification main shaft system is utilized
System parameter, detailed process is as follows:
As shown in Fig. 2, using milling cutter point of a knife as coordinate axis origin, using milling feed direction as X-direction, perpendicular to feeding
Direction and cutter axially direction are Y direction, establish two-freedom rectangular coordinate system, wherein 1 is workpiece, 2 be milling cutter.
Acceleration transducer is arranged along the x axis in milling cutter point of a knife, motivates milling cutter point of a knife in sensor opposite side using power hammer,
Frequency response function curve is measured, and picks out the modal mass m of master modex, rigidity kxWith damping cx.It is carried out in Y direction same
Operation, picks out modal mass my, rigidity kyWith damping cy。
2) milling experiment is carried out using specified workpiece and cutter, cutting force system is picked out by the Milling Force measured
Number KtWith radial cutting force COEFFICIENT Kr.Milling experiment is carried out using specified workpieces processing and cutter, picks out and tangentially and radially cuts
Force coefficient is cut, detailed process is as follows:
Using the workpiece and cutter of specified material, under same determining revolving speed, change feed speed, carries out multiple groups and cut entirely
Wide milling experiment.Cutting force data is measured and recorded in cutting process.Being averaged for different directions under different feed speeds is calculated to cut
Power is cut, and then acquires radial cutting force COEFFICIENT KrWith cutting force COEFFICIENT Kt, formula is as follows:
In formula, N is cutter tooth quantity, and a is axial cutting-in, ExAnd EyIt is that X-direction is put down under Y-direction difference feed speed respectively
The slope of equal Milling Force fitting a straight line.
3) it according to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) that identification obtains in step 1), builds
Found asymmetric rigidity main shaft-milling system kinetic model.Asymmetric rigidity main shaft-milling system kinetic model is established, is had
Body process is as follows:
According to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) recognized in step 1), it is non-right to establish
Claim main shaft-milling system kinetics equation as follows:
In formula, X (t)=[x (t) y (t)]TIt is point of a knife in X, the vibration displacement vector of Y-direction；mx、my、cx、cy、kxAnd ky
It is major axis X, the modal mass of Y-direction, damping and rigidity respectively；nxAnd nyRespectively axis system X-direction and Y-direction rigidity is put
Big multiple, and nx≠ny, that is, pass through nxAnd nyThe non-equivalent assignment of two constants realizes axis system X, Y both direction rigidity
Asymmetric adjusting.F (t) is dynamic milling force, and expression is as follows:
In formula, H is to orient dynamic cutting force coefficients matrix, expression such as formula (4), wherein hxx、hxy、hyxAnd hyy
Value is different under climb cutting, the two different milling modes of upmilling, expression such as formula (5).τ is the time lag period, is equal to milling
The cutter tooth of process is cut by the period, i.e. τ=60/N Ω, wherein N is cutter tooth quantity, and Ω is the speed of mainshaft, and unit is r/min.
In formula, Krc=Kr/Kt；φ is the instantaneous tooth position angle of cutter tooth；φenAnd φexIt is cutter tooth entrance angle and to cut out angle respectively, it is suitable
When milling, φen=arccos (2d/D-1), φex=π；φ when upmillingen=0, φex=arccos (1-2d/D), wherein D is cutter
Diameter, d are radial cutting depth.
4) according to the kinetic model established in step 3), its characteristic equation is calculated, and is directed to two kinds of climb cutting, upmilling differences
Milling mode, draw the milling stability flap under asymmetric rigidity different adjustment degree using Nyquist stability criterion
Figure analyzes milling stability, and detailed process is as follows:
Formula (3), formula (4) in step 3) is substituted into formula (2), and pull-type transformation is carried out simultaneously to equation both sides, is obtained:
Enable Ψ=NaKt(1-e-iωτThe π of)/4, and then know the characteristic equation of asymmetric rigidity main shaft-milling system are as follows:
This feature equation is major axis X, Y-direction rigidity amplification factor nx、nyFunction, while having with suitable, upmilling cutting way
It closes.For climb cutting and upmilling, constantly increase n respectivelyxAnd ny, the stabilization of milling process is judged using Nyquist stability criterion
Property, draw the milling stability flap figure under different milling modes, asymmetric rigidity different adjustment degree.
5) using stability analysis in step 4) as a result, according to different processing operating conditions, when climb cutting is cut, to the main shaft side Y
Suitable amplification factor is chosen to rigidity；When upmilling is cut, suitable amplification factor is chosen to major axis X directional stiffness, realizes master
The asymmetric rigidity regulation of axis X, Y-direction.According to the analysis of step 4) as a result, milling stability to be improved, in upmilling cutting process,
Operating condition (rotating speed of target and axial cutting-in) is cut according to target, chooses suitable X-direction rigidity amplification factor, so that original place is in quivering
The target cutting operating condition in vibration region is realized after asymmetric stiffness tuning stablizes cutting, as shown in Figure 3.In climb cutting cutting process,
Operating condition is cut also according to target, chooses suitable Y-direction rigidity amplification factor, realizes target cutting operating condition by flutter to stabilization
The control target of cutting.
6) the integrated piezoelectric actuator in main shaft knife handle utilizes piezoelectric actuator pair according to the parameter chosen in step 5)
Main shaft application is used as power, and realizes the physical regulating of the asymmetric rigidity suitable parameters of axis system.
In the step 6), as shown in figure 4, complete using two pairs of piezoelectric actuators being integrated on the orthogonal direction of knife handle position
At the physics realization that asymmetric rigidity regulates and controls, wherein 3 be knife handle, 4 be bearing, and 5 be piezoelectric actuator.Detailed process is as follows:
For axis system shown in Fig. 4, axis system X, Y-direction stiffness variation ratio and right are determined by experimental method first
The corresponding relationship of piezoelectric actuator power output on direction is answered, then using passive and active control two ways, realizes main shaft system
Asymmetric rigidity of uniting regulates and controls, and then controls flutter.It is inverse according to the analysis in step 4) and step 5) as a result, for passively regulating and controlling
During milling is cut, corresponding torque is applied to X-direction piezoelectric actuator using torque spanner, by the rigidity tune of axis system X-direction
Control selected ratio；In climb cutting cutting, benefit applies torque to the piezoelectric actuator of Y-direction in the same way, realizes asymmetric
Rigidity regulation.The passive control methods are suitable for being adjusted before cutting according to selected cutting parameter.The output of piezoelectric actuator
Power and input voltage are directly proportional, determine the ratio according to handbook first.According to the analysis in step 4) and step 5) as a result, in master
In dynamic regulation, upmilling is cut, applies target stiffness variation ratio using piezoelectric actuator of the signal generator to major axis X direction
The corresponding DC voltage value of example, by the rigidity regulation of axis system X-direction to selected ratio；Climb cutting is cut, using same
Mode corresponding DC voltage value is applied to the piezoelectric actuator of axis system Y-direction, realize target proportion it is asymmetric just
Degree regulation.The active control method is not only suitable for cutting preceding adjusting, and is able to achieve in cutting process according to cutting operating condition variation
Online regulation.
Embodiment
Embodiment of the present invention is analyzed using milling spindle system as shown in Figure 4.
Using 3 blade milling cutters of diameter 10mm, using milling cutter point of a knife as coordinate axis origin, using milling feed direction as X-direction,
, as Y direction, to establish two-freedom rectangular coordinate system perpendicular to direction of feed and cutter axially direction.
Acceleration transducer is arranged along the x axis in milling cutter point of a knife, motivates milling cutter point of a knife in sensor opposite side using power hammer,
Frequency response function curve is measured, and picks out the modal mass m of master modex, rigidity kxWith damping cx.It is carried out in Y direction same
Operation, picks out modal mass my, rigidity kyWith damping cy.The results are shown in Table 1 for Modal Parameter Identification.
1 Modal Parameter Identification result of table
Milling revolving speed is set as 8000r/min, in 240mm/min, 720mm/min, 1200mm/min and 1680mm/min
Wide cutting experiment is cut entirely under four groups of feed speeds, and records the cutting force of cutting process.Utilize X, Y under different feed speeds
The average cutting force in direction carries out curve fitting, and calculates radial cutting force COEFFICIENT KrWith cutting force COEFFICIENT Kt, as a result such as table 2
It is shown.
2 Cutting Force Coefficient identification result of table
Using the modal parameter and Cutting Force Coefficient picked out, asymmetric rigidity main shaft-milling system kinetic simulation is established
Type, such as formula (8).
Wherein, dynamic milling force F (t) may be expressed as:
In formula,Ω indicates the speed of mainshaft, unit r/min；Dynamic milling force coefficient matrix H can be indicated
Are as follows:
In formula, hxx、hxy、hyxAnd hyyIt is respectively as follows:
In formula, Krc=Kr/Kt=0.21, φ indicate instantaneous tooth position angle, φen、φexIt respectively indicates cutter tooth entrance angle and cuts out
Angle.
Wushu (9) and formula (10) substitute into formula (8), carry out pull-type transformation to equation both sides, and enable Ψ=NaKt(1-e-iωτ)/
4 π=597a (1-e-iωτ)/π can be obtained:
It can thus be concluded that the characteristic equation of asymmetric rigidity main shaft-milling system are as follows:
This feature equation is major axis X, Y-direction rigidity amplification factor nx、nyFunction, while having with suitable, upmilling cutting way
It closes.For climb cutting and upmilling, constantly increase n respectivelyxAnd ny, the stabilization of milling process is judged using Nyquist stability criterion
Property, draw the milling stability flap figure under different milling modes, asymmetric rigidity different adjustment degree.
Using 3 blade milling cutters of above-mentioned diameter 10mm, stability analysis is carried out in the case where 5mm cuts width.When climb cutting is cut, enable first
nx=1, ny1,1.1,1.2,1.3,1.4 are taken respectively, and the stability lobes diagram under available 5 groups of stiffness combines is specific such as Fig. 5
It is shown.Then, n is enabledy=1, nx1,1.1,1.2,1.3,1.4 are taken respectively, the stability lobes diagram such as Fig. 6 under this 5 groups of stiffness combines
It is shown.Under upmilling cutting, the stability analysis under above two combination, n are equally carried outx=1, ny=1,1.1,1.2,1.3,1.4
The stability lobes diagram under stiffness combine is as shown in fig. 7, nx=1,1.1,1.2,1.3,1.4, nyStabilization under=1 stiffness combine
Property flap figure is as shown in Figure 8.
According to above-mentioned analysis result it can be found that the rigidity for increasing axis system Y-direction when climb cutting can effectively improve and be
The milling stability of system, and the rigidity for increasing X-direction when upmilling can be obviously improved the milling stability of system.Therefore, climb cutting
When, in order to expand stability region, processing efficiency is improved, operating condition can be processed according to target and choose suitable Y-direction rigidity times magnification
Number.As shown in figure 9, stablizing cutting under A point operating condition (revolving speed 10000r/min, axial direction cutting-in 3.2mm) to be realized, by main shaft Y
The rigidity in direction increases to 1.2 times of original rigidity；Under B point operating condition (revolving speed 8200r/min, axial direction cutting-in 3.6mm) to be realized
Stablize cutting, the rigidity of main shaft Y-direction is increased to 1.3 times of original rigidity.When upmilling, in order to inhibit flutter, improves and add
Work precision and efficiency can process operating condition according to target and choose suitable X-direction rigidity amplification factor.As shown in Figure 10, C to be realized
Stablize cutting under point operating condition (revolving speed 9600r/min, axial direction cutting-in 4.7mm), the rigidity in major axis X direction is increased to original rigid
1.2 times of degree；Stablize cutting under D point operating condition (revolving speed 8500r/min, axial direction cutting-in 4.8mm) to be realized, by major axis X direction
Rigidity increase to 1.4 times of original rigidity.Compared to Limit cutting depth of the former axis system under corresponding revolving speed, A, B, C and D tetra-
The corresponding cutting parameter of point significantly improves processing efficiency, that is, is directed to suitable, two kinds of milling modes of upmilling, by suitable asymmetric
Rigidity regulation, significantly improves processing efficiency while guaranteeing machining accuracy.
Asymmetric rigidity regulation multiple is had chosen respectively according to above-mentioned operating condition, passes through integrated piezoelectric actuator shown in Fig. 4
Main axle structure can complete physics realization.It determines and is pressed on axis system X, the stiffness variation amplitude of Y-direction and corresponding direction first
Functional relation between motor-driven cylinder power output.On this basis, stiffness variation amplitude and pre- when further obtaining passive control
Function when functional relation and active control between clamp force square between stiffness variation amplitude and actuator input voltage closes
System.Regulate and control multiple according to the corresponding asymmetric rigidity of above-mentioned different target operating condition, determines the pretightning force or input for needing to apply
Voltage value.By taking the A point operating condition in Fig. 9 as an example, according to the function relation curve that experimental method obtains, main shaft Y-direction rigidity to be realized
1.2 times of amplification applies the torque of 1.78Nm or the DC voltage of 7V to a pair of of piezoelectric actuator of Y-direction.
Claims (6)
1. the milling parameter control method based on the asymmetric rigidity regulation of axis system, which is characterized in that include the following steps:
1) using milling cutter point of a knife as coordinate origin, using milling feed direction as X-axis, perpendicular to direction of feed and milling cutter axis direction
Rectangular coordinate system is established for Y-axis；It measures the frequency response function of point of a knife X, Y-direction respectively using power hammer excitation experiment, and recognizes mode
Quality, rigidity and the several parameters of damping；
2) milling experiment is carried out using specified workpiece and cutter, cutting force COEFFICIENT K is picked out by the Milling Force measuredt
With radial cutting force COEFFICIENT Kr；
3) it according to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) that identification obtains in step 1), establishes non-
Symmetrical rigidity main shaft-milling system kinetic model；
4) according to the kinetic model established in step 3), its characteristic equation is calculated, and is directed to climb cutting, the two different millings of upmilling
Mode is cut, draws the milling stability flap figure under asymmetric rigidity different adjustment degree using Nyquist stability criterion,
Analyze milling stability；
5) rigid to main shaft Y-direction when climb cutting is cut using stability analysis in step 4) as a result, according to different processing operating conditions
Degree chooses suitable amplification factor；When upmilling is cut, suitable amplification factor is chosen to major axis X directional stiffness, realizes major axis X, Y
The asymmetric rigidity regulation in direction, and then realize that milling stability promotes the Flutter Control with target operating condition.
2. the milling parameter control method according to claim 1 based on the asymmetric rigidity regulation of axis system, feature
It is, in the step 3), establishes asymmetric rigidity main shaft-milling system kinetic model, detailed process is as follows:
According to the Cutting Force Coefficient recognized in the axis system modal parameter and step 2) recognized in step 1), asymmetric master is established
Axis-milling system kinetics equation is as follows:
In formula, X (t)=[x (t) y (t)]TIt is point of a knife in X, the vibration displacement vector of Y-direction；mx、my、cx、cy、kxAnd kyRespectively
It is major axis X, the modal mass of Y-direction, damping and rigidity；nxAnd nyRespectively axis system X-direction and Y-direction rigidity times magnification
Number, and nx≠ny, that is, pass through nxAnd nyThe non-equivalent assignment of two constants realizes the non-right of axis system X, Y both direction rigidity
Claim to adjust；F (t) is dynamic milling force, and expression is as follows:
In formula, H is to orient dynamic cutting force coefficients matrix, expression such as formula (4), wherein hxx、hxy、hyxAnd hyySuitable
Value is different under milling, the two different milling modes of upmilling, expression such as formula (5)；τ is the time lag period, is equal to milling
The cutter tooth of journey is by the period, i.e. τ=60/N Ω, wherein N is cutter tooth quantity, and Ω is the speed of mainshaft, and unit is r/min；
In formula, Krc=Kr/Kt；φ is the instantaneous tooth position angle of cutter tooth；φenAnd φexIt is cutter tooth entrance angle and to cut out angle, climb cutting respectively
When, φen=arccos (2d/D-1), φex=π；φ when upmillingen=0, φex=arccos (1-2d/D), wherein D is that cutter is straight
Diameter, d are radial cutting depth.
3. the milling parameter control method according to claim 2 based on the asymmetric rigidity regulation of axis system, feature
It is, in the step 4), according to the kinetics equation in step 3), calculates corresponding characteristic equation, it is fixed using Nyquist
Milling stability under reason analysis climb cutting, two kinds of upmilling different milling modes, detailed process is as follows:
Formula (3), formula (4) in step 3) is substituted into formula (2), and pull-type transformation is carried out simultaneously to equation both sides, is obtained:
Enable Ψ=NaKt(1-e-iωτThe π of)/4, and then know the characteristic equation of asymmetric rigidity main shaft-milling system are as follows:
This feature equation is major axis X, Y-direction rigidity amplification factor nx、nyFunction, while with suitable, upmilling cutting way is related；
For climb cutting and upmilling, constantly increase n respectivelyxAnd ny, the stability of milling process is judged using Nyquist stability criterion,
Draw the milling stability flap figure under different milling modes, asymmetric rigidity different adjustment degree.
4. the milling parameter control method according to claim 3 based on the asymmetric rigidity regulation of axis system, feature
It is, in the step 5), according to the analysis of step 4) as a result, milling stability to be improved, in upmilling cutting process, according to mesh
Mark cutting operating condition, including rotating speed of target and axial cutting-in, choose suitable X-direction rigidity amplification factor, so that original place is in flutter
The target cutting operating condition in region, which is realized to stablize after asymmetric stiffness tuning, cuts, wherein suitable rigidity amplification factor is with can
Effectively the minimum rigidity amplification factor of flutter is preferential selective value under control target cutting operating condition；In climb cutting cutting process, equally
Operating condition is cut according to target, chooses suitable Y-direction rigidity amplification factor, realizes that target cutting operating condition is cut by flutter to stable
Control target.
5. the milling parameter control method according to claim 4 based on the asymmetric rigidity regulation of axis system, feature
It is, in the step 5), by the integrated piezoelectric actuator in main shaft knife handle, and the parameter chosen according to the step, it utilizes
Piezoelectric actuator is used as power to main shaft application, realizes the physical regulating of the asymmetric rigidity suitable parameters of axis system.
6. the milling parameter control method according to claim 5 based on the asymmetric rigidity regulation of axis system, feature
It is, the physics for completing asymmetric rigidity regulation using two pairs of piezoelectric actuators being integrated on the orthogonal direction of knife handle position is real
Existing, detailed process is as follows:
It is integrated with the axis system of two pairs of piezoelectric actuators using on the orthogonal direction of knife handle position, is determined first by experimental method
Then the corresponding relationship of piezoelectric actuator power output on axis system X, Y-direction stiffness variation ratio and corresponding direction uses quilt
Dynamic and active control two ways realizes the asymmetric rigidity regulation of axis system, and then controls flutter；According to step 4) and step
5) analysis in upmilling cutting, applies X-direction piezoelectric actuator using torque spanner and corresponds to as a result, for passively regulating and controlling
Torque, by the rigidity of axis system X-direction regulation to selected ratio；In climb cutting cutting, benefit is in the same way to Y-direction
Piezoelectric actuator applies torque, realizes asymmetric rigidity regulation；And the passive control methods can be according to selected cutting parameter
It completes to adjust before cutting；The power output and input voltage of piezoelectric actuator are directly proportional, determine the ratio according to handbook first；Root
According to the analysis in step 4) and step 5) as a result, in active control, upmilling is cut, using signal generator to major axis X
The piezoelectric actuator application in direction makes major axis X directional stiffness change to DC voltage value required for target proportion, by main shaft system
The rigidity for X-direction of uniting regulates and controls to selected ratio；Climb cutting is cut, benefit is in the same way to the piezoelectricity of axis system Y-direction
Actuator applies corresponding DC voltage value, realizes the asymmetric rigidity regulation of target proportion；The active control method, is cutting
Preceding completion is adjusted, or is regulated and controled online according to the variation of cutting operating condition during the cutting process.
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| CN110850903A (en) * | 2019-11-07 | 2020-02-28 | 西安交通大学 | Active control system and active control method for radial vibration of rotating shaft |
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| CN104298799A (en) * | 2014-05-07 | 2015-01-21 | 上海交通大学 | Method for designing key geometric parameters of end mill on basis of machining vibration |
| CN105629920A (en) * | 2014-09-22 | 2016-06-01 | 财团法人工业技术研究院 | Processing monitoring system and method |
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