CN108334722A - Consider micro- milling cutter point frequency response function modeling method of main shaft rotation - Google Patents
Consider micro- milling cutter point frequency response function modeling method of main shaft rotation Download PDFInfo
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Abstract
The present invention consider main shaft rotation micro- milling cutter point frequency response function modeling method belong to micro- milling technology field, be related to it is a kind of consideration main shaft high speed rotation when centrifugal force and gyroscopic effect micro- milling point of a knife frequency response function modeling method.The frequency response function of the considerations of main shaft is reduced to several sections of multi-diameter shafts by modeling method, and every section of multi-diameter shaft is reduced to Rotating Timoshenko Beams model of element, finds out each section of multi-diameter shaft centrifugal force and gyroscopic effect.After the frequency response function for solving each section of multi-diameter shaft, the frequency response function that coupling calculating solves axis system is carried out by each section using minor structure response coupled method, centrifugal force and main shaft bearing characteristic when using structural modification method by main shaft high speed rotation are introduced into axis system frequency response function.This method effectively avoids causing cutter life to reduce because vibration is excessive, to improve the micro- Milling Process quality of micro parts and efficiency.Various micro- milling machines can be adapted to extensively, realize the accurate fast prediction of micro- Milling Process stability.
Description
Technical field
The invention belongs to micro- milling technology field, centrifugal force when being related to a kind of consideration main shaft high speed rotation and gyroscopic effect
Micro- milling point of a knife frequency response function modeling method.
Background technology
Micro- milling technology based on micro- milling machine is a kind of emerging processing skill for processing micro parts and high precision part
Art, has that rapidoprint range is wide, can realize three-dimension curved surface milling, high precision machining, energy consumption is small, equipment investment is few, efficient
Outstanding advantages of.However, because the mutual vibration between cutter and workpiece can cause chatter phenomenon, micro- milling to quiver in micro- Milling Process
Shake is to lead to that surface quality is poor, the serious one of the main reasons of tool wear ensures the steady of micro- Milling Process in order to avoid flutter
It is qualitative, the method frequently with the stability lobes diagram as pre- micrometer milling parameter, and the premise for obtaining stable flap figure is to learn
Micro- milling system point of a knife kinetic characteristics obtain point of a knife frequency response function.Currently, real frequently with FInite Element, hammering both at home and abroad
It tests and minor structure response coupled method is combined and solves micro- milling system point of a knife frequency response function, but hammer experimental method and be only applicable to
Certain specific lathe, and take time and effort.In addition, taking into account, micro- milling is high-accuracy, superfast machining feature, main during high-speed milling
Axle system high speed rotation generates centrifugal force and gyroscopic effect easily leads to micro- milling parameter and shows dynamic instability phenomenon.Cause
This, micro- milling system point of a knife frequency response function computational methods based on the static hypothesis of lathe have certain limitation in practical applications
Property.
For example, Xiaohong L of Dalian University of Technology etc. 2017 are in Journal of Manufacturing
Paper " the Tool Point Frequency that Science and Engineering periodicals the 3rd phase of volume 139 delivers
Response Prediction for Micro-milling by Receptance Coupling Substructure
Based on minor structure response coupled method (RCSA) and consideration rotational freedom in Analysis ", and combine Timoshenko and Euler
Two kinds of beam theories and Hammering Test obtain the point of a knife frequency response function of oligodynamics system.By comparing
The point of a knife frequency response function that Timoshenko and Euler beam theories obtain.Finally, frequency response function is identified as mode ginseng
It counts, and modal parameter is converted to the equivalent structure parameter of physical system.However, the point of a knife frequency response function computational methods do not have
There are centrifugal force and gyroscopic effect caused by considering main shaft high speed rotation, to can not theoretically Accurate Prediction main shaft high speed revolve
Stability under turning.
Invention content
The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art, main shaft high speed rotation in micro- milling is considered
When centrifugal force and gyroscopic effect, it is theoretical based on Rotating Timoshenko Beams, entire axis system is modeled, and main shaft bearing
Equivalent parameters is introduced into axis system modeling, responds the rigid coupling condition of coupled method using minor structure and elastic damping couples item
Part solves its frequency response function, and this method is more in line with the actual processing operating mode of micro- milling, it can be achieved that micro- Milling Process stability
Accurate fast prediction.This method greatly improves efficiency under the premise of ensureing prediction result precision.
The technical solution adopted by the present invention is to consider micro- milling cutter point frequency response function modeling method of main shaft rotation, feature
It is that modeling method is based on Rotating Timoshenko Beams model, main shaft is reduced to several sections of multi-diameter shafts, every section of multi-diameter shaft is reduced to
Rotating Timoshenko Beams model of element, so the considerations of find out each section of multi-diameter shaft centrifugal force and gyroscopic effect frequency response function.
After the frequency response function for solving each section of multi-diameter shaft, coupling calculating is carried out by each section using minor structure response coupled method and solves main shaft
The main shaft bearing characteristic for considering centrifugal force is introduced into axis system frequency response function by the frequency response function of system using structural modification method
In, solve its frequency response function using rigid coupling condition and elastic damping coupling condition；Method is as follows：
Main shaft is reduced to several sections of multi-diameter shafts by step 1, and each section of multi-diameter shaft is all reduced to Timoshenko beam element moulds
Type, then solve each frequency response function of this section of multi-diameter shaft；
First, under broad sense three-dimensional coordinate, the equation of motion of Rotating Timoshenko Beams is expressed as：
Wherein, ρ, A, I are respectively density, cross-sectional area and the cross sectional moment of inertia of beam, k, G, E be respectively for shearing factor,
Modulus of shearing and elasticity modulus, u, φ are the displacement in all directions, corner, and Ω is beam rotary speed.
According to the boundary condition of rotating beam-free end, by taking the directions y as an example, the torque at beam both ends and shearing force are zero, by with
Lower formula indicates：
Wherein, L is the length of beam.It carries it into the equation of motion and can obtain the equation of motion abbreviation in the directions y and be：
Due to the presence of Ω, there is coupling in the direction x, y.Assuming that simple harmonic motion is made in the direction x, y, i.e.,：
uy(z, t)=Uy(z)ejωt (10)
ux(z, t)=Ux(z)ejωt (11)
φx(z, t)=θx(z)ejωt (12)
In the free vibration analysis of beam element, it is in the vibration shape relationship of orthogonal plane：
Wherein, f, b are respectively the forward, backward vibration shape.
Formula (10) is brought into formula (9) and can be obtained to formula (13)：
With reference to the solution of common beam, it is to the rear characteristic solution to vibration shape freedom-free end vibration equation：
Wherein：
D11=(α-λ) cos (α L)+(λ-α) cosh (β L) (17)
D22=λ α (cosh (β L))-cos (α L) (20)
Finally the expression formula of characteristic function is：
Wherein, αr、βrFor each first order mode corresponding α, β, ArIt is characterized the constant that function normalization obtains：
Forward mode need to only be become b, d：
Formula (25) and formula (26) are brought into frequency response function formula：
Remember that g and w indicates the endpoint of beam, Hgw(Lgw、Ngw、Pgw) indicating that w is excitation point, g is the frequency response function of response point.R is
Exponent number, ωrFor r rank intrinsic frequencies, as r=0：
It is 0 and L to enable Z respectively, that is, acquires H00、H0L、HL0、HLLIt equally can be in the hope of corresponding Lgw、Ngw、Pgw.Thus it asks
Solve each frequency response function value of the fixed one section of beam of radius, length；
Each section of beam after solving the frequency response function of each section of beam, is carried out the frequency response letter that coupling calculates the system that solves by step 2
Number responds coupled method using minor structure, and cutter and the respective coupled modes of main shaft body are coupled using rigidity, coupling between the two
Conjunction mode is coupled using elastic damping.Adjacent two sections of rigidity couples formula：
[V11]=[W11]-[W12]([W22]+[B11])-1[W21] (32)
[V12]=[W12]([W22]+[B11])-1[B12] (33)
[V21]=[B21]([W22]+[B11])-1[W21] (34)
[V22]=[B22]-[B21]([W22]+[B11])-1[B12] (35)
WhereinX=W, B, V；G=1,2；W=1,2.
If n is multi-diameter shaft hop count.As n=2, can directly be calculated using coupling formula；
When n=3, result of calculation when using n=2, in this way can with third section beam as the frequency response function of one section of new beam
It is calculated with still coupling formula according to two sections of beams, repeats down in this way, then when n is any number, can all be solved.
Rigidity need to only be coupled matrix [W in formula by the elastic damping coupling between cutter and main shaft22]+[B11] become [W22]+
[K]-1+[B11], i.e.,：
[V11]=[W11]-[W12]([W22]+[K]-1+[B11])-1[W21] (36)
[V12]=[W12]([W22]+[K]-1+[B11])-1[B12] (37)
[V21]=[B21]([W22]+[K]-1+[B11])-1[W21] (38)
[V22]=[B22]-[B21]([W22]+[K]-1+[B11])-1[B12] (39)
WhereinWherein kyf、kym、kθf、kθmIndicate power to displacement, displacement respectively
To torque, angular displacement is to power, and angular displacement is to torque rigidity, cyf, cym, cθf, cθmPower is indicated respectively to displacement, and displacement is to torque, angle
Displacement damps torque power, angular displacement；
Main shaft bearing is introduced into axis system frequency response function by step 3 using structural modification method, and C is coupling unit, C1
For the left end of coupling unit, and coupled with main shaft bearing, C2For the right end of coupling unit；Application structure modification method can be coupled
The frequency response function matrix of new unit C' is afterwards：
[αC']=[[I4]+[αC][D]]'[αC] (40)
Wherein, aCFor frequency response matrix before coupling, aC′For the frequency response unit after coupling, expression formula is：
I4For 4 rank unit matrixs, D is bearing characteristics unit related with rotating speed, and expression formula is：
Wherein Ky、Kθ、Cy、CθRespectively be translatable rigidity, translation damping, rotational stiffness and rotary damping, and has with rotating speed
It closes.
Accurate characteristic parameters of bearing is solved, its related ginseng is obtained to the method that empirical equation is combined using economics analysis
Number.Bearing rigidity and contact stiffness kcWith oil film rigidity kzCorrelation, respective solution formula are：
Wherein A ' is the set physics relating to parameters with bearing, also coefficient related with radial load and rotating speed, Q0iFor rolling
The Maximum Contact load of kinetoplast, t are index coefficient, and spot contact bearing generally takes 2/3, and line generally takes 0.9 when contacting；ki、keIt is interior
The contact coefficient of outer ring, FCFor centrifugal force；
t1For the load factor in Elastic fluid theory, when point contact, generally takes 0.16, and line contact takes 0.073.djiFor supporting region
The Oil Film Coefficient that rolling element is contacted with inner ring, djeThe Oil Film Coefficient contacted with outer ring for the rolling element of supporting region；Further according to bearing
Rolling element number and the angle of each rolling element can calculate oil film rigidity kz；
The integral stiffness of bearing is defined as being connected in series i.e. by contact stiffness and oil film rigidity：
And for other three translation dampings, rotational stiffness and damping are answered then by empirical equation with reference to lathe rolling bearing
It is solved with handbook, is finally completed the modeling of point of a knife frequency response function.
The notable advantageous effect of the present invention is theoretical based on Rotating Timoshenko Beams, while considering that main shaft high speed rotation is produced
Raw centrifugal force and gyroscopic effect, zygote structural response coupled method and structural modification method obtain point of a knife frequency response function modeling side
Method, this method are more in line with the actual processing operating mode of micro- milling, can adapt to various micro- milling machines, Accurate Prediction point of a knife frequency extensively
Function is rung, forecasting efficiency is greatly improved, is laid the foundation for the stability prediction research under main shaft high speed rotation.
Description of the drawings
Micro- milling point of a knife frequency response function modeling procedure figures of the Fig. 1 based on Rotating Timoshenko Beams.
Fig. 2 tool parts are reduced to multi-diameter shaft figure, T-1 sections-cutting edge part, T-2 to T-6 sections-it is respectively transition centrum
Each component part, the coupling part of T-7 sections-main shaft and cutter.
Fig. 3 main shaft portions are reduced to multi-diameter shaft figure, and S-1 to S-11- is respectively each unit axis of main shaft component part.
Fig. 4 a) be n=2 rigidly coupling figures, Fig. 4 b) it is n=3 rigidly coupling figures.Wherein, W1, B1, V1- coupling unit
Left end, the right end of W2, B2, V2- coupling unit.
Fig. 5 structural modification method schematic diagrames, KyBe translatable rigidity, KθTranslation damping, CyRotational stiffness, CθRotary damping, C-
Coupling unit, C1The left end of coupling unit, C2The right end of coupling unit, coupling unit new C'-.
Fig. 6 a) point of a knife frequency response function real part curve graph, wherein 1- bibliography as a result, 2- the present embodiment as a result, level
Axis-frequency (HZ), longitudinal axis-real part (m/N).
Fig. 6 b) point of a knife frequency response function imaginary part curve graph.Wherein, 1- bibliography as a result, 2- the present embodiment as a result, level
Axis-frequency (HZ), longitudinal axis-imaginary part (m/N).
Specific implementation mode
Below in conjunction with the accompanying drawings with the technical solution specific implementation mode that the present invention will be described in detail.
The present invention is by taking the HT42S120C electro spindles that IBAG companies of common Switzerland in micro- milling machine produce as an example, to modeling
Journey is described in detail.The minimum speed of the main shaft is 40000r/min, and maximum speed 140000r/min, main shaft is using oil
Gas mixed lubrication, ceramic ball bearing improve support stiffness.
Condition used in embodiment is as follows：
As shown in Fig. 2, tool parts are reduced to 7 sections of multi-diameter shaft figures, specific size is：T-1 sections of length is 1.5mm,
Outer diameter is 0.41mm, and T-2 segment length is 2.15mm, and the length that 0.6mm, T-3 section of outer diameter is 2.15mm, outer diameter 1.28mm,
T-4 segment length is 2.15mm, and outer diameter 1.96mm, T-5 segment length is 2.15mm, and outer diameter 2.64mm, T-6 segment length is
2.15mm, outer diameter 3.32mm, T-7 segment length are 4mm, outer diameter 7.77mm.
Main shaft portion is reduced to 11 sections of multi-diameter shafts, as shown in Figure 3.S-1 sections of length is 10mm, outer diameter 12.3mm, S-2
The length of section is 15mm, and outer diameter 10mm, the length that 5mm, S-3 sections of internal diameter is 2.9mm, the length that 10mm, S-4 sections of outer diameter
For 4mm, the length that 10mm, S-5 sections of outer diameter is 6mm, and the length that 14.6mm, S-6 sections of outer diameter is 3.2mm, and outer diameter is
13.5mm, S-7 sections of length is 26.4mm, and the length that 7.36mm, S-8 sections of outer diameter is 4mm, the length that 14mm, S-9 sections of outer diameter
Degree is 9.5mm, and the length that 7.7mm, S-10 sections of outer diameter is 3mm, and the length that 6mm, S-11 sections of outer diameter is 8.3mm, and outer diameter is
6mm。
The density of cutter is 14300kg/m3, elasticity modulus 580GPa, Poisson's ratio 0.28, fissipation factor 0.02.
The density of main shaft is 7860kg/m3, elasticity modulus 200GPa, Poisson's ratio 0.30, fissipation factor 0.06.Connection performance is joined
Number：kyf=4.2 × 107, kym=2.1 × 106, kθf=2.1 × 106, kθm=6.5 × 104, cyf=54, cym=22, cθf=22,
cθm=1.0.
Fig. 1 is micro- milling point of a knife frequency response function modeling procedure figure based on Rotating Timoshenko Beams, and modeling method is based on
Axis system is reduced to several sections of multi-diameter shafts by Rotating Timoshenko Beams model, and every section of multi-diameter shaft is reduced to rotate
Timoshenko beam element models, and then find out each frequency response function of multi-diameter shaft axis.Solve the frequency response letter of each section of multi-diameter shaft
After number, the frequency response function that coupling calculates the system that solves is carried out by each section using minor structure response coupled method, utilizes structural modification
The main shaft bearing characteristic for considering centrifugal force is introduced into axis system frequency response function by method, to realize the prediction of micro- milling stability
It lays the foundation.Method is as follows：
Step 1, in order to obtain the frequency response function of axis system, several sections of multi-diameter shafts, each section of multi-diameter shaft are reduced to
It can be all reduced to Rotating Timoshenko Beams model of element, and then solve each frequency response function of this section of multi-diameter shaft.Such as Fig. 3 institutes
Show, main shaft-collet segment is reduced to 11 sections of multi-diameter shafts, distinguishes phase marked as S-3 and S-4 sections, S-10 and S-11 sections of internal-and external diameters
Deng being distinguished here due to bearing characteristics to be added between S-3 and S-4 sections, between S-10 and S-11 sections for position of bearings
Regard two sections as.Assuming that S-1 sections of entities, material property is identical as main shaft, and S-2 sections of cutter outer diameters are less than main shaft internal diameter, it is therefore assumed that
It is hollow；Between micro- milling cutter point of a knife and handle of a knife there is cross-sectional area be the circular truncated cone, be for its motion control equation
The differential equation group of variable coefficient is that can not solve the solution of its free vibration using analytic method, therefore, micro- milling cutter is divided into 7 sections
Multi-diameter shaft, as shown in Figure 2.The T-1 sections of multi-diameter shafts that original diameter 68% is equivalent to for micro- milling cutter cutting edge portion point, T-2 to T-6 sections is
Transition pyramidal portion is equivalent to 5 corresponding multi-diameter shafts.Axis system rotor portion entire so is just divided into 18 sections of multi-diameter shafts, often
One section of multi-diameter shaft can all regard one section of Rotating Timoshenko Beams model as, be calculated according to Rotating Timoshenko Beams frequency response function public
Formula (29) and (30) can solve the frequency response function of each section of axis system simplified model.
Step 2, after the frequency response function for solving each section of beam, the frequency response letter that coupling calculates the system that solves need to be carried out by each section
Number responds coupled method using minor structure.It includes three kinds of coupled modes that minor structure, which responds coupled method,：Rigidity, elasticity and elastic damping
Coupling, cutter and the respective coupled modes of main shaft body are coupled using rigidity, couple formula such as (32) to (35)；Between the two
Coupled modes are coupled using elastic damping, couple formula such as (36) to (39).In connection performance Parameter Conditions wherein in matrix
It has provided.As shown in Fig. 4 (a, b), as n=2, can directly it be calculated using coupling formula, as n=3, when n=2
Frequency response function of the result of calculation as one section of new beam, in this way can be still according to two sections of beams coupling formula with third section beam
It calculates, repeats down in this way, then when n is any number, can all be solved.
Step 3, using structural modification method as shown in figure 5, calculated according to formula (40), (41), (42), and with reference to machine
Bed rolling bearing application manual can acquire accurate characteristic parameters of bearing, fore bearing characterisitic parameter：Ky=3.0 × 107N/m, Kθ=
67Nm/rad, Cy=9.5Ns/m, Cθ=0.042Nms/rad.Characteristic parameters of bearing afterwards：Ky=8.7 × 106N/m, Kθ=19Nm/
Rad, Cy=0.026Ns/m, Cθ=0.00011Nms/rad.Characteristic parameters of bearing is introduced into new unit frequency response function matrix
In, it is final to obtain the point of a knife frequency response function for considering centrifugal force and gyroscopic effect.
The present embodiment result and bibliography are compared, shown in analysis result such as Fig. 6 (a, b) of the two, curve 1 is reference
Result by references, curve 2 are the present embodiment results.Using the least square method of LMS TestLab softwares to the frequency response function of acquisition
Modal idenlification is carried out, analytical error is 1 rank in rank number of mode and 2 rank mistiming differences are respectively 1.74% and 0.028%.The present invention is real
Result and the bibliographic reference result for applying example are more accurate for the prediction of the low mode of two ranks and experimental result, can improve small zero
The quality and efficiency of part processing.
Claims (1)
1. a kind of micro- milling cutter point frequency response function modeling method considering main shaft rotation, characterized in that modeling method simplifies main shaft
For several sections of multi-diameter shafts, every section of multi-diameter shaft is reduced to Rotating Timoshenko Beams model of element, and then finds out each section of multi-diameter shaft
Consider the frequency response function of centrifugal force and gyroscopic effect；After the frequency response function for solving each section of multi-diameter shaft, coupling is responded using minor structure
It is legal to carry out the frequency response function that coupling calculating solves axis system by each section, the master of centrifugal force will be considered using structural modification method
Axle bearing characteristic is introduced into axis system frequency response function, its frequency is solved by rigid coupling condition and elastic damping coupling condition
Ring function；Method is as follows：
Main shaft is reduced to several sections of multi-diameter shafts by step 1, and each section of multi-diameter shaft is all reduced to Timoshenko beam element models,
Each frequency response function of this section of multi-diameter shaft is solved again；First, under broad sense three-dimensional coordinate, the movement of Rotating Timoshenko Beams
Equation is expressed as：
Wherein, ρ, A, I are respectively density, cross-sectional area and the cross sectional moment of inertia of beam, and k, G, E are respectively for shearing factor, shearing
Modulus and elasticity modulus, u, φ are the displacement in all directions, corner, and Ω is beam rotary speed；
According to the boundary condition of rotating beam-free end, by taking the directions y as an example, the torque at beam both ends and shearing force are zero, by following public affairs
Formula indicates：
Wherein, L is the length of beam；It carries it into the equation of motion and can obtain the equation of motion abbreviation in the directions y and be：
Due to the presence of Ω, there is coupling in the direction x, y；Assuming that simple harmonic motion is made in the direction x, y, i.e.,：
uy(z, t)=Uy(z)ejωt (10)
ux(z, t)=Ux(z)ejωt (11)
φx(z, t)=θx(z)ejωt (12)
In the free vibration analysis of beam element, it is in the vibration shape relationship of orthogonal plane：
Wherein, f, b are respectively the forward, backward vibration shape；Formula (10)-(13) are brought into formula (9) and are obtained：
With reference to the solution of common beam, it is to the rear characteristic solution to vibration shape freedom-free end vibration equation：
Wherein：
D11=(α-λ) cos (α L)+(λ-α) cosh (β L) (17)
D22=λ α (cosh (β L))-cos (α L) (20)
Finally the expression formula of characteristic function is：
Wherein, αr、βrFor each first order mode corresponding α, β, ArIt is characterized the constant that function normalization obtains：
Forward mode need to only be become b, d：
Formula (25), (26) are brought into frequency response function formula：
Remember that g and w indicates the endpoint of beam, Hgw(Lgw、Ngw、Pgw) indicating that w is excitation point, g is the frequency response function of response point；R is rank
Number, ωrFor r rank intrinsic frequencies, as r=0：
It is 0 and L to enable Z respectively, that is, acquires H00、H0L、HL0、HLLIt equally can be in the hope of corresponding Lgw、Ngw、Pgw；Thus it solves
Each frequency response function value of the fixed one section of beam of radius, length；
Each section of beam after solving the frequency response function of each section of beam, is carried out the frequency response function that coupling calculates the system that solves by step 2,
Coupled method is responded using minor structure, cutter and the respective coupled modes of main shaft body are coupled using rigidity, coupling between the two
Mode is coupled using elastic damping；Adjacent two sections of rigidity couples formula：
[V11]=[W11]-[W12]([W22]+[B11])-1[W21] (32)
[V12]=[W12]([W22]+[B11])-1[B12] (33)
[V21]=[B21]([W22]+[B11])-1[W21] (34)
[V22]=[B22]-[B21]([W22]+[B11])-1[B12] (35)
Wherein,X=W, B, V；G=1,2；W=1,2；
If n is multi-diameter shaft hop count；As n=2, can directly be calculated using coupling formula；When n=3, meter when n=2
Frequency response function of the result as one section of new beam is calculated, still can couple formula meter according to two sections of beams with third section beam in this way
It calculates, repeats down in this way, then when n is any number, can all be solved；
Rigidity need to only be coupled matrix [W in formula by the elastic damping coupling between cutter and main shaft22]+[B11] become [W22]+[K]-1
+[B11], i.e.,：
[V11]=[W11]-[W12]([W22]+[K]-1+[B11])-1[W21] (36)
[V12]=[W12]([W22]+[K]-1+[B11])-1[B12] (37)
[V21]=[B21]([W22]+[K]-1+[B11])-1[W21] (38)
[V22]=[B22]-[B21]([W22]+[K]-1+[B11])-1[B12] (39)
Wherein,Wherein kyf、kym、kθf、kθmPower is indicated respectively to displacement, and displacement is to power
Square, angular displacement is to power, and angular displacement is to torque rigidity, cyf, cym, cθf, cθmPower is indicated respectively to displacement, and displacement is to torque, angular displacement
To power, angular displacement damps torque；
Main shaft bearing is introduced into axis system frequency response function by step 3 using structural modification method, and C is coupling unit, C1For coupling
Close the left end of unit, C2For the right end of coupling unit, C1 is bearing and the Coupling point with main shaft, and it is available that application structure changes method
The frequency response function matrix of new unit C' is after coupling：
[αC']=[[I4]+[αC][D]]'[αC] (40)
Wherein, aCFor frequency response matrix before coupling, aC′For the frequency response unit after coupling, expression formula is：
I4For 4 rank unit matrixs, D is bearing characteristics unit related with rotating speed, and expression formula is：
Wherein Ky、Kθ、Cy、CθRespectively be translatable rigidity, translation damping, rotational stiffness and rotary damping, and related with rotating speed；
Accurate characteristic parameters of bearing is solved, the method being combined using economics analysis and empirical equation obtains its relevant parameter；
Bearing rigidity and contact stiffness kcWith oil film rigidity kzCorrelation, respective solution formula are：
Wherein, A ' is the set physics relating to parameters with bearing, also coefficient related with radial load and rotating speed, Q0iFor rolling element
Maximum Contact load, t is index coefficient, and spot contact bearing generally takes 2/3, and line generally takes 0.9 when contacting；ki、keFor Internal and external cycle
Contact coefficient, FCFor centrifugal force；
t1For the load factor in Elastic fluid theory, when point contact, generally takes 0.16, and line contact takes 0.073；djiIt is rolled for supporting region
The Oil Film Coefficient that body is contacted with inner ring, djeThe Oil Film Coefficient contacted with outer ring for the rolling element of supporting region；Further according to bearing element
Body number and the angle of each rolling element can calculate oil film rigidity kz；The integral stiffness of bearing is defined as by contact stiffness
It is connected in series i.e. with oil film rigidity：
And for other three translation dampings, rotational stiffness and damping, then by empirical equation, with reference to lathe rolling bearing application hand
Volume is solved, and the micro- milling cutter point frequency response function modeling for considering main shaft rotation is finally completed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810375930.3A CN108334722A (en) | 2018-04-19 | 2018-04-19 | Consider micro- milling cutter point frequency response function modeling method of main shaft rotation |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110210179A (en) * | 2019-06-28 | 2019-09-06 | 合肥工业大学 | A kind of acquisition methods of elastic element dynamic stiffness and its both ends load |
| CN111291479A (en) * | 2020-01-21 | 2020-06-16 | 清华大学 | Method for predicting milling stability of series-parallel machine tool |
| CN112069611A (en) * | 2020-08-06 | 2020-12-11 | 清华大学 | Complete machine modeling method for swing angle milling head based on block modeling and experimental parameter identification |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103894884A (en) * | 2014-03-21 | 2014-07-02 | 西北工业大学 | Milling cutter tip frequency-response function prediction method |
| CN105058166A (en) * | 2015-09-11 | 2015-11-18 | 上海理工大学 | Cutter tip frequency-response function predicting method based on accurate milling cutter modeling |
-
2018
- 2018-04-19 CN CN201810375930.3A patent/CN108334722A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103894884A (en) * | 2014-03-21 | 2014-07-02 | 西北工业大学 | Milling cutter tip frequency-response function prediction method |
| CN105058166A (en) * | 2015-09-11 | 2015-11-18 | 上海理工大学 | Cutter tip frequency-response function predicting method based on accurate milling cutter modeling |
Non-Patent Citations (6)
| Title |
|---|
| A.ERTURK等: "Analytical modeling of spindle–tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF", 《INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE》 * |
| O. ÖZSAHIN等: "A closed-form approach for identification of dynamical contact parameters in spindle-holder-tool assemblies", 《INTERNATIONAL JOURNAL OF MACHINE TOOLS & MANUFACTURE》 * |
| O. ÖZSAHIN等: "Analytical modeling of asymmetric multi-segment rotor-bearing systems with Timoshenko beam model including gyroscopic moments", 《COMPUTERS AND STRUCTURES》 * |
| S.A.TAJALLI等: "Size dependent vibrations of micro-end mill incorporating strain gradient elasticity theory", 《JOURNAL OF SOUND AND VIBRATION》 * |
| 唐云冰等: "高速陶瓷滚动轴承等效刚度分析与试验", 《航空动力学报》 * |
| 朱坚民等: "一种新的预测铣刀刀尖频响函数的方法", 《中国机械工程》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110210179A (en) * | 2019-06-28 | 2019-09-06 | 合肥工业大学 | A kind of acquisition methods of elastic element dynamic stiffness and its both ends load |
| CN110210179B (en) * | 2019-06-28 | 2023-03-24 | 合肥工业大学 | Method for acquiring dynamic stiffness of elastic element and loads at two ends of elastic element |
| CN111291479A (en) * | 2020-01-21 | 2020-06-16 | 清华大学 | Method for predicting milling stability of series-parallel machine tool |
| CN112069611A (en) * | 2020-08-06 | 2020-12-11 | 清华大学 | Complete machine modeling method for swing angle milling head based on block modeling and experimental parameter identification |
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