CN108664709A - Effect analysis method is rolled over based on 3D constitutive models pendulum under a kind of alternating load - Google Patents
Effect analysis method is rolled over based on 3D constitutive models pendulum under a kind of alternating load Download PDFInfo
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Abstract
The invention belongs to machinery manufacturing technology fields, it discloses and effect analysis method is rolled over based on 3D constitutive models pendulum under a kind of alternating load, 3D bulk effects are carried out to vibration rotary forging viscoelastic-plastic constitutive model using MATLAB softwares and skin effect is analyzed, Three-dimensional Contact Problem is described by the Contact Boundary during Multi-parameter coupling analog vibration rotary forging；Viscoplasticity space matrix and visco-plasticity space matrix have been derived respectively using the generalized Hooke law in Elasticity and the incremental theory in plasticity, and the skin effect analysis model in vibration rotary forging forming is established with this；By proposing rational it is assumed that carrying out FEM Simulation and skin effect analysis to the vibration rotary forging model under different modal parameters.Present invention is disclosed vibration roll milling forming mechanism, improve material vibrating roll milling forming process analysis procedure analysis under three-dimensional constitutive model, have important theory significance and practical value to establishing vibration roll milling forming equipment.
Description
Technical field
The invention belongs to be based on 3D constitutive models pendulum under machinery manufacturing technology field more particularly to a kind of alternating load to roll over effect
Answer analysis method.
Background technology
Currently, the prior art commonly used in the trade is such：
With the rapid development of machine industry, vibration rotary forging Precision Forming Technology is increasingly by the weight of people
Depending on.Since rotary forging has the characteristics that low energy consumption, forming accuracy is high, noise is small, small investment, by the general of countries in the world
All over attention and increasingly wider application is obtained in actual production.But due to the complexity of its building motion, people are to the skill
Art forms the understanding of regularity not yet, is still a weak link so far in theoretical side, related agricultural technology problem lacks
Weary effective theoretical direction, many produce reality problems can only use experiment and the method to accumulate experience to explore be subject in practice
It solves, these greatly limit the application and development of rotary forging technique.
Vibrate a kind of citation form as the nature motion of matter, Theory of Vibration is macro mechanical engineering and material engineering
Sight has obtained significant progress in field.In the 1950s, University Vienna Austria B.Langernecker is single in test
It is found when the yield strength of crystal, the vibration effect that test result generates when passing through beside laboratory with truck is very big.
Thus him has been caused and had explored influence of the mechanical oscillation to metal plastic deformation later, and then delivered in zinc crystal stretching experiment
Metal has the analysis bulletin of stronger ruckbildung after attached supersonic vibration.After grinding for F.Blaha and B.Langernecker
After studying carefully work, the country such as the U.S., Germany, Japan and former Soviet Union expands extraneous vibration (especially ultrasonic vibration) condition in succession
Under metal forming is theoretical and applied analysis.Therefore, it vibrates plastic working technique and technology is come into being.
As the rotary forging new technology and vibrotechnique of monotechnics, different degrees of development is respectively obtained and has answered
With.In order to overcome the shortcomings of rotary forging, can attempt friendly neighbour's science and engineering technology --- mechanical vibration theory and engineering
Technology is combined with rotary forging technique, that is, vibration is attached in rotary forging technique, and vibration is consequently formed and swings rolling
Press new technology.Vibration rotary forging is on the basis of routinely pendulum is rolled over, by a certain specific frequency and the pendulum of regular waveform again
Power is rolled over to be applied in workpiece-mold vibration system along assigned direction.The plastic processing that mechanical oscillation are introduced to metal, can drop
External force needed for low material deformation.There are two aspects for the reason of generating this effect, are on the one hand bulk effects, are on the other hand
Skin effect.
Rotary forging technology originates from the U.S. earliest, and Si Like first proposed pendulum rolling technology early in 1918, and make
United States Patent (USP) is obtained at the Slick milling trains of his naming, and in nineteen twenty.Then, the Marseille of Britain proposes pendulum
The basic conception for rolling over movement obtains British patent in nineteen twenty-nine.Until Marseille company in 1966 just produces the pendulum of a 700KN
Rolling machine.Warsaw, POL Polytechnics Ma Erxinni professors invented four track PXW types rotary forging presss in 1967 and by Warsaw machineries
Research institute designs.After Poland, Switzerland's Schmid companies eighties and Mori companies of Japan produce the nineties in succession
There are four types of the rotary forging presss of track as commodity selling for tool.
China began to rotary forging research work from 1972.It is that Shanghai Electric-motor Forging Factory develops single-track pendulum earliest
Rolling machine is mainly used for the hot rotary roll of automobile axle shaft.Then Wuhan automobile gear factory trial-produces First 120KN vertical pendulums successfully
Roll over testing machine.In recent years, Institutes Of Technology Of Jiangxi has carried out Primary Study to rotary forging, and draws in conventional pendulum spreading technology
Vibration is entered, has had developed the extensional vibration that one carries out the inner spline housing in fuel-saving apparatus for motor cycle rotary forging processing and put rolling
Testing machine so that pendulum rolling technology has new leap.In addition, the school is also made to vibration rotary forging press progress PLC control aspects
Very big achievement is analysed in depth and obtains, this provides wide space for the development and popularization of rotary forging technology.
Bulk effect initially finds under ultrasonic vibration, initially disclose bulk effect be F.Blaha and
What B.Langenecker was done in nineteen fifty-five starts sex work, F.Blaha and B.Langenecker and later major part
Scientific research personnel generally uses ultrasonic vibration, but according to later related studies have shown that low-frequency vibration can also reduce plastic deformation
Mean stress in deformation process generates bulk effect.How to explain that the mechanism of bulk effect is always to vibrate in plastic processing
Hot issue, due to generate bulk effect vibration frequency range usually in 15Hz between 1.5MHz, frequency range is very
Width, this mechanism more essential to research bulk effect brings larger difficulty.Mould based on accurate experiment and quantitative description
There are no formation so far for type, so the view of many scholars in this regard still is limited to the description of the seventies substantially.I.e. for body
Two kinds of explanations of product effect：One is thermally softening related with crystal dislocation；The second is the Stress superposition based on phenomenological mechanics
Principle.So-called Stress superposition refers to that another computable cyclic stress is superimposed in quiet machining stress, and total stress is in each cycle
Interior peak value is consistent with the static stress under operating mode without friction, and in the case of no Wen Sheng, zerofriction force, principle of stacking can be with
Illustrate the entire reason that machining stress reduces.
Some are usually to be carried out under relatively small normal pressure in relation to the basic experiment to rub under vibration operating mode, it is difficult to
The skin effect of true description plastic processing.Skin effect Producing reason has been deemed likely to following several respects at present：
(1) moment occurs and detaches due to vibration between workpieces processing and tool；(2) friction force vector is reversed so that in the vibration period
Part-time in frictional force be conducive to deformation processing instead；(3) effect of local heat effect so that local weldbonding phenomenon subtracts
It is few；(4) vibration improves processing and lubrication condition, makes new machined surface by oxygen since the moment of machining tool and workpiece separates
Change, generate oxide, generates lubricating action；(5) due to effect of vibration, lubricating fluid is easier to enter deformed area, so as to improve
Lubricating condition, friction coefficient are reduced.
Practice is lagged behind for vibrating the Analysis on Mechanism of plastic processing deformation at present, analysis results are confined to ultrasound mostly
In frequency range, the explanation of some microcosmic mechanisms during ultrasonic vibrating machining still lacks the quantitative description of science；Ultrasound is shaken
Dynamic excitation system power is small, to influence the popularization and application of ultrasonic vibration.Due to low-frequency vibration system can be more convenient obtain
Higher exciting power is obtained, effect similar with ultrasonic vibration can be reached when low-frequency vibration is machined with, therefore low-frequency vibration adds
The industrial applications value of work technology becomes apparent.
Many methods have had been established to describe METHOD IN METAL FORMING PROCESSES at present, including slip line method, slab method, upper bound method and
FInite Element etc..
Slip line method establishes sliding field for specific deformation process, seeks each point stress shape in plane when flow of metal
State and flow tendency.This method has many advantages, such as that theory is complete, computational accuracy is high in terms of handling plane strain problems, but this
Kind method is only adapted to the plane strain problems of processing rigid-perfectly plastic body.And for deforming, complicated, sliding field is unknown and examines
The problems such as considering thermal stress caused by material hardening, strain rate influence, deformation temperature, skid wire rule is difficult to meet the requirements.
Principal stress collimation method mathematics calculation it is fairly simple, but this method can only determine the power on contact surface size and its
Distribution situation, the accuracy of result of calculation and made by assume it is related with the degree that actual conditions are close.
Upper bound method is built upon on the basis of the suitable exercise-induced sudden death pattern of deformable body proposition, it solves speed
The construction problem for spending field, can analyze all kinds of stable states and unstable state, two and three dimensions forming process.The calculation amount of the algorithm is small,
Processing method is simple, can be not only used for positive simulation, it can also be used to inverse analog.But it is poor for the simulation precision of complex boundary, and
More accurate stress distribution law in deformable body can not be acquired.
In conclusion problem of the existing technology is：
Existing Visco-elastic Constitutive Relations theory cannot explain comprehensively vibration roll milling forming mechanism, and it is acquired at
Fruit is to be based on one-dimensional, two-dimentional compacting mechanism research mostly, lacks theory analysis and experimental demonstration for 3D compacting mechanisms, also can not
Theoretically effective guidance is provided to vibrate the production practices of spreading.
Solve the difficulty and meaning of above-mentioned technical problem：
Difficulty：
(1) it in establishing three-D volumes effect finite element analysis model, due to the division of cell node in model and takes a little
Some errors can be brought, are affected to visco-plasticity stiffness matrix and model solution, are needed further perfect；
(2) in the derivation of the viscoplasticity stiffness matrix of space problem and visco-plasticity stiffness matrix, ginseng is assumed in contact
Several establishments can also introduce error, affect the accuracy of calculating；
(3) in MATLAB solution procedurees, iterations are inadequate in program, cause the convergency value of result of calculation undesirable；
Meaning：Although there are many deficiencies for research, the bulk effect mechanism study side in vibration pendulum rolles over Plastic Forming
Fruitful work has been made in face, has filled up the research shortage that vibration pendulum rolles over three-dimensional volume effect field, can be plasticity at
The development of shape processing provides theory and technology and supports, can greatly improve forming accuracy and prouctiveness, shortening production cycle.
Invention content
In view of the problems of the existing technology, the present invention provides be based on 3D constitutive models pendulum under a kind of alternating load to roll over effect
Analysis method is answered, roll milling forming is vibrated by Multi-parameter coupling, inquires into three-dimensional of the metal material under vibration spreading effect
Mechanism is established shake shape parameter and material characteristic parameter, force parameter, edge load and is applied related between the multi-parameters such as load mode
Property, and orthogonal experiment is carried out, to disclose vibration roll milling forming mechanism, improve material vibrating roll milling forming under three-dimensional constitutive model
Process analysis procedure analysis, establishing vibration roll milling forming equipment has important theory significance and practical value.
The invention is realized in this way rolling over effect analysis method based on 3D constitutive models pendulum under a kind of alternating load, utilize
MATLAB softwares carry out 3D bulk effects to vibration rotary forging viscoelastic-plastic constitutive model and skin effect is analyzed, by joining more
Three-dimensional Contact Problem is described in Contact Boundary during number coupled simulation vibration rotary forging；Using in Elasticity
Incremental theory in generalized Hooke law and plasticity has derived viscoplasticity space matrix and visco-plasticity space matrix respectively, and
The skin effect analysis model in vibration rotary forging forming is established with this；It is rational it is assumed that in the different vibration shapes by proposing
Vibration rotary forging model under parameter carries out FEM Simulation and skin effect analysis.
Further, effect analysis method is rolled over based on 3D constitutive models pendulum under the alternating load to include the following steps：
(1) using three-dimensional constitutive model, (the sine wave signal, square-wave signal) vibration pendulum under different vibration signals is established
The display expression formula of the Numerical Simulation of Three Dimensional Viscoelastic plasticity model of rolling system；
(2) related technological parameter and vibration parameters are determined, and combine plastic deformation ess-strain it is assumed that finding technique ginseng
The optimum matching scheme of number and the shape parameter that shakes；
(3) by Multi-parameter coupling mechanism, induction and conclusion is carried out to model constitutive relation, boundary condition, load-up condition, from
And further study its 3D compacting mechanism；
(4) vibration forming process of roll milling parameter, modal parameters etc., histological examination, on-line checking are determined according to theoretical research
Each parameter is shaped, the theoretical research of early period is verified with this and it is further corrected perfect；
(5) model is analyzed and is calculated by softwares such as MATLAB and MARC.
Further, the derivation of the viscoplasticity space matrix [D] is：
In the visco-elastic portions of viscoelastic-plastic constitutive model, elastic part and glued portion are in parallel, at all moment, two
Partial elongation epsilon is identical always, and total force σ is divided into σ ' (elasticity) and σ " (viscosity)；
Elastic stress σe'=E εe
Viscous stress
Elastic total stress
Equipped with primary condition ε (0)=0, simultaneous equations can acquire：
In Numerical Simulation of Three Dimensional Viscoelastic constitutive model, for isotropic material, when deformation very little and in linear-elastic range, line is answered
Become only related with direct stress, and it is unrelated with shearing stress, and shearing stress is only related and unrelated with direct stress with shear strain, can obtain in this way：
Above formula is write as matrix form, is
It is abbreviated as：{ ε }=[D]-1{ σ } transformation can obtain：{ σ }=[D] { ε }
I.e. viscoplasticity space matrix [D] is
Further, visco-plasticity space matrix [D]pDerivation is：
Theoretical according to row dimension- meter Sai Si, some materials are being surrendered in a bit of, stress-strain diagram and ideal plasticity material
Expect similar, also some degree of hardening of material are weaker, assume that material is ideal modeling close to perfectl plastic material, therefore in its theory
Property；
It is larger due to being plastically deformed after material reaches plasticity, elastic part can be ignored, that is, think that overall strain is equal to
Plastic strain, that is to say, that assuming that material meets rigid plastic model, i.e. d ε=d εe+dεp≈dεp；According to incremental theory and row
The analysis that dimension- meter Sai Si theories deform material in the plastic stage, it is believed that influence of the viscosity in plastic period
It is smaller, it can be ignored in the derivation of plastic matrix, be formula by the space visco-plasticity matrix equation being derived from：
Further, finite element modelling is carried out by the way of displacement load, the displacement course of load is shown below：
(1) displacement loading sequence when common rotary forging：
(2) displacement loading sequence when vibration rotary forging：
In formula, U- load deflections (mm), the t- load times (s), A- amplitudes (mm), f- vibration frequencies (Hz), n- yaws turn
Fast (r/min), S- feed of every rotation (mm/r).
In conclusion advantages of the present invention and good effect are：
Fig. 3 to Fig. 5 indicates the nodal force of 16 nodes of common rotary forging and vibration rotary forging cell node, section respectively
The 3-D view of point displacement curve, every width figure from left to right indicate the nodal force and modal displacement in tri- directions X, Y, Z respectively.Three
In dimensional view the axis of vertical direction indicates the size of nodal force and modal displacement, below in two axis the left side be time, the right
Be node curve number, expression be respectively 1~16 16 nodes corresponding to curve.
Comparing can obtain, and in a model from top to bottom, nodal force is also to be sequentially reduced to node, identical in load deflection
In the case of, the nodal force that vibration rotary forging generates is much smaller than general pendulum rolling, is primarily due to metal after extraneous vibration
Internal resistance of deformation reduces.Simultaneously again it can be found that after extraneous vibration, modal displacement variation is rolled over greatly than general pendulum
It is more, and the variation of each modal displacement is evenly.
Therefore the present invention can obtain, on the basis of general pendulum is rolled over after extraneous vibration, the resistance of deformation of metal inside
It reduces, the volume change of bigger can be obtained in the case where smaller displacement loads, the essence of this and bulk effect is kissing
It closes.It can be seen that compared with existing general pendulum rolles over technology, vibration rotary forging can improve product shaping quality, reduce energy
Consumption, process advantage are apparent.
Vibration pendulum is rolled under alternating load rolles over forming effect contrast table with general pendulum
The present invention vibrates roll milling forming by Multi-parameter coupling, inquire into metal material under vibration spreading effect it is three-dimensional at
Shape mechanism establishes shake shape parameter and material characteristic parameter, force parameter, edge load and applies phase between the multi-parameters such as load mode
Guan Xing, and orthogonal experiment is carried out, to disclose vibration roll milling forming mechanism, improves material vibrating under three-dimensional constitutive model and be rolled into
Shape process analysis procedure analysis, establishing vibration roll milling forming equipment has important theory significance and practical value.
Description of the drawings
Fig. 1 is to roll over effect analysis method flow based on 3D constitutive models pendulum under alternating load provided in an embodiment of the present invention
Figure；
Fig. 2 is to roll over effect analysis method vibration pendulum based on 3D constitutive models pendulum under alternating load provided in an embodiment of the present invention
Roll over device roll milling forming schematic diagram.
Fig. 3 is that general pendulum rolling node provided in an embodiment of the present invention is tried hard to.
Vibration pendulum when Fig. 4 is amplitude A provided in an embodiment of the present invention=1 frequency f=80 is rolled over node and is tried hard to.
Vibration pendulum when Fig. 5 is amplitude A provided in an embodiment of the present invention=0.5 frequency f=20 is rolled over node and is tried hard to.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Using metal material as experimental study object, carries out vibration roll milling forming experiment, choose vibration parameters (exciting appropriate
Power, amplitude, frequency), roll over pressure size, loading velocity, displacement parameter and edge load parameter as experiment parameter.By to shaking
The calculating of movable pendulum rolling wheel exterior feature Contact Boundary, the shape and yaw and blank on obtained simulating contact boundary are in forming process
The shape of practical Contact Boundary is consistent substantially.And on this basis, vibration rotary forging model finite element discretization is proposed false
If；
Utilize the mesh discretization thought of FInite Element, the forming of contact and vibration rotary forging according to pendulum swaging with workpiece
Principle, it is discrete to column progress in conjunction with the characteristics of volume effect study, establish finite element analysis model；
On the basis of analyzing three-dimensional viscoelastic-plastic constitutive model, in conjunction with Lie Wei- meter Sai Si theories and material in plasticity shape
Incremental theory when state is deduced the viscoplasticity stiffness matrix and visco-plasticity stiffness matrix of 3d space problem, by establishing table
Lattice have clearly obtained the connectivity of relationship and unit between quadrangular internal tetrahedrons unit and node；
By orthogonal experiment, show that different wave (such as sine wave, rectangular wave) is right under different frequency and various amplitude
Vibrate the influence curve during spreading precision form.It, can be smaller after applying vibration compared with conventional rotary roll
Pendulum obtains the deformation of bigger in the case of rolling over power, to disclose vibration rotary forging compacting mechanism under 3D constitutive models.
By the existing vibration rotary forging equipment of school different modal parameters and technique are selected under the conditions of vibration pendulum is rolled over
Parameter carries out sunykatuib analysis and verification experimental verification to the theoretical analysis model established and computer simulation.
(1) load is rolled over by designing test material vibration pendulum under exciting device, utilizes vibrating motor (hydraulic exciting
Device) alternating load is provided, its vibration frequency is changed using frequency converter, with different vibration frequencies, amplitude, edge load, main shaft
The parameters such as rotating speed, the amount of feeding, forming angle carry out orthogonal test, and motion mode is as shown in Figure 2；
(2) vibration acquisition and dynamic signal analyzer acquire the signal from tension-compression sensor, record in forming process
Shape each three-dimensional parameter；
(3) data are handled and is analyzed by matlab softwares, and carry out vibration roll milling forming on this basis
3D effect studies.
In the setting of technique and modal parameters, there are many factor for influencing vibration rotary forging forming effect, such as yaw
Rotating speed n, feed of every rotation S, vibration frequency f, amplitude A etc., the present invention choose two Parameter analysis circles of vibration frequency f and amplitude A
Nodal force, modal displacement, node accumulation displacement and cell cube deformation of the column in vibration rotary forging deformation process, to real
The analysis of existing vibration rotary forging process volume effector mechanism.
In FEM Simulation, workpiece material chooses Q235, and related technological parameter is：Elastic modulus E=
220Gpa, Poisson's ratio v=0.3, viscosity η 1=52GPa.s, yieldlimitσs=235MPa.
In the case of yaw rotating speed and constant feed of every rotation, by change two parameters of vibration frequency f and amplitude A come
Analyze the shaping law of metal during vibration pendulum is rolled over.Scheme is divided to two groups of progress, changes frequency (scheme in the case that amplitude is constant
1, scheme 2, scheme 3) and change amplitude (scheme 4, scheme 5, scheme 6) in the case that frequency is constant, as shown in the table.
Vibration rotary forging modeling scheme table
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement etc., should all be included in the protection scope of the present invention made by within refreshing and principle.
Claims (5)
1. rolling over effect analysis method based on 3D constitutive models pendulum under a kind of alternating load, which is characterized in that under the alternating load
Based on 3D constitutive models put roll over effect analysis method, using MATLAB softwares to vibration rotary forging viscoelastic-plastic constitutive model into
Row 3D bulk effects and skin effect analysis, pass through the Contact Boundary pair three during Multi-parameter coupling analog vibration rotary forging
Dimension contact problems are described；It is derived respectively using the generalized Hooke law in Elasticity and the incremental theory in plasticity
Viscoplasticity space matrix and visco-plasticity space matrix, and mould is analyzed with this skin effect established in vibration rotary forging forming
Type；By proposing rational it is assumed that carrying out FEM Simulation to the vibration rotary forging model under different modal parameters
And skin effect analysis.
2. rolling over effect analysis method based on 3D constitutive models pendulum under alternating load as described in claim 1, which is characterized in that institute
It states and is included the following steps based on 3D constitutive models pendulum rolling effect analysis method under alternating load：
(1) using three-dimensional constitutive model, the Numerical Simulation of Three Dimensional Viscoelastic plasticity model that the vibration pendulum under different vibration signals rolles over system is established
Display expression formula；
(2) determine related technological parameter and vibration parameters, and combine plastic deformation ess-strain it is assumed that find technological parameter and
Shake the optimum matching scheme of shape parameter；
(3) by Multi-parameter coupling mechanism, induction and conclusion is carried out to model constitutive relation, boundary condition, load-up condition, thus into
One step studies its 3D compacting mechanism；
(4) vibration forming process of roll milling parameter, modal parameters etc., histological examination, on-line checking forming are determined according to theoretical research
Each parameter is verified the theoretical research of early period with this and is further corrected to it perfect；
(5) model is analyzed and is calculated by MATLAB and MARC.
3. rolling over effect analysis method based on 3D constitutive models pendulum under alternating load as described in claim 1, which is characterized in that institute
The derivation for stating viscoplasticity space matrix [D] is：
In the visco-elastic portions of viscoelastic-plastic constitutive model, elastic part and glued portion are in parallel, at all moment, two parts
Elongation epsilon be identical always, total force σ is divided into σ ' (elasticity) and σ " (viscosity)；
Elastic stress σ 'e=E εe
Viscous stress
Elastic total stress
Equipped with primary condition ε (0)=0, simultaneous equations can acquire：
In Numerical Simulation of Three Dimensional Viscoelastic constitutive model, for isotropic material, when deformation very little and in linear-elastic range, line strain is only
It is related with direct stress, and it is unrelated with shearing stress, and shearing stress is only related and unrelated with direct stress with shear strain, can obtain in this way：
Above formula is write as matrix form, is
It is abbreviated as：{ ε }=[D]-1{ σ } transformation can obtain：{ σ }=[D] { ε }
I.e. viscoplasticity space matrix [D] is
4. rolling over effect analysis method based on 3D constitutive models pendulum under alternating load as described in claim 1, which is characterized in that viscous
Plasticity space matrix [D]pDerivation is：
After material reaches plasticity, ignores elastic part and be equal to plastic strain to get overall strain, is i.e. material meets rigid -plastic mould
Type, i.e. d ε=d εe+dεp≈dεp；
It is formula to obtain visco-plasticity space matrix equation：
5. rolling over effect analysis method based on 3D constitutive models pendulum under alternating load as described in claim 1, which is characterized in that adopt
Finite element modelling is carried out with the mode that displacement loads, the displacement course of load is shown below：
(1) displacement loading sequence when common rotary forging：
(2) displacement loading sequence when vibration rotary forging：
In formula, U- load deflections (mm), the t- load times (s), A- amplitudes (mm), f- vibration frequencies (Hz), n- yaw rotating speeds (r/
), min S- feed of every rotation (mm/r).
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