CN107160990A - A kind of oscillation damping method of the longitudinally twisted vibration of vehicle motor - Google Patents
A kind of oscillation damping method of the longitudinally twisted vibration of vehicle motor Download PDFInfo
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- CN107160990A CN107160990A CN201710218821.6A CN201710218821A CN107160990A CN 107160990 A CN107160990 A CN 107160990A CN 201710218821 A CN201710218821 A CN 201710218821A CN 107160990 A CN107160990 A CN 107160990A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60K—ARRANGEMENT OR MOUNTING OF PROPULSION UNITS OR OF TRANSMISSIONS IN VEHICLES; ARRANGEMENT OR MOUNTING OF PLURAL DIVERSE PRIME-MOVERS IN VEHICLES; AUXILIARY DRIVES FOR VEHICLES; INSTRUMENTATION OR DASHBOARDS FOR VEHICLES; ARRANGEMENTS IN CONNECTION WITH COOLING, AIR INTAKE, GAS EXHAUST OR FUEL SUPPLY OF PROPULSION UNITS IN VEHICLES
- B60K5/00—Arrangement or mounting of internal-combustion or jet-propulsion units
- B60K5/12—Arrangement of engine supports
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Abstract
The present invention relates to a kind of vibration control method based on internal resonance, this method belongs to the vibration control technology field of vehicle motor towards the longitudinally twisted vibration of engine.This method includes：Set up engine six-degree of freedom vibration equation；Construct the Controlling model of bump leveller；Set up the seven freedom vibration equation of the engine with bump leveller；Seven freedom vibration equation is decoupled, adjustment bump leveller frequency is controlled modal frequency half；Controlled mode and bump leveller modal vibration equation are extracted, it is solved using Method of Multiple Scales.The present invention forms internal resonance, by the engine luggine energy that on the vibrational energy transfer of engine to bump leveller, dissipated by the damping of bump leveller by constructing Non-linear coupling.Substantially, simple in construction, consumed energy is few for effectiveness in vibration suppression of the present invention.
Description
Technical field
The present invention relates to a kind of vibration control method based on internal resonance, in the longitudinally twisted mode of oscillation of four cylinder engine
Non-linear coupling is constructed between bump leveller mode, using distinctive internal resonance phenomenon in nonlinear kinetics, by engine
Vibrational energy transfer on bump leveller, and by the Damping work of bump leveller, so as to realize the vibration damping of engine.The invention belongs to
The vibration control technology field of vehicle motor.
Background technology
The engine of vehicle is the power source of automobile, while being also the main source of automobile vibration.Turn in engine crankshaft
In the presence of the impulsive force that the inertia force and gasoline combustion that dynamic and piston translation is produced are produced, engine can produce violent shake
Dynamic, this vibration, which is passed to, can cause the vibration of vehicle body on vehicle body.Driver works long hours easily feels tired in such a case
Labor, slow in reacting, life security is on the hazard.
For the vibration of engine, mainly there are two kinds of vibration reducing measures：Vibration isolation and absorbing.The vibration isolation of engine is main by suspending
System is realized, is suspended equivalent to spring-damp system, is installed between engine and vehicle body.According to whether extraneous input energy
Amount, the suspension of engine is divided into passive suspension, active engine mount and Semi-active mount.Suspension can reduce engine and pass to vehicle body
Vibration, the characteristics of due to many vibration sources of engine luggine, wideband, suspension system not can effectively improve the vibration feelings of engine
Condition.
The absorbing of engine is mainly realized that bump leveller is installed on engine by bump leveller.Bump leveller is divided into three species
Type：Passive type bump leveller, semi-active type bump leveller and active bump leveller.Passive type bump leveller is simple in construction, its intrinsic frequency
Must be equal with the frequency of external excitation, frequency of use narrow range.Active bump leveller adds equivalent on passive type bump leveller
One main power units, the power unit produces a power opposite with controlled object acceleration.Active bump leveller energy consumption is big, body
Product is big, and control effect is unstable.Some parameters of semi-active type bump leveller can voluntarily change according to demand, and energy consumption is small, stability
Good, bandwidth.
As classical Theory of Vibration, linear oscillator theory has developed quite perfect, and is obtained in practice in engineering
Extensive use.But with the continuous development of scientific technology, it is increasingly recognised that, solving many engineering problems
When can obtain satisfied result with linear oscillator theory, and in many situations, such as large-amplitude vibration, with linearly shaking
Dynamic theory analysis can bring about very big error even qualitatively mistake.The theory of nonlinear oscillation was rapidly sent out in recent years
Exhibition, nonlinear vibration shows jump, self-excited vibration, over harmonic and many linear oscillators such as Asia harmonic motion, internal resonance and chaos
Without phenomenon, can for control engine luggine new thinking be provided.
Nonlinear system is vibrated distinctive internal resonance phenomenon and shown as when system has two intrinsic frequencies, and satisfaction can commensurability pass
When being, two mode of oscillations are consumingly coupled, a kind of another vibration of vibrational excitation.It is so-called can commensurability relation refer to two it is solid
There is frequency satisfaction(wherein m1、m2It is positive integer, ω1、ω2It is intrinsic frequency).Disregarding the condition of resistance
Under, the energy of system is constantly changed and unattenuated, amplitude and phase cycling change between being vibrated at two kinds.Add damping
Afterwards, the energy of system can be dissipated, and realize the vibration damping of engine.A kind of half master based on internal resonance is proposed in present patent application
Dynamic formula oscillation damping method, internal resonance is constructed between the controlled mode and bump leveller mode of four cylinder engine.
Therefore, in order to control the longitudinally twisted vibration of engine, the present invention is from the angle of nonlinear kinetics, construction hair
Non-linear coupling between motivation longitudinal vibration mode and bump leveller, proposes a kind of semi-active type vibration damping side based on internal resonance
Method.
The content of the invention
It is an object of the invention to provide a kind of oscillation damping method towards four cylinder engine extensional vibration based on internal resonance, it
The amplitude of engine can be substantially reduced, reduces the vibration that engine passes to vehicle body, comfortable working environment is provided for driver.
Present invention is mainly applied to four cylinder engine vibration control field, it can in addition contain the vibration damping applied to reciprocating machinery.
The present invention proposes a kind of four cylinder engine oscillation damping method based on internal resonance, includes modeling and the internal resonance of engine
Construction.Engine is considered as a particle, ignores its internal structure.This method is comprised the following steps that：
Step one：The kinetics equation of engine six degree of freedom is set up using Lagrangian method.The shape of Lagrange's equation
Formula is,
Above-mentioned coefficient ETThe kinetic energy of expression system, EVThe potential energy of expression system, EDThe Dissipated energy of expression system, XPTRepresent wide
Adopted coordinate,Generalized velocity is represented, Q represents generalized force,Represent to time derivation.
The kinetic energy of power assembly includes translational kinetic energy and rotational kinetic energy, if servo-actuated coordinate origin displacement is XPT=[x, y,
z,θx,θy,θz]T, position of the Motor Mass Centre under with moving coordinate system is (xc,yc,zc), then system kinetic energy is,
Above-mentioned Coefficient m represents engine quality, Ixx,Iyy,IzzRotary inertia of the difference engine under with moving coordinate system,
Ixy,Iyz,IzxFor with the product of inertia under moving coordinate system.
The potential energy of system is,
Above-mentioned coefficient kuk、kvk、kwkRepresent the rigidity in three directions of engine mounting, Δ uk、Δvk、ΔwkExpression is suspended at
Displacement on three directions.
System Dissipated energy is,
Above-mentioned coefficient cuk、cvk、cwkThe damping in three directions of engine mounting is represented,Represent outstanding
Put the speed on three directions.
Formula (2), formula (3), formula (4) are substituted into formula (1), the free vibration equation of engine six can be obtained,
Above-mentioned coefficient MPRepresent mass matrix, CPRepresent damping matrix, KPRepresent stiffness matrix, FpRepresent generalized force.
Step 2：The Controlling model of bump leveller is designed as,
WhereinThe desired angular velocity of satellite motion of servomotor and angular displacement, k are represented respectivelyd、kpServo is represented respectively
The velocity feedback gain and position feedback oscillator of motor, T represent the driving moment that servomotor is acted on vibration absorber, and χ is
The Non-linear coupling for forming internal resonance and constructing, e1、e2It is adjusted as needed for constructing variable.
In this model, the desired locations of servomotor are zero, it is therefore desirable for angular speedAnd angular displacementIt is zero.This
Pattern (6a) is changed into,
Step 3：The seven freedom kinetics equation of engine and bump leveller is set up using Lagrangian method.Due to absorbing
Device is swing type, itself meeting additional non-linearity exciting force, moves on on the right of equation these exciting forces using Taylor expansion, obtains
The seven freedom Lagrange's dynamical equations of engine with bump leveller,
Fall=FP+Fremain (8b)
M=MP+Mstator+Mrotor (8c)
Wherein：
Above-mentioned coefficient M represents the mass matrix of system, and C represents the damping matrix of system, and K represents the stiffness matrix of system,
FpThe suffered generalized force of expression system, FremainRepresent the additional non-linear exciting-vibration force of bump leveller；ω represents engine rotation frequency
Rate, mpRepresent piston mass, ml2Connecting rod reciprocating mass is represented, r represents engine crank radius, and λ represents engine crank and company
The length ratio of bar, MeoRepresent engine output torque amplitude, eyRepresent two, three cylinder center lines to barycenter X-direction distance；mγRepresent
The mover quality of bump leveller, l represents bump leveller mover length, xε、yεAnd zεRepresent the installation position of bump leveller stator on the engine
Put.
Step 4：Engine and bump leveller vibration equation are obtained by step 3, system can be utilized in the hope of its sytem matrix S
The main formation matrix P that system matrix S characteristic vector is constituted is decoupled to equation (8a), obtains the vibration side under modal coordinate
Journey,
S=M-1K (9a)
X=Pq (9b)
Wherein：Mde=PTMP,Cde=PTCP, Kde=PTKP, Q=PTFall,
Step 5：Adjust the intrinsic frequency of bump leveller.Vibration equation under the modal coordinate in step 4, longitudinal direction
The vibration frequency of torsion modes is ω5.By the position feedback oscillator k for adjusting bump levellerp, make bump leveller natural frequency ω7
To be controlled mode ω5The half of intrinsic frequency, i.e.
Step 6：Main vibration mode is longitudinally twisted vibration and vertical vibration for vehicle motor, and this is specially
Profit solves its longitudinally twisted vibration.The vertical vibration of engine can produce influence to bump leveller mode, can not in solution procedure
Ignore vertical vibration.Longitudinally twisted modal vibration equation, vertical mode vibration equation and bump leveller mode are extracted from formula (9e)
Vibration equation,
In formula, q7For bump leveller modal coordinate, q5For the longitudinally twisted mode of oscillation coordinate of engine, q3It is vertical for engine
Mode of oscillation coordinate.
Wherein：
fi=di1+di2χ+di3sin2ωt+(di4+di5)ω2cos2ωt
+φi1+φi2+φi3+φi4+φi5+φi6+φi7
di1=-ai4Meo
di2=ai7
di3=-1.3ai4Meo
di4=-4ai3(ml2+mp)rλ
di5=-4ai5ey(ml2+mp)rλ
φi1=0+O (ε)
φi3=0
φi5=0+O (ε)
I=5,7, neglect high-order a small amount of in above-mentioned coefficient.Then formula (11a), (11b) can be written as,
Wherein：
φi=φi1+φi2+φi3+φi4+φi5+φi6+φi7,
Step 7：Using Method of Multiple Scales solve equation (12a), (12b) (12c) approximate solution, by equation (12a),
Engine vertical mode coordinate, engine torque modal coordinate and bump leveller modal coordinate in (12b), (12c), respectively according toNondimensionalization is carried out to obtain,
Wherein：
By the time according to τ=ω7T carries out nondimensionalization, while utilizing replacementThe above-mentioned equation of abbreviation (13a), (13b), (13c) are obtained,
By equation (14a), (14b), (14c) left and right simultaneously divided byAnd make
Obtain,
Solved using Method of Multiple Scales, it is a small amount of with nonlinear terms to make damping term, makees following replacement,
ξi=ε ηi
Tk=εkτ (k=0,1)
If the first approximation solution of equation is,
Wherein T0What is represented is fast change time, T1What is represented is the slow change time.
ε can be solved0The corresponding equation of rank is,
ε1The corresponding equation of rank is,
Wherein：
C in above formulai1=ai2mrl-ai4mrlze+ai6mrlxe。
Step 8：Equation (17a), (17b), the solution of (17c) can be expressed as：
In formula, AiFor on T1Unknown complex function, cc is above every conjugation.Remaining parameters is,
Work as q7With q5Mode occurs 1:During 2 internal resonance, following detuning parameter σ is introduced,
ωs5=2+ ε σ (20)
Formula (19a), (19b), (19c) and (20) are substituted into equation (18a), (18b), (18c), the length on the equation right side is eliminated
Phase can obtain,
In formula：
OrderWherein a3、a5、a7、θ3、θ5、θ7It is with becoming time T slowly1
Relevant complex constant, substitutes into equation (21a), (21b), (21c), and is that zero can obtain according to real and imaginary parts,
Wherein ai′、θi' it is respectively aiWith θiBecome time T for slow1Derivative.
In above formula：
Order：
γ=θ5-2θ7+εσT0
Imaginary part in formula (22a), (22b), (22c) and real part are separated, obtained after arrangement,
a′3=-η3ωs3a3 (23e)
Step 9：(the η in the case of undamped3=η5=η7=0), formula (23f) is multiplied by a5, formula (23g) be multiplied by a7, so
After do and obtain,
Because steady state solution corresponds to a5'=a7'=γ '=0, then can obtain,
It can be obtained by formula (24),
It can know from formula (25b), select appropriate e1、e2Value can make ν be more than 0.Substituted into formula (26) and understand a5And a7
Always bounded, and be presented shifting relation.This demonstrate that can be in the longitudinally twisted vibration of engine using the method
Internal resonance is formed between mode and the mode of motion of bump leveller, energy can be transmitted between two mode.
From formula (26) as can be seen that v characterizes the degree of energy exchange between flexible engine and bump leveller, v ＞ 0 represent two
Person has energy exchange, when v is bigger, a5The amplitude of decay is bigger, illustrates that now energy exchange is more abundant.
Step 10：It was found from from step 9, system is under the conditions of undamped, and energy can be passed between two mode
Pass.Damping is introduced into bump leveller mode, i.e. η7≠ 0, the now damping of bump leveller can dissipate the vibrational energy from engine
Amount, the damping for adjusting bump leveller is worth to suitable so that bump leveller can farthest reduce the vibration of engine.
The present invention forms internal resonance by constructing the coupling terms between bump leveller and controlled mode.Formed after internal resonance,
Energy is transmitted that there is provided a set of oscillation damping method possible in theory controlled between mode and bump leveller.
Advantage and effect：
(1) present invention proposes a kind of new absorbing principle based on internal resonance energy consumption, two of system formation internal resonance
Energy can be transmitted mutually between mode, engine luggine be controlled to further expand to non-linear field, effectiveness in vibration suppression is bright
It is aobvious.The present invention is formed internal resonance, engine is shaken by construction controlled Non-linear coupling between mode and bump leveller mode
Energy is transferred on bump leveller, using bump leveller damping come the vibrational energy of consumption of engine.
(2) compared to passive type bump leveller, the present invention is not limited by external excitation frequency, while having passive type bump leveller
Feature simple in construction.Internal resonance between engine and bump leveller is realized by adjusting the position feedback factor of servomotor, because
And for different control objects, bump leveller can meet the requirement of frequency matching；Introduced and hindered by governing speed feedback factor
Buddhist nun fully absorbs the vibrational energy from engine into vibration absorber, suppresses the significantly vibration of engine.
(3) compared to active bump leveller, consumed energy of the present invention is few, as long as basic when providing bump leveller normal work
Voltage, it is not necessary to which additional input energy offsets vibrational energy；And it assign servomotor as the activation part of bump leveller, control
Tactful very simple, the stability of system is fine.
Brief description of the drawings
Fig. 1 is the connection diagram of engine and bump leveller.
Fig. 2 is the control block schematic diagram of bump leveller servomotor.
Fig. 3 is undamped bump leveller and engine modal amplitudes variation diagram.
Fig. 4 is to have damping absorber and engine modal amplitudes variation diagram.
Fig. 5 is the Vibration Condition without bump leveller engine.
Fig. 6 is the Vibration Condition for installing bump leveller rear engine.
Numbers and symbols is described as follows in Fig. 1：
1 represents four cylinder engine, and 2 represent acceleration transducer, and 3 represent bump leveller servomotor, and 4 represent bump leveller mover
Swing rod, 5 represent bump leveller device, and 6 represent engine mounting.
OXYZ represent to connect firmly on the engine with moving coordinate system, O'ijk represents to connect firmly servomotor on the engine
Kinetic coordinate system, θrRepresent the corner of servomotor.
Symbol description in Fig. 2 is as follows：
θrdRepresent the desired motion angular displacement of bump leveller servomotor, θrRepresent servomotor actual motion angular displacement, kp
Represent the position feedback oscillator of servomotor, kdS represents the velocity feedback gain of servomotor, and τ represents control moment, e1、e2Table
Show constructing variable,The acceleration of six direction of motion of engine is represented,Expression is watched
Take motor angular acceleration, P-1Represent the transition matrix that actual motion Coordinate Conversion is modal coordinate.
Embodiment
Below in conjunction with the accompanying drawings and example the present invention will be described in detail.
See Fig. 1, bump leveller 5 is made up of servomotor 3, rigid pole 4.Bump leveller 5 is arranged on four cylinder engine 1,
Servomotor 3 drives rigid pole 4 in Oij move in plane.Coordinate system Oijk is identical with coordinate system OXYZ direction.Engine
1 is connected by 4 engine mountings 6 with vehicle body.Acceleration transducer 2 is arranged on engine 1, for measuring engine 1
The acceleration of six direction.
A kind of vibration control method based on internal resonance energy consumption of the present invention, including add the engine seven freedom of bump leveller
The foundation of kinetics equation and Analysis of Internal Resonance.Specific implementation steps are as follows.
Step one：The kinetics equation of engine six degree of freedom is set up using Lagrangian method.The shape of Lagrange's equation
Formula is,
Above-mentioned coefficient ETThe kinetic energy of expression system, EVThe potential energy of expression system, EDThe Dissipated energy of expression system, XPTRepresent wide
Adopted coordinate,Generalized velocity is represented, Q represents generalized force.
The kinetic energy of power assembly includes translational kinetic energy and rotational kinetic energy, if servo-actuated coordinate origin displacement is XPT=[x, y,
z,θx,θy,θz]T, position of the Motor Mass Centre under with moving coordinate system is (xc,yc,zc), then system kinetic energy is
Above-mentioned Coefficient m represents engine quality, Ixx,Iyy,IzzRotary inertia of the difference engine under with moving coordinate system,
Ixy,Iyz,IzxFor with the product of inertia under moving coordinate system.
The potential energy of system is,
Above-mentioned coefficient kuk、kvk、kwkFor the rigidity in three directions of engine mounting, Δ uk、Δvk、ΔwkFor three sides of suspension
Upward displacement.
Then system Dissipated energy is,
Above-mentioned coefficient cuk、cvk、cwkFor the damping in three directions of engine mounting, the suspension damping of engine in this example
Very little, makes cuk=a × kuk, cvk=a × kvk, cwk=a × kwk, a represents damping proportional coefficient；It is outstanding
Put the speed on three directions.
Formula (2), formula (3), formula (4) are substituted into formula (1), the free vibration equation of engine six can be obtained,
Above-mentioned coefficient MPRepresent mass matrix, CPRepresent damping matrix, KPRepresent stiffness matrix, FpRepresent generalized force.
Step 2：The Controlling model of bump leveller is designed as,
WhereinThe desired angular velocity of satellite motion of servomotor and angular displacement, k are represented respectivelyd、kpServo is represented respectively
The velocity feedback gain and position feedback oscillator of motor, T represent the driving moment that servomotor is acted on vibration absorber, and χ is
The Non-linear coupling for forming internal resonance and constructing, e1、e2It is adjusted as needed for constructing variable.
In this model, the desired locations of servomotor are zero, it is therefore desirable for angular speedAnd angular displacementIt is zero.This
Pattern (6a) is changed into,
Step 3：The seven freedom kinetics equation of engine and bump leveller is set up using Lagrangian method.Due to absorbing
Device is swing type, itself meeting additional non-linearity exciting force, moves on on the right of equation these exciting forces using Taylor expansion, obtains
The seven freedom Lagrange's dynamical equations of engine with bump leveller,
Fall=FP+Fremain (8b)
M=MP+Mstator+Mrotor (8c)
Wherein：
Above-mentioned coefficient M represents the mass matrix of system, and C represents the damping matrix of system, and K represents the stiffness matrix of system, F
The suffered inertia force of expression system, FremainRepresent the additional non-linear exciting-vibration force of bump leveller；mpRepresent piston mass, ml2Table
Show connecting rod reciprocating mass, r represents engine crank radius, and λ represents the length ratio of engine crank and connecting rod, MeoRepresent engine
Output torque amplitude, eyRepresent two, three cylinder center lines to barycenter X-direction distance；mγThe end mass block quality of bump leveller is represented,
meBump leveller stator quality is represented, l represents bump leveller strut lengths, xε、yεAnd zεRepresent the peace of bump leveller stator on the engine
Holding position.
Step 4：Engine and bump leveller vibration equation are obtained by step 3, system can be utilized in the hope of its sytem matrix S
The main formation matrix P that system matrix S characteristic vector is constituted is decoupled to equation (8a), obtains the vibration side under modal coordinate
Journey,
S=M-1K (9a)
X=Pq (9b)
Wherein：Mde=PTMP,Cde=PTCP, Kde=PTKP, Q=PTFall,
Step 5：Adjust the intrinsic frequency of bump leveller.Vibration equation under the modal coordinate in step 4, longitudinal direction
The vibration frequency of torsion modes is ω5.By the position feedback oscillator k for adjusting bump levellerp, make bump leveller natural frequency ω7
To be controlled mode ω5The half of intrinsic frequency, i.e.
Adjust bump leveller position on the engine, the influence of the Non-linear coupling of limit structure to other mode.
Step 6：Main vibration mode is longitudinally twisted vibration and vertical vibration for vehicle motor, and this is specially
Profit solves its longitudinally twisted vibration.The vertical vibration of engine can produce influence to bump leveller mode, can not in solution procedure
Ignore vertical vibration.Longitudinally twisted modal vibration equation, vertical mode vibration equation and bump leveller mode are extracted from formula (9e)
Vibration equation,
In formula, q7Represent bump leveller modal coordinate, q5Represent the longitudinally twisted mode of oscillation coordinate of engine, q3Expression is started
Machine vertical vibration modal coordinate.
Wherein：
fi=di1+di2χ+di3sin2ωt+(di4+di5)ω2cos2ωt
+φi1+φi2+φi3+φi4+φi5+φi6+φi7
di1=-ai4Meo
di2=ai7
di3=-1.3ai4Meo
di4=-4ai3(ml2+mp)rv
di5=-4ai5ey(ml2+mp)rλ
φi1=0+O (ε)
φi3=0
φi5=0+O (ε)
I=5,7, neglect high-order a small amount of in above-mentioned coefficient.Then formula (11a), (11b) can be written as,
Wherein：
φi=φi1+φi2+φi3+φi4+φi5+φi6+φi7,
Step 7：Using Method of Multiple Scales solve equation (12a), (12b) (12c) approximate solution, by equation (12a),
Engine vertical mode coordinate, engine torque modal coordinate and bump leveller modal coordinate in (12b), (12c), respectively according toNondimensionalization is carried out to obtain,
Wherein：
By the time according to τ=ω7T carries out nondimensionalization, while utilizing replacement
The above-mentioned equation of abbreviation (13a), (13b), (13c) are obtained,
By equation (14a), (14b), (14c) left and right simultaneously divided byAnd make
Obtain,
Solved using Method of Multiple Scales, it is a small amount of with nonlinear terms to make damping term, makees following replacement：
ξi=ε ηi
Tk=εkτ (k=0,1)
If the first approximation solution of equation is,
Wherein T0What is represented is fast change time, T1What is represented is the slow change time.
ε can be solved0The corresponding equation of rank is：
ε1The corresponding equation of rank is,
Wherein：
C in above formulai1=ai2mrl-ai4mrlze+ai6mrlxe。
Step 8：Equation (17a), (17b), the solution of (17c) can be expressed as,
In formula, AiFor on T1Unknown complex function, cc is above every conjugation.Remaining parameters is：
Work as q7With q5Mode occurs 1:During 2 internal resonance, following detuning parameter σ is introduced,
ωs5=2+ ε σ (20)
Formula (17a), (17b), (17c) and (20) are substituted into equation (18a), (18b), (18c), the length on the equation right side is eliminated
Phase can obtain,
In formula：
OrderWherein a3、a5、a7、θ3、θ5、θ7It is with becoming time T slowly1
Relevant complex constant, substitutes into equation (21a), (21b), (21c), and is that zero can obtain according to real and imaginary parts,
Wherein ai′、θi' it is respectively aiWith θiBecome time T for slow1Derivative.
In above formula：
Order：
γ=θ5-2θ7+εσT0
Imaginary part in formula (22a), (22b), (22c) and real part are separated, obtained after arrangement,
a3'=- η3ωs3a3(23e)
Step 9：(the η in the case of undamped5=η7=0), formula (23f) is multiplied by a5, formula (23g) be multiplied by a7, then
Do and obtain,
Because steady state solution corresponds to a5'=a7'=γ '=0, then can obtain,
It can be obtained by formula (24),
It can know from formula (25b), select appropriate e1、e2Value can make ν be more than 0.Substituted into formula (26) and understand a5And a7
Always bounded, and be presented shifting relation.This demonstrate that can be in the longitudinally twisted vibration of engine using the method
Internal resonance is formed between mode and the mode of motion of bump leveller, energy can be transmitted between two mode.
From formula (26) as can be seen that v characterizes the degree of energy exchange between flexible engine and bump leveller, v ＞ 0 represent two
Person has energy exchange, when v is bigger, a1The amplitude of decay is bigger, illustrates that now energy exchange is more abundant.
Step 10：It was found from from step 9, system is under the conditions of undamped, and energy can be passed between two mode
Pass.Damping is introduced into bump leveller mode, i.e. η7≠ 0, the now damping of bump leveller can dissipate the vibrational energy from engine
Amount, the damping for adjusting bump leveller is worth to suitable so that bump leveller can farthest reduce the vibration of engine.
For the superiority of the further visual representations present invention, following examples are given.
Setting models parameter such as table 1：
Parameter in the model of table 1
Given a3, a5, a7, γ initial value is：A3 (0)=0.000001, a5(0)=0.00001, a7(0)=0.03,
γ (0)=0.Adjust the position feedback factor k of servomotorp=6.65 make detuning parameter σ=0 in formula (20), such internal resonance
Frequency compares ωs5=2, the longitudinally twisted mode of oscillation of engine forms complete internal resonance with bump leveller.Make the exciting force F of engineP
=0, the damping η of system3=0, η5=0, η7=0.Now the energy exchange between the longitudinal Torsional Vibration of engine and bump leveller is as schemed
Shown in 3, from the figure, it can be seen that there is anti-phase modulated motion in the longitudinally twisted vibration of engine and the mode of bump leveller two.Due to
The damping of engine is damped essentially from suspension, makes Damping Scale Coefficient a=0.00001, adjusts the velocity feedback of servomotor
Coefficient kd=0.0001, the energy exchange having under damping condition between the now longitudinally twisted vibration of engine and bump leveller is as schemed
Shown in 4, from the figure, it can be seen that the longitudinally twisted vibrational energy of engine progressively decays to disappearance in the presence of damping.
Engine is in the presence of external excitation, and its longitudinally twisted Vibration Condition is as shown in Figure 5 during without bump leveller.Regulation is inhaled
Shake the parameters of device, and the longitudinally twisted vibration of rear engine for obtaining adding bump leveller is as shown in Figure 6.Comparison diagram 5 and Fig. 6 can
Know, using the longitudinally twisted vibratory output based on internal resonance vibration control method, engine relatively reduced in 10s 80% with
On.It is effective to prove the oscillation damping method based on internal resonance, and the particularly oscillation damping method can make the significantly vibration of engine exist
Decay rapidly in the very short time.
The example that the above is implemented is only that checking illustrates that the present invention's realizes effect, but is not intended to limit the invention.It is all
That implements within Principle Method framework proposed by the invention should be included in this hair without substantial modification, conversion and improvement
In bright protection domain.
Claims (1)
1. a kind of oscillation damping method of the longitudinally twisted vibration of vehicle motor, it is characterised in that the controlled mode of construction and bump leveller mould
Coupling terms between state, are formed internal resonance, by engine luggine energy transfer to bump leveller, are consumed using bump leveller damping
The vibrational energy of engine, this method is comprised the following steps that：
Step one：The kinetics equation of engine six degree of freedom is set up using Lagrangian method, the form of Lagrange's equation is,
Above-mentioned coefficient ETThe kinetic energy of expression system, EVThe potential energy of expression system, EDThe Dissipated energy of expression system, XPTRepresent that broad sense is sat
Mark,Generalized velocity is represented, Q represents generalized force,Represent to time derivation；
The kinetic energy of power assembly includes translational kinetic energy and rotational kinetic energy, if servo-actuated coordinate origin displacement is XPT=[x, y, z, θx,
θy,θz]T, position of the Motor Mass Centre under with moving coordinate system is (xc,yc,zc), then system kinetic energy is,
Above-mentioned Coefficient m represents engine quality, Ixx,Iyy,IzzRotary inertia of the difference engine under with moving coordinate system, Ixy,
Iyz,IzxFor with the product of inertia under moving coordinate system；
The potential energy of system is,
Above-mentioned coefficient kuk、kvk、kwkRepresent the rigidity in three directions of engine mounting, Δ uk、Δvk、ΔwkExpression is suspended at three
Displacement on direction；
System Dissipated energy is,
Above-mentioned coefficient cuk、cvk、cwkThe damping in three directions of engine mounting is represented,Represent suspension three
Speed on individual direction；
Formula (2), formula (3), formula (4) are substituted into formula (1), the free vibration equation of engine six can be obtained,
Above-mentioned coefficient MPRepresent mass matrix, CPRepresent damping matrix, KPRepresent stiffness matrix, FpRepresent generalized force；
Step 2：The Controlling model of bump leveller is designed as,
WhereinThe desired angular velocity of satellite motion of servomotor and angular displacement, k are represented respectivelyd、kpServomotor is represented respectively
Velocity feedback gain and position feedback oscillator, T represents the driving moment that servomotor is acted on vibration absorber, and χ is forms
Internal resonance and the Non-linear coupling that constructs, e1、e2It is adjusted as needed for constructing variable；
In this model, the desired locations of servomotor are zero, it is therefore desirable for angular speedAnd angular displacementIt is zero, this pattern
(6a) is changed into,
Step 3：The seven freedom kinetics equation of engine and bump leveller is set up using Lagrangian method, because bump leveller is
Swing type, itself meeting additional non-linearity exciting force, these exciting forces are moved on on the right of equation, had using Taylor expansion
The seven freedom Lagrange's dynamical equations of the engine of bump leveller,
Fall=FP+Fremain (8b)
M=MP+Mstator+Mrotor (8c)
Wherein：
Above-mentioned coefficient M represents the mass matrix of system, and C represents the damping matrix of system, and K represents the stiffness matrix of system, FpRepresent
The suffered generalized force of system, FremainRepresent the additional non-linear exciting-vibration force of bump leveller；ω represents engine speed frequency, mp
Represent piston mass, ml2Connecting rod reciprocating mass is represented, r represents engine crank radius, λ represents engine crank and connecting rod
Length ratio, MeoRepresent engine output torque amplitude, eyRepresent two, three cylinder center lines to barycenter X-direction distance；mγRepresent absorbing
The mover quality of device, l represents bump leveller mover length, xε、yεAnd zεRepresent the installation site of bump leveller stator on the engine；
Step 4：Engine and bump leveller vibration equation are obtained by step 3, system square can be utilized in the hope of its sytem matrix S
The main formation matrix P that battle array S characteristic vector is constituted is decoupled to equation (8a), obtains the vibration equation under modal coordinate,
S=M-1K (9a)
X=Pq (9b)
Wherein：Mde=PTMP,Cde=PTCP, Kde=PTKP, Q=PTFall,
Step 5：The intrinsic frequency of bump leveller is adjusted, the vibration equation under the modal coordinate in step 4 is longitudinally twisted
The vibration frequency of mode of oscillation is ω5, by the position feedback oscillator k for adjusting bump levellerp, make bump leveller natural frequency ω7For quilt
Control mode ω5The half of intrinsic frequency, i.e.,：
Step 6：Main vibration mode is longitudinally twisted vibration and vertical vibration, this patent solution for vehicle motor
Certainly its longitudinally twisted vibration, the vertical vibration of engine can produce influence to bump leveller mode, can not ignore in solution procedure
Vertical vibration, extracts longitudinally twisted modal vibration equation, vertical mode vibration equation and bump leveller modal vibration from formula (9e)
Equation,
In formula, q7For bump leveller modal coordinate, q5For the longitudinally twisted mode of oscillation coordinate of engine, q3For engine vertical vibration
Modal coordinate；
Wherein：
fi=di1+di2χ+di3sin2ωt+(di4+di5)ω2cos2ωt
+φi1+φi2+φi3+φi4+φi5+φi6+φi7
di1=-ai4Meo
di2=ai7
di3=-1.3ai4Meo
di4=-4ai3(ml2+mp)rλ
di5=-4ai5ey(ml2+mp)rλ
φi1=0+O (ε)
φi3=0
φi5=0+O (ε)
I=5,7 in above-mentioned coefficient, neglect high-order in a small amount, then formula (11a), (11b) can be written as：
Wherein：
φi=φi1+φi2+φi3+φi4+φi5+φi6+φi7,
Step 7：Using Method of Multiple Scales solve equation (12a), (12b) (12c) approximate solution, by equation (12a), (12b),
Engine vertical mode coordinate, engine torque modal coordinate and bump leveller modal coordinate in (12c), respectively according toNondimensionalization is carried out to obtain,
Wherein：
By the time according to τ=ω7T carries out nondimensionalization, while utilizing replacementAbbreviation
Above-mentioned equation (13a), (13b), (13c) are obtained,
By equation (14a), (14b), (14c) left and right simultaneously divided byAnd makeObtain,
Solved using Method of Multiple Scales, it is a small amount of with nonlinear terms to make damping term, makees following replacement,
ξi=ε ηi
Tk=εkτ (k=0,1)
If the first approximation solution of equation is,
Wherein T0What is represented is fast change time, T1What is represented is the slow change time；
ε can be solved0The corresponding equation of rank is,
ε1The corresponding equation of rank is,
Wherein：
C in above formulai1=ai2mrl-ai4mrlze+ai6mrlxe；
Step 8：Equation (17a), (17b), the solution of (17c) can be expressed as,
In formula, AiFor on T1Unknown complex function, cc is above every conjugation, and remaining parameters is,
Work as q7With q5Mode occurs 1:During 2 internal resonance, following detuning parameter σ is introduced,
ωs5=2+ ε σ (20)
Formula (17a), (17b), (17c) and (20) are substituted into equation (18a), (18b), (18c), the secular term on the equation right side is eliminated
It can obtain,
In formula：
OrderWherein a3、a5、a7、θ3、θ5、θ7It is with becoming time T slowly1It is relevant
Complex constant, substitute into equation (21a), (21b), (21c), and be that zero can obtain according to real and imaginary parts,
Wherein a 'i、θ′iRespectively aiWith θiBecome time T for slow1Derivative；
In above formula：
y71=h72g31+h73g51+h74g71,
Order：
γ=θ5-2θ7+εσT0
Imaginary part in formula (22a), (22b), (22c) and real part are separated, obtained after arrangement,
a′3=-η3ωs3a3 (23e)
Step 9：(the η in the case of undamped3=η5=η7=0), formula (23f) is multiplied by a5, formula (23g) be multiplied by a7, then do
With,
Because steady state solution corresponds to a '5=a '7=γ '=0, then can obtain,
It can be obtained by formula (24),
It can know from formula (25b), select appropriate e1、e2Value can make ν be more than 0, substituted into formula (26) and understand a5And a7Always
Bounded, and shifting relation is presented, this demonstrate that can be in the longitudinally twisted mode of oscillation of engine using the method
Internal resonance is formed between the mode of motion of bump leveller, energy can be transmitted between two mode；
From formula (26) as can be seen that v characterizes the degree of energy exchange between flexible engine and bump leveller, v ＞ 0 represent that the two has
Energy exchange, when v is bigger, a5The amplitude of decay is bigger, illustrates that now energy exchange is more abundant；
Step 10：It was found from from step 9, system is under the conditions of undamped, and energy can be transmitted between two mode,
Damped when being introduced into bump leveller mode, i.e. η7≠ 0, now the damping of bump leveller, which can dissipate, carrys out the vibrational energy of engine,
The damping for adjusting bump leveller is worth to suitable so that bump leveller can farthest reduce the vibration of engine.
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| CN110712491A (en) * | 2019-10-16 | 2020-01-21 | 湖南大学 | Layered control method, system and medium for vehicle modal decoupling |
| CN111062143A (en) * | 2019-12-30 | 2020-04-24 | 重庆长安汽车股份有限公司 | Method for identifying inertial parameters of automobile engine |
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