CN109145514A - A kind of Numerical Simulation Analysis method of loudspeaker distortions - Google Patents
A kind of Numerical Simulation Analysis method of loudspeaker distortions Download PDFInfo
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Abstract
The invention discloses a kind of Numerical Simulation Analysis methods of loudspeaker distortions, belong to loudspeaker design field.Firstly, drawing the geometrical model in loudspeaker and its surrounding air domain in mapping software.Then, material property definition, the setting of physical field interface and grid dividing are carried out to the geometrical model of foundation in finite element analysis software, obtains finite element model.Secondly, carrying out the solution of THM coupling transient state to finite element model by finite element solving device, the time domain sound pressure signal that loudspeaker generates at the specified point of space is obtained.Finally, the stability region to time domain sound pressure signal carries out spectrum analysis, distortion, including harmonic distortion, intermodulation distortion and subharmonic distortion of loudspeaker etc. can be calculated after extracting the amplitude of different frequency point.This method can be analyzed to obtain the distorted characteristic of loudspeaker at loudspeaker design initial stage before not yet making sample, to make the design and production rapid and convenient of loudspeaker.
Description
Technical field
The present invention relates to a kind of Numerical Simulation Analysis methods of loudspeaker distortions, belong to loudspeaker design of Simulation neck
Domain.
Background technique
Loudspeaker distortions are divided into linear distortion and non-linear distortion, the latter be as caused by the amplitude non-linearity of loudspeaker,
Its ability for verily resetting sound to loudspeaker has an adverse effect, including harmonic distortion, intermodulation distortion and subharmonic distortion
Deng.
Harmonic distortion refers to when loudspeaker inputs the sinusoidal signal of a certain frequency, in the acoustical signal of loudspeaker output, removes
Outside the signal of former input, while there are the harmonic components such as secondary, triple-frequency harmonics.Usual harmonic distortion of loudspeaker appears in low frequency
Section, especially in vibrational system resonant frequency f0Larger when nearby, there are three main sources: vibrational system is non-linear, leads
Loudspeaker is caused third harmonic distortion occur in large-amplitude vibration；Nonlinear Magnetic Circuit, Magnetic Induction Density Distribution is uneven in magnetic gap
It will lead to loudspeaker and second harmonic distortion occur in large-amplitude vibration；Non-linear, the closed sky under dust cap of aeroelastic
Closed air will lead to second harmonic distortion between gas, centring disk and frame.
Intermodulation distortion refers to when two frequencies are respectively f1And f2Sinusoidal signal simultaneously when being added to loudspeaker, due to loudspeaking
Device it is non-linear, in its output acoustic pressure, it may appear that f1And f2And difference frequency (f2±f1、f2±2f1...) signal.In addition to loudspeaking
Other than device amplitude non-linearity, due to Doppler effect, the directive property of loudspeaker, the originals such as interference of speaker medium-high frequency woofer
Because can all generate intermodulation distortion.
Subharmonic distortion refers to when the sinusoidal signal reinforced to loudspeaker, middle low-frequency range can generate frequency be 1/2 or
The blurred signal of the signal frequencies such as 1/3 is referred to as " semitone " in factory, discontinuously occurs, it is caused by vibrating diaphragm is non-linear
's.
Distortion is a very important performance indicator of loudspeaker, is directly related to the sound reproduction matter of loudspeaker
Amount, therefore each loudspeaker manufacturing enterprise pays much attention to the distortion of loudspeaker, but loudspeaker distortions are analyzed in enterprise at present
Method is still traditional empirical method, and generally sample has a fling at, tests, improving the iterative cycles process of sample, re-test again, this
Mode must could find speakerphone problem until the design later period, and the development cycle is long, at high cost.
With the development of computer technology, carrying out Computer Aided Design using Numerical Simulation Analysis method becomes more and more extensive,
It Numerical Simulation Analysis method is applied to loudspeaker design can have a fling in sample estimate the performance of loudspeaker early period, to accelerate
The design schedule of loudspeaker reduces development cost.
Summary of the invention
The purpose of the present invention is obtain a kind of Numerical Simulation Analysis method of loudspeaker distortions；
The present invention is to solve must wait until that the design later period could find to raise existing for empirical method when analysis loudspeaker distortions
Sound device problem and development cycle length, problem at high cost.The present invention is based on three couplings of magnetic circuit of loudspeaker, vibrational system and sound field
Analysis is closed to carry out distortion analysis, analysis result is more comprehensive and accurate compared to single game or two independent analyses；
A kind of Numerical Simulation Analysis method of loudspeaker distortions of the invention, specific steps are as follows:
(1) the geometrical model figure in loudspeaker and its surrounding air domain is established
Loudspeaker and its surrounding sky using mapping software or are directly drawn in the finite element analysis software with CAD function
The 3D geometrical model figure in gas domain, wherein the geometrical model of loudspeaker should including the magnetic circuit of loudspeaker and vibrational system, if
Loadspeaker structure has the axisymmetric geometrical characteristic of 2D, then draws the 2D axial symmetry geometrical model in loudspeaker and its surrounding air domain
Figure；
(2) finite element model of loudspeaker distortions Numerical Simulation Analysis is established, the specific steps are as follows:
A. definition material parameter defines the material parameter of each component in geometrical model, the magnetic including upper clamp plate and magnetic conductor bowl
Hysteresis curves, Young's modulus, Poisson's ratio, density and the Rayleigh damping of each component of characteristic and vibrational system of air；
B., physical field interface is set, and loudspeaker can be related to electromagnetic field, vibration and sound field multiple physical field in the operating condition
Coupling, it is therefore desirable to each physical field interface is respectively set, comprising: 1) magnetic field constitutive relation, be arranged the magnetic circuit of loudspeaker in
Residual magnetic flux density, the magnetic characteristic of upper clamp plate and magnetic conductor bowl of magnet steel；2) multiturn coil, due to voice coil be by enameled wire coiling and
At, and the voice coil in geometrical model is a rectangular area, therefore to define the number of turns, end voltage and the conductor cross-section of voice coil
Product；3) perfect domination set is added in outer air layer；
C. grid division carries out grid dividing to the geometrical model of loudspeaker, obtains analysis list used in finite element analysis
Member selects face unit, if 3D model, then select body unit if 2D model；
D. boundary condition is defined, 1) fixed boundary condition, since loudspeaker ring and centring disk are fixed in frame
, it needs in its Edge definition fixed boundary condition；2) apply load, apply driving force at the voice coil position of model.Analysis is not
With distorted characteristic when, the loading of application is also different, when analyzing harmonic distortion of loudspeaker and subharmonic and being distorted, needs to apply
The driving force for adding a single frequency sinusoidal signal then needs to apply one by two frequencies when analyzing the intermodulation distortion of loudspeaker
The driving force of sinusoidal signal superposition；
(3) finite element model is solved with finite element solving device
Solution is divided into two steps: solving the Maxwell equation of magnetic circuit part static magnetic field first, obtains the stable state of loudspeaker
Magnetic flux distribution；Then it carries out magnetic circuit and acoustic power flow transient state solves, including solving the Maxwell side under electromagnetic fiele
Journey, many-degrees of freedom system forced vibration equation and sound and vibration coupled wave equation complete the THM coupling wink of magnetic circuit, vibrational system and sound field
State analysis, and obtain the time domain sound pressure signal that loudspeaker generates at specified point；
A. magnetic circuit steady-state analysis is carried out to finite element model
By solving the Maxwell equation of magnetic circuit of loudspeaker part static magnetic field, where obtaining loudspeaker voice coil at magnetic gap
Stable state magnetic flux distribution；
B. THM coupling transient analysis is carried out to finite element model
A. the coupling transient analysis of magnetic circuit and vibrational system
The coupling of magnetic circuit of loudspeaker and vibrational system shows themselves in that on the one hand energized coils are in magnetic field by Lorentz force
Effect and generate movement, so that entire vibrational system be pushed to be vibrated, while the voice coil moved can be due to cutting magnetic induction line
And induced electromotive force is generated, and then influence voice coil drive force size；On the other hand, the induced electricity generated by alternating current on voice coil
Magnetic field also will affect the Magnetic Induction Density Distribution of magnetic circuit system；
Maxwell equation under electromagnetic fiele can be expressed as:
In above formula, σ is conductivity,For partial differential symbol, A is magnetic vector potential, and t is the time,For Hamilton operator, H is
Magnetic field strength, JeFor the current density in voice coil comprising signal code density and induced current density.It can be in the hope of by above formula
Solution obtains A, so as to calculated magnetic induction intensity B:
In addition, due in the oscillating region of voice coil, magnetic induction intensity is unevenly distributed, therefore magnetic circuit is non-thread
Property will lead to the non-linear of voice coil drive force；
Hot-wire coil power suffered in magnetic field are as follows:
F=BLIe=B (2 π rN) Ie
In above formula, L is the length of magnetic gap coil, and N is the coil turn of voice coil, and r is voice coil radius, IeFor in voice coil
Electric current, including signal code and induced current；
B. coupled vibro-acoustic transient analysis
The coupling of speaker vibration system and sound field shows themselves in that one side, vibrational system radiative acoustic wave into air；It is another
Aspect, sound wave also can generate reaction force to vibrational system, and have an impact to vibrational state；
Vibration mode of the loudspeaker under the effect of humorous load can be characterized by many-degrees of freedom system forced vibration, vibrate position
It moves { u (t) } and meets following many-degrees of freedom system forced vibration equation:
In above formula, [m] is comprising the vibrational system mass matrix including airequivalent quality, and [c] is resistance coefficient matrix,
[k] is stiffness matrix, and F is driving force amplitude, and i is imaginary unit, and ω is the angular frequency of humorous load, and t is the time, and F ' (t) is sound
Reaction force of the wave to vibrational system；
It solves equation (1), obtains:
{ u (t) }={ u1(t)}+{u2(t)}
The solution consists of two parts, { u1It (t) } is the general solution of corresponding homogeneous equation, it is related with primary condition, it is to be
System does the transient silution of free vibration attenuation；{u2(t) } it is the particular solution of corresponding nonhomogeneous equation, is that system does the steady of forced vibration
State solution；When carrying out loudspeaker distortions specificity analysis, need to study the steady state solution { u of equation2(t)}；
At the position that air is coupled with vibrational system, the vibration of vibration acceleration and air normal direction in structure normal direction
Dynamic acceleration is identical, sets acceleration ü (t) in this way at coupling boundary, obtains producing on boundary by coupled vibro-acoustic equation calculation
Raw atmospheric pressure p:
Wherein, ρ is density of material, and n is the normal direction unit vector on coupling boundary.It can realize that vibrational system is shaken by above formula
It is dynamic that air vibration is driven to form sound wave, the acceleration sound source being equivalent in sound field；
Simultaneously on the boundary of vibrational system and sound field, atmospheric pressure generates acoustic pressure load on boundary to vibrational system
Stress:
Pn=δ n (2)
Wherein, 6 be structural stress.Sound wave can be achieved by formula (2), reaction force is generated to vibrational system；
(4) calculated distortion
The mistake of loudspeaker can be calculated by the loudspeaker time domain sound pressure signal obtained by THM coupling transient analysis
True characteristic, including harmonic distortion, intermodulation distortion and subharmonic distortion, provide the calculating side of harmonic distortion and intermodulation distortion herein
Method；
A. harmonic distortion is calculated.If f is exciting signal frequency, FFT spectrum is carried out to the stabilization sub stage of time domain sound pressure signal
Analysis, and higher hamonic wave is extracted, it is then calculate by the following formula to obtain the nth harmonic distortion H of loudspeakernWith total harmonic distortion THD:
Nth harmonic distortion:
Total harmonic distortion:
In above formula, PnfFor the acoustic pressure component at frequency nf, PtIt is total acoustic pressure including fundamental frequency；
B. intermodulation distortion is calculated.If f1And f2It is two frequencies of input signal, wherein f1Less than f2, and two frequencies it
Between not no integral multiple relationship.FFT spectrum analysis is carried out to the stabilization sub stage of time domain sound pressure signal, and extracts frequency f2±(n-
1)f1Corresponding intermodulation acoustic pressure componentThen it is calculate by the following formula to obtain the n times intermodulation distortion M of loudspeakern:
N times intermodulation distortion:
The invention has the advantages that the method for the present invention considers the phase of the magnetic circuit of loudspeaker, vibrational system and sound field comprehensively
Mutual coupling relationship is calculated by THM coupling transient analysis solution and spectrum analysis, obtains the distortion of loudspeaker, therefore the present invention
Can quickly, low cost and accurately estimate the distortion of loudspeaker and improve loudspeaker so as to shorten the R&D cycle of loudspeaker
Performance.
Detailed description of the invention
Fig. 1 is implementation method flow figure of the present invention.
Fig. 2 is THM coupling transient analysis schematic diagram
Fig. 3 is the 3D geometrical model of a 6.5 inches of auto loud hailers.
Fig. 4 is the 2D axial symmetry geometrical model in a 6.5 inches of auto loud hailers and its surrounding air domain.
Fig. 5 is the BH value of upper clamp plate and magnetic conductor bowl.
Fig. 6 is the material parameter of each component of vibrational system.
Fig. 7 is the Rayleigh damping coefficient of vibrational system.
Fig. 8 is multiturn coil parameter.
Fig. 9 is the grid dividing result of the finite element model.
Figure 10 is the loudspeaker time domain pressure response curve.
Figure 11 is the spectrum analysis figure of the loudspeaker time domain pressure response.
Figure 12 is preceding 5 order harmonics distortion component.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and specific embodiments.
The present invention is imitated by taking a 6.5 inches of auto loud hailers as an example using COMSOL Multiphysics 5.3a respectively
Its harmonic distortion and intermodulation distortion are really analyzed, and has directly given the simulation analysis result of harmonic distortion.Fig. 1 is implementation of the present invention
Method flow diagram mainly has the following steps:
Step 1: since this loudspeaker is axially symmetric structure, as shown in figure 3, therefore for ease of calculation, in COMSOL
It selects 2D axial symmetry to analyze environment in software first, then selects magnetic field analysis module, sound solid phase interaction-transient state module and shifting
Dynamic mesh module, because to carry out the transient analysis of THM coupling, the analytical model of last selection and time correlation；
Step 2: the 2D axial symmetry geometrical model in loudspeaker and its surrounding air domain, such as Fig. 4 are created using COMSOL software
It is shown.As seen from the figure, which consists of two parts: (1) magnetic circuit system, including magnetic conductor bowl, magnet steel and upper clamp plate, main to produce
Magnetisation field generates driving force to energized coils；(2) vibrational system, including dust cap, speech coil framework, voice coil, centring disk and folding
Ring.In order to avoid the interference of loudspeaker front in anti-phase with rear sound wave, infinitely great baffle model is established at the edge of ring, before loudspeaker
Air-shed separates afterwards；
Step 3: the finite element model of loudspeaker is established using COMSOL software, the specific steps are as follows:
1) average function of voice coil is set, and is named as coil_av, this is to define inverse electromotive force in voice coil domain
Arithmetic mean of instantaneous value.
2) definition material characteristic.For the loudspeaker of this example, the material of upper clamp plate and magnetic conductor bowl is soft iron, is needed defeated manually
Enter itself BH and HB value, as shown in Figure 5；Magnetic steel material is equivalent to air；The material of voice coil is copper, defines each component of vibrational system
Young's modulus, Poisson's ratio and density, as shown in Figure 6；The Rayleigh damping coefficient of vibrational system is set, as shown in Figure 7；
Rayleigh damping parameter alphadMAnd βdKCalculation formula be respectively as follows:
With
Wherein f1、f2It is any two resonant frequency of loudspeaker, δ1、δ2It is and f respectively1、f2Corresponding damping factor, can
By half-power method, obtained from loudspeaker amplitude-versus-frequency curve；
3) physical field environment is set.The z durection component that the residual magnetic flux density of magnet steel is arranged is 0.37T；It upper clamp plate and leads
The constitutive relation of magnetic bowl is set as HB curve；Multiturn coil is defined, as shown in Figure 8, wherein for different distortion analyses, sound
The driving voltage of circle is also different, but is all divided into two, for Research of Analysis System for Harmonic Distortion: driving voltage expression formula is 8.484
[V] * sin (2*pi*50 [Hz] * t), indicate amplitude be 8.484V, the single-frequency voltage excitation signals that frequency is 50Hz.For intermodulation
For distortion analysis: driving voltage expression formula is 8.484 [V] * (sin (2*pi*45 [Hz] * t)+sin (2*pi*400 [Hz] *
T)), indicate amplitude be 8.484V, single-frequency voltage excitation signals that frequency is 45Hz and amplitude is 8.484V, frequency is 400Hz's
The superposition of single-frequency voltage excitation signals；In one layer of air-shed outermost upper addition perfect domination set；
4) boundary condition is defined.Since the edge of loudspeaker ring and centring disk is fixed in frame, in loudspeaking
The Edge definition fixed boundary condition of device ring and centring disk.Setting unit body force Fv is Lorentz force contribution on voice coil
(mf)；
5) grid dividing.The trellis-type that outer air layer is arranged is map unit, interior air-shed, vibrational system and magnetic circuit system
The trellis-type of system is free triangular unit, and unit size is all set as Extra fine.Boundary is added to upper clamp plate and magnetic conductor bowl
Layer, the number of plies 3, first layer thickness are set as 0.2mm.It is Free Transform region that air section is arranged in mobile grid module, Gu
Determine the boundary being connected in Free Transform region with magnetic circuit system, the boundary r being connected in Free Transform region with vibrational system is set
Direction displacement is u, and the displacement of the direction z is w；
Step 4: setting calculates total time and time step as range (0,0.25 [ms], 550 [ms]), and chooses geometry
Non-linear option, setting tolerance are 0.001.It clicks Study to start to carry out THM coupling transient analysis, solution is divided into two steps: first
The stable state for first carrying out magnetic circuit part solves, the stable state magnetic flux density of magnetic gap part where available loudspeaker, especially voice coil
Distribution, so that the coupling transient analysis for next step magnetic circuit and vibrational system provides necessary parameter；Then magnetic circuit harmony is carried out
Admittedly coupling transient state to solve, the THM coupling transient analysis of magnetic circuit, vibrational system and sound field is completed, and obtains loudspeaker in specified point
Locate the time domain sound pressure signal generated；
A. the coupling transient analysis of magnetic circuit and vibrational system
The coupling of magnetic circuit of loudspeaker and vibrational system shows themselves in that on the one hand energized coils are in magnetic field by Lorentz force
Effect and generate movement, so that entire vibrational system be pushed to be vibrated, while the voice coil moved can be due to cutting magnetic induction line
And induced electromotive force is generated, and then influence voice coil drive force size；On the other hand, the induced electricity generated by alternating current on voice coil
Magnetic field also will affect the Magnetic Induction Density Distribution of magnetic circuit system；
Maxwell equation under electromagnetic fiele can be expressed as:
In above formula, σ is conductivity,For partial differential symbol, A is magnetic vector potential, and t is the time,For Hamilton operator, H is
Magnetic field strength, JeFor the current density in voice coil comprising signal code density and induced current density.It can be in the hope of by above formula
Solution obtains A, so as to calculated magnetic induction intensity B:
In addition, due in the oscillating region of voice coil, magnetic induction intensity is unevenly distributed, therefore magnetic circuit is non-thread
Property will lead to the non-linear of voice coil drive force；
Hot-wire coil power suffered in magnetic field are as follows:
F=BLIe=B (2 π rN) Ie
In above formula, L is the length of magnetic gap coil, and N is the coil turn of voice coil, and r is voice coil radius, IeFor in voice coil
Electric current, including signal code and induced current；
B. coupled vibro-acoustic transient analysis
The coupling of speaker vibration system and sound field shows themselves in that one side, vibrational system radiative acoustic wave into air；It is another
Aspect, sound wave also can generate reaction force to vibrational system, and have an impact to vibrational state；
Vibration mode of the loudspeaker under the effect of humorous load can be characterized by many-degrees of freedom system forced vibration, vibrate position
It moves { u (t) } and meets following many-degrees of freedom system forced vibration equation:
In above formula, [m] is comprising the vibrational system mass matrix including airequivalent quality, and [c] is resistance coefficient matrix,
[k] is stiffness matrix, and F is driving force amplitude, and i is imaginary unit, and ω is the angular frequency of humorous load, and t is the time, and F ' (t) is sound
Reaction force of the wave to vibrational system；
It solves equation (3), obtains:
{ u (t) }={ u1(t)}+{u2(t)}
The solution consists of two parts, { u1It (t) } is the general solution of corresponding homogeneous equation, it is related with primary condition, it is to be
System does the transient silution of free vibration attenuation；{u2(t) } it is the particular solution of corresponding nonhomogeneous equation, is that system does the steady of forced vibration
State solution；When carrying out loudspeaker distortions analysis, need to study the steady state solution { u of equation2(t)}；
At the position that air is coupled with vibrational system, the vibration of vibration acceleration and air normal direction in structure normal direction
Dynamic acceleration is identical, sets acceleration ü (t) in this way at coupling boundary, obtains producing on boundary by coupled vibro-acoustic equation calculation
Raw atmospheric pressure p:
Wherein, ρ is density of material, and n is the normal direction unit vector on coupling boundary.It can realize that vibrational system is shaken by above formula
It is dynamic that air vibration is driven to form sound wave, the acceleration sound source being equivalent in sound field；
Simultaneously on the boundary of vibrational system and sound field, atmospheric pressure generates acoustic pressure load on boundary to vibrational system
Stress:
Pn=δ n (4)
Wherein, 6 be structural stress.Sound wave can be achieved by formula (4), reaction force is generated to vibrational system；
Time domain pressure response signal of the loudspeaker in air-shed at specified point (0,150mm) is extracted after calculating, is seen
Figure 10；
Step 5: calculated distortion.
A. harmonic distortion is calculated.FFT spectrum analysis is carried out to the stabilization sub stage of time domain sound pressure signal, and it is humorous to extract high order
Then wave is calculate by the following formula to obtain the second harmonic distortion of loudspeaker, third harmonic distortion and the mistake of total harmonic wave as shown in figure 12
Very (take preceding 5 order harmonic component as approximate):
Second harmonic distortion:
Third harmonic distortion:
Total harmonic distortion:
Wherein,The total acoustic pressure being approximately equal to including fundamental frequency；
B. intermodulation distortion is calculated.FFT spectrum analysis is carried out to the stabilization sub stage of time domain sound pressure signal, and extracts frequency
400Hz, (400Hz ± 45Hz) and (400Hz ± 90Hz) corresponding intermodulation component, are then calculate by the following formula to obtain loudspeaker
Second and third secondary intermodulation distortion:
Secondary intermodulation distortion:
Intermodulation distortion three times:
Finally, it should be noted that the above case study on implementation is only to illustrate realization process of the invention, and not limit this hair
Bright described technical solution.Therefore, although this specification is referring to above-mentioned each step, invention is explained in detail,
But those skilled in the art should understand that, it still can modify to the present invention or equivalent replacement, and all are not
It is detached from the technical solution and its improvement of the spirit and scope of the present invention, should all be covered in scope of the presently claimed invention.
Claims (4)
1. a kind of Numerical Simulation Analysis method of loudspeaker distortions, it is characterised in that this method at least includes the following steps:
(1) the geometrical model figure in loudspeaker and its surrounding air domain is established
Loudspeaker and its surrounding air domain using mapping software or are directly drawn in the finite element analysis software with CAD function
3D geometrical model figure, wherein the geometrical model of loudspeaker should be including the magnetic circuit of loudspeaker and vibrational system, if loudspeaking
Device structure has the axisymmetric geometrical characteristic of 2D, then draws the 2D axial symmetry geometrical model figure in loudspeaker and its surrounding air domain；
(2) finite element model of loudspeaker distortions Numerical Simulation Analysis is established, the specific steps are as follows:
A. definition material parameter, defines the material parameter of each component in geometrical model, and the magnetic hysteresis including upper clamp plate and magnetic conductor bowl is returned
Line, Young's modulus, Poisson's ratio, density and the Rayleigh damping of each component of characteristic and vibrational system of air；
B., physical field interface is set, and loudspeaker can be related to the coupling of electromagnetic field, vibration and sound field in the operating condition, therefore need
Each physical field interface is respectively set, comprising: 1) residual flux of magnet steel in the magnetic circuit of loudspeaker is arranged in magnetic field constitutive relation
The magnetic characteristic of density, upper clamp plate and magnetic conductor bowl；2) multiturn coil, since voice coil is and the geometry mould as made of enameled wire coiling
Voice coil in type is a rectangular area, therefore to define the number of turns, end voltage and the sectional area of wire of voice coil；3) in outer air layer
Add perfect domination set；
C. grid division carries out grid dividing to the geometrical model of loudspeaker, obtains analytical unit used in finite element analysis, if
It is 2D model, face unit is selected, if 3D model, then select body unit；
D. define boundary condition, 1) fixed boundary condition is needed since loudspeaker ring and centring disk are fixed in frame
It will be in its Edge definition fixed boundary condition；2) apply load, apply driving force at the voice coil position of model；Analyze different mistakes
When true characteristic, the loading of application is also different, when analyzing harmonic distortion of loudspeaker and subharmonic is distorted, needs to apply one
The driving force of single frequency sinusoidal signal then needs to apply one and is believed by two the sinusoidal of frequency when analyzing the intermodulation distortion of loudspeaker
Number superposition driving force；
(3) finite element model is solved with finite element solving device
Solution is divided into two steps: solving the Maxwell equation of magnetic circuit part static magnetic field first, obtains the stable state magnetic flux of loudspeaker
Density Distribution；Then it carries out magnetic circuit and acoustic power flow transient state to solve, including solving the Maxwell equation under electromagnetic fiele, more
Thus system with one degree of freedom forced vibration equation and sound and vibration coupled wave equation complete the THM coupling wink of magnetic circuit, vibrational system and sound field
State analysis, and obtain the time domain sound pressure signal that loudspeaker generates at specified point；
A. magnetic circuit steady-state analysis is carried out to finite element model
It is steady at magnetic gap where obtaining loudspeaker voice coil by solving the Maxwell equation of magnetic circuit of loudspeaker part static magnetic field
State magnetic flux distribution；
B. THM coupling transient analysis is carried out to finite element model
A. the coupling transient analysis of magnetic circuit and vibrational system
The coupling of magnetic circuit of loudspeaker and vibrational system shows themselves in that on the one hand energized coils are in magnetic field by the work of Lorentz force
With and generate movement, so that entire vibrational system be pushed to be vibrated, while the voice coil moved can be produced due to cutting magnetic induction line
Raw induced electromotive force, and then influence voice coil drive force size；On the other hand, the induction field generated by alternating current on voice coil
Also it will affect the Magnetic Induction Density Distribution of magnetic circuit system；
Maxwell equation under electromagnetic fiele can be expressed as:
In above formula, σ is conductivity,For partial differential symbol, A is magnetic vector potential, and t is the time,For Hamilton operator, H is magnetic field
Intensity, JeFor the current density in voice coil comprising signal code density and induced current density.It can be solved by above formula
To A, so as to calculated magnetic induction intensity B:
In addition, due in the oscillating region of voice coil, magnetic induction intensity is unevenly distributed, therefore the non-linear meeting of magnetic circuit
Lead to the non-linear of voice coil drive force；
Hot-wire coil power suffered in magnetic field are as follows:
F=BLIe=B (2 π rN) Ie
In above formula, L is the length of magnetic gap coil, and N is the coil turn of voice coil, and r is voice coil radius, IeFor the electric current in voice coil,
Including signal code and induced current；
B. coupled vibro-acoustic transient analysis
The coupling of speaker vibration system and sound field shows themselves in that one side, vibrational system radiative acoustic wave into air；Another party
Face, sound wave also can generate reaction force to vibrational system, and have an impact to vibrational state；
Vibration mode of the loudspeaker under the effect of humorous load can be characterized by many-degrees of freedom system forced vibration, vibration displacement { u
(t) } meet following many-degrees of freedom system forced vibration equation:
In above formula, [m] is comprising the vibrational system mass matrix including airequivalent quality, and [c] is resistance coefficient matrix, [k]
For stiffness matrix, F is driving force amplitude, and i is imaginary unit, and ω is the angular frequency of humorous load, and t is the time, and F (t) is sound wave pair
The reaction force of vibrational system；
It solves equation (1), obtains:
{ u (t) }={ u1(t)}+{u2(t)}
The solution consists of two parts, { u1It (t) } is the general solution of corresponding homogeneous equation, it is related with primary condition, it is that system is done certainly
By the transient silution of decaying vibration；{u2(t) } it is the particular solution of corresponding nonhomogeneous equation, is the steady state solution that system does forced vibration；
When carrying out loudspeaker distortions specificity analysis, need to study the steady state solution { u of equation2(t)}；
At the position that air is coupled with vibrational system, the vibration of vibration acceleration and air normal direction in structure normal direction adds
Speed is identical, and acceleration is set in this way at coupling boundaryThe sky generated on boundary is obtained by coupled vibro-acoustic equation calculation
The strong p of air pressure:
Wherein, ρ is density of material, and n is the normal direction unit vector on coupling boundary.It can realize that vibrational system vibrates band by above formula
Dynamic air vibration forms sound wave, the acceleration sound source being equivalent in sound field；
Simultaneously on the boundary of vibrational system and sound field, atmospheric pressure answers acoustic pressure load on boundary to vibrational system generation
Power:
Pn=δ n (2)
Wherein, δ is structural stress, and sound wave can be achieved by formula (2) and generate reaction force to vibrational system；
(4) calculated distortion
The distortion of loudspeaker can be calculated by the loudspeaker time domain sound pressure signal obtained by THM coupling transient analysis, wrap
Harmonic distortion, intermodulation distortion and subharmonic distortion are included, provides the calculation method of harmonic distortion and intermodulation distortion herein；
A. it calculates harmonic distortion and sets f as exciting signal frequency, FFT spectrum analysis is carried out to the stabilization sub stage of time domain sound pressure signal,
And higher hamonic wave is extracted, it is then calculate by the following formula to obtain the nth harmonic distortion H of loudspeakernWith total harmonic distortion THD:
Nth harmonic distortion:
Total harmonic distortion:
In above formula, PnfFor the acoustic pressure component at frequency nf, PtIt is total acoustic pressure including fundamental frequency.
B. it calculates intermodulation distortion and sets f1And f2It is two frequencies of input signal, wherein f1Less than f2, and do not have between two frequencies
The relationship of integral multiple.FFT spectrum analysis is carried out to the stabilization sub stage of time domain sound pressure signal, and extracts frequency f2±(n-1)f1It is corresponding
Intermodulation acoustic pressure componentThen it is calculate by the following formula to obtain the n times intermodulation distortion M of loudspeakern:
N times intermodulation distortion:
2. the Numerical Simulation Analysis method of loudspeaker distortions characteristic as described in claim 1, it is characterised in that the loudspeaking of selection
Device includes various moving oil electric loudspeakers.
3. the Numerical Simulation Analysis method of loudspeaker distortions characteristic as described in claim 1, it is characterised in that loudspeaker distortions
It is distorted including harmonic distortion, intermodulation distortion and subharmonic.
4. the Numerical Simulation Analysis method of loudspeaker distortions characteristic as described in claim 1, it is characterised in that Drawing package
Include SolidWorks, Pro/E；Finite element analysis software includes COMSOL Multiphysics and ANSYS.
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