CN104809342B - A kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM - Google Patents
A kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM Download PDFInfo
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Abstract
A kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM of the present invention, belong to Vibration Using Engineering field, the present invention is in the case where ensureing the synchronization of vibrational system and being stable, considering vibrational system has material ginseng when shaking, the amplitude response of plastid that works and the vibration isolating effect of system, so that the twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM designed manufacturing cost on the premise of vibration isolating effect is ensured is more economical, operating efficiency is higher；Due to there is no the kinetic parameter design method for the SELF-SYNCHRONOUS VIBRATION SYSTEM for finding complete set both at home and abroad at present and thering is material to join design method when shaking, therefore, the present invention has not only filled up the design method of domestic and international SELF-SYNCHRONOUS VIBRATION SYSTEM but also has given the design method of vibrational system when material ginseng is shaken, a complete mentality of designing is provided for the scientific worker of this area, being that motor synchronizing is theoretical is combined there is provided a reference frame with engineering is actual.
Description
Technical field
The invention belongs to Vibration Using Engineering field, and in particular to a kind of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM
Parameter determination method.
Background technology
Self-synchronous vibrating machine is extensively using in the industrial all departments such as mine, metallurgy, manufacture of cement, transport of materials；From motion
In form, Self-synchronous vibrating machine is divided into plane motion bobbing machine and spatial movement bobbing machine two types；Plane motion from same
Walk bobbing machine species is various, form is different, it is very universal in engineering department application, wherein there is self-synchronous vibration feed
Machine, self-synchronous vibration conveyer, self-synchronous vibration cooler, motor synchronizing probability screen, self-synchronous vibration dryer, self-synchronous vibration
Shakeout, self-synchronizing linear vibration sieve, the cold ore deposit vibratory sieve of motor synchronizing and thermal mineral vibrating screen etc..It is this kind of machinery material supply, it is defeated
Send, sieve, cooling down, drying, being molded and casting falling sand in terms of be widely used.It is flat except promoting in industrial department
Face motion elemental body and double mass Self-synchronous vibrating machine (for example, self-synchronization vibration feeder, self-synchronous vibration conveyer, from
Synchronous probability sieve, self-synchronous vibration cooler, self-synchronous vibration shakeout, self-synchronizing linear vibration sieve) outside, also using space
The elemental body of motion and double mass Self-synchronous vibrating machine, this kind of machinery have spiral vertical vibrating conveyer, self-synchronous vibration to dry
Dry machine, self-synchronous vibration feeder, self-synchronous vibration cooler and long length double mass Near resonance oscillating formula jigging conveyer etc.；From same
Step bobbing machine has the following advantages：
(1) gear drive in forced synchronism formula bobbing machine is instead of using self synchronization theory, makes such mechanical transmission
The structure in portion is comparatively simple；
(2) due to eliminating gear drive, make the lubrication of machine, safeguard and overhaul greatly simplified；
(3) for some Self-synchronous vibrating machines, the amplitude started when passing through resonance region with parking can be reduced；
(4) the Self-synchronous vibrating machine majority applied at present in industry makes its construction more using shock electric machine direct drive
To be simple, cost is significantly reduced, and is easily installed；
(5) two main shafts of Self-synchronous vibrating machine vibrator can be installed under the conditions of relatively large distance；
(6) such bobbing machine is easy to implement seriation, generalization and standardization；
Current above-mentioned vibrating machine its common be structurally characterized in that：Two are driven to be arranged on same respectively by two motor
Two vibrators on individual rigid vibrating body, driving vibrational system makes vibrational system realize Vibration Synchronization stable drive；But, and
Do not account in vibrational system containing ginseng shake material when system vibration isolating effect and production efficiency；Due in produce reality,
The noise of vibration would generally be caused larger, the problem of production efficiency is not high；And the method for solving this problem is work plastid
Amplitude, ginseng shakes the mass change of material and the factor of vibration isolating effect is taken into account, and realizes the synchronization and synchronization of vibrational system
It is stable.
The content of the invention
In view of the shortcomings of the prior art, the present invention proposes that a kind of parameter of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM is true
Method is determined, in the case where ensureing the synchronization of vibrational system and being stable, it is contemplated that when vibrational system has the material ginseng to shake, work plastid
Amplitude response and system vibration isolating effect so that the twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM designed ensure
Manufacturing cost is more economical on the premise of vibration isolating effect, and operating efficiency is higher.
A kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, comprises the following steps：
Step 1, the structural model according to twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, obtain the total kinetic energy, total of system
Potential energy and total power consumption, so as to set up the kinetic model of twin-engined drives double-mass vibrating system；
Step 2, the condition of the synchronism stability operation determined in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM running,
Comprise the following steps that：
Step 2-1, determine two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM realize synchronous condition；
Step 2-2, the stable operation condition for determining two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM；
Step 3, synchronism stability operation under conditions of, with reference to the kinetic model of twin-engined drives double-mass vibrating system,
Obtain can meet synchronism stability operation kinetic parameter it is interval, described kinetic parameter include as received basis body frequency ratio, every
Plastid frequency of shaking than, work plastid and total system mass mass ratio；
Step 4, determine that the ginseng of twin-engined drives double-mass vibrating system is shaken material coefficient, and shaken material system according to above-mentioned ginseng
Number, the quality for obtaining critical frequency than the span of difference, work plastid and total system mass compares span；
Step 5, the critical frequency obtained than difference span in and work plastid and total system mass mass ratio
Span in, when determining that work plastid amplitude amplification degree is maximum, corresponding critical frequency is than difference and the plastid that works with being
The mass ratio for gross mass of uniting；
Step 6, work plastid and the mass ratio of total system mass according to acquisition, with reference to work plastid and total system mass
Mass ratio and work plastid critical frequency ratio between relation, obtain work plastid critical frequency ratio；
Step 7, according to the critical frequency that is obtained than difference and work plastid critical frequency ratio, further obtain work plastid
Frequency ratio：
Step 8, judge obtained as received basis body frequency than with work plastid and total system mass mass ratio whether in step 3
In described kinetic parameter is interval, if so, then performing step 9, otherwise, returns and perform step 4；
Step 9, according to the actual requirements, in vibration isolation plastid frequency than carrying out value in span, and by itself and obtained work
Make plastid frequency than, work plastid and total system mass mass ratio substitute into combine twin-engined drives double-mass vibrating system power
Learn in model, obtain all parameters of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, including as received basis weight, vibration isolation plastid
Quality, vibrating spring rigidity, isolation spring rigidity, working amplitude, eccentric rotor eccentric throw and eccentric block quality；
Step 10, the parameter according to obtained twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, build twin-engined drives double mass
SELF-SYNCHRONOUS VIBRATION SYSTEM.
The kinetic model for setting up twin-engined drives double-mass vibrating system described in step 1, is comprised the following steps that：
Step 1-1, the total kinetic energy T for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, J01Represent the rotary inertia of twin-engined drives double-mass vibrating the first eccentric rotor of system；J02Represent double-engine driving
The rotary inertia of dynamic double-mass vibrating the second eccentric rotor of system；J1Represent rotary inertia of the work plastid around itself barycenter；J2Table
Show rotary inertia of the vibration isolation plastid around itself barycenter；Represent the vibration velocity of i-th of eccentric rotor；Represent work plastid
Barycenter vibration velocity；Represent the vibration velocity of the barycenter of work plastid；The phase angle of i-th of eccentric rotor is represented,
I=1,2；m1Represent as received basis weight；m2Represent vibration isolation plastid quality；m0iThe quality of i-th of eccentric rotor is represented, ψ is represented
The angle of the rotation around center of mass of work plastid and vibration isolation plastid；
Step 1-2, the total potential energy U for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, XK2jRepresent the deformation vector of four isolation springs being connected with vibration isolation plastid, j=1,2,3,4；XKiRepresent
The deformation vector of two slinky springs worked between plastid and vibration isolation plastid, i=1,2；XK3Represent to be y-axis in the horizontal direction, erect
The deformation vector of Nogata spring that y directions are connected with vibration isolation plastid into the coordinate system for x-axis；K represents the rigidity of vibrating spring
Matrix, K2Represent stiffness matrix, the K of x directions isolation spring3Represent the stiffness matrix of y directions isolation spring；
Step 1-3, the total power consumption D for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein,Represent the vibration velocity of four isolation springs being connected with vibration isolation plastid, j=1,2,3,4；Represent
The vibration velocity of two slinky springs worked between plastid and vibration isolation plastid, i=1,2；XK3Represent to be y-axis in the horizontal direction, erect
The vibration velocity of Nogata spring that y directions are connected with vibration isolation plastid into the coordinate system for x-axis；F represents the damping of vibrating spring
Matrix, F2Represent damping matrix, the F of x directions isolation spring3Represent the damping matrix of y directions isolation spring；fdiRepresent double-engine driving
The damped coefficient of motor in dynamic double-mass vibrating system；
Step 1-4, bring the total kinetic energy of the twin-engined drives double-mass vibrating system of acquisition, total potential energy and total power consumption into glug
In bright day equation, the kinetic model of twin-engined drives double-mass vibrating system is obtained；
Formula is as follows：
Wherein,
M1For the gross mass of twin-engined drives double-mass vibrating system, M1=m01+m02+m1+m2；
M2Represent the gross mass of vibration isolation plastid, M2=m01+m02+m2；
JψRepresent total rotary inertia of twin-engined drives double-mass vibrating system, Jψ=J1+J2+(m01+m02)(r2+l0 2), formula
In, l0Represent the barycenter of eccentric rotor to the distance of twin-engined drives double-mass vibrating system barycenter；R represents the inclined of two eccentric rotors
Heart radius；
fψ=fxl2+f2x1ly1 2+f2x2ly0 2+f2y1lx1 2, in formula, fxRepresent damping of the vibrating spring in x directions；f2x1Represent
Damping of the x directions isolation spring in x directions；f2x2Represent damping of the y direction isolation springs in x directions；When l represents system quiescence
The original of vibrating spring is long；ly0Represent the distance of the isolation spring in y directions and the tie point of vibration isolation plastid to vibration isolation plastid barycenter；
ly1The tie point of expression isolation spring and vibration isolation plastid is to vibration isolation plastid barycenter in the distance in y directions, lx1Represent isolation spring with
The tie point of vibration isolation plastid to vibration isolation plastid barycenter x directions distance；
f2xy=f2x2ly0；
f2x=f2x1+f2x2；
f2y=f2y1+f2y2, in formula, f2y1Represent the damping of the isolation spring in y directions in x directions；f2y2Represent y directions every
Shake damping of the spring in y directions；
k2x=k2x1+k2x2, in formula, k2x1Represent the rigidity of the isolation spring in x directions in x directions；k2x2Represent y directions every
Shake rigidity of the spring in x directions；
kψ=kxl2+k2x1ly1 2+k2x2ly0 2+k2y1lx1 2, in formula, kxRepresent rigidity of the vibrating spring in x directions；k2y1Represent
Rigidity of the isolation spring in x directions in y directions；
k2xy=k2x2ly0；
k2y=k2y1+k2y2, in formula, k2y1Represent the rigidity of the isolation spring in y directions in x directions；K in formula2y2Represent y directions
Isolation spring y directions rigidity；
kyRepresent rigidity of the vibrating spring in y directions；
Te1Represent the electromagnetic torque of motor 1；
fd1Represent the damped coefficient of motor 1；
Te2Represent the electromagnetic torque of motor 2；
fd2Represent the damped coefficient of motor 2；
β represents the angle between two eccentric rotors rotation center and the line and x-axis of the plastid barycenter of inactive state two；
Step 1-5, the kinetic model of solution twin-engined drives double-mass vibrating system steady-state response solution；
Steady-state response solution x, y1、y2Formula it is as follows：
Wherein,
rm=m01/m1；
η=m02/m01；
Represent the average phase of vibrator；
α represents the half of two eccentric rotor phase differences；
C in formula1x=η2nx 2(1-nψ 2), d1x=2 η2ξψnψnx 2, η2Represent work plastid and system
The mass ratio of gross mass, a1=(1-nx 2)(1-nψ 2)+4ξxξψnxnψ(τ1-1)-τ2, b1=2 ξxnx(1-2τ3-nψ 2)+2ξψnψ(1-
nx 2)；τ1=f2xy 2/f2xfψ, τ2=k2xy 2/k2xkψ, τ3=f2xyk2xy/
f2xkψ, nx=ωm/ωx, nψ=ωm/ωψ,ωmRepresent the average angle speed of vibrator
Degree；
In formula, c2x=r1η2nx 2, d2x=2r2η2ξψnψnx 2, r1=k2xyl0/kψ；
In formula, c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2, r2=f2xyl0/fψ；
In formula, c2ψ=r3η2nx 2(1-nx 2), d2ψ=2r4η2ξψnψnx 2, r3=
k2xl0 2/kψ, r4=f2xl0 2/fψ；
In formula, a=(1-ny1 2)(1-ny2 2)-ny2(η1ny2+4ξy1ξy2ny1), η1=m1/M2；η2
=m1/M1；ny1Represent as received basis body frequency ratio, ny1=ωm/ωy1,ny2Represent vibration isolation plastid frequency ratio, ny2=ωm/ωy2,
B=2 ξy1ny1(1-η1ny2 2-ny2 2)+2ξy2ny2(1-ny1 2)；cy1=η1ny2 2；dy1=dy2=2 η1ξy1ny1ny2 2；
In formula, cy2=η1ny2 2(1-ny1 2)；
Two vibrators realizes synchronization bar in determination twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM described in step 2-1
Part, synchronous condition is：It is poor that broad sense dynamic symmetry torque is more than motor electromagnetism surplus torque；
Specific formula is as follows：
Wherein,
Represent the average value of two eccentric rotor phase differences in the monocycle；
ΔTRRepresent the difference of the remaining electromagnetic torque of two eccentric sons；
TuThe kinetic energy of expression standard eccentric rotor；
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ], formula
In,c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2,c2ψ=r3η2nx 2(1-
nx 2), d2ψ=2r4η2ξψnψnx 2；
Due toTherefore realize that self synchronous condition is：
System broad sense dynamic symmetry torque is poor more than motor electromagnetism surplus torque, that is, obtains WccCos α ＞ 0, are obtained as follows
Formula：
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ]cosα
＞ 0 (7).
The stable operation bar of two vibrators in determination twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM described in step 2-2
Part, stable operation condition is：
H0＞ 0, H1＞ 0, H3＞ 0, H ＞ 0；
Wherein,
In formula, Represent synchronous
Under service condition, two eccentric rotor phase angle average values；；
H1=ρ1κ2+ρ2κ1-WccWcs, in formula,ke01
It is ω in angle bullet degree to represent motor 1mWhen angle bullet degree stiffness coefficient；ke02It is ω in angle bullet degree to represent motor 2mWhen angle bullet degree it is firm
Spend coefficient, ωm0Represent under the conditions of running simultaneously, the synchro angle bullet degree of two eccentric rotors, m0The amount of the being eccentric rotor quality represented
The quality of eccentric rotor when identical, i.e.,：m01=m02=m0；
H=4H1H2-H0H3；
The kinetic parameter that acquisition described in step 3 can meet synchronism stability operation is interval, and specific method is：
Under the conditions of synchronous operation, in the range of 0~1, set as received basis body frequency than value, according to twin-engined drives
The actual conditions of double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, determine the value of the mass ratio of work plastid and total system mass, so as to obtain
When must run simultaneously vibration isolation plastid frequency than parameter it is interval；In the range of 4~6, set vibration isolation plastid frequency than value,
According to the actual conditions of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, the mass ratio of work plastid and total system mass is determined
Value, thus obtain as received basis body frequency during synchronous operation than parameter it is interval；The mass ratio of work plastid and total system mass
Span be 0~1；
Under the conditions of stable operation, in the range of 0~1, set as received basis body frequency than value, according to twin-engined drives
The actual conditions of double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, determine the value of the mass ratio of work plastid and total system mass, so as to obtain
Stable operation when vibration isolation plastid frequency than parameter it is interval；In the range of 4~6, set vibration isolation plastid frequency than value,
According to the actual conditions of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, the mass ratio of work plastid and total system mass is determined
Value, thus obtain as received basis body frequency during stable operation than parameter it is interval；The mass ratio of work plastid and total system mass
Span be 0~1；
The span obtained under the conditions of synchronous operation and the span obtained under the conditions of stable operation are taken into common factor,
Under conditions of synchronism stability operation, with reference to the kinetic model of twin-engined drives double-mass vibrating system, twin-engined drives are obtained double
The span of the key parameter of plastid SELF-SYNCHRONOUS VIBRATION SYSTEM.
The ginseng of determination twin-engined drives double-mass vibrating system described in step 4 is shaken material coefficient, and is shaken thing according to above-mentioned ginseng
Expect coefficient, quality of the critical frequency than the span of difference, work plastid and total system mass is obtained than span, using line
Property interpolation method, the ginseng for drawing twin-engined drives double-mass vibrating system shakes the isopleth of material coefficient, ordinate be work plastid and
The mass ratio of total system mass, abscissa is that critical frequency ratio is poor.
When determination as received basis body amplitude amplification degree described in step 5 is maximum, corresponding critical frequency is than difference and as received basis
The mass ratio of body and total system mass, using linear interpolation method, the isopleth of drawing plastid amplitude amplification degree, ordinate is
The mass ratio of work plastid and total system mass, abscissa is that critical frequency ratio is poor.
Advantage of the present invention：
A kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM of the present invention, is ensureing vibrational system
In the case of synchronous and stable, it is contemplated that when vibrational system has the material ginseng to shake, the amplitude response of the plastid that works and system every
Shake effect so that the twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM designed is manufactured on the premise of vibration isolating effect is ensured
This is more economical, and operating efficiency is higher；Due to there is no the dynamics for the SELF-SYNCHRONOUS VIBRATION SYSTEM for finding complete set both at home and abroad at present
Parameters design and there is design method of material ginseng when shaking, therefore, the present invention has not only filled up domestic and international self-synchronous vibration system
The design method of system and the design method for giving vibrational system when material ginseng is shaken, are provided for the scientific worker of this area
One complete mentality of designing, which is that motor synchronizing is theoretical, to be combined there is provided a reference frame with engineering is actual.
Brief description of the drawings
Fig. 1 is the parameter determination method flow of the twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM of an embodiment of the present invention
Figure；
Fig. 2 is the kinetic model schematic diagram of the twin-engined drives double-mass vibrating system of an embodiment of the present invention, wherein,
It is system structure model to scheme (a), and figure (b) is the simplified structural modal of system；
Fig. 3 is the stability parameter numerical result schematic diagram of an embodiment of the present invention, wherein, figure (a) is stable
Property index H0, H1, H phase difference be 0 and 2 π when, compare n with frequencyxSituation of change schematic diagram；It is stability indicator H to scheme (b)3
When phase difference is 0 and 2 π, compare n with frequencyxSituation of change schematic diagram, figure (c) is stability indicator H3It is 0 and 2 in phase difference
During π, compare n with as received basis body frequencyy1Situation of change schematic diagram, figure (d) be stability indicator H3When phase difference is 0 and 2 π,
Compare n with vibration isolation plastid frequencyy2Situation of change schematic diagram；
Fig. 4 realizes that Vibration Synchronization is driven the parameter interval diagram of simultaneously stable operation for an embodiment of the present invention, its
In, figure (a) is that than in nx, vibrational system can realize the frequency of synchronism stability operation than interval diagram in frequency, figure (b) be
Frequency is than in ny1, vibrational system can realize the frequency of synchronism stability operation than interval diagram, and figure (c) is to compare ny2 in frequency
In, vibrational system can realize that the frequency of synchronism stability operation compares interval diagram；
Fig. 5 is the n of an embodiment of the present inventiony1 ny2Plane internal force carry-over factor and feature amplitude isopleth schematic diagram；
Fig. 6 is the unloaded feature amplitude of an embodiment of the present invention, maximum ginseng is shaken material coefficient, amplification degree and power transmission system
Several isopleth is in Δ η2Distribution schematic diagram in plane, wherein, figure (a) is the isopleth of unloaded feature amplitude in Δ η2Plane
On distribution schematic diagram, figure (b) for maximum ginseng shake material coefficient isopleth in Δ η2Distribution schematic diagram in plane, schemes (c)
For amplification degree isopleth in Δ η2Distribution schematic diagram in plane, figure (d) is the isopleth of power carry-over factor in Δ η2In plane
Distribution schematic diagram；
Fig. 7 is the critical frequency of an embodiment of the present invention than the change schematic diagram with as received basis body mass ratio.
Embodiment
An embodiment of the present invention is described further below in conjunction with the accompanying drawings.
In the embodiment of the present invention, illustrated by taking twin-engined drives plane motion double-mass vibrating system as an example, twin-engined drives
The parameter determination method of double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, method flow diagram are as shown in figure 1, comprise the following steps：
Step 1, the structural model according to twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, obtain the total kinetic energy, total of system
Potential energy and total power consumption, so as to set up the kinetic model of twin-engined drives double-mass vibrating system, are comprised the following steps that：
Fig. 2 is the kinetic model of twin-engined drives plane motion double-mass vibrating system；By work plastid m1, vibration isolation plastid
m2And two eccentric rotor m01And m02Composition；Work plastid m1By orthogonal connecting rod and spring and vibration isolation plastid m2It is connected
Connect, spacer plastid m2It is arranged on by resilient support on ground, and vibrator (eccentric rotor) m01And m02On vibration isolation plastid,
By the ac motor driving of two reversed turnings, shown in such as Fig. 2 (a).Because two plastids are connected in x directions for bar, in y directions
Connected by spring, axle of spring is vertical with rod axis, bar can be handled with beam, in the absence of displacement in the axial direction, so two matter
The relative motion in y directions is only existed between body, so system can simplify the mechanical model such as Fig. 2 (b).Select m1In y directions
Move y1、m2Motion x, y in x and y directions2And two plastid around respective barycenter rotate ψ, two eccentric rotor phase anglesWithFor
Generalized coordinates.Using coordinate transformation method, two plastids and eccentric rotor barycenter displacement component, each spring variable can be tried to achieve, and then obtain
System kinetic energy, potential energy and dissipative function；
In the embodiment of the present invention, when the attachment coefficient of material is 0.2, the quality of material of addition is mm=250kg, work
The quality of plastid is m1=950kg, the gross mass for the plastid that now works is M=m1+kmmm=1000kg；
Step 1-1, the total kinetic energy T for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, J01Represent the rotary inertia of twin-engined drives double-mass vibrating the first eccentric rotor of system；J02Represent double-engine driving
The rotary inertia of dynamic double-mass vibrating the second eccentric rotor of system；J1Represent rotary inertia of the work plastid around itself barycenter；J2Table
Show rotary inertia of the vibration isolation plastid around itself barycenter；XiFor the barycenter displacement of i-th of eccentric rotor；XG1Represent the matter of work plastid
Heart displacement；XG2Represent the barycenter displacement of vibration isolation plastid；Represent the phase angle of i-th of eccentric rotor, i=1,2；m1Represent work
Plastid quality；m2Represent vibration isolation plastid quality；m0iThe quality of i-th of eccentric rotor is represented, ψ represents work plastid and vibration isolation plastid
Rotation around center of mass angle；
Step 1-2, the total potential energy U for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, XK2iRepresent the deformation vector of four isolation springs being connected with vibration isolation plastid, j=1,2,3,4；XKiRepresent
The deformation vector of two slinky springs worked between plastid and vibration isolation plastid；XK3Expression is that y-axis, vertical direction are in the horizontal direction
The deformation vector for the spring that y directions are connected with vibration isolation plastid in the coordinate system of x-axis；K represents the stiffness matrix of vibrating spring, K2Table
Show stiffness matrix, the K of x directions isolation spring3Represent the stiffness matrix of y directions isolation spring；
Step 1-3, the total power consumption D for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, F represents the damping matrix of vibrating spring, F2Represent damping matrix, the F of x directions isolation spring3Represent y directions
The damping matrix of isolation spring；fdiRepresent the damped coefficient of motor in twin-engined drives double-mass vibrating system；
Step 1-4, bring the total kinetic energy of the twin-engined drives double-mass vibrating system of acquisition, total potential energy and total power consumption into glug
In bright day equation, the kinetic model of twin-engined drives double-mass vibrating system is obtained；
Formula is as follows：
Wherein,
M1For the gross mass of twin-engined drives double-mass vibrating system, M1=m01+m02+m1+m2；
M2Represent the gross mass of vibration isolation plastid, M2=m01+m02+m2；
JψRepresent total rotary inertia of twin-engined drives double-mass vibrating system, Jψ=J1+J2+(m01+m02)(r2+l0 2), formula
In, l0Represent the barycenter of eccentric rotor to the distance of twin-engined drives double-mass vibrating system barycenter；R represents the inclined of two eccentric rotors
Heart radius；
fψ=fxl2+f2x1ly1 2+f2x2ly0 2+f2y1lx1 2, in formula, fxRepresent damping of the vibrating spring in x directions；f2x1Represent
Damping of the x directions isolation spring in x directions；f2x2RepresentyDamping of the direction isolation spring in x directions；When l represents system quiescence
The original of vibrating spring is long；ly0Represent the distance of the isolation spring in y directions and the tie point of vibration isolation plastid to vibration isolation plastid barycenter；
ly1The tie point of expression isolation spring and vibration isolation plastid is to vibration isolation plastid barycenter in the distance in y directions, lx1Represent isolation spring with
The tie point of vibration isolation plastid to vibration isolation plastid barycenter x directions distance；
f2xy=f2x2ly0；
f2x=f2x1+f2x2；
f2y=f2y1+f2y2, in formula, f2y1Represent the damping of the isolation spring in y directions in x directions；f2y2Represent y directions every
Shake damping of the spring in y directions；
k2x=k2x1+k2x2, in formula, k2x1Represent the rigidity of the isolation spring in x directions in x directions；k2x2Represent y directions every
Shake rigidity of the spring in x directions；
kψ=kxl2+k2x1ly1 2+k2x2ly0 2+k2y1lx1 2, in formula, kxRepresent rigidity of the vibrating spring in x directions；k2y1Represent
Rigidity of the isolation spring in x directions in y directions；
k2xy=k2x2ly0；
k2y=k2y1+k2y2, in formula, k2y1Represent the rigidity of the isolation spring in y directions in x directions；K in formula2y2Represent y directions
Isolation spring y directions rigidity；
kyRepresent rigidity of the vibrating spring in y directions；
Te1Represent the electromagnetic torque of motor 1；
fd1Represent the damped coefficient of motor 1；
Te2Represent the electromagnetic torque of motor 2；
fd2Represent the damped coefficient of motor 2；
β represents the angle between two eccentric rotors rotation center and the line and x-axis of the plastid barycenter of inactive state two；
Step 1-5, the kinetic model of solution twin-engined drives double-mass vibrating system steady-state response solution；
Steady-state response solution x, y1、y2Formula it is as follows；
Wherein,
rm=m01/m1；
η=m02/m01；
Represent the average phase of vibrator；
α represents the half of two eccentric rotor phase differences；
C in formula1x=η2nx 2(1-nψ 2), d1x=2 η2ξψnψnx 2, η2Represent work plastid and system
The mass ratio of gross mass, a1=(1-nx 2)(1-nψ 2)+4ξxξψnxnψ(τ1-1)-τ2, b1=2 ξxnx(1-2τ3-nψ 2)+2ξψnψ(1-
nx 2)；τ1=f2xy 2/f2xfψ, τ2=k2xy 2/k2xkψ, τ3=f2xyk2xy/
f2xkψ, nx=ωm/ωx, nψ=ωm/ωψ,ωmRepresent the average angle speed of vibrator
Degree；
In formula, c2x=r1η2nx 2, d2x=2r2η2ξψnψnx 2, r1=k2xyl0/kψ；
In formula, c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2, r2=f2xyl0/fψ；
In formula, c2ψ=r3η2nx 2(1-nx 2), d2ψ=2r4η2ξψnψnx 2, r3=
k2xl0 2/kψ, r4=f2xl0 2/fψ；
In formula, a=(1-ny1 2)(1-ny2 2)-ny2(η1ny2+4ξy1ξy2ny1), η1=m1/M2；η2
=m1/M1；ny1Represent as received basis body frequency ratio, ny1=ωm/ωy1,ny2Represent vibration isolation plastid frequency ratio, ny2=ωm/ωy2,
B=2 ξy1ny1(1-η1ny2 2-ny2 2)+2ξy2ny2(1-ny1 2)；cy1=η1ny2 2；dy1=dy2=2 η1ξy1ny1ny2 2；
In formula, cy2=η1ny2 2(1-ny1 2)；
Step 2, the condition of the synchronism stability operation determined in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM running,
Comprise the following steps that：
Step 2-1, the synchronous condition of realizing for determining two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, it is synchronous
Service condition is：It is poor that broad sense dynamic symmetry torque is more than motor electromagnetism surplus torque；
If system can realize the synchronization of two eccentric rotors, the angular speed momentary fluctuation system of two eccentric rotors within the monocycle
Several averages is 0；
Specific formula is as follows：
Wherein,
Represent the average value of two eccentric rotor phase differences in the monocycle；
ΔTRRepresent the difference of the remaining electromagnetic torque of two eccentric sons；
TuThe kinetic energy of expression standard eccentric rotor；
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ], formula
In,c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2,c2ψ=r3η2nx 2(1-
nx 2), d2ψ=2r4η2ξψnψnx 2；
Due toTherefore realize that self synchronous condition is：System broad sense dynamic symmetry torque is more than electronic electromechanics
Magnetic surplus torque is poor, that is, obtains WccCos α ＞ 0 obtain equation below：
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ]cosα
＞ 0 (7).
Step 2-2, the stable operation condition for determining two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM are stable
Service condition is：
H0＞ 0, H1＞ 0, H3＞ 0, H ＞ 0；
If system meets Self synchronous conditions, the same of phase angle and two eccentric rotors is obtained using numerical computation method
Angular speed is walked, is designated asAnd ωm0。
Formula (8) is existedAnd ωm0Field is linearized, and is consideredTake Represent
Average coefficient of variation of the angular speed of two eccentric rotors worked on plastid in a cycle,Represent on work plastid
Two eccentric rotors average coefficient of variation of the phase difference in a cycle,Represent the phase difference of two eccentric rotors
Average undulating value in a cycle.It can obtain differential equation of first order matrix form as follows：
In formula, C=A '-1B ',
By C=A '-1B ' obtains Matrix C；The characteristic equation of Matrix C is obtained by det (C- λ I)=0：
λ3+c1λ2+c2λ+c3=0 (9)
In formula,
c1=4 ωm0H1/H0,
H1=ρ1κ2+ρ2κ1-WccWcs；
H=4H1H2-H0H3；
From Routh-Hurwitz criterions, when characteristic equation (9) parameter of Matrix C is met
c1＞ 0, c3＞ 0, c1c2＞ c3 (10)
When, trivial solution z=0 is stable.
For vibrating machine, because the structure of system is always satisfied with H0＞ 0, can further be write as：
H0＞ 0, H1＞ 0, H3＞ 0, H ＞ 0 (11)
Step 3, synchronism stability operation under conditions of, with reference to the kinetic model of twin-engined drives double-mass vibrating system,
Obtain can meet synchronism stability operation kinetic parameter it is interval, described kinetic parameter include as received basis body frequency ratio, every
Plastid frequency of shaking than, work plastid and total system mass mass ratio；
The kinetic parameter that described acquisition can meet synchronism stability operation is interval, and specific method is：
Under the conditions of synchronous operation, it is 0.7 than value to make as received basis body frequency, is shaken according to twin-engined drives double mass motor synchronizing
The actual conditions of dynamic system, determine the value of the mass ratio of work plastid and total system mass, thus obtain synchronous operation after
Plastid frequency of shaking than parameter it is interval；It is 4 than value to make vibration isolation plastid frequency, according to twin-engined drives double mass self-synchronous vibration system
The actual conditions of system, determine the value of the mass ratio of work plastid and total system mass, so that as received basis when obtaining synchronous operation
Body frequency than parameter it is interval；The span of the mass ratio of work plastid and total system mass is 0~1；
Under the conditions of stable operation, it is 0.7 than value to make as received basis body frequency, is shaken according to twin-engined drives double mass motor synchronizing
The actual conditions of dynamic system, determine the value of the mass ratio of work plastid and total system mass, thus obtain stable operation after
Plastid frequency of shaking than parameter it is interval；It is 4 than value to make vibration isolation plastid frequency, according to twin-engined drives double mass self-synchronous vibration system
The actual conditions of system, determine the value of the mass ratio of work plastid and total system mass, so that as received basis when obtaining stable operation
Body frequency than parameter it is interval；The span of the mass ratio of work plastid and total system mass is 0~1；
The span obtained under the conditions of synchronous operation and the span obtained under the conditions of stable operation are taken into common factor,
Under conditions of synchronism stability operation, with reference to the kinetic model of twin-engined drives double-mass vibrating system, twin-engined drives are obtained double
The span of the key parameter of plastid SELF-SYNCHRONOUS VIBRATION SYSTEM.
In the embodiment of the present invention, when system meets formula (9) condition, two eccentric turns of synchronous operations are stable.By system
Synchronous operation stability condition is known：As H0 ＞ 0, H1 ＞ 0, H3 ＞ 0, H ＞ 0, system stable operation.From above analyzing,
Possible stable intervals have 2 α0∈ (- pi/2, pi/2) and 2 α0Two intervals of ∈ (pi/2,3 pi/2s)；Therefore, 2 α are selected herein0=0
With 2 α0=π, you can represent two interval stability.
Figure (a) is visible in such as Fig. 3, H0And H1Two parameters do not change with the change of synchronous extreme point, and H is varied less, and
Three parameters are all satisfied with stability of synchronization condition, and two kinds of situations are also same result of calculation in addition.Therefore, machinery is tied herein
In structure, H3Then it is to determine the foundation of synchronous operation stability.Table 2, which is listed, schemes (b), figure (c) and figure (d) stabilization in corresponding diagram 3
The interval of parameter result of calculation.According to table 1 and 2, it may be determined that realize Vibration Synchronization transmission and operation stability while meeting
Parameter is interval, in such as Fig. 4 shown in figure (a), figure (b) and figure (c), in figure, and 0 represents the minimum synchronous stable region of limit 0, and 0 represents pole
Big synchronization limit 0 stable region,Minimum synchronous limit π stable regions are represented,Represent greatly synchronization limit π stable regions；
Table 1
Table 2
Step 4, determine that the ginseng of twin-engined drives double-mass vibrating system is shaken material coefficient, and shaken material system according to above-mentioned ginseng
Number, the quality for obtaining critical frequency than the span of difference, work plastid and total system mass compares span；
In the embodiment of the present invention, using linear interpolation method, the ginseng for drawing twin-engined drives double-mass vibrating system is shaken material system
Several isopleth, ordinate is the mass ratio of work plastid and total system mass, and abscissa is that critical frequency ratio is poor.
If as received basis weight is m when vibrational system is unloaded1, vibrational system feedstock mass is mm, material combination coefficient is
km, the ginseng material coefficient that shakes is designated as σm：
σm=kmmm/m1 (12)
In the embodiment of the present invention, σm=0.2；
Consider ginseng shake quality of material when, the dimensionless group of system is：
Fig. 5 is ny1、ny2Plane internal force carry-over factor and feature amplitude isopleth, according to Fig. 5, by unloaded operation point selection
Parameter region is surrounded in λ=0.1 and ab；Work as ny2When larger, n2=1 isopleth is approximately perpendicular to ny1Axis, so by n2=1 etc.
It is worth line and ny2=6 straight-line intersections correspondence ny1Value is defined as work plastid critical frequency ratio, is designated as ny10This
If setting ny1EAs received basis body frequency compares n when unloadedy1It should be less than ny10, define critical frequency is than difference：
Δ=ny10-ny1 (14)
Because the amplitude for the plastid that works is rrmμy1, and rmWith material factor sigmamIncrease and reduce, therefore, by feature amplitude amendment
For：
μ′y1=μy1/(1+σm) (15)
As the above analysis, as Δ ＞ 0, feature amplitude may be shaken with ginseng material coefficient increase and increase；If being
Feature amplitude is μ when system is unloadedy10, and reach maximum and join material factor sigma of shakingmWhen its feature amplitude be μ 'y1max, definition is characterized
Amplitude amplification degree, abbreviation amplification degree：
δ=(μ 'y1max-μy10)/μy10× 100% (16)
Fig. 6 give the unloaded feature amplitude of system, maximum ginseng shake material coefficient and its corresponding maximum, force carry-over factor and
Amplification degree is in Δ η2Distribution of contours in plane, by scheming in Fig. 6 it can be seen from (a) as the unloaded kinetic parameter of system deviates
The feature amplitude extreme point of system, unloaded feature amplitude declines.As shown in figure (b) in Fig. 6 and figure (c), in Δ η2Parameter plane
On, the isopleth that maximum joins shake material coefficient and its correspondence amplification degree is approximately one and half cucurbit appearance curves, and internal layer value is big, outside
Layer value is small, and increases with critical frequency than difference, and each isopleth is to η2=0.1 approaches.Mass ratio is bigger, and maximum joins the material coefficient that shakes
It is smaller with amplification degree, work as η2During ＞ 0.57, amplification degree is 0；Corresponding power carry-over factor, which is always less than in 10%, such as Fig. 6, schemes (d)
It is shown.
In the embodiment of the present invention, shaken material coefficient according to the ginseng that obtains is calculated, work plastid is determined in Fig. 6 figure (b)
With the mass ratio η of total system mass2Span with critical frequency than poor Δ, i.e. (Δ, η2) point set coordinate；
Step 5, the critical frequency obtained than difference span in and work plastid and total system mass mass ratio
In span, when determining that work plastid amplitude amplification degree is maximum, corresponding critical frequency is than difference and work plastid and system
The mass ratio of gross mass；
In the embodiment of the present invention, using linear interpolation method, the isopleth of drawing plastid amplitude amplification degree, ordinate is
The mass ratio of work plastid and total system mass, abscissa is that critical frequency ratio is poor.
In the embodiment of the present invention, according to in rapid 4 determined by η2With the span of Δ, found in Fig. 6 figure (c)
When the plastid amplitude amplification that works degree is maximum, the mass ratio η of corresponding work plastid and total system mass2With critical frequency than poor Δ
Value；
In the embodiment of the present invention, according to figure (a) in Fig. 6 and figure (c), it is determined that (Δ, η2) coordinate be (0.1,0.3), this
When, μy10=1.312, η is worked as in corresponding δ=20.833, λ=0.0507 of maximum material coefficient2When=0.3, the quality m of lower plastid2
=2333kg；
Step 6, work plastid and the mass ratio of total system mass according to acquisition, with reference to work plastid and total system mass
Mass ratio and work plastid critical frequency ratio between relation, obtain work plastid critical frequency compare ny10；
Fig. 7 gives critical frequency and compares ny10With η2Changing rule；Understood to check in by calculating data, work as η2When=0.645,
System zero load feature amplitude maximum 2.67, and critical frequency ratio now, n are checked in by Fig. 7y10=1.69.Herein by ny2When=6
(η2, ny1) correspond to the feature amplitude extreme point that idle condition point (0.645,1.69) is defined as such system.
In the embodiment of the present invention, according to the work plastid and the mass ratio η of total system mass of acquisition2, obtain ny10=
1.24；
Step 7, according to the critical frequency that is obtained than difference and work plastid critical frequency ratio, further obtain work plastid
Frequency ratio；
In the embodiment of the present invention, according to the n of acquisitiony10Value, in its generation, is back in formula (14), as received basis when obtaining unloaded
Body frequency compares ny1E, compare n using its value as received basis body frequencyy1；
Step 8, judge obtained as received basis body frequency than with work plastid and total system mass mass ratio whether in step 3
In described kinetic parameter is interval, if so, then performing step 9, otherwise, returns and perform step 4；
Step 9, according to the actual requirements, in vibration isolation plastid frequency than carrying out value in span, and by itself and obtained work
Make plastid frequency than, work plastid and total system mass mass ratio substitute into combine twin-engined drives double-mass vibrating system power
Learn in model, obtain all parameters of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, including as received basis weight m1, vibration isolation matter
Weight m2, vibrating spring rigidity kx、ky, isolation spring rigidity k2y, working amplitude A, eccentric rotor eccentric throw r and eccentric block matter
Measure m01；
ky=7.776 × 103KN/m, by ny2=6, nx=4.0, nψ=4.0, it is known that k2y=281KN/m, kx=kψ=
632KN/m；By A=2rrmμ′maxUnderstand, rrm=0.0656, it is eccentric if the eccentric rotor radius of power taking machine is r=0.06m
Rotor quality is m01=1.1kg.
Step 10, the parameter according to obtained twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, build twin-engined drives double mass
SELF-SYNCHRONOUS VIBRATION SYSTEM.
Claims (7)
1. a kind of parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, it is characterised in that comprise the following steps：
Step 1, the structural model according to twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, obtain the total kinetic energy of system, total potential energy
Consumed energy with total, so as to set up the kinetic model of twin-engined drives double-mass vibrating system；
Step 2, the condition of the synchronism stability operation determined in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM running, specifically
Step is as follows：
Step 2-1, determine two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM realize synchronous condition；
Step 2-2, the stable operation condition for determining two vibrators in twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM；
Step 3, under conditions of synchronism stability operation, with reference to the kinetic model of twin-engined drives double-mass vibrating system, obtain
The kinetic parameter that synchronism stability operation can be met is interval, and described kinetic parameter includes as received basis body frequency ratio, vibration isolation matter
Body frequency than, work plastid and total system mass mass ratio；
Step 4, determine that the ginseng of twin-engined drives double-mass vibrating system is shaken material coefficient, and shaken material coefficient according to above-mentioned ginseng, obtained
The quality that critical frequency is obtained than the span of difference, work plastid and total system mass compares span；
Step 5, take with the mass ratio of work plastid and total system mass in the span of the critical frequency that is obtained than difference
In the range of value, when determining that work plastid amplitude amplification degree is maximum, corresponding critical frequency is more total than difference and work plastid and system
The mass ratio of quality；
Step 6, work plastid and the mass ratio of total system mass according to acquisition, with reference to the matter of work plastid and total system mass
Amount obtains work plastid critical frequency ratio than the relation between work plastid critical frequency ratio；
Step 7, according to the critical frequency that is obtained than difference and work plastid critical frequency ratio, further obtain as received basis body frequency
Than；
Step 8, judge obtained as received basis body frequency than with work plastid and total system mass mass ratio whether described in step 3
Kinetic parameter it is interval in, if so, then performing step 9, otherwise, return and perform step 4；
Step 9, according to the actual requirements, in vibration isolation plastid frequency than carrying out value in span, and by itself and obtained as received basis
Body frequency than, work plastid and total system mass mass ratio substitute into combine twin-engined drives double-mass vibrating system kinetic simulation
In type, all parameters of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, including as received basis weight, vibration isolation plastid matter are obtained
Amount, vibrating spring rigidity, isolation spring rigidity, working amplitude, eccentric rotor eccentric throw and eccentric block quality；
Step 10, the parameter according to obtained twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, build twin-engined drives double mass from same
Walk vibrational system.
2. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
In the kinetic model for setting up twin-engined drives double-mass vibrating system described in step 1 is comprised the following steps that：
Step 1-1, the total kinetic energy T for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein, J01Represent the rotary inertia of twin-engined drives double-mass vibrating the first eccentric rotor of system；J02Represent that twin-engined drives are double
The rotary inertia of the eccentric rotor of mass vibrating system second；J1Represent rotary inertia of the work plastid around itself barycenter；J2Represent every
Shake rotary inertia of the plastid around itself barycenter；Represent the vibration velocity of i-th of eccentric rotor；Represent the matter of work plastid
The vibration velocity of the heart；Represent the vibration velocity of the barycenter of vibration isolation plastid；Represent the phase angle of i-th of eccentric rotor, i=
1,2；m1Represent as received basis weight；m2Represent vibration isolation plastid quality；m0iThe quality of i-th of eccentric rotor is represented, ψ represents work
The angle of the rotation around center of mass of plastid and vibration isolation plastid；
Step 1-2, the total potential energy U for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
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Wherein, XK2jRepresent the deformation vector of four isolation springs being connected with vibration isolation plastid, j=1,2,3,4；XKiRepresent work
The deformation vector of two slinky springs between plastid and vibration isolation plastid, i=1,2；XK3Represent in the horizontal direction as y-axis, vertical side
The deformation vector for the spring that y directions are connected with vibration isolation plastid into the coordinate system for x-axis；K represents the stiffness matrix of vibrating spring,
K2Represent stiffness matrix, the K of x directions isolation spring3Represent the stiffness matrix of y directions isolation spring；
Step 1-3, the total power consumption D for determining twin-engined drives double-mass vibrating system；
Formula is as follows：
Wherein,Represent the vibration velocity of four isolation springs being connected with vibration isolation plastid, j=1,2,3,4；Represent work
The vibration velocity of two slinky springs between plastid and vibration isolation plastid, i=1,2；Represent in the horizontal direction as y-axis, vertical side
The vibration velocity for the spring that y directions are connected with vibration isolation plastid into the coordinate system for x-axis；F represent vibrating spring damping matrix,
F2Represent damping matrix, the F of x directions isolation spring3Represent the damping matrix of y directions isolation spring；fdiRepresent that twin-engined drives are double
The damped coefficient of motor in mass vibrating system；
Step 1-4, bring the total kinetic energy of the twin-engined drives double-mass vibrating system of acquisition, total potential energy and total power consumption into Lagrange
In equation, the kinetic model of twin-engined drives double-mass vibrating system is obtained；
Formula is as follows：
Wherein,
M1For the gross mass of twin-engined drives double-mass vibrating system, M1=m01+m02+m1+m2；
M2Represent the gross mass of vibration isolation plastid, M2=m01+m02+m2；
JΨRepresent total rotary inertia of twin-engined drives double-mass vibrating system, JΨ=J1+J2+(m01+m02)(r2+l0 2), in formula, l0
Represent the barycenter of eccentric rotor to the distance of twin-engined drives double-mass vibrating system barycenter；R represents eccentric the half of two eccentric rotors
Footpath；
fψ=fxl2+f2x1ly1 2+f2x 2ly0 2+f2y1lx1 2, in formula, fxRepresent damping of the vibrating spring in x directions；f2x1Represent x directions
Damping of the isolation spring in x directions；f2x2Represent damping of the y direction isolation springs in x directions；L represents to vibrate bullet during system quiescence
The original of spring is long；ly0Represent the distance of the isolation spring in y directions and the tie point of vibration isolation plastid to vibration isolation plastid barycenter；ly1Represent
The tie point of isolation spring and vibration isolation plastid is to vibration isolation plastid barycenter in the distance in y directions, lx1Represent isolation spring and vibration isolation matter
The tie point of body to vibration isolation plastid barycenter x directions distance；
f2xy=f2x2ly0；
f2x=f2x1+f2x2；
f2y=f2y1+f2y2, in formula, f2y1Represent the damping of the isolation spring in y directions in x directions；f2y2Represent the vibration isolation bullet in y directions
Damping of the spring in y directions；
k2x=k2x1+k2x2, in formula, k2x1Represent the rigidity of the isolation spring in x directions in x directions；k2x2Represent the vibration isolation bullet in y directions
Rigidity of the spring in x directions；
kψ=kxl2+k2x1ly1 2+k2x2ly0 2+k2y1lx1 2, in formula, kxRepresent rigidity of the vibrating spring in x directions；k2y1Represent x directions
Isolation spring y directions rigidity；
k2xy=k2x2ly0；
k2y=k2y1+k2y2, in formula, k2y1Represent the rigidity of the isolation spring in y directions in x directions；K in formula2y2Represent y directions every
Shake rigidity of the spring in y directions；
kyRepresent rigidity of the vibrating spring in y directions；
Te1Represent the electromagnetic torque of motor 1；
fd1Represent the damped coefficient of motor 1；
Te2Represent the electromagnetic torque of motor 2；
fd2Represent the damped coefficient of motor 2；
β represents the angle between two eccentric rotors rotation center and the line and x-axis of the plastid barycenter of inactive state two；
Step 1-5, the kinetic model of solution twin-engined drives double-mass vibrating system steady-state response solution；
Steady-state response solution x, y1、y2Formula it is as follows：
Wherein,
rm=m01/m1；
η=m02/m01；
Represent the average phase of vibrator；
α represents the half of two eccentric rotor phase differences；
C in formula1x=η2nx 2(1-nψ 2), d1x=2 η2ξψnψnx 2, η2Represent work plastid and total system mass
Mass ratio, a1=(1-nx 2)(1-nψ 2)+4ξxξψnxnψ(τ1-1)-τ2, b1=2 ξxnx(1-2τ3-nψ 2)+2ξψnψ(1-nx 2)；τ1=f2xy 2/f2xfψ, τ2=k2xy 2/k2xkψ, τ3=f2xyk2xy/f2xkψ, nx
=ωm/ωx, nψ=ωm/ωψ,ωmRepresent the mean angular velocity of vibrator；
In formula, c2x=r1η2nx 2, d2x=2r2η2ξψnψnx 2, r1=k2xyl0/kψ；
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In formula, c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2, r2=f2xyl0/fψ；
In formula, c2ψ=r3η2nx 2(1-nx 2), d2ψ=2r4η2ξψnψnx 2, r3=k2xl0 2/kψ,
r4=f2xl0 2/fψ；
In formula, a=(1-ny1 2)(1-ny2 2)-ny2(η1ny2+4ξy1ξy2ny1), η1=m1/M2；η2=m1/
M1；ny1Represent as received basis body frequency ratio, ny1=ωm/ωy1,ny2Represent vibration isolation plastid frequency ratio, ny2=ωm/ωy2,B=2 ξy1ny1(1-η1ny2 2-ny2 2)+2ξy2ny2(1-ny1 2)；cy1=η1ny2 2；dy1=dy2=2 η1ξy1ny1ny2 2；
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In formula, cy2=η1ny2 2(1-ny1 2)；
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c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2,c2ψ=r3η2nx 2(1-
nx 2), d2ψ=2r4η2ξψnψnx 2。
3. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
In two vibrators realizes synchronous condition, synchronization in the determination twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM described in step 2-1
Condition is：It is poor that broad sense dynamic symmetry torque is more than motor electromagnetism surplus torque；
Specific formula is as follows：
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Wherein,
Represent the average value of two eccentric rotor phase differences in the monocycle；
ΔTRRepresent the difference of the remaining electromagnetic torque of two eccentric sons；
TuThe kinetic energy of expression standard eccentric rotor；
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ], in formula,c1ψ=r1η2nx 2, d1ψ=2r2η2ξψnψnx 2,c2ψ=r3η2nx 2(1-nx 2),
d2ψ=2r4η2ξψnψnx 2；
Due toTherefore realize that self synchronous condition is：
System broad sense dynamic symmetry torque is poor more than motor electromagnetism surplus torque, that is, obtains WccCos α ＞ 0, obtain following public
Formula：
Wcc=-η rm[μ1xcosγ1x-μ2xsin(γ2x-β)-μy2cosγy2+μ1ψsin(γ1ψ+β)+μ2ψcosγ2ψ] cos α ＞ 0 (7).
4. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
In the stable operation condition of two vibrators in the determination twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM described in step 2-2 is stable
Service condition is：
H0＞ 0, H1＞ 0, H3＞ 0, H ＞ 0；
Wherein,
In formula, synchronous fortune is represented
Under the conditions of row, two eccentric rotor phase angle average values；
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H1=ρ1κ2+ρ2κ1-WccWcs, in formula,ke01Represent electricity
Machine 1 is ω in angular speedmWhen angular speed stiffness coefficient；ke02It is ω in angular speed to represent motor 2mWhen angular speed rigidity system
Number, ωm0Represent under the conditions of running simultaneously, the synchronous angular velocity of two eccentric rotors, m0The amount of the being eccentric rotor represented is identical in quality
When eccentric rotor quality, i.e.,：m01=m02=m0；
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H=4H1H2-H0H3；
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5. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
In the kinetic parameter that the acquisition described in step 3 can meet synchronism stability operation is interval, and specific method is：
Under the conditions of synchronous operation, in the range of 0~1, set as received basis body frequency than value, according to the double matter of twin-engined drives
The actual conditions of body SELF-SYNCHRONOUS VIBRATION SYSTEM, determine the value of the mass ratio of work plastid and total system mass, so as to obtain same
During step operation vibration isolation plastid frequency than parameter it is interval；In the range of 4~6, set vibration isolation plastid frequency than value, according to
The actual conditions of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, determine that the mass ratio of work plastid and total system mass takes
Value, thus obtain as received basis body frequency during synchronous operation than parameter it is interval；Work the mass ratio of plastid and total system mass
Span is 0~1；
Under the conditions of stable operation, in the range of 0~1, set as received basis body frequency than value, according to the double matter of twin-engined drives
The actual conditions of body SELF-SYNCHRONOUS VIBRATION SYSTEM, determine the value of the mass ratio of work plastid and total system mass, so as to obtain steady
When running surely vibration isolation plastid frequency than parameter it is interval；In the range of 4~6, set vibration isolation plastid frequency than value, according to
The actual conditions of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM, determine that the mass ratio of work plastid and total system mass takes
Value, thus obtain as received basis body frequency during stable operation than parameter it is interval；Work the mass ratio of plastid and total system mass
Span is 0~1；
The span obtained under the conditions of synchronous operation and the span obtained under the conditions of stable operation are taken into common factor, same
Walk under conditions of stable operation, with reference to the kinetic model of twin-engined drives double-mass vibrating system, obtain twin-engined drives double mass
The span of the key parameter of SELF-SYNCHRONOUS VIBRATION SYSTEM.
6. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
Shake material coefficient, and shaken material system according to above-mentioned ginseng in the ginseng of, the determination twin-engined drives double-mass vibrating system described in step 4
Number, is obtained quality of the critical frequency than the span of difference, work plastid and total system mass than span, is inserted using linear
Value method, the ginseng for drawing twin-engined drives double-mass vibrating system is shaken the isopleth of material coefficient, and ordinate is work plastid and system
The mass ratio of gross mass, abscissa is that critical frequency ratio is poor.
7. the parameter determination method of twin-engined drives double mass SELF-SYNCHRONOUS VIBRATION SYSTEM according to claim 1, its feature exists
In when the determination as received basis body amplitude amplification degree described in step 5 is maximum, corresponding critical frequency ratio difference and work plastid are with being
The mass ratio for gross mass of uniting, using linear interpolation method, the isopleth of drawing plastid amplitude amplification degree, ordinate is as received basis
The mass ratio of body and total system mass, abscissa is that critical frequency ratio is poor.
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| CN106547946A (en) * | 2016-09-30 | 2017-03-29 | 北京建筑大学 | Non-linear vibrating system synchronizing characteristicss analysis method and device that shock electric machine drives |
| CN106503307B (en) * | 2016-09-30 | 2019-09-13 | 北京建筑大学 | The synchronizing characteristics analysis method and device of the vibrational system of Double -motor excitation driving |
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| CN107330156A (en) * | 2017-06-07 | 2017-11-07 | 北京建筑大学 | Double -motor excitation synchronizing characteristics simulating analysis based on frequency catching |
| CN107194105A (en) * | 2017-06-07 | 2017-09-22 | 北京建筑大学 | A kind of Double -motor excitation synchronizing characteristics analysis method based on frequency catching |
| CN109307500B (en) * | 2018-11-02 | 2020-06-26 | 常州大学 | Method for calculating eccentricity of motor shaft based on vibration speed peak value |
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| CN109499695B (en) * | 2018-12-17 | 2019-11-08 | 东北大学 | A kind of multimachine drives the parameter determination method of large-scale high-frequency vibration grinding machine |
| CN109794329B (en) * | 2018-12-17 | 2019-12-17 | 东北大学 | Parameter determination method for double-mass four-machine driven circular motion high-frequency vibration mill |
| CN109635453B (en) * | 2018-12-17 | 2023-05-12 | 东北大学 | Design parameter determining method of double-machine-driven high-frequency vibration ball mill |
| CN109701697B (en) * | 2018-12-17 | 2020-03-24 | 东北大学 | Four-machine-driven double-mass vibration impact crusher and parameter determination method thereof |
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