CN107469702A - A kind of nonlinear chaotic vibration rod - Google Patents
A kind of nonlinear chaotic vibration rod Download PDFInfo
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- CN107469702A CN107469702A CN201710657775.XA CN201710657775A CN107469702A CN 107469702 A CN107469702 A CN 107469702A CN 201710657775 A CN201710657775 A CN 201710657775A CN 107469702 A CN107469702 A CN 107469702A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
- B01F—MIXING, e.g. DISSOLVING, EMULSIFYING OR DISPERSING
- B01F31/00—Mixers with shaking, oscillating, or vibrating mechanisms
- B01F31/44—Mixers with shaking, oscillating, or vibrating mechanisms with stirrers performing an oscillatory, vibratory or shaking movement
- B01F31/449—Stirrers constructions
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Abstract
The present invention relates to a kind of nonlinear chaotic vibration rod, and it belongs to the nonlinear chaotic vibration rod that the industries such as a kind of building, food, medicine use.The present invention mainly solve existing vibrating head existing for vibrational excitation be difficult to reach material region, leakiness of vibrating and the uneven technical problem of stirring comprehensively.The technical solution adopted by the present invention is：A kind of nonlinear chaotic vibration rod, including motor, driving snake and chaos caput, wherein：Described motor and the drive end of driving snake connect, rotating shaft is provided with the inner chamber of the chaos caput, one end of the rotating shaft is fixed on the opening of chaos caput inner chamber, the other end of the rotating shaft is provided with eccentric block, the end of the driving snake couples with the fixing end of rotating shaft, L section curve of the chaos caput inwall from rotating shaft fixing end to eccentric block working chamber along axis section is one section of parabolic segment, first set L sections curve as：G (x)=acos (bx)+d, then verify whether the L sections curve meets that eccentric block reaches the critical condition of chaotic motion.
Description
Technical field
The present invention relates to a kind of nonlinear chaotic vibration rod, it belong to the industries such as a kind of building, food, medicine use it is non-
Linear chaotic vibration rod.
Background technology
Vibrating head in present society using extensive, therefore, the selection of vibrating head whether rationally, stirring extent it is whether uniform
Directly affect the quality of product.Vibrating head is a kind of mechanization tamping tool, by vibrating the bubble excluded in material, is eliminated
Gap.But in actual use, the vibration rail of existing vibrating head is mostly that circle or regular figure, vibrational excitation are difficult to arrive comprehensively
Up to material region, bubble is caused to discharge completely, leakiness of vibrating, stirring is uneven, has had a strong impact on stirring of vibrating
Quality.
Macroscopical nonlinear system that chaos refers to determine shown under certain condition it is uncertain, similar with
The motion of machine.Using the method for machinery, theoretical by non-linear chaotic dynamics introduces vibrating head technology, is allowed and shaken by chaos
Dynamic rod is activated to each region up to material to be mixed so that stirring is especially uniform, and Vibratory Mixing quality greatly improves.
The content of the invention
It is difficult to reach material region comprehensively present invention aim to address vibrational excitation existing for existing vibrating head, vibrates not
A kind of technical problem closely knit and that stirring is uneven, there is provided nonlinear chaotic vibration rod.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of nonlinear chaotic vibration rod, including motor, driving snake and chaos caput, wherein：Described motor
It is connected with the drive end of driving snake, horizontal direction is provided with rotating shaft in the inner chamber of the chaos caput, and one end of the rotating shaft leads to
The opening that bearing is fixed on chaos caput inner chamber is crossed, the other end of the rotating shaft is provided with eccentric block, the end of the driving snake
End couples with the fixing end of rotating shaft, L of the chaos caput inwall from rotating shaft fixing end to eccentric block working chamber along axis section
Section curve is the parabolic segment of one section of small curvature, first set the L sections curve as：G (x)=acos (bx)+d, in formula, g (x) is turns
The contact position of axle and chaos caput inwall is to the distance of chaos caput axis, the contact position of x-rotating shaft and chaos caput inwall
Put to the distance of fixing end；Verify whether the L sections curve meets that eccentric block reaches the critical condition of chaotic motion again, if L sections are bent
Line meets the critical condition of chaotic motion, then the curve is that the chaos caput inwall works from rotating shaft fixing end to eccentric block
Cross section curve of the chamber along axis, otherwise, it is necessary to separately set curve, repeated authentication step, until meeting that chaotic motion occurs for eccentric block
Critical condition.
Further, whether the checking L sections curve meets that the step of eccentric block reaches chaotic motion critical condition is as follows：
(1) rigidity of rotating shaft is calculated
In formula：The amplitude of y-rotating shaft free end；a1- Taylor series expansion constant term；b1- Taylor series expansion is once
Term coefficient；c1The secondary term coefficient of-Taylor series expansion；
(2) nonlinear dynamic equation of rotating shaft free end eccentric block is established
In formula：P=me ω2, m-eccentric block quality；E-eccentric throw；ω-angular speed,N-rotating speed, c-resistance
Buddhist nun's coefficient；
(1) formula is brought into (2) formula to obtain
In formula：ε is one a small amount of,
(3) α is judged by Melnikov functions1、α2、α3Whether meet that eccentric block reaches the critical condition of chaotic motion
In formula：η1The imaginary part of-the first limit,
η2The imaginary part of-the second limit,
(4) dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks is combined
Whether system occurs chaos
The eccentric distance e and damped coefficient c that are determined by critical condition formula (3) are brought into (2-1) formula, obtained power
System is
Phase plane trajectory figure, timeamplitude map and Poincare are drawn according to the dynamical system using matlab softwares to map
Whether figure, send out with reference to the dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks
Raw chaos；The L sections curve is verified if chaos occurs to produce the cross section curve of chaotic motion.
The present invention uses above-mentioned technical proposal, makes chaos caput inwall curve that the critical bar of chaotic motion occur according to rotating shaft
Part designs, and in high-speed rotation, eccentric block is reached chaotic motion state, under the exciting effect of eccentric block, from
And barred body is driven to produce nonlinear chaotic vibration.Because non-linear chaotic motion never repeats in finite region inner orbit, utilize
Motion state is extremely complex and the characteristics of ergodic, solves usual vibrating poker and is difficult to reach material region comprehensively, vibrates
The leakiness technical problem uneven with stirring, compared with background technology, the present invention, which has, significantly improves Vibratory Mixing effect
Fruit and the advantages of improving mixing quality.
Brief description of the drawings
Fig. 1 is the structural representation of the present invention；
Fig. 2 is the structural representation of the chaos caput of nonlinear chaotic vibration rod of the present invention；
Fig. 3 is the phase plane trajectory figure of eccentric block of the present invention；
Fig. 4 is the timeamplitude map of eccentric block of the present invention；
Fig. 5 is the Poincare mapping graphs of eccentric block of the present invention.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and examples.
As depicted in figs. 1 and 2, a kind of nonlinear chaotic vibration rod in the present embodiment, including motor 1, driving snake 2
With chaos caput 7, wherein：Described motor 1 is connected with the drive end of driving snake 2, the inner chamber reclaimed water of the chaos caput 7
The opening of the inner chamber of chaos caput 7, the rotating shaft 4 square are fixed on by bearing 3 to one end provided with rotating shaft 4, the rotating shaft 4
The other end be provided with eccentric block 6, the end of the driving snake 2 couples with the fixing end of rotating shaft 4, the chaos caput inwall 5
L section curve of 6 working chambers along axis section is the parabolic segment of one section of small curvature from rotating shaft fixing end to eccentric block, is first set described
L section curves are：G (x)=acos (bx)+d, in formula, g (x) is rotating shaft 4 and the contact position of chaos caput inwall 5 to chaos rod
The distance of first 7 axis, the contact position of x-rotating shaft 4 and chaos caput inwall 5 from fixing end with a distance from, a, b, d are constant and ﹥
0；Verify whether the L sections curve meets that eccentric block 6 reaches the critical condition of chaotic motion again, if L section curves meet chaotic motion
Critical condition, then the curve is that the chaos caput inwall 5 section along axis of 6 working chambers from fixing end to eccentric block is bent
Line, otherwise, it is necessary to separately set curve, repeated authentication step, until meeting that the critical condition of chaotic motion occurs for eccentric block 6.
Whether the checking L sections curve meets that the step of eccentric block 6 reaches chaotic motion critical condition is as follows：
(1) rigidity of rotating shaft 4 is calculated
In formula：The amplitude of y-rotating shaft free end；a1- Taylor series expansion constant term；b1- Taylor series expansion is once
Term coefficient；c1The secondary term coefficient of-Taylor series expansion；
(2) nonlinear dynamic equation of the free end eccentric block of rotating shaft 4 is established
In formula：P=me ω2, m-eccentric block quality；E-eccentric throw；ω-angular speed,N-rotating speed, c-
Damped coefficient；
(1) formula is brought into (2) formula to obtain
In formula：ε is one a small amount of,
(3) α is judged by Melnikov functions1、α2、α3Whether meet that eccentric block reaches the critical condition of chaotic motion
In formula：η1The imaginary part of-the first limit,
η2The imaginary part of-the second limit,
(4) dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks is combined
Whether system occurs chaos
The eccentric distance e and damped coefficient c that are determined by critical condition formula (3) are brought into (2-1) formula, obtained power
System is
Phase plane trajectory figure, timeamplitude map and Poincare are drawn according to the dynamical system using matlab softwares to map
Whether figure, send out with reference to the dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks
Raw chaos；The L sections curve is verified if chaos occurs to produce the cross section curve of chaotic motion.
The present invention implementation verification process be：
In the vibrating head course of work, the inwall of chaos caput plays a part of support, thus chaos caput inwall is from rotating shaft 4
Section L section curve g (x) of the free end to eccentric block working chamber along axis should be smaller than flexure curvature of a curve, now sets L section curvilinear equations
For g (x)=acos (bx)+d (a, b, d are constant), then verified according to calculating.
(1) rigidity of L section curve g (x) and rotating shaft 4 under the support of the inwall of chaos caput 7 is determined
Y=g (x)=acos (bx)+d is substituted into (1-1) formula, and obtained by Taylor series expansion：
Will(1-2) formula of substitution, is obtained：
Order
：
It is set to meet following condition：
In the vibrating head course of work, the inwall of caput plays a part of supporting rotating shaft, thus curve g (x) should be than without branch
Rotating shaft flexure curvature of a curve is small during support, therefore according to the deflection curve equation without rotating shaft when supporting
Condition in (1-4) takes a=0.001, b=0.5, d=-0.0016.That is g (x)=0.001cos (0.5x) -0.0016.
By a, b, d value substitute into a respectively1, b1And c1, obtain：
By a1, b1, and c1Value substitute into (1) formula, obtain：
(2) nonlinear dynamic equation of the free end eccentric block of rotating shaft 4 is established
In formula：C-damped coefficient；P-exciting force, P=me ω2；E-eccentric throw；ω-angular speed；N-rotating speed；
Take eccentric block quality m=0.1kg, exciting force P=50N, rotating speed n=2840r/min.
(1-5) formula substitution (2) formula is obtained into the nonlinear dynamic equation of eccentric block is：
Wherein
(3) α is judged by Melnikov functions1、α2、α3Whether meet that eccentric block 6 reaches the critical condition of chaotic motion
Defining Melnikov functions is：
Wherein
Then
It is computed：
In formula：
The real part of two limits of ζ-integrand,
η1The imaginary part of-the first limit,
η2The imaginary part of-the second limit,
When Melnikov functions have zero point, the perturbed system considered has the chaos under Smale horseshoe meanings, i.e. M
(τ)=0：
To make equation (3-4) have root, it is necessary to make sin ω (t+ τ)≤1, and due toTherefore, eccentric block is obtained to reach
Chaotic motion α1、α2、α3The critical condition must being fulfilled for：
By α1、α2And α3Value bring into (3) formula, by (3-5) formula understand exist e and c cause (3) formula set up, i.e. α1、α2With
α3Value can meet eccentric block occur chaotic motion critical condition.
(4) dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determinations eccentric block 6 is combined
Whether system occurs chaos.
E=0.005653m, c=0.1 are taken according to the critical condition that chaos occurs, are brought into (2-1) formula, what is obtained is dynamic
Force system is：
Matlab softwares are utilized according to the dynamical system, it is y=-0.0006 to take primary condition,Draw
Whether phase plane trajectory figure, timeamplitude map and Poincare mapping graphs, the dynamical system of synthetic determination eccentric block occur chaos.
The Poincare mapping graphs shown in timeamplitude map and Fig. 5 shown in phase plane trajectory figure as shown in Figure 3, Fig. 4
As can be seen that time-history curves have no rule, phase plane trajectory is even more disorderly and unsystematic just like inverted 8, Poincare mappings, with reference to
This group of parameter has fallen in the chaotic region that Melnikov functions give, and therefore, dynamical system corresponding to determining type (2-1) has been enter into
Chaos state, rotating shaft are issued to chaotic motion in the support of rod shell inwall.Therefore determine g (x)=0.001cos (0.5x) -0.0016
For the present embodiment chaos caput inwall (5) from rotating shaft fixing end to eccentric block L section curve of (6) working chamber along axis section.
Claims (2)
1. a kind of nonlinear chaotic vibration rod, including motor (1), driving snake (2) and chaos caput (7), it is characterised in that：
Described motor (1) is connected with the drive end of driving snake (2), and horizontal direction is provided with the inner chamber of the chaos caput (7)
Rotating shaft (4), one end of the rotating shaft (4) are fixed on the opening of chaos caput (7) inner chamber, the rotating shaft (4) by bearing (3)
The other end be provided with eccentric block (6), the end of the driving snake (2) couples with the fixing end of rotating shaft (4), the chaos caput
Inwall (5) the L sections curve of (6) working chamber along axis section from rotating shaft fixing end to eccentric block is the parabola of one section of small curvature
Section, first set the L sections curve as：G (x)=a cos (bx)+d, in formula, g (x) is rotating shaft (4) and chaos caput inwall (5)
Contact position is to the distance of chaos caput (7) axis, the contact position of x-rotating shaft (4) and chaos caput inwall (5) to fixing end
Distance；Verify whether the L sections curve meets that eccentric block (6) reaches the critical condition of chaotic motion again, if L sections curve meets to mix
The critical condition of ignorant motion, then the curve is chaos caput inwall (5) (6) working chamber from rotating shaft fixing end to eccentric block
Along the cross section curve of axis, otherwise, it is necessary to separately set curve, repeated authentication step, until meeting that chaotic motion occurs for eccentric block (6)
Critical condition.
A kind of 2. nonlinear chaotic vibration rod according to claim 1, it is characterised in that：Whether the checking L sections curve
Meet that the step of eccentric block (6) reaches chaotic motion critical condition is as follows：
(1) rigidity of rotating shaft (4) is calculated
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(3) α is judged by Melnikov functions1、α2、α3Whether meet that eccentric block reaches the critical condition of chaotic motion
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η1The imaginary part of-the first limit,
η2The imaginary part of-the second limit,
(4) it is with reference to the dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks
No generation chaos
The eccentric distance e and damped coefficient c that are determined by critical condition formula (3) are brought into (2-1) formula, obtained dynamical system
For
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Whether mixed with reference to the dynamical system of phase plane trajectory figure, timeamplitude map and Poincare mapping graph synthetic determination eccentric blocks
It is ignorant；The L sections curve is verified if chaos occurs to produce the cross section curve of chaotic motion.
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| CN201710657775.XA Active CN107469702B (en) | 2017-08-03 | 2017-08-03 | Nonlinear chaotic vibrating spear |
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| CN113164950A (en) * | 2018-11-05 | 2021-07-23 | Hycor生物医学有限责任公司 | Apparatus and method for mixing fluids or media by vibrating a pipette using a non-concentric mass |
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