CN103267087A - Simple method for restraining harmonic-waves of single-gear transmission system - Google Patents
Simple method for restraining harmonic-waves of single-gear transmission system Download PDFInfo
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- CN103267087A CN103267087A CN2013102064709A CN201310206470A CN103267087A CN 103267087 A CN103267087 A CN 103267087A CN 2013102064709 A CN2013102064709 A CN 2013102064709A CN 201310206470 A CN201310206470 A CN 201310206470A CN 103267087 A CN103267087 A CN 103267087A
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Abstract
The invention provides a simple method for restraining harmonic-waves of a single-gear transmission system. According to the method, a model of the single-spur-gear system is built for gear side clearances, time-varying meshing rigidity, comprehensive meshing errors and other factors, conditions for generating the chaos harmonic waves are given, a simplest self-adaptation controller is utilized for achieving rapid restraint of the harmonic waves of the single-gear transmission system, and correctness of the conclusion is verified through testing.
Description
Technical field
The present invention relates to a kind of single gear transmission system harmonic wave and suppress simple and easy method, belong to mechanical engineering field.
Background technique
Harmonic vibration is the distinctive a kind of form of nonlinear dynamics system because the backlash in the gear train, engagement damping, the time become non-linear factor such as rigidity, cause system to produce very strong nonlinear vibration.In certain parameter region, system shows as the chaos harmonic vibration, and harmonic vibration is harmful to service behaviour and the reliability of transmission system.Therefore,, the chaotic vibration in the gear train assembly is needed effective, feasible control.People have proposed the measure of a lot of inhibition harmonic vibrations from different angles, have obtained a lot of achievements in research.In the single gear transmission system, obtained a lot of useful laboratory datas and rule, the measure of different inhibition harmonic vibrations has been proposed.And the adaptive approach of single gear transmission system inhibition harmonic wave is rarely had report.The present invention adopts simple controller, can realize the quick inhibition of single gear transmission system harmonic vibration.
The present invention adopts simple controller, can realize the quick inhibition of single gear transmission system harmonic vibration.
Summary of the invention
The invention provides a kind of single gear transmission system harmonic wave and suppress simple and easy method, it is characterized in that: at first in backlash, time, become factors such as mesh stiffness and comprehensive meshing error and set up single-stage straight-tooth gear transmission system model this method, provide the condition that it produces the chaos harmonic wave, and utilize simple controllers to realize that single gear transmission system harmonic wave suppresses fast, verifies the correctness of conclusion by experiment.
The technological scheme concrete steps that the present invention proposes comprise:
The single gear transmission system is only considered the torsional vibration of gear for the single gear transmission system as shown in Figure 1, adopts concentrated quality method to set up gear pair analysis on Torsional Vibration model.Wherein,
Engagement damping for gear pair;
With
It is rotary inertia main, driven gear;
With
It is Base radius main, driven gear;
For gear pair the time become mesh stiffness;
With
It is torsional vibration displacement main, driven gear;
With
For acting on the torque on master, the driven gear;
Be gear engagement resultant error.The kinetic equations that can obtain the single gear transmission system is:
Gear clearance is 2b, and the backlash nonlinearity function is
The model dimensionless differential equation is
Wherein,
Be the dimensionless Gear Meshing Stiffness,
Be the dimensionless damping,
Be dimensionless frequency,
Be gear-driven external excitation amplitude;
Be gear-driven equivalent external excitation.
Single gear transmission system harmonic wave suppresses adaptive controller
Wherein,
For the adaptive updates rule also can be expressed as
Utilize above-mentioned adaptive controller can realize that single gear transmission system harmonic wave suppresses fast.
Technique effect of the present invention: above-mentioned a kind of single gear transmission system harmonic wave that the present invention proposes suppresses technological scheme, this method at first provides the dynamic model of single gear transmission system, carry out the dimensionless conversion then, and utilize an adaptive controller the simplest to realize the quick inhibition of single gear transmission system harmonic wave, verify the correctness of conclusion by experiment.
Description of drawings
Fig. 1 is single gear transmission system model.
Fig. 2 be before embodiment's single gear transmission system suppresses harmonic component (
).
Fig. 3 be after embodiment's single gear transmission system suppresses harmonic component (
).
Fig. 4 is embodiment's single gear transmission system adaptive updates rule
Response.
Embodiment
Embodiment:
The single gear transmission system is only considered the torsional vibration of gear for the single gear transmission system as shown in Figure 1, adopts concentrated quality method to set up gear pair analysis on Torsional Vibration model.Wherein,
Engagement damping for gear pair;
With
It is rotary inertia main, driven gear;
With
It is Base radius main, driven gear;
For gear pair the time become mesh stiffness;
With
It is torsional vibration displacement main, driven gear;
With
For acting on the torque on master, the driven gear;
Be gear engagement resultant error.The kinetic equations that can obtain the single gear transmission system is:
(1)
Gear clearance is 2b, and the backlash nonlinearity function is
The model dimensionless differential equation is
Wherein,
Be the dimensionless Gear Meshing Stiffness,
Be the dimensionless damping,
Be dimensionless frequency,
Be gear-driven external excitation amplitude;
Be gear-driven equivalent external excitation.
Single gear transmission system harmonic wave suppresses adaptive controller
Wherein,
For the adaptive updates rule also can be expressed as
Utilize above-mentioned adaptive controller can realize that single gear transmission system harmonic wave suppresses fast.
Before controlled, work as parameter in the single gear transmission system
Gear clearance is
The time, can obtain the harmonic component of single gear transmission system
As shown in Figure 2.
Utilize the simplest and easy above-mentioned adaptive controller, when
The time, the harmonic component after can being inhibited as shown in Figure 3, its adaptive updates rule
Response as shown in Figure 4.
From the contrast of Fig. 2, Fig. 3 as can be seen, this kind said method can effectively suppress the harmonic component of single gear transmission system.
Harmonic component output result after the inhibition of this single gear transmission system is good.Use the result to show that this method has the good restraining degree for noise level and the harmonic wave of single gear transmission system, compare with similar single gear transmission system, can obtain better transmission effect.
Claims (3)
1. a single gear transmission system harmonic wave suppresses simple and easy method, it is characterized in that: at first in backlash, time, become factors such as mesh stiffness and comprehensive meshing error and set up single-stage straight-tooth gear transmission system model this method, provide the condition that it produces the chaos harmonic wave, and utilize simple controllers to realize that single gear transmission system harmonic wave suppresses fast, verifies the correctness of conclusion by experiment.
2. method according to claim 1 is characterized in that: only consider the torsional vibration of gear for the single gear transmission system, adopt concentrated quality method to set up gear pair analysis on Torsional Vibration model; Wherein,
Engagement damping for gear pair;
With
It is rotary inertia main, driven gear;
With
It is Base radius main, driven gear;
For gear pair the time become mesh stiffness;
With
It is torsional vibration displacement main, driven gear;
With
For acting on the torque on master, the driven gear;
Be gear engagement resultant error, the kinetic equations that can obtain the single gear transmission system is:
Gear clearance is 2b, and the backlash nonlinearity function is
Method according to claim 1 is characterized in that: the model dimensionless differential equation is
Wherein,
Be the dimensionless Gear Meshing Stiffness,
Be the dimensionless damping,
Be dimensionless frequency,
Be gear-driven external excitation amplitude;
Be gear-driven equivalent external excitation.
3. method according to claim 1 is characterized in that: single gear transmission system harmonic wave suppresses adaptive controller and is
Wherein,
For the adaptive updates rule also can be expressed as
Utilize above-mentioned adaptive controller can realize that single gear transmission system harmonic wave suppresses fast.
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|---|---|---|---|
| CN2013102064709A CN103267087A (en) | 2013-05-30 | 2013-05-30 | Simple method for restraining harmonic-waves of single-gear transmission system |
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| CN2013102064709A CN103267087A (en) | 2013-05-30 | 2013-05-30 | Simple method for restraining harmonic-waves of single-gear transmission system |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103470744A (en) * | 2013-09-26 | 2013-12-25 | 中国航天科工信息技术研究院 | Control method and system for eliminating influence of transmission gear gap |
| CN103486239A (en) * | 2013-09-26 | 2014-01-01 | 中国航天科工信息技术研究院 | Control method and system for eliminating transmission gear clearance influence |
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| JPH04152454A (en) * | 1990-10-17 | 1992-05-26 | Fujitsu Ltd | Limit sufficing solution sequential calculation method for linear limit condition |
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| CN101702188A (en) * | 2009-09-28 | 2010-05-05 | 南京理工大学 | Method for evaluating state of hydraulic machine based on multilayer fuzzy matching algorithm |
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2013
- 2013-05-30 CN CN2013102064709A patent/CN103267087A/en active Pending
Patent Citations (3)
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|---|---|---|---|---|
| JPH04152454A (en) * | 1990-10-17 | 1992-05-26 | Fujitsu Ltd | Limit sufficing solution sequential calculation method for linear limit condition |
| US6792584B1 (en) * | 2001-10-30 | 2004-09-14 | Lsi Logic Corporation | System and method for designing an integrated circuit |
| CN101702188A (en) * | 2009-09-28 | 2010-05-05 | 南京理工大学 | Method for evaluating state of hydraulic machine based on multilayer fuzzy matching algorithm |
Non-Patent Citations (2)
| Title |
|---|
| 王少夫: "电力系统混沌振荡分析及其自适应控制", 《中国优秀硕士学位论文全文数据库（工程科学Ⅱ辑）》, 15 December 2012 (2012-12-15) * |
| 王靖岳等: "单级齿轮传动系统混沌的非反馈法抑制", 《机械传动》, vol. 36, no. 12, 31 December 2012 (2012-12-31), pages 12 - 15 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103470744A (en) * | 2013-09-26 | 2013-12-25 | 中国航天科工信息技术研究院 | Control method and system for eliminating influence of transmission gear gap |
| CN103486239A (en) * | 2013-09-26 | 2014-01-01 | 中国航天科工信息技术研究院 | Control method and system for eliminating transmission gear clearance influence |
| CN103470744B (en) * | 2013-09-26 | 2016-07-20 | 中国航天科工信息技术研究院 | A kind of control method eliminating influence of transmission gear gap and system |
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Application publication date: 20130828 |