基于动态特性的大型减速齿轮装置试验系统的振动控制研究

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Sep．2013机 床 与 液 压Hydromechatronics Engineering Vo1．41 No．18DOI：10．3969／j．issn．1001-3881．2013．18．032Vibration Analysis of a Large-size Reduction GearboxTest System Based on Its Dynamic CharacteristicsCHEN Xuehua ，FENG Jian． Chongqing Radio& TV University，Chongqing 400052，China；2．Technical center of CN ower Gearbox Co，Ltd，Chongqing 402263，China1．IntroductionAbstract：In testing process of a large—size reduction gearbox lest system．its vibration and noiseare the key parameters used to estimate its performance，which are caused by the vibration ofthe test gearbox and the support saddles．In this paper，a new simulation method is proposed toanalyze vibrations of a large-size reduction gearbox test system，which consists of a finite ele—ment(FE)method and a torsional vibration analysis method．In this method，the natural fre-quencies，the mode shape and the vibration response of the large—size reduction gearbox testsystem are studied using the FE method，and the factors of the resonance of the system are dis-cussed．Furthermore，a torsional vibration model of the large-size reduction gearbox test systemis proposed to study the torsional vibration of the gearbox test system．Also，the factors of thetorsionaI vibration are discussed．The simulation results show that the vibration analysis and theoptimization design of the gearbox test system should be considered at the beginning of its designstage．The results also show that the proposed method can be used to improve the vibration andnoise level of a large-size reduction gearbox test system.

Key words：Large-size reduction gearbox test system ，FE method，dynamic characteristics，tor-sional vibrationA large—size reduction gearbox test system is oneof key experimental equipment used for test the per—formance of a large—-size reduction gearbox in the in-·dustry．Its vibration and noise characteristics are veryimportant for predicting the performance of the testgearbox．The current design method of the gearboxtest system is based on a static design method，whichonly considers the experimental functions and cannotdescribe its dynamic characteristics．When a staticdesign method is used，its vibration problem may befound when the test system is completed，and it isdifficult to analyze the reasons of the vibration prob—Received：2013—06—22FENG Jian．E—mail：fengjia0508###sohu．cornlem for a whole test system．In addition．it is dificultto control the vibration and noise of the large·-size re—-duction gearbox using an experimental method be—cause its structure is very complex．Hence it is veryimportant to investigate the dynamic characteristics ofthe large—size reduction gearbox，which can providesome guidance for its vibration and noise contro1．Alot of research works have been done in this area.

For instance，Richards and Pines[1]proposeda passive method to reduce transmitted vibrationcaused by the gear mesh contact dynamics base onthe dynamic characteristics of the periodic structuralcomponents．Guan et a1．[2]developed a compara-tive analysis method for the dynamic perform ances offour potentialy feasible actuation concepts used tocontrol the housing vibration in a gearbox test sys—tern．Cheon et a1．[3]presented a new approach tocontrol the vibration of a simple spur gear pair withCHEN Xuehua，et al：Vibration Analysis of a Large—size Reduction GearboxTest System Based oi1 Its Dynamic Characteristics 159phasing，which is based on controling the vibrationin mesh stiffness by adding another pair of gears withhalf-pith phasing．Zhang et a1．[4]proposed a dy-namic model coupling bending and torsional vibrationof a gear pair system to study the vibration of the gearpair system caused by the mass unbalance．Li et a1.

r 5]developed a three degree of freedom numericalmodel of a spur gear pair system using a lumped massmethod．They provided an active control method tocontrol the gear meshing point vibration caused by thetransmission error based on the numerical results.

Some other researchers also studied the different vi—bration control method for various gearboxes as shownin Refs．『6—8]．However，the above research worksonly focused on the vibration control of a simple gearpair system． There are few research works on thelarge．size reduction gearbox test system．Hence it isnecessary to investigate the dynamic characteristics ofthe large-size reduction gearbox test system f0r its Vi-bration and noise contro1.

In this paper．a new simulation method is devel—oped to analyze the vibration of a large—size reductiongearbox test system，which consists of a FE methodand a torsional analysis method．Tl1e natural frequen.

eies，the mode shapes and the harmonic response ofthe gearbox test system are studied using the FEmethod． The torsional vibration of the gearbox testsystem is analyzed by a proposed torsional mode1.

The simulation results show that the proposed methodmay be used to the vibration and noise analysis andcontrol of a large．size test gearbox test system.

2．Finite Element analysis2．1．Analysis of natural frequencies and modeshapesA large-size reduction gearbox test system isstudied in this section，which consists of two motors，shaft couplings，a speed—increasing gearbox，a dyna-mometer，and other support saddles as shown in Fig.

1．Since the whole test system has a complex struc—ture，it is dificult to obtain the natural frequenciesand the model shapes of the large—-size reduction gear·-box test system using an experimental method．Hencea FE method is utilized to calculate its natural fre—quencies and mode shapes using commercial FE soft—ware．Here．because the technica1 know．how of thenew large—size reduction gearbox test system，the re—suits from the speed—increasing gearbox is given inthis study．But it has slight efects on the quality ofthis paper because the analysis method of the othercomponent of the gearbox test system is similar．Thefirst ten natural frequencies of the speed—increasinggearbox is show in Tab．1，and one typical mbde atthe eighth natural frequency of the speed-increasinggearbox is shown in Fig．2.

Fig．1 Schematic of a large—size reductiongearbox test systemTab．1 FIrst ten natural frequencies of the speed-increasing gearbox with its support saddlesTab．2 plots the rotational frequencies of the in—put shaft of the speed—increasing gearbox． Compari—sons analysis between the natural frequencies of thespeed-increasing gearbox and the rotational frequen-cies of the input shaft of the speed—increasing gearboxshow that the resonance vibration may be causedwhen the input shaft speed is at 1 020 r／min(4L and)and 1 060 r／min( ， and 5f,)．The modeshape at the eighth natural frequency shows the reso‘nance vibration at the bottom of the speed—increasingbox when the input shaft speed is at 1 060 r／min(5 =90 Hz)．The simulation results show that thevibration problem can be predicted at the beginningof the design stage of the large—size reduction gearboxtest system using the proposed method，which cannotbe predicted using the traditional static design meth—od.

Hydromechatronics EngineeringTab．2 Rotational frequencies( )of the input shaftof the speed—increasing gearbox(in Hz)NODAL SOLUTlONSTEP=lSUB —RFREQ-90．077USUM (^V0)DSYS=0DMXn7 579SMN-0．002 276SMX=7 5790002276 l 686 3 37 5．053 6．7374 2Il 5．895 7,579Fig．2 Mode shape at the eighth natural frequencyof the speed·increasing gearbox2．2．Analysis of the vibration responseTo analysis the vibration response of the large-size reduction gearbox test system caused by the of-center rotational components， a harmonic responsemethod iS presented using the FE method．A refer—ence point at the input shaft of the large·-size reduc-tion gearbox test system iS chosen to study its vibra.

tion response as shown in Fig．3．The vibration re.

sponse along the Z direction is discussed as given inTab．3 and Fig．4．which iS chosen to be tested inpractice．Fig．4 plots that peaks occur at the 1 00Hz，1 10 Hz，150 Hz，160 Hz，175 Hz，190 Hz，and 2O 1 Hz．It can be seen that the vibration level ofthe large-size reduction gearbox test system is largewhen the rotational frequencies of its shaft are closedto those above frequencies。which should be considered during its design process.

Fig．3 Reference point at the input shaft of the large-sizereduction gearbox test systemTab．3 Amplitude of the vibration response of thereference point 76961 at the input shaft of the large·size reduction gearbox test system6．4：星 4．0：O40E．20 20 4O 60 80 10O 120 140 160 l 8O 200f／HzFig．4 Vibration response of the referencepoint al0ng the Z direction3．Torsional Vibration Analysis3．1．Torsional vibration modelAs another key vibration problem of the large—size gearbOX。torsional vibration of the rotational tom.

ponnets should be considered too． Furhermore。thetorsional vibration contol iS one of the major mthod ofthe vibration and noise contol methods for the large.

size reduction gearbox test system． According toeshematic of the large·size reduction gearbox test sys·—tem ．a seven degree of freedom torsional vibrationmodel of the rotaional component system of the large·size gearbox test sytem is proposed as shown inFig．5jlMj4r 2Shaft ClutchcouplingFig．5 A rotational vibration model of the relation componentsystem of the large-size reduction gearbox test systemCHEN Xuehua，et al：Vibration Analysis of a Large—size Reduction GearboxTest System Based on Its Dynamic CharacteristicsThe propose mdoel incorparates the folowing re-alistic assumptions and considerations.

1)Each rotational component is considered as arigid plate，which are connected by massless roation.

al springs.

2)The component with a large rotational inertiais assumed as an inertia element．and the componentwith a small rotational jnertia is assumed as a elasticelement.

3)A1l the excitation moments are applied on theinertia elements.

4)The mass of the shafts between two mass ele.

ments are shared by the two mass elements connectedby the shafts.

5)The rotational inertia and the stifnesses ofthe shafts with different rotational speeds are changedinto equivalent rotational inertia and equivalent stif-nesses.

6)The deformation of the gears are ignored dur-ing their meshing process．The rotational inertias ofthe gears are applied on the lumped mass on the cen.

ter 1ine of the master gears based on their transmis.

sion ratios.

7)The deformations of the components withlarge stiffness are ignored.

。

Based on the above assumptions and considera.

tions，the equations of motion for eache element arederived as follows.

Jl 01+K1(0l一02)M (1)1in whic+ ( 一0s)一Kl(0l一 )+C1 =003+K3(03—04)一K2(02—03)=004+ (04—05)一Ks(03—04)+C：( 一 )=005+ (05—06)一／q(04—05)一C2(04—05)+C3(05一 6)=006一 (05—06)一C3( 5一 )=M2(2)(3)(4)(5)(6)h J1， ，Js，J4，J5 and J6 are the rotationalinertia of each inertia element，Kl，K2，K3，／q andare the stiffnesses of each elastic element，Cl，C2and C3 are the damping ratios，0l，02，03，04，05and 06 are the rotational displacement vectors，andM1 and M2 are the driving moment and load，respec-tively.

3．2．Analysis of the Torsional Vibration3．2．1．Analysis of themode shapenatural Frequencies and theLet[C]=0 and[M]=0，Eqs．(1)．(6)be.

COm e[I，]{0}+[ ]{0}=0 (7)The general solution of Eq．(7)is{0}={A}8in(tot+ ) (8)Then the eigensolutions of Eq．(7)is{A}=[．，] [K]{A} (9)Based on Eq．(9)，the natural frequencies and themode shapes of the rotational component system canbe obtained．which are listed in Tab．4.

Tab．4 Natural frequencies and mode shapes of the rotational component system3．2．2．Forced responseIn this study，Matlab／Simulink module in Mat.

1ab software is used to solve the Eq．(1)一(6)。Theloads are based on the experimental date．which aregiven in Tab．5.

The excitation moment is assumed to be causedby the motor，which is given byM=M0+0．04M0sin(tot) (10)where Mo is the constant moment of the motor；t isthe time，and w is the fluctuation frequency of themotor，which is described as162 Hydromechatronics Engineering=
2竹 × Nin which N is thefluctuation of the一 4％ to 4％ .

(11) 4
． Conclusionsinput speed of the motor，and themoment of the motor ranges fromTab．5 Experimental load parameters3．2．3．Results and discussionsFig．6(a)and(b)show the rotational speed ofthe output shaft of the test gearbox when the inputspeed of the motor is 565 rpm and the frequency ofthe load is 9．58 Hz．It can be seen that a beat phe—nomenon is observed in the time domain rotationalspeed of the output shaft of the test gearbox．The en—velope frequency of the beat phenomenon is closed to1 Hz and it is a periodic signa1． According to theEq．(10)，the input speed of the motor 1 rangesfrom 563 rpm to 565 r／min．The simulation resultsshow that a large vibration level of the test gearboxmay be caused when the input speed of the large—sizereduction gearbox test system is about 565±1 r／min.

575 5575 O574 5574 0573 5573 0572 5575 0574 5574 0573 5573 O572 5150 152 154 15 6 15．8 16．0 16．2 l6．4 166 168 170t／s(b)Fig．6 Time domain rotational speed of the output shaftof the test gearbox with the input speed of 565 rpmA new simulation method is proposed to controlthe vibration of a large-size reduction gearbox testsystem．It consists of a finite element(FE)methodand a torsional vibration analysis method．The naturalfrequencies，the mode shape and dynamic responseof the key components of the large—size reductiongearbox test system are calculated by the FE method.

Also．a torsional vibration model of the large—size re.

duction gearbox test system is proposed to investigatethe torsional vibration of the gearbox test system．Thesimulation results show that the vibration analysis andthe optimization design of the large—size reductiongearbox test system should be investigated at the be—ginning of its design stage，which can improve its vi—bration and noise leve1．The results also show that theproposed model can be used to analyze and optimizethe vibration characteristics of a large—size reductiongearbox test system.

References：[1] Richards D，Pines D J．Passive reduction of gear meshv—ibration using aperiodic drive shaft[J]．Journal of Sound’ and Vibration，2003，264：317—342.

[2] Yuan H G，Li M F，Lim T C，et a1．Comparative analy—sis of actuator concepts for activegear pair vibration con—trol[J]．Journal of Sound and Vibration，2004，269：273—294.

[3] Cheonng G J．Numerical study on reducing the vibrationof spur gear pairs with phasing[J]．Journal of Sound andVibration，2010，329：3915—3927.

[4] Kun Zhang，Yingsheng Li，Bailin Zheng．Numerical a—nalysis of the efects of the mass unbalance on the vibra—tion of a gear transmission system[J]．Journal of Engi—neering for Thermal Energy and Power，2010，25(3)：312—316[5] Yinong Li，Zhenhua Fan，Guiyang Li，et a1．Activevibtaiton control and simulation of gear transmission sys—tem based on fuzzy algorithm{J 1．Journal of Jiansu Uni—versity：Natural Science Edition，2011，32(3)：281— 286.

[6] Guan Y H，Lim T C，Jr W S S．Experimental study onactive Vibration control a gearbox system[J]．Journal ofSound and Vibration，2005，282(3—5)：713—733.

[7] Tuma J R．Gearbox noise and vibration prediction andcontrol[J]．International Journal of Acoustics and Viba—tion，2009，14(2)：1—11.

[8] Liang J，Wang D F，Jiang Y S，et a1．The Noise sourceidentification and noise control of automobile gearbox[J]．Noise and Vibration Control，2006，3：67—69.

一一口一鲁．JJ／p ds一日口0【]B】0加9 8 7 6 ㈨4 3 2 O 一一口一宕 ．JJ／p0uq∞ q0【I旦0CHEN Xuehua，et al：Vibration Analysis of a Large—size Reduction GearboxTest System Based on Its Dynamic Characteristics 1 63基于动态特性的大型减速齿轮装置试验系统的振动控制研究陈雪华 ，冯 健(1．重庆广播电视大学，重庆 400021；2．重庆齿轮箱有限责任公司技术中心，重庆 402263)摘要：在大型减速齿轮装置的试验过程中，振动与噪声是试验过程的控制关键因素，其受到被测产品、陪试产品及试验台架振动指标影响。针对这个问题，采用有限元方法，对试验台系统进行 了模态分析和谐响应分析，研究了试验系统各部套的模态频率和振型，分析 了发生共振的可能性，并建立了试验台系统的扭转振动模型，对试验 台的扭转振动特性进行了研究，分析了可能引起试验台系统发生扭转振动的因素，找到了试验 台系统振动控制的最佳方案。研究表明：在设计初期就应用仿真技术对大型减速齿轮装置试验 系统的振动进行分析与优化设计，能解决大型减速齿轮装置在实际运转中的振动与噪音问题，从而加快大型减速齿轮装置试验和开发的进程。

关键词：减速齿轮装置；振动控制；动态特性；试验系统中图分类号：TH13(Continued on 152 page)基于遗传算法的液压压上系统的PID优化仿真分析徐秀芬新乡学院 机电工程学院，河南 新乡 453003摘要：为了进一步提高冷轧平整机液压压上系统的动态特性 ，提 出了新的 PID参数设计方法：遗传算法．利用Matlab／sIMuLINK软件求解优化模型，实现了PID控制参数自整定。对优化得到的PID参数和 z—N整定 PID控制效果进行比较，结果表明：遗传算法PID控制优于 z—N整定 PID控制，验证了遗传算法的可行性和实用性。

关键词：遗传算法；PID；液压压上系统；优化；仿真中图分类号：TP18