vibration characteristic analysis

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2011 International Conference on Electronic & Mechanical Engineering and Information Technolog y

Vibration Characteristic Analysis of Spot-Welding Robot Based onADAMS/Vibration1 2H ai tao Luo, *Y uw ang L iu , ^o ng gu an g W an g/W ei j ia Zhou

1. State Key Laboratory of Robotics , Shenyang Inst i tute of Automation, CAS, Shenyang 110016, P .R. China2.Graduate School of the Chinese Academy of Sciences , Beij ing 1 00049, P .R. C hina

{luohaitao, l iuyuwang, hgwang, zhouweij ia}@sia .cnAbstractAiming to improving the performance of high-power,heavy-load, high-speed and high-precision robots, this paperproposes a simulation method for vibration analysis based onvirtual prototyping technology. In ADAMS/Vibration, we firstestablish the rigid-flexible coupling vibration system of a spot-welding robot, then solve the natural frequencies and modalshapes of the system, and finally calculate the frequencyresponse under certain forced vibration. In order to buildvibration system, the principle and simulation process ofvibration analysis are given by inputting sine sweep signal onend effector. With the help of the getting frequency response,we can avoid the failure of damage due to the resonancevibration of the system and create the conditions for theoptimal design and reliability research of a spot-welding robot.

Keywords-Vibration analysis; ADAM S; Spot-welding robot;Rigid-flexible coupling;I. I N T R O D U C T I O N

Spot-welding robot , combination of robotics technologyand welding technique, is high-power , heavy- load, highspeed, high-precision, f lexible-operation, large-workspaceand so on. I t is widely used in vehicles, ships and otherengineering filed at the present stage. And the highperformance is more and more needed. How ever , the quali tyof vibration characteristic is an important factor to improveits performa nce [1]. Th erefore, how to limit the vibrationeffect so as to improve its anti-vibration performance hasbecome a key factor to the design.

In the process of spot-welding, there are lots of vibrationsources on the robot, which caused by the low installationaccuracy, t ransmiss ion gap and uninter rupted impact loadsand so on. And the vibrat ions are common nonlinear andstrong coupling. If the vibrations pass to the machine, theywill seriously affect the robot's dynamic characteristic, theworking life and performance of the robot. Especially whenthe vibration frequency of exciting force is equal or close tothe natural frequency of the robot, and then resonan ce willhappen [2-5], Which can seriously affect the quality oftransmission system and result in key part 's fatigue failure.Therefore, vibration analysis has become an important andnon-ignored indicator to evaluate the vibration characteristicof spot-welding robot.

In recent years, scholars from different country havedone many valuable researches on the vibrat ioncharacteristic of industry robot. Jinwook and park putforward to the first order stiffness and vibration analysismethod based on geometr ic method and ins t i tut ions of the

stiffness and deformation [6]. Han m ade the test modalanalysis of the robot by using hammer multi-point excitationmeth od [7]. Kris.K calculated the vibration characteristics oflittle degree of freedom robot using linear method [8]. YSakural analyzed the vibration of cylinder block under f ir ingcondition s [9] . Zha ng studied the dynam ics characteristic ofhigh speed machine tool [10] . These theory analyses ab oveare mainly based on linear method, and ignore the impact offlexible body. However, the cost of experiment method isover high. So, we combine the advantages of these methodsand give a more intuitive and accurate method.This paper mainly considers the impact and vibrat ioncaused by the exciting force on the end effector of spot-welding robot. In ADAMS/Vibration, we first establish therigid-flexible coupling vibration system of a spot-weldingrobot, then solve the natural frequencies and modal shapes ofthe system, and finally calculate the frequency responseunder certain forced vibration. In order to calculate thevibration response of the end measuring point in thefrequency dom ain, the external exciting force is used as animpact load. Through vibrat ion s imulat ion analysis , we get

the natural frequency and mode shapes which are negative tothe system, and obtain frequency response curve of the robot.This provides scientif ic proof for the restraint of vibrationand the improvem ent of the robot ' s per formance.II . V I B R A T I O N A N A L Y S I S P R I N C I P L E O F R I G I D - F L E X I B L E

C O U P L I N G S Y S T E MFor simple vibration system, the inherent characteristic ofthe system mainly refers to the natural frequency. Forcomplex systems, the inherent characteristics included thedifferent order natural frequencies, mode shapes, dampingand so on [11]. Th e calculation and determin ation oninherent characteristics of the system, which can avoid

system resonance at work on the one hand, on the other hand,it can also lay the foundation for further dynamic analysis.A. Vibration theory basis

Differential equation of motion of single degree offreedom, second-order and damped linear mass-springsystem is as follows:mx + ex + kx = F 0 sin co t, (1)

w her e , mmass;c damping coeff ic ient ;

978-l-61284-088-8/ll/$26.00 2011 IEEE 691 12-14 August, 2011


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k spring stiffness;x displacement ;

F0amplitude of harm onic excitation force;Solution of equation under harmonic excitation:

FJkVa-A2)2+(2a)2

2 l (2 )q> = arctanl-A 2A = co I co n is the frequency ratio, C, = c I cn is the dampingratio.

Differential equations for damped vibration systemexpressed by complex number are as follows:mx + ex + kx = Faelc (3 )

Using the relationship of exponential and trigonometricfunctions, the frequency response function can be obtainedas follows:

H(a)) = 1e~FJk l-A2+i2CJl (4 )The most practical mechanical systems and mechanicalstructure are continuous and non-uniform elastic body. To beable to analyze, they are always equivalent to finite degree offreedom system under meeting accuracy requirements.Equations of motion of discrete multi-freedom system are:

[m]{x} + [c]{i} + [k]{x} = {F0(t)}9 (5)here, [m], [k], [c] is respectively the system mass matrix,damping matrix and stiffness matrix; {x} , {^0(0} lsrespectively displacement response and excitation of thesystem. So system frequency response function matrix is:

H U((D) H 12 (CD) H^ico)H 2l(co) H 22{coi) H 2j(co) |[H(w)] =Ha(co) H l2(co) HU{G>)

(6 )

here, FL^co) represents frequency response functionbetween the excitation point / and j . When i = j , itrepresents the origin frequency response function;when i j , it represents cross-point frequency responsefunction.B. Representation of flexible-body

In ADAMS, flexible body is generated by using acombination method of finite element analysis and modalanalysis. The discretization result of the finite element is notdirectly imported to A D A M S , but firstly generated a modalneutral file (.mnf file) by modal analysis in A N S Y S . The file

includes lots of information about mass, center of mass,inertia, frequency and mode shape of flexible-body [12-13].By calculating the deformation in dynamic simulationprocess and the forces on connecting nodes using modalsuperposit ion method, we can introduce flexible-body todynamics model, and improve the simulation accuracy of themechanical system.In ADAMS/Vibration module, flexible body is addedconstraint, exerted force and measured the dynamiccharacteristics by using the coordinate point [14]. Shown inFig . l , the posit ion vector of flexible body at any node can beexpressed as:

= X+B A{Sp+ Up)> (7 )where , GBA transformation matrix of coordinate system B

relative to coordinate system G ;sp posi t ion of point P under coordinate system

B when body is non-deformed;u direction vector of point P' on deformed

body with respect to point P on non-deformed body;xposition vector of object coordinate system B

under base coordinate system;Among them, u =(& pq , O represents modal matrix

sub-block corresponding to the node translational degrees offreedom. Th e Velocity of node P is:= [J-U{SP+UP)BGBA%]4: (8 )

where, tilde indicates the posit ion vector is non-symmetricalmatrix; matrix B is defined as first-order derivative ofEulerian angle relative to t ime or angular velocity transitionmatrix. So the kinetic and potential energy can be expressed

T = \-\pvTvd V = hTM(Z)%. (9)

v = vg(4)+-4T K4. (io)Establish the differential equation of motion of flexiblebody using Lagrange multipliers method:

M+M%- 1 dM S + KZ+f+D + A = fi(ll)here, K modal st iffness matrix;

D modal damping matr ix;/ g eneralized gravity;Q generalized external force;

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X L agrange mult ipl ier of constraint equation;

Figure 1. Moving schematic of flexible-body on node PIn this study, the vibration response value is obtained byusing corresponding marker ' s measurement on outputchannels .

III. V I B R A T I O N M O D E L O F S P O T - W E L D I N G R O B O TBased on the theory above, we establish the structural

model in ADAMS, and create the vibrat ion system model inADAMS/Vibrat ion. With the combination of the two models ,we can smoothly run the simulation analysis.A. Structural model

The structural model of spot welding-robot is as shown inFig.2.

1-base; 2-waist; 3-cylinder block; 4-cylinder rod; 5-upper armflexible body; 6-forearm flexible body; 7-wrist; 8-end effector

Figure 2. Rigid-flexible coupling model of Spot-welding robotIn the finite element analysis software ANSYS, we makeupper arm and forearm of spot welding-robot become

flexible-body, and then in AD AM S, read the modal neu tralfile generated in ANSYS, respectively replace the rigidupper arm and forearm of mult i- r igid-body dynamics modelwith flexible body, so the rigid-flexible coupling dynamicsmodel of spot-welding robot is generatedWhere, adding a f ixed pair between the base and earthand six revolute pairs on rotational joints. In addition, arevolute pair is added between balance cylinder rod andupper arm and a translational pair is added between cylinderblock and cylinder rod. In order to prevent the generation ofredundant constraints, an inline pair need to be built betweencylinder block and lug. To simulate the role of balancecylinder, a spring should be added between cylinder block

and cylinder rod and corresponding parameters must bespecified. The spring stiffness is \tfNlm , damping is10* N/(m / s2) and preload value is 15681 N .

B. System ModelVibration test system mainly consists of excitation source,vibration model, input channels, and output channels, asshown in Fig.3 . External excitation is regarded as the signalsource of vibration test, the input channels are used to definethe position and direction of vibration input and outputchannels are used to measure the vibration response [15].Because the deformation of some components is not toolarge under external force, but little effect on the weldingprecision, so these parts of the robot can be considered asrigid bodies. In addition, the flexible body of model has agreat influence to simulation speed, so in order to improvesimulat ion process , only the more imp or tant components canwe transformed to flexible body, while other elementsremain r igid body.From the structure of spot-welding robot, we can seeupper arm and forearm are its major parts, which have agreat influence to the welding accuracy of end effector. Sowe mainly considered part 5 and part 6 as f lexible body toform a rigid-flexible coupling system of entire model.

Figure 3. Vibration system modelIn order to effectively simulate the vibration impactcaused by the welding load, we selected the sine sweepsignal as the external excitation. As a result of largeexcitation power and high signal-to-noise ratio of sine sweep,we can obtain more accurate measurements . S ine sweepsignal have the steady amplitude and increasing frequency,when the sine signal acted on the model, we only provide the

initial amplitude and phase angle. The expression of sinesweep signal in time domain is:f(t) = F[cos(o)t + 0) + js'm(a)t + 6) ], (12)

here, f(t) is the time domain form of forced signal onfrequency domain equation; F is the amplitude of excitationforce; co is the circular frequency; 6 is the phase angle.

IV . D Y N A M I C S S I M U L A T I O N A N A L Y S I S O F S P O T -W E L D I N G R O B O T

Free vibration analysis mainly calculates the naturalfrequency and solves the each order 's mod e shape of system.ADAMS/Vibrat ion transformed the s imulat ion model into a

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linear matrix by using Laplace transform in a state point, andcalculated the natural frequency and dam ping ratio of systemthrough eigenvalues.A. Free vibration

The real and imaginary coordinates of eigenvalues are asshown in Fig.4. Table I shows the top 10 naturalfrequencies, damping ratios and corresponding mode shapesdescription of spot-welding robot system.

Figure 4. System modes

TABLE I. NATURAL FREQUENCY, DAMPING RATIO AND VIBRATIONM O D E OF S Y S TEM

Order12

345678910

frequency (Hz)0.00E+0000.00E+0000.00E+0001.59E-0013.42E-0017.68E-0012.58E+0013.76E+0016.17E+0011.15E+002

Dampingratio0.00E+0000.00E+0000.00E+0001.00E+0001.00E+0001.00E+0001.72E-0021.15E-0023.14E-0024.45E-002

Mode shapeno significantvibrationno significantvibrationno significant

vibrationno significantvibrationno significantvibrationno significantvibrationside-to-sidevibrationup and downvibrationface-to-backvariationtorsionalvibrationAs can be seen from the table above, the top 6 shapemodes only show slight vibration, and the vibration began tointensify from the 7th-order. In practical work of spot-welding robot, modal tests should be completed combinedwith damping sheet attached to suppress the excitation ofcorresponding order's mode and ensure the welding accuracyof end effector.

B. Forced vibrationApplied the excited force on end position of the robot andanalyzed with the analysis method of sine sweep, the valueof amplitude is 2000 N , the direction is vertical, and theinitial phase is zero. Response of end measuring point is

given by using displacement response value of X, Y, Z andspatial synthesis direction, thus the graph of frequen cyresponse can be created.When the robot vibration system is excited by externalfore, frequency response curve of 0-200Hz can be obtainedin post-processing module of ADAMS. The response curveof X direction is as shown in Fig.5 (a). The frequen cyresponse of end measuring point in X direction is 25Hz andthe maximum displacement response amplitude is 0.017mm.The response curve of Y direction is as shown in Fig.5 (b).The frequency response of end measuring point in Ydirection is 37Hz and the maximum displacement responseamplitude is 0.085mm. The response curve of Z direction isas shown in Fig.5 (c). The frequency response of endmeasuring point in Z direction is 25Hz and the maximumdisplacement response amplitude is 0.115mm. The responsecurve of spatial synthesis direction is as shown in Fig.6 (d).

The frequency response of end measuring point in thisdirection is also 25Hz and the maximum displacementresponse amplitude is 0.088mm.

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Figure 5. Frequency response of marker point in every directionFrom the graphs above, we can see the maximumfrequency response happened on the 25H z in the Z direction,when the robot subjected to 2000 7V excitation force. Highfrequency components have little effect on the system

vibration, it can be ignored. Through the vibration analysis offrequency response, we can reasonably improve anti-vibration design of the robot by changing the relevantparameters of virtual prototype, such as center of mass,spring stiffness and damping etc.V. CONCLUSION

This paper deals with simulation analysis of vibrationcharacteristics in ADAMS, a practical and effective methodwas put forward to improve the dynamic performance ofspot-welding robot. In order to create rigid-flexible couplingsystem of entire model, we considered upper arm 5 andforearm 6 as flexible body in ADAMS/Flex module. Then inADAMS/Vibration module, we obtained the naturalfrequencies and mode shapes under free vibration, and gotthe displacement response of end measuring point under theexternal excitation force. Simulation analysis has drawn thefollowing conclusions:

1) All eigenvalues have the negative real-parts underfree vibration analysis, which indicate that the vibrationsystem is stable. From the beginning of the 7th-orderfrequency 25.8Hz, the system appeared obvious vibration.2) Within the range of 0-200Hz, when welding plierssubjected to an excitation force w ith the frequency 25Hz andamplitude 2000 N , the displacement response of endmeasuring point is maximal in vertical direction, and the

maximum displacement value is 0.1125mm.3) High frequen cy components (61 Hz above) have littleeffect on the system vibration, which can be ignored.ACKNOWLEDGMENT

This work was supported by the National Science andTechnology Major Project on High Grade CNC MachineTool and Fundamental Manufacturing Equipment underGrant 2009ZX04013.REFERENCES

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