a new concept of active vibration controller through a...

A new concept of active vibration controller through a fric-tion interface driven by piezos

H. Bouaziz 1,2,3, N. Peyret 2, M.S. Abbes 2, G. Chevallier 1, M. Haddar 3

1 FEMTO-ST Institute UMR 6174, CNRS-UFC-ENSMM-UTBM, 24 Chemin de l’Epitaphe, F-25000 Be-sanon, Francee-mail: [email protected]

2 QUARTZ, SUPMECA-PARIS, 3 Rue Fernand Hainaut, F-93400 Saint-Ouen, France

3 LA2MP, ENI-SFAX, Route de Soukra km 4 Sfax, 3038 Sfax, Tunisie

AbstractFor extreme temperatures (< −20oC and > 100oC), Coulomb friction might provide more structural damp-ing than polymers. Nevertheless, there is a consensus to say that these friction-damping values are oftenlower than 5%. Moreover friction damping is amplitude-dependent. Therefore, engineers have to tune thenormal load in order to get the maximum damping for the average vibration level. In this paper we mentionfirst the limitations of the ordinary passive friction-dampers. Then we propose an active friction damper.This device aims to drive the normal load or the tightening inside the bolted joints, in real time. Firstly, thisallows to obtain optimal damping based on the measured vibration level. Secondly, the active friction damperallows to modify the global rigidity of the structure and thus its eigenfrequencies to avoid the critical fre-quencies of excitation. The paper shows and justify the design of an active friction damper and demonstrateits efficiency on a simple structure.

1 Introduction

Many devices are made to emphasize in friction induced damping, see [1–11]. Moreover some devicesare designed with an asset of a screw control [10, 11]. We inspired of these devises. We adopt the benchconfiguration that avoid the coupling between the vibration motion and the normal stresses on the one hand.On the other hand, we adopt the configuration that has a larger joint interface with the same screw. The mostinnovative aim of our device, is the energy pumping from one part of the structure to the added part. Anotheraim of our devise is to command the global rigidity to avoid the critical frequencies. Thus in this paper wewill talk about active control for friction dampers. The active control is assured by the clamping force of ascrew. The role of the active bolt is to control the stiffness of the structure and the friction induced damping.The control of the active bolt can be done with the piezoelectric stack actuators to apply an adjustable normalforce exerted by a bolt. In the first part of this paper, we mention the ordinary passive friction-dampers limits. In the second part, we present our bench which contains the added friction damper. The third part is devotedto the experimental results presentation and the comments. Finally, we summarize this paper.

2 Limitation of the ordinary passive friction-dampers

Friction dampers are recommended for their high energy-dissipation potential, their low cost and the facilityof their manipulation. Adding friction dampers is mainly discussed for civil engineering structure under

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earthquake [12–14].

The dynamic response of a structure which we add a friction damper depends on the vibration amplitude(first limitation). According to the relative movement there is three states of friction: stick, total slip andmicroslip. In [12], the authors treated the three cases and they showed that there is optimum slip force inthe damper for which the peak displacement of the structure attains the minimum value. A large slip mayreduce the structural displacement response but not the acceleration response and the situation is reversedif a small slip force is used (second limitation) [17]. The same result it is shown in [15] where the authorspresented a method which can be used to find the optimum sliding friction force in a bladed disk assembly.But unfortunately this optimum value is different for each resonance frequency (third limitation).

In [16], the author emphasized on the difficult on the friction dampers sizing (fourth limitation). In fact theyshowed that the frequency domain simulations undersized the optimum damper weight.

Adding a friction damper to a mechanical structure is a new aspect even if the dissipation of energy in theassembly structure is widely discussed . In [18], the authors proposed an add-on joint in order to change itsglobal stiffness and therefore to change its eigenfrequencies depending on the external load frequencies.

Adding active friction damper device can surpass the limitations presented above.

3 Conception of the active friction damper

Figure 1: The geometry of our bench

The ultimate objective of the desired bench is to absorb the vibrations of the chassis and shells in the auto-motive and aerospace fields. Commercially, the device has to be light, easy to plug, energy efficient, and,of course, it has to give satisfaction in term of vibration damping. Thus the experimental design goal is toabsorb the low frequency vibrations specifically in the interval [20,300] Hz.

To control the parameters of such a device, it is necessary to go through an academic device that meets therequirements listed above. Our device will include an active bolt that can have two patches ”PICMA ChipActuators” reference ”PD080.30”.

So after changing shapes, masse, dimension and thickness, we ended with the geometry presented in figure 1.This devices is composed from two stages. The principal structure is a free-free beam and it will be attachedto an upper stage. We used the sandwich configuration of the upper stage to maximise the disspated energyby the friction damper. To reduce the device size, we include the mass of the screws, patches and theirsupport to the secondary mass.

One of the two bolts of the upper stage is fully tightened and the other is the controled one. The command ofthe tightening force controls the rigidity and the friction of the secondary stage. The aim of the added upperstage is to eliminate the vibration of the extremity of the main beam (see figure 2). In the design phase, the

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sensors geometries and masses are added in order to have the masses distribution presented in table 1. Theratio of the masses is about 8%.

Excitation

Fully tightening Variable tightening The part of the

structure where

the vibrations

must be canceled

Figure 2: A simplified schema representing the experimental bench

Length (mm) Width (mm) Thickness (mm) Mass (g)Main beam 500 30 2 264,5Upper stage 108 15 0,4 22,5

Table 1: Device description

A modal and frequency response analyses are performed using Ansys Workbench. Despite the analysis arelimited in the linear formulation, it allows the prediction of the natural frequencies and the energy pumpingphenomena bandwidth. The pumping energy direction should be from the extremity of the main beam to theupper stage. We can use the deformed shape of the 4th and 5th mode or the 13th and 14th mode. As wecan see in table 2, in the 4th and 13th mode, the energy vibration is located in the upper stage while in the5th and the 14th mode the vibration energy is located in the primary stage. Thus, it is hoped that changingthe clamping force of the active bolt, switch between these consecutive modes. The frequency responsesimulation will be presented in the next section to compare the numerical and the experimental results.

Table 2: The deformed shape at the 4th mode 228, 65Hz, 5th mode 236, 36Hz, 13th mode 625, 77Hz and14th mode 702, 39Hz

4 Experimental results

For our experiment we use a shaker, an amplifier and a laptop to control the experience and record the signalsof the sensors. We used three accelerometers type Dytran 3214A fixed to main beam, another type Bruel andKjaer-4517 fixed to the upper stage and a force sensor type Endevco-2311-100 fixed between the shaker andthe structure. The experience is as follows;

• We excite the structure at a constant frequency for a duration that allows the structure to stabilize.

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Figure 3: The experimental structure fixed on the shaker with the abbreviation of the sensors

• We swept the frequency from 10 Hz to 1 kHz with a Logarithmic step.

• We record and process the collected data with Matlab.

Coupling the structure with the shaker, results a non-constant excitation amplitude. Without a servo unitfor the excitation force; the excitation depend of the frequency. By comparing the critical frequencies andthe average amplitude of the simulation and the experimental resalts we confirmed that there is an almostcoincidence for the bending modes especially in the lowest frequency. The differences are mainlly for theupper stage. These differences are due to the nonlinearities of the friction and the large displacement in thisstage.

Several excitation varying from 0.4 N to 8 N are made. We will comment the result of the higher excitationwith some preservation. For these excitation levels a plastic deformation of the blades can occur at theresonance frequencies.

Figure 4: Effect of the excitation force on the main beam for a tightening torque of 0.2Nm


Figure 5: Tightening torque effect on the acceleration of the upper stage with an excitation force of 2 N

In the figure 4 we showed that there is a minimal excitation force to have influence on the critical vibrationfrequencies. For the lower excitations (for the excitation swept between 0.4N and 4N), the critical vibrationfrequencies are independent of the excitation force and still located in the linear domain.

Below the 500Hz frequency, the tightening force has no effects on the vibration amplitude of the extremityof the main beam (the point of visualization). However, above the 500Hz the evolution of the pics ampli-tude evolves nonlinearly for the higher excitation and changes linearly for the lower excitation. Unlike thevibration of the extremity of the main beam, the acceleration of the upper stage is affected for the wholefrequency bandwidth. In figure 5 we show that the tightening force affects the vibration of the upper stagewith a nonlinear modification.

The tightening force has a more effect on the medium and the higher frequencies of the bandwidth frequencyexcitation than at the lower frequency. The more the clamping force increase, the more the rigidity ofthe upper stage increases. Then, the vibration amplitude in resonance frequency decreases. Moreover, theresonance frequencies shift to the right. This effect is as visible as we increase the excitation frequency.

Figure 6: comparing the vibratory response of the end of the main beam for an excitation started of 2N for atightening torque of 20cNm (bleu line) and 250cNm (black line)

In term of shifting of the critical frequencies, the results are promising; taking the case to the resonantfrequency at 238 Hz; the vibration gain is reduced to 23% at the end of the main beam (see figure 6). But interm of pumping energy from the extremity of the beam to the upper stage there’s just a small band wherethe upper stage vibrates intensely unlike the rest of the structure as it is shown in figure 7. This band can beexploited as pumping energy area. For the same experimental conditions shown in the figure 7, we capturedthe quasi-periodic regime for the pumping area before the signal stabilization.

This bench, is the new conceptual try of added friction dampers and absorber, has more than one limitationto improve;


Figure 7: Comparison of frequency responses of the end of the main beam and the upper stage for a tighteningtorque of 0.2 Nm and an excitement of 2 N

• The upper blade must be replaced with two spring for each lame to improve the pumping effect and toavoid the plasticity of the lames

• The conception of the upper stage has to be improved to have more shifting effect on the criticalfrequency

• The excitation force must be constant to compare the tighten force effect only, so we can use a servounit for the excitation force.

A mathematical base or a combined mathematical and experimental base are necessary to success the visual-ization of the pumping and damping effect for an academicals bench and then for a real industrial application

5 Conclusion

The dimensions and the capacity of the active bolt are indeed a difficult tasks. The experimental resultslead to the conclusion that the bench is slightly nonlinear. Then the clamping action has not the full abilityto switch between two successive modes. Thus the coupling between the two stages must be studied thenincreased. Increasing the clamping force effects results two effects. The first is the vibration pumpingfrom the main beam to the upper stage (the switch between two modes). The second is the ability to havethe lower vibrational amplitudes for each amplitudes and frequency bandwidth excitement. Using a fictiondamper with active control will increase the field frequency controlling and will absorb vibration better thantraditionaly method.

Another key strength that is added to the new concept of friction damper and absober is that with the samebench, we proved that we can have an active tunned mass damper effect with a lighter added mass and forthe several critical frequency.

References

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[2] J. Esteban, C.A. Rogers, Energy dissipation through joints: theory and experiments, Comput. Struct.,Vol. 75, (2000), pp. 347-359.


[3] Y. Song, Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam ele-ments, Journal of sound and vibration, Vol. 273, No. 12,(2004), pp. 249-276.

[4] B.K. Nanda, A.K. Behera, Study on damping in layered and jointed structures with uniform pressuredistribution at the interfaces, Journal of sound and vibration, Vol. 226, No. 4,(1999), pp. 607-624.

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[6] H. Nouira,E. Foltete, B. A. Brik, L. Hirsinger, S. Ballandras, Experimental characterization and mod-eling of microsliding on a small cantilever quartz beam, Journal of sound and vibration, Vol. 317, No.12,(2008), pp. 30-49.

[7] C. Beards, J. Williams, The damping of structural vibration by rotational slip in joints, Journal of soundand vibration, Vol. 53, No. 3,(1977), pp. 333-340.

[8] S. Bograd, P. Reuss, A. Schmidt, L. Gaul, M. Mayer, Modeling the dynamics of mechanical joints,Mechanical Systems and Signal Processing, Vol. 25, No. 8,(2011), pp. 2801-2826.

[9] J. Dion, L., G. Chevallier, N. Peyret, Improvement of measurement techniques for damping induced bymicro-sliding, Mechanical Systems and Signal Processing, Vol. 34, No. 1,(2013), pp. 106-115.

[10] J. Becker, L. Gaul. Semiactive Control of Adaptive Friction Dampers for Structural Vibration Control,25th IMAC, (2007).

[11] R. Nitsche, L. Gaul, Lyapunov design of damping controllers, Archive of Applied Mechanics, Vol. 72,No. 11-12,(2003), pp. 865-874.

[12] A.V. Bhaskararao, R.S. Jangid, Harmonic response of adjacent structures connected with a frictiondamper, Journal of sound and vibration, Vol. 292, No. 3,(2006), pp.710-725 .

[13] L.Y. Lu, Semi-active modal control for seismic structures with variable friction dampers, Engineeringstructures, Vol. 26, No. 4,(2004), pp. 437-454 .

[14] I. H. Mualla, B. Belev, Performance of steel frames with a new friction damper device under earthquakeexcitation, Engineering Structures, Vol. 24, No. 3,(2002), pp. 365-371.

[15] E. Cigeroglu, H.N. Ozguven, Nonlinear vibration analysis of bladed disks with dry friction dampers,Journal of Sound and Vibration, Vol. 295, No. 3,(2006), pp. 1028-1043.

[16] G. Csaba, Forced response analysis in time and frequency domains of a tuned bladed disk with frictiondampers, Journal of Sound and Vibration, Vol. 214, No. 3,(1998), pp. 395-412.

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[18] Y. Karim, C. Blanze, Vibration reduction of a structure by design and control of a bolted joint, Com-puters & Structures , Vol. 138, (2014), pp. 73–85.


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