Stiffness and damping coefficients for rubber mounted ...web.iitd.ac.in/~hirani/lijesh-lubrication-science.pdf · Stiffness and damping coefﬁcients for rubber mounted hybrid bearing

LUBRICATION SCIENCELubrication Science 2014; 26:301–314Published online 26 February 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ls.1252

Stiffness and damping coefficients for rubber mountedhybrid bearing

Lijesh K. P.*,† and Harish Hirani

Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India

ABSTRACT

A non-contact passive magnetic bearing has a low friction compared with other passive (journal or ball)bearings. But these bearings have negligible damping due to which even small rotor vibration impacts thebearing magnet. It results in breakage of brittle magnetic materials. To overcome this problem, a hybridbearing (passive magnet + elastomer) has been proposed in the present manuscript. To select an appropriaterubber, a step-by-step approach, using pendulum and hysteresis tests, has been followed. A parametric studyon thickness of selected rubber was carried out. Experiments were conducted on three configurations: (i) astand-alone magnetic bearing, (ii) magnetic bearing with a butyl rubber having a thickness of 1mm, and (iii)magnetic bearing with a butyl rubber having a thickness of 1.5mm. To investigate the effect of rubberYoung’s modulus on the damping, rubber was made softer by immersing in aromatic liquid, and theexperiments were repeated using softer rubber. Copyright © 2014 John Wiley & Sons, Ltd.

Received 29 July 2013; Revised 7 November 2013; Accepted 15 December 2013

KEY WORDS: hybrid bearing; rubbers; damping; stiffness; thickness

INTRODUCTION

Permanent magnetic bearings consist of ring magnets in rotor and ring or sector magnets in thestator. In these bearings, rotor is levitate in air using either attraction or repulsion force betweenthe stator and rotor magnets. Since the rotor rotates in air, magnetic bearings provide zero wearand frictionless operation. These bearings have been used in many industrial applications likeflywheel,1 axial magnet spindle motor2 and brushless direct current motors,3 and one of the maindisadvantages of magnetic bearing is negligible damping.4 Rare earth magnets used for magneticbearing are very brittle,5,6 and low amplitude vibration may damage rotor and stator magnets. Inone of our experimental study, stator was damaged as shown in Figure 1. In this figure, crackson a stator magnet are shown. Measurement of the magnetic field on this cracked stator indicatedthe formation of new north and south poles at the breaking points. Such formation of new northand south poles disturbs the complete magnetic field and can be treated as complete failure of

*Correspondence to: Lijesh K. P., Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India.†E-mail: [email protected]

Copyright © 2014 John Wiley & Sons, Ltd.

Figure 1. Cracks on stator magnet.

302 LIJESH K. P. AND H. HIRANI

magnetic bearing. One way to overcome this drawback is isolation. In the present work, elastomersare experimented as rubber bearings to absorb the vibration energy.Rubber bearings have been used for isolation of structure from external vibration like earthquake7,8

and also been practised in machinery and equipment’s.9 In the present work, two sets of experimentswere conducted to understand the behaviour of the rubber bearing as an isolator. In initial experiments,dynamic characteristics of rubber were tested, and best rubber material was selected to fabricate rubberbearings. In second set of experiments, rubber bearings were hybridised with permanent magnet andtested for their dynamic characteristics.In the present work, a step-by-step approach, using pendulum and hysteresis tests, has been used to

select an appropriate rubber as an isolator. The pendulum test was used as a screening step to shortlisttop two rubbers among: (i) natural rubber, (ii) nitrile butadiene rubber,(iii) Hypalon rubber, and (iv)butyl rubber. Costlier hysteresis test10,11 was performed on the shortlisted rubbers.There is a relation between the thickness of the rubber and the vibration amplitude. An increase in

the rubber thickness decreases the value of vibration amplitude and reduces the damping time.12 Toinvestigate the effect of rubber thickness on damping, hammer test was performed on the following:(i) 1, (ii) 1.5, and (iii) 2mm thick rubbers. Logarithmic decrement results are plotted and presentedin the present manuscript.It is always necessary to test the samples in the actual system because the isolation properties

(stiffness and damping) vary with different amplitude and frequency of vibration.13 To measure theperformance of the rubber bearing with permanent magnet, an experimental setup was developed.The amplitude of vibration for different thicknesses and different Young’s moduli of rubber bearingswas measured.

DAMPING AND STIFFNESS OF RUBBER

Rubber bearing increases the damping but at the cost of stiffness. So it is always necessary to choosethe rubber thickness that provides good damping without compromising the stiffness.

Copyright © 2014 John Wiley & Sons, Ltd. Lubrication Science 2014; 26:301–314DOI: 10.1002/ls

303STIFFNESS AND DAMPING COEFFICIENTS FOR RUBBER MOUNTED HYBRID BEARING

Hamaguchi et al.14 studied the effect of ageing on the rubber bearing stiffness and concludedthat after 20 years, the vertical stiffness of the bearing increased by less than 20% to the initialvalue. This phenomenon is due to reduction in the height of the rubber with ageing. Xianget al.15 conducted accelerated test on the butyl rubber and concluded that specimen heightwas reduced by 1/16 times of the height of the specimen in 371 days at room temperature;i.e. for a 1mm specimen, the reduction of rubber height will be 62 μm. In the present setup,the reduction in height can be adjusted by adding shims at the bottom to increase the heightof bearing. In other words, rubber ageing is not a severe problem; however, rubber shall bereplaced during overall maintenance period.To select an appropriate rubber for isolating the permanent magnet from vibration, four most

commonly used rubbers, natural rubber, nitrile butadiene rubber, Hypalon rubber and butyl rubberas isolators, were selected. Pendulum test was performed to select two rubbers having higher lossfactor among those four rubbers. Hysteresis test was performed on the two shortlisted rubbers tochoose the best rubber. Finally, a parametric study on rubber thickness was performed using hammertest and compression tests.

Pendulum and hysteresis tests

The pendulum test provides the qualitative results of absorbed energy during the impact. In thistest, a bob (a steel ball suspended with the help of inextensible thread) is allowed to hit on thestructure from constant angular distance (i.e. angle of 45° measured with a protractor fixed onexperimental setup) as shown in Figure 2a. The neodymium magnet was attached to the structureby sandwiching rubbers of different thicknesses (1, 1.5 and 2mm) between them. Whenever thebob hits the structure, a high amplitude signal was observed initially that dies out with time. Theamplitude of signal is directly proportional to the amplitude of the hit.In the present study, number and magnitude of the hits were found by using accelerometer. The

accelerometer was fixed on the surface of the structure just near the point where the bob hits thestructure. Charge amplifier was used to convert and amplify the signals from the accelerometers into

(a) Pendulum Test (b) Hysteresis Test

Figure 2. Experimental setup for (a) pendulum and (b) hysteresis tests.



displacement signals. Data acquisition system (DAQ) along with LabVIEW software fromNational Instruments were used to record and analyse the signals. Under periodic or cyclic loading cycle,every material dissipates energy that is represented by a hysteresis loop. The area of hysteresis loopindirectly indicates the amount of energy dissipated, which means that the material having larger areaof hysteresis (such as viscoelastic compared with elastic material) dissipates more energy.To find the hysteresis loop of any rubber, universal testing machine (UTM) (shown in Figure 2b)

was used. A rubber mould of 60mm in height and 30mm in diameter was attached to two metalliccircular discs. The metallic circular discs were required for gripping the rubber mould to the jawsof UTM.

Hammer and compression tests

Hammer test16 was used in identifying the behaviour of mechanical systems. The test wasperformed by hitting the material by hammer and measuring the displacement of the material usingaccelerometers.Hammer test was performed by varying the rubber thickness to find the damping ratio using

logarithmic decrement curve. Damping ratio of the rubber is calculated from the logarithmic decrementplot of displacement, as expressed in equation (1):

ξ ¼ 12πn

lnAi

Aiþn

� �(1)

where A is the amplitude of the displacement and n is the nth cycle of decrement.In the present work, three different thicknesses, 1, 1.5 and 2mm rubbers having the same projected

area, were tested. The rubber was sandwiched between the surfaces of the magnet and the aluminiumstructure. Accelerometer was attached to the bottom of the aluminium structure as shown in Figure 3.Hammer blow was made on the magnet, and the displacement signal was measured using theaccelerometer signal.The stiffness was found by plotting force versus deflection curve. Stiffness of the different thickness

rubbers was measured by compressing the rubber in UTM for desired range of load and measuring thecompression of the rubber. In the present work, rubbers of the same length (30mm) and breadth(30mm) but with different thicknesses (1, 1.5 and 2mm) were compressed with the load of 5000N

Figure 3. Damping test for rubber.



at a speed of 1mmmin�1. The stiffness of the rubber is obtained from the slope of the curve betweenload versus deflection.A magnetic bearing setup, as shown in Figure 4a, has been developed for testing the perfor-

mance of the hybrid bearing. The experimental setup consists of motor, a spiral coupling, anonmagnetic shaft on which permanent magnet is mounted and casing made of nonmagneticmaterial (aluminium) consisting of stator magnet. The speed of the motor was controlled byusing a frequency drive. Two accelerometers and hall sensors were mounted on the casing inx and y direction. The signals from accelerometers and hall sensors were measured using anaccelerometer and voltage data acquisition systems (DAQ) as shown in Figure 4b. The dataacquisition systems were connected to the computer, and signals (at the rate of 50 μs) wereacquired using LabVIEW software. The following precautions were taken while convertingmagnetic bearing to hybrid bearing:

1) The inner diameter of the casing and outer diameter of the hybrid bearing must exactly the same.If the rubber is inserted into casing either tightly (rubber will be in compression) or loosely(bearing will not be attached properly to the casing), the hybrid bearing would not perform itsdesired operations.

2) High strength glue was used to attach rubber to the magnet.3) Smooth surface of the magnet was roughened using sandpaper.

(a) Experimental Setup

(b) Data Acquisition system

Figure 4. (a) Experimental setup with (b) DAQ.



4) When rubber reacts with oil, the surface of the rubber becomes oily, and it becomes difficult toattach with the magnet and casing. So the whole setup (hybrid bearing [magnet + rubber] and thecasing) was fully immersed in the oil for 72 h.

These precautions are necessary to maintain the stator and rotor magnets in concentric position andaxially aligned. If the magnets are not properly aligned, the performance of the magnetic bearing interms of magnetic force reduces.

RESULTS AND DISCUSSION

Pendulum test

Pendulum test does not provide absolute results, but relative results obtained from this test helpin making fast and easy decisions. The displacement signal of pendulum test, carried on thedifferent types of rubbers, is shown in Figure 5, and loss factor and number of hits are tabulatedin Table I.As per Table I, the number of hits in butyl rubber is two compared with three hits for other

rubbers. Further, it can be noted that butyl rubber has highest loss factor among all fourrubbers. To increase the accuracy of the obtained results, hysteresis testing was performed onHypalon and butyl rubbers, which have higher damping compared with natural rubber andnitrile butadiene rubber.

Hysteresis test

The hysteresis test was conducted on butyl and Hypalon rubbers for extensions ±1, ±3 and ±5mm. Thechange in force is plotted against the extension as shown in Figure 6a and 6b. From Figure 6, it can beinferred that, with an increase in the rubber deformation, the area of hysteresis increases, henceindicating the enhancement in the energy absorption by the rubbers. The values of area of thehysteresis for different extensions for both butyl and Hypalon rubber are tabulated in Table II. FromTable II, it can be inferred that the area of hysteresis plot for butyl rubber is higher compared thatfor with Hypalon rubber. Hence, it validates the pendulum test results. So, in the present work, butylrubber is considered for developing rubber bearing.

Hammer test

The displacement versus time for different thicknesses of rubber to estimate the damping ratio isplotted in Figure 7. The damping ratio is tabulated in Table III.From Figure 7 and Table III, it can be concluded that damping ratio increases with increase in

thickness of rubber.

Compression test

The plot for different thickness rubbers is plotted in Figure 8. From Figure 8, it can be concluded thatthe stiffness reduces by increasing the thickness. If the application requires low stiffness and highdamping, a rubber of higher thickness has to be used. If the application requires low damping but highstiffness, then low thickness rubber has to be used.


Table I. Pendulum test results for different rubbers.

Type of rubber Amplitude of first peak No. of hits Loss factor

Natural rubber 0.51 3 0.948433Nitrile butadiene rubber 0.4991 3 1.225878Hypalon rubber 0.4672 3 1.377013Butyl rubber 0.391 2 1.905

Figure 5. Pendulum test for different rubbers: (a) natural rubber, (b) nitrile butadiene rubber, (c) Hypalonrubber and (d) butyl rubber.



Figure 6. Hysteresis plot for different extensions: (a) butyl rubber and (b) Hypalon rubber.

Table II. Area of hysteresis curve for different elongation for Hypalon and butyl rubbers.

Type of rubber

Area of hysteresis curve for different elongation (Nmm)

�/+1 �/+3 �/+5

Hypalon 10 98.7 185Butyl 33 151 327


Performance of permanent magnet and hybrid bearings

Isolation of the bearings was tested at 5 to 30Hz rotational frequencies. Initially, the performanceof a magnetic bearing was evaluated, and the test was extended for hybrid (permanent bearingmounted on rubber) bearing. Figure 9 shows the acceleration and displacement signals at 12Hzrotational frequency. In Figure 9a and 9b, the peaks indicate the hitting of rotor on stator, andthe number of hits is found to be equal to 12 in 1 s. It means that in each rotation, the rotor hitsthe stator in both horizontal and vertical directions. In comparing Figure 9a and 9b, it can be statedthat higher amplitude acceleration occurs in the vertical direction compared with horizontaldirection. Figure 9c and 9d shows the displacement signals of the rotor from the centre position(value zero) of the bearing. The radial clearance of the bearing is 1mm, which means +1 inFigure 9c indicates the right side and �1 indicates the left side of the bearing. Similarly, inFigure 9d, +1 and �1 indicate the top and bottom sides of the bearing, respectively. It can beinferred from Figure 9c and 9d that rotor hits the left side and bottom side of the bearing. The sameinference can be reached from the orbit plot shown in Figure 10.The magnitude of acceleration at different frequencies in both horizontal and vertical directions is

plotted in Figure 11. From this figure, it is observed that in horizontal direction, amplitude ofacceleration increases with the increase in the frequency. However, two peaks, one at 11Hz and theother 18Hz, are observed in vertical direction acceleration.


Figure 7. Damping ratio for (a) magnet and different thicknesses of the rubber: rubber of (b) 1, (c) 1.5 and(d) 2mm thickness.

Table III. Damping ratio for different thicknesses of rubber.

Condition Damping ratio

Magnet 2.34Magnet with 1mm thick rubber 3.54Magnet with 1.5mm thick rubber 3.85Magnet with 2mm thick rubber 4.13


In the next set, hybrid bearing, as shown in Figure 12, was experimented. Three hybrid bearingsconsisting of concentric magnet and butyl rubber thickness (1, 1.5 and 2mm) arrangement wereexperimented. Buckling in hybrid bearing, having 2mm thick annulus rubber, restricted to acquireany meaningful data.The magnitude of acceleration in horizontal and vertical directions, at different frequencies for both

hybrid bearing and magnetic bearing, is compared in Figure 13a and 13b, respectively. From thesefigures, it is inferred that the amplitude of acceleration is greatly reduced by rubber bearing and thereduction of the amplitude is directly proportional to the thickness of the rubber. Incorporation ofthe rubber reduces the magnitude and frequency at which the peak acceleration occurred. The shiftingof peak frequency is due to reduction in stiffness of the bearing.


Figure 8. Force versus deflection for different thickness rubbers.

Figure 9. Acceleration and displacement signals of magnet bearing. Acceleration signals in (a) horizontaland (b) vertical directions. Displacement signals in (c) horizontal and (d) vertical directions.



Figure 10. Orbit plot of magnetic bearing.

Figure 11. Acceleration at different frequencies for magnetic bearing.


EFFECT OF YOUNG’S MODULUS OF BUTYL RUBBER ON HYBRID BEARING

In the previous section, it was concluded that with increase in the thickness of butyl rubber, isolation ofhybrid bearing increases. However, the experiments on hybrid bearing having 2mm thickness couldnot be performed as bearing started to buckle. Alternative method to increase the isolation propertyof the rubber is to reduce its Young’s modulus. To reduce the Young’s modulus of the rubber, liquidscontaining aromatic and non-aromatic compounds were selected. Butyl rubber was dipped in theseliquids for 72 h, and the percentage change in Young’s modulus at different elongation was studied.The results are listed in Table IV.


Figure 12. Hybrid bearing.

Figure 13. Acceleration at different frequencies for hybrid bearing. (a) Vertical acceleration and (b)horizontal acceleration.


From Table IV, it can be inferred that the behaviour of butyl rubber in two liquids are giving twoextreme results. The modulus for butyl rubber was not much affected by the non-aromatic liquid whilein an aromatic liquid, the Young’s modulus value is reduced by 27%.To evaluate the performance of the hybrid bearing, the reduced Young’s modulus butyl rubber of

1mm thickness was attached to the magnet and was fully immersed in the liquid for 72 h. The testperformed in the section on Performance of Permanent Magnet and Hybrid Bearings was repeated,and the results are plotted in Figure 14. From the plot, it can be inferred that with reduction of Young’smodulus, equivalent isolation value of 1.5mm thick rubber is achieved using a 1mm thick rubber.From Figure 14, it can be observed that the damping of the hybrid bearing has increased in both


Table IV. Modulus change for different elongation for butyl in different liquids.

% Elongation Original rubber (kg cm�2) Non-aromatic liquid (kg cm�2) Aromatic liquid (kg cm�2)

50 18.41 17.69 10.71100 28.08 26.44 19.79150 39.51 37.23 28.79200 52.18 48.03250 64.93 60.40300 77.88 72.89

Figure 14. Acceleration at different frequencies for hybrid bearing. (a) Vertical acceleration and (b)horizontal acceleration.


horizontal and vertical directions. It is hence concluded that by reducing the Young’s modulus of therubber, the isolation property of the hybrid bearing has increased.

CONCLUSION

Due to vibration, breakage of stator magnet occurred. To avoid such breakage, a hybrid (magnetic + rubber)bearing is proposed. Pendulum test was performed to screen out the two high damping rubbers. Hysteresistest was conducted to choose the best rubber and confirmed the results of pendulum test. From the testresults, it was concluded that butyl rubber provides more isolation compared with other rubbers.On executing hammer and compression tests, an increase in isolation property with increase in

rubber thickness was observed.In comparing the results obtained from the experiments performed on magnetic and hybrid bearings,

it was concluded that the hybrid bearing with higher thickness and reduced Young’s modulus providedhigher isolation.

REFERENCES

1. Kumbernuss J, Jian C, Wang J, Yang HX, Fu WN. A novel magnetic levitated bearing system for vertical axis wind turbines(VAWT). Applied Energy 2012; 90:148–153.

2. Dunfield JC, Oveyssi K. Integrated passive magnetic bearing system and spindle magnet for use in an axial magnet spindlemotor. U.S. Patent No. 5,587,617. 1996; 24.



3. Wang F, Wang J, Kong Z, Zhang F. Radial and axial force calculation of BLDC motor with passive magnetic bearing.Power Electronics and Motion Control Conference, 2004. IPEMC 2004. The 4th International 2004; 1:14–16.

4. Filatov AV, Maslen EH. Passive magnetic bearing for flywheel energy storage systems. IEEE Transactions on Magnetics2001; 37(6):3913–3924.

5. Brown D, Ma BM, Chen Z. Developments in the processing and properties of NdFeb-type permanent magnets. Journal ofMagnetism and Magnetic Materials 2002; 248:432–440.

6. Smith DJB, Mecrow BC, Atkinson GJ, Jack AG, Mehna AAA. Shear stress concentrations in permanent magnet rotorsleeves, The XIX International Conference on Electrical Machines - ICEM 2010; 1–6.

7. Derham CJ, Thomas AG. The design and use of rubber bearings for vibration isolation and seismic protection of structures.Engineering Structures 1980; 2:171–175.

8. Derham CJ, Kelly JM, Thomas AG. Nonlinear natural rubber bearings for seismic isolation. Nuclear Engineering andDesign 1985; 84:417–428.

9. Gobel EF. Rubber Springs Design. Newnes-Butterworth, London 1978.10. Ciambella J, Paolone A, Vidoli S. A comparison of nonlinear integral-based viscoelastic models through compression tests

on filled rubber. Mechanics of Materials 2010; 42(10):932–944.11. Mordini A, Strauss A. An innovative earthquake isolation system using fiber-reinforced rubber bearings. Engineering

Structures 2008; 30(10):2739–2751.12. Baltac A, Sarıkanat M, Yıldız H. Damping effects of rubber layer in laminated composite circular plate during forced

vibration. The Seventh International Conference on Vibration Problems: ICOVP, 2005; 64–69.13. Nel CB, Steyn AJ. Stiffness and damping characterisation for a hydraulic engine mount. Topics in Modal Analysis II,

Proceedings of the 30th IMAC, A Conference on Structural Dynamics, vol. 6. 2012; 129–136.14. Hamaguchi H, Samejima Y, Kani N. A study of aging effect on rubber bearings after about twenty years in use. 11th World

Conference on Seismic Isolation, Energy Dissipation and Active Vibration Control of Structures, vol. 15, no. 30. 2009;393–398.

15. Xiang K, Huang G, Zheng J, Wang X, Huang J. Investigation on the thermal oxidative aging mechanism and lifetimeprediction of butyl rubber. Macromolecular Research 2012; 21(1):10–16.

16. Rahman Bhuiyan A, Alam MS. Seismic performance assessment of highway bridges equipped with super-elastic shapememory alloy-based laminated rubber isolation bearing. Engineering Structures 2013; 49:396–407.


Documents

Stiffness and damping coefficients for rubber mounted ...web.iitd.ac.in/~hirani/lijesh-lubrication-science.pdf · Stiffness and damping coefﬁcients for rubber mounted hybrid bearing