Jtam-A4.dvi JOURNAL OF THEORETICAL SHORT RESEARCH COMMUNICATION AND APPLIED MECHANICS 54, 1, pp. 311-316, Warsaw 2016 DOI: 10.15632/jtam-pl.54.1.311 SEMI-ACTIVE LINEAR VACUUM PACKED PARTICLES DAMPER Robert Zalewski, Paweł Chodkiewicz Warsaw University of Technology, Institute of Machine Design Fundamentals, Warsaw, Poland e-mail: robertzalewski@wp.pl; pawel@chodkiewicz.com.pl In this paper, the authors focus on thepropositionof an innovative semi-active lineardamper prototypeworkingonthebasisof granularmaterials.VacuumPackedParticles (VPP)belong to theclassofmaterialswhosemechanical (rheological,dissipative)propertiesmaybequickly changedby applying a partial vacuum inside the system.The concept of an innovative linear damper based onVPP is presented in the paper. Typical experimental results are presented to reveal changeable damping characteristics of the device. Additionally, the mathematical model is proposed to capture extraordinary features of the investigated damper. Keywords: VacuumPacked Particles, modeling, underpressure, experiments 1. Introduction VacuumPacked Particles (VPP) are a class of “smart structures”whose physical propertiesmay be rapidly changed by pulling out the pressure from the system and generating the so called underpressure. This change is in proportion to the magnitude of the internal partial vacuum generated and is quickly reversible. VPP, from the macroscopic point of view, are viscoplastic solid bodies and can bemodeled by various constitutive models (Zalewski and Pyrz, 2013). The VPPstructure canbealso compared tomagnetorheologicalmaterials and, consequently,modeled by typical rheological models developed forMRfluids. Typical, well commercialized engineering applications ofVPPare universal robot grippers (Brown et al., 2010), flexible endoscopes (Loeve et al., 2010), “smart layers” in sandwich beam structures (Bajkowski et al., 2015) or vacuum mattresses (Luscombe andWilliams, 2003). The discussed granular structures are conglomerates that consist of loose granularmaterials placed in a soft and hermetic envelope. When exposed to a partial vacuum, the so called “jam- ming mechanism” occurs and loose particles interact to form a solid-like structure that resists various types of deformations or flow (Cates et al., 1998). This change in the structure appears as a dramatic increase in apparent viscosity, and the “plastic” structure develops characteristics of a semisolid state (Majmudar et al., 2007). Themagnitude of this transformation is controlled by the value of the partial vacuum and is immediately reversed upon removing the underpressure. Noting the apparent similarities of the considered VPP andmagnetorheological (MR) fluids (Makowski andKnap, 2014), the authors propose an “innovative” semi-active linear VPP dam- per prototype. Taking advantage of the previous, fundamental research on VPP, in this paper the authors propose an original engineering application of the previously mentioned granular conglomerates. In the modeling Section, a mathematical model including damage functions is proposed.Typical laboratory tests results are presented in the experimental Section.The impact of underpressure on recorded dissipative characteristics is introduced and discussed. Themodel has been calibrated using an Evolutionary Algorithm. 312 R. Zalewski, P. Chodkiewicz 2. Model of the system In our experiment we consider a system that consists of a spring that is attached to a rigid support at the top and has amass attached to it at the bottom end (Fig. 1). The spring encloses a flexible and hermetically sealed sleeve that is full with a granular material, which acts as the damper. Fig. 1. Model of the nonlinear mass-spring-damper system Tocapture real behavior of theproposedVPPdamperprototype, the followingmathematical model is proposed v̇+ cζv+kx+µg sgn(v) = f D(t)= ds t ∫ 0 |v(s)| ds ζ̇ =−df(|x|−λf)+−D x(0)=x0 v(0)= v0 ζ(0)= ζ0 (2.1) where m, k, c are positive material coefficients, µ is the coefficient of friction and g is the gravitational acceleration. The introduced D function with the rate ds is related to gradual wear of single grains caused by the “intergranular” friction phenomenon. The global damage function ζ also consists of the part related to rearrangement of the grains along the total path traveled. The damping damage coefficients df and ds are based on experiments, and we assume that they depend on the underpressure. λf is the critical amplitude below which the granular material does not change its internal arrangement. The problem is rewritten as a system of three first order deferential equations with appro- priate initial conditions. A forward-typeEuler algorithm (2.2) has been used to solve the system (2.1) vn+1 = vn− cvn−kxn+µgsgn(vn)+fn+1 m h xn+1 =xn+vn+1h Dn+1 =Dn+ds|vn+1|h ζn+1 = ζn− [df(|xn+1|−λf)+−Dn+1]h (2.2) 3. Experiments The structural scheme of the device is depicted in Fig. 2. It consists of two rigid discs (3, 5), coupled by themain spring (2). The heart of the device is a granular core (4). It is formed of a cylindrical envelope filled by loose plastomer grains (also small cylinders). Thanks to the special valvemounted in a handle (1), it is possible to connect the core to a vacuumpumpand generate the appropriate value of a partial vacuum inside the system. Short Research Communication – Semi-active linear Vacuum Packed Particles damper 313 Fig. 2. Scheme of the investigated damper; 1 – handles, 2 – spring, 3 – upper disc, 4 – granular core, 5 – lower disc The VPP damper prototype has been investigated on a specially designed laboratory stand (Fig. 3). A kinematical sine excitation rule with various frequencies was considered in the la- boratory tests. Different underpressure values from the range 0.01 to 0.09MPa were taken into considerations. Typical experimental results are depicted in Fig. 4. Fig. 3. Laboratory stand for investigations of VPP dampers Fig. 4. Damping characteristics of the VPP damper for various values of underpressure and the excitation frequency f =1.4Hz Analyzing the experimental results presented in Fig. 4, it can be observed that the un- derpressure parameter has a great impact on the recorded energy dissipation loops. A higher 314 R. Zalewski, P. Chodkiewicz underpressurevalue results in increased damping properties of theVPPdamper prototype. This phenomenon shows that changing the value of partial vacuum inside the system enables one to control the global properties of the discussed devices. In the authors opinion, it confirms that investigated devices can be placed among the family of “smart dampers” next to MR or ER devices. The recorded data also reveal a nonsymmetrical response of the damper, which complicates the mathematical description of the damper. The results of laboratory tests, in the next stage of research, are the base for the mathematical model calibration process. 4. Model calibration The model has been calibrated for two various values of the underpressure.We used the Evo- lutionary Algorithm (EA) optimization method to find 6 parameters of the model presented in Section 2. TheEAdeveloped in theMathematica software applies a population of 40 individuals and simulated the evolution process for 200 generations. Each iterative step includes three sta- ges: selection, mutation and crossover. Crossover andmutation operators are applied randomly with 50% probability. The following fitness function is taken into consideration Er = 1 n n ∑ i=1 |F iexp−F i| |F iexp| →min (4.1) whereFexp is a temporary experimental force value,F – numerical force value,n – total number of discrete points. Fig. 5. Verification of the model calibration processes for (a) P =0.01MPa; (b) P =0.07MPa Theold population is replaced bynew individuals forwhichnewfitness values are calculated. Thebest results obtained after 200 iterations are presented inTable 1.Thenumerical simulation results carriedout for the identifiedmodelparametershavebeenverifiedwithdirect experimental data (Fig. 5). In the initial stepofnumerical investigations, damage functions (2.1)2,3were turned off during the calibration process. As the properties of the VPP damper are influenced by the underpressure value and the direction of velocity (Fig. 4), we assumed that all investigated parameters can be described as c(P, sgn(v)) = { c0 for v­ 0 c1 for v < 0 k(P, sgn(v)) = { k0 for v­ 0 k1 for v< 0 n(P, sgn(v))= { n0 for v­ 0 −n1 for v < 0 Short Research Communication – Semi-active linear Vacuum Packed Particles damper 315 Finally, the estimated values of the model parameters for two selected underpressures (0.01 and 0.07MPa) are presented in Table 1. For the simplicity of calculations it has been assumed that n=µg. Table 1.Model parameters for various underpressure values P [MPa] c0 [kg/s] k0 [kN/mm] c1 [kg/s] k1 [kN/mm] n0 [kN] n1 [kN] 0.01 34.14 42.22 50.57 145.51 0.40 0.44 0.07 72.53 117.96 51.10 297.13 0.82 0.69 5. Conclusions In the paper, an innovative semi-active damper prototype, based on Vacuum Packed Particles is proposed and investigated. The experimental results confirmed the possibility of controlling the dissipative properties of the device by changing the value of partial vacuum. Higher un- derpressure provides intensification of grains compaction and results in increasing the damping properties of the device. The proposedmathematical model assumes two types of damage functions.Most important damagemechanisms, encountered during experimental research, are related to the ongoingwear of single grainsmaterial and large, exceeding the assumed range, rearrangements of the granular system. The model has been calibrated basing on the obtained experimental results using the EA strategy. Verification of the numerical and laboratory tests results revealed quite a good correct- ness of the proposedmodel (global error less than 7%). Theprevious experimental research didnot include destructive tests of the investigated VPP prototype.To identify the damage functions, amulti-cycle loading of the testing device has to be applied. Moreover, the nonlinear underpressure functions have to be identified and introduced to the proposedmodel. Futuredesignworks shouldbe focused ondeveloping semi-active granular deviceswith optio- nal, not necessarily nonsymmetrical damping characteristics. In the authors’ opinion, semi-active linear VPP dampersmay in a near future replace much more expensive and complex magnetorheological or electrorheological devices. More than 500 times cheaper and uncomplicated VPP dampers seem to be competitive to already well com- mercialized and popular “intelligent” dampers. References 1. Bajkowski J.M.,DyniewiczB.,BajerC.I., 2015,Dampingproperties of a beamwithvacuum- -packed granular damper, Journal of Sound and Vibration, 341, 74-85 2. Brown E., Rodenberg N., Amend J., et al., 2010, Universal robotic gripper based on the jamming of granularmaterial,Proceedings of theNational Academy of Sciences of theUnited States of America, 107, 44, 18809-18814 3. Cates M.E., Wittmer J.P., Bouchaud J.P., Claudin P., 1998, Jamming, force chains and fragile matter,Physical Review Letters, 81, 1841-1844 4. LoeveA.J., Van deVenO.S., Vogel J.G., Breedveld P., Dankelmann J., 2010,Vacuum packedparticles as flexible endoscopeguideswith controllable rigidity,GranulMatter,12, 6, 543-54 5. LuscombeM.D.,Williams J.L., 2003,Comparison of a long spinal board and vacuummattress for spinal immobilization,Emergency Medicine Journal, 20, 1, 476-478 316 R. Zalewski, P. Chodkiewicz 6. MajmudarT.S., SperlM., LundigS.,BehringerR.P., 2007, Jamming transition in granular systems,Physical Reviews Letters, 98, 058001 7. Makowski M., Knap L., 2014, Reduction of wheel force variations with magnetorheological devices, Journal of Vibration and Control, 20, 10, 1552-1564 8. Zalewski R., Pyrz M., 2013, Experimental study andmodeling of polymer granular structures submitted to internal underpressure,Mechanics of Materials, 57, 75-85 Manuscript received June 10, 2014; accepted for print November 29, 2015