Trillingsdempende materialen basis & eigenschappen Berekenen en toepassen op trillingsisolatie van technische installaties.

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Trillingsdempende materialen basis & eigenschappen Berekenen en toepassen op trillingsisolatie van technische installaties Patrick Carels KVIV Studiedag Ingenieurshuis - Antwerpen

1 Trillingsdempende materialen basis & eigenschappen Berekenen en toepassen op trillingsisolatie van technische installaties Patrick Carels KVIV Studiedag Ingenieurshuis - Antwerpen 23/9/206 Content Vibrations Basic Concepts Vibration Isolation Basic Concepts Vibration Isolation Resilient Material Technology Vibration Isolation Applications in Buildings 2

j j j 2 3 i BASICS ON VIBRATIONS Vibrations - Basic Concepts v(t) C f(hz) vibrations can be approached in the same way as noise basis: vibration velocity v(t) instead of air pressure p(t) human

force F = split up in 3 different parts: F m = Newton force (mass movement) F c = viscous damping (damper velocity) F k = Hooke s law (spring deflection) every force can be written as a combination

2 j j j 2 3 i BASICS ON VIBRATIONS Vibrations - Basic Concepts v(t) C f(hz) vibrations can be approached in the same way as noise basis: vibration velocity v(t) instead of air pressure p(t) human sensitivity = 0, mm/sec spectrum of importance = to 00 Hz Vibrations can be harmonic, periodic, impulsive/shock or random complex model: single degree of freedom system (SDOF) (>>) applied harmonic force F = split up in 3 different parts: F m = Newton force (mass movement) F c = viscous damping (damper velocity) F k = Hooke s law (spring deflection) every force can be written as a combination of individual harmonic forces, having a frequency f and an amplitude F spectral analysis when considering one individual harmonic force as input, the output (a, v, x) will be of the same shape but dephased over a constant φ the involved (kinetic) energy E is related to v², so the spectrum is also often set for v² instead of v, since this gives a better visualisation of the energy involvement F = Fm + Fc + Fk F = m a + c v + k x d²x(t) dx(t) F(t) = m + c + k x(t) dt² dt F(t) = m x"(t) + c x'(t) + k x(t) j ω t+ φ F(t) = F cos( ω t + φ ) = F e with ω= 2πf φ= const = ω t + φ x(t) X cos( ) ω t X e = + φ = cos( ω t + φ v(t) V ) 2 dx(t) ω t+φ V e = = dt = j ω x(t) = cos( ω t + φ a(t) A ) 3 t+φ A = ω e dv(t) = dt = j ω v(t) = ω 2 x(t) L vt () = 20 log( ) v v 0 with v = 5 0 mm /sec 5 0 also : v = 0 mm / sec 0 L = 0 log 0 v tot 6 Lv / 0 ( ) BASICS ON VIBRATIONS Vibrations - Basic Concepts T SCR AMPLIFICATION DCR ISOLATION ξ =0.5 MCR ξ =0.8 ξ = ξ =0.2 ξ = β the isolation efficiency I can be defined as follows: function of the transmissibility T T=f(β,ξ) = spectral function of k, c, m β <0,5 SCR 0,5 < β <2 DCR 2<β MCR if f = f r then β = and there is maximum amplification, so the damping becomes very important vibration isolation starts at the mass controlled region; damping becomeslessimportantthenandisconsideredasasecondary phenomenon, which is often neglected; this results in an interesting simplification of the formula I (% ) = 00 ( T) I (dbv) = 20 Log(T) with F T = = + ( 2 ξ β) 2 T F 2 ( β ) + ( 2 ξ β ) 2 2 with f β= f ω exc = fr k = ω r 2 π m c ξ= = c c 0 2 k m T = β 2

Vibration Isolation - Basic Concepts simplified approach We assume system to be

AMPLIFICATION ISOLATION STATIC EVALUATION x = ΔP k stat ξ =0.5 ξ =0.2 ξ =0 ξ =0.

3 Vibration Isolation - Basic Concepts simplified approach We assume system to be a SDOF system with resilient material ΔP mx + cx + kx = ΔP (kdyn/kstat = r ) m x(t), v(t), a(t) with x = X.e j(ωt+φ) T SCR k DCR c x 0 (t), v 0 (t), a 0 (t) MCR f res = 2π k dyn m AMPLIFICATION ISOLATION STATIC EVALUATION x = ΔP k stat ξ =0.5 ξ =0.2 ξ =0 ξ =0.8 ξ = β DYNAMIC EVALUATION IL 40log( f f res ) xm IL 40log 2πf + 20log rδp Vibration Isolation - Basic Concepts simplified approach

Materials T SCR DCR MCR AMPLIFICATION ISOLATION ξ =0.5 ξ =0.

4 Vibration Isolation - Basic Concepts simplified approach TL = 20 log (A ic /B ic ) IL = 20 log (B ic /B ref ) IL = 20 log IL (B ic /B 40 ref log ) (f TL ref /f = ic 20 ) log TL ic (A ic /B ic ) f ref : base resonance frequency of reference case f ic : base resonance frequency of isolated case Vibration Isolation - Basic Concepts Resilient Materials T SCR DCR MCR AMPLIFICATION ISOLATION ξ =0.5 ξ =0.8 ξ = IDEAL VIBRATION ISOLATION MATERIAL used in should be a combination A linear spring best transmissibility T With some damping for practical reasons (limit response after excitation) Linear elastic material with no damping β k m ξ =0.2 ξ =0 Linear elastic material + damper m k c

5 Vibration Isolation Resilient Material Technology What about real life resilient materials? Helicoidal springs with or without damping Resilient materials with spring and damping action combined Examples Cork PU foam Rubber Lead Etc... A good resilient material is combination Spring action (=action immediate reaction ) Damping action (= action time dependent reaction) Ok to work in the load window imposed by the application (between DL and DL+LL) and typical boundary conditions (creep, environment, water, acids, alkalines, temperature, ozone, etc...) Vibration Isolation Resilient Material Technology F Helicoidal spring? Yes constant stiffness in wide load range but no damping Plain Rubber? No stiffness changes too much with strain - strain hardening (because of noncompressibility) - non-linear elasticity how to make products compressible? Introduce AIR bubbles make it microcellular! H x R Δr R MICRINLOSS technology M Strain ( ) R = Rubber M = Microcellular material

Vibration Isolation Micrinloss Technology How to make a

because load is taken by thin cells walls (collapse!

because load is taken by plain rubbery granules and air can

All little air balloons next to each other Resilient Closed

incompressible and loss of pressure via osmosis (creep!

PU foams with combined open/closed cells (PUF) OK for dry

6 Vibration Isolation Micrinloss Technology How to make a rubber compressible = introduce air microcellular structure of the resilient material! Ease of air flow defines damping quantity Air flow through porosity! Via open cells? With thin cells walls sponges not OK for load bearing because load is taken by thin cells walls (collapse!) and PU hydrolisis With plain rubbery granules (RR) OK because load is taken by plain rubbery granules and air can move in/out Via closed cells? All little air balloons next to each other Resilient Closed cell rubbers Material not OK because Technology incompressible and loss of pressure via osmosis (creep!) Via mixed cells combination open/closed? PU foams with combined open/closed cells (PUF) OK for dry conditions attention problem to PU hydrolisis Cork&rubbers cork being the mixed cell! (HR) OK Vibration Isolation Resilient Material Technology CDM Resilient Materials High Resilience Rubbers (HR) Helicoidal Metal Springs (MS) Cork & Rubber (CR) Polyurethane Foams (PF) Recycled Rubber (RR) Noise & Vibration Isolation Systems 2

7 Vibration Isolation Resilient Material Technology Performance (Hz) 20 5 CDM SOLIDS Performance/Load Overview 5 RR 7 Materials: Helicoidal Metal Springs Polyurethane Foams Polyurethane Foams & High Resilience Rubbers High Resilience Rubbers 0 PF PF & HR HR 6 5 Recycled Rubber METAL SPRINGS 0,0 0,0,00 0,0 Load (MPa) 3 Vibration Isolation Resilient Material Technology solids 4

Vibration Isolation Resilient Material Technology So real life fit-to-use resilient elastomer materials with broad load range and excellent spring/damping action are Springs in combination with

accepted : Resilient Material Technology Type ST-RR (Resin bonded rubber): Revalorised rubber granules, bonded in a polyurethane matrix Type 2 ST-PU (PolyUrethane Foam): Polymer foam with mixed open

8 Vibration Isolation Resilient Material Technology So real life fit-to-use resilient elastomer materials with broad load range and excellent spring/damping action are Springs in combination with mechanical or elastomer material damping (COMBIPAD) PU Resin bonded rubber materials (RR) Mixed cells PU foam materials (PF) Example for mat foundations generally 2 material types are widely used and accepted : Resilient Material Technology Type ST-RR (Resin bonded rubber): Revalorised rubber granules, bonded in a polyurethane matrix Type 2 ST-PU (PolyUrethane Foam): Polymer foam with mixed open and closed cells Vibration Isolation Resilient Material Technology Resilient material becomes stiffer with load less deformation at incremental overload Soft behavior at low loads Stiffer at higher loads 3 clear stress strain zones A first zone with stiff behavior A 2 nd zone with softer behavior A 3 rd zone with strain hardening (cfr. Type )

Vibration Isolation Resilient Material Technology Type vs Type 2 - Stress Strain considerations for model Dead Load point σ 0 = 0.03 MPa Evaluation Load point σ 2 : oq=80 kn σ 2 = 0.

04 MPa Vibration Isolation Resilient Material Technology Simple Beam on Elastic Foundation model Type vs Type 2 Q=80 kn (rolling stock empty) : Type ST-RR c dyn almost everywhere << ( better

9 Vibration Isolation Resilient Material Technology Type vs Type 2 - Stress Strain considerations for model Dead Load point σ 0 = 0.03 MPa Evaluation Load point σ 2 : oq=80 kn σ 2 = MPa oq=20 kn σ 2 = MPa Maximum Load point σ3 : o Q=80 kn σ 3 = MPa o Q=20 kn σ 3 = 0.04 MPa Vibration Isolation Resilient Material Technology Simple Beam on Elastic Foundation model Type vs Type 2 Q=80 kn (rolling stock empty) : Type ST-RR c dyn almost everywhere << ( better vibration isolation performance) though with present known specs focusing mainly on cdyn/cstat ratio at maximum load, Type 2 ST-PU would have been the material choice. Q=20 kn (rolling stock at full capacity with dynamic factor) : in this case at maximum deflection points, c dyn Type 2 ST-PU mats < Type ST-RR. The real c dyn seen by the wheels is defined by < load than maximum load under the bogie. c dyn and hence also on c dyn /c stat ratio, measured at maximum load = not OK when optimizing for vibration isolation performance. c dyn measured at an equivalent load level with 50 to 70% participation of LL

10 Vibration Isolation Resilient Material Technology MultiBody / FEM Analysis model Type vs Type 2 IL results compared to simple model Vibration Isolation Applications in Buildings Vibration Isolation 20

11 Vibration Isolation Applications in Buildings Without Vibration Control 2 Vibration Isolation Applications in Buildings With Vibration Control 22

12 Vibration Isolation Applications in Buildings Sound Insulation 23 Vibration Isolation Applications in Buildings Without Sound Insulation 24

13 Vibration Isolation Applications in Buildings With Sound Insulation 25 Vibration Isolation Applications in Buildings Vibration Isolation Technical Installations 26

14 CDM in a NutShell KEY FACTS VIBRATION & STRUCTURE BORNE NOISE ISOLATION SPECIALISTS IN BUILDING & INDUSTRY APPLICATIONS PIONEERING since 95 & REX with long list references specifically in Building Base Isolation High Performance Floating Floors Heavy Machine Isolation WORLDWIDE ACTIVE 8 branches IN DEPT KNOW HOW ON ELASTOMERS & VIBRATION ISOLATION TECHNOLOGY BESPOKE SOLUTIONS at lowest TOTAL COST OF OWNERSHIP 27

Lecture 9: Harmonic Loads (Con t)

Lecture 9: Harmonic Loads (Con t) Reading materials: Sections 3.4, 3.5, 3.6 and 3.7 1. Resonance The dynamic load magnification factor (DLF) The peak dynamic magnification occurs near r=1 for small damping