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1994 by Alexander H. SlocumPrecision Machine DesignTopic 11Vibration control step 2:DampingPurpose:Damping is one of the most important, yet misunderstood, factors inmachine design. Without proper damping, a machine or process canshake itself into ineffectiveness.Outline: The importance of damping Damping, stiffness and mass effects on system servo bandwidth Material damping Tuned mass dampers Constrained layer dampers Replicated internal viscous dampers"Be always sure you're right - then go ahead"David Crockett11-11

1994 by Alexander H. SlocumThe importance of damping Damping is needed to absord energy from the process: To prevent chatter and damage to the surface. To absorb energy from structural modes excited by the servos. Damping can be obtained by internal means: Material damping. Damping by microslip in joints. Damping can be obtained by external means: Tuned mass dampers. Constrained layer dampers. Active dampers. Velocity feedback in servos Actively controlled damped masses attached to thestructure.11-22

1994 by Alexander H. SlocumDamping, stiffness and mass effects on system servobandwidth There are three primary sources of excitation in a system thatrequire the servo to have a minimum bandwidth: Self-excited structural vibrations Step response Contouring speed requirements A simple model can help the designer ensure that sufficientdamping is made available. External disturbance force requirements Difficult to determine the effects of system parameters withouta complete dynamic simulation including the controller.11-33

1994 by Alexander H. Slocum For determining system parameters to prevent self-excitedstructural vibrations: Model the system with a motor driving a carriage in the followingmanner:k2Fm1m2c1c2 m1 is the mass of a linear motor forcer or: m1 is the reflected inertia of the motor rotor and leadscrew (orjust a linear motor's moving part):M reflected4 p2 J 2l M2 is the mass of the carriage. C1 is the damping in the linear and rotary bearings. C2 is the damping in the actuator-carriage coupling and thecarriage structure. K2 is the stiffness of the actuator and actuator-carriage-toolstructural loop.11-44

1994 by Alexander H. Slocum The equations of motion are:m1 0 x 1 c1 c 2 - c2 x 1k2 0 m2 x 2- c2c2 x 2 - k 2- k 2 x1 F(t) 0k 2 x2 The transfer function x2/F (dynamic response of the carriage) is:x2k 2 c2 s F c1 s( k 2 c 2 s m2 s2) ( m1 m2 ) s2 (k 2 c2 s ) m1 m2 s4 Note the product of the masses term which tends to dominate thesystem.11-55

1994 by Alexander H. Slocum Calculated parameters of four possible systems are:ActuatorBearingsStructural dampingmaterial damping zetaactuator to ground zetam1 (actuator) (kg)m2 (carriage), kgc1 (N/m/s)c2 (N/m/s)k1 (N/m)Bandwidth (Hz)ballscrewlinear balllin. motorlinear balllin. motorairlin. motorairno0.0050.055050355191.75E 08no0.0050.03550187191.75E 08no0.00505500191.75E 08yes0.1055003741.75E 082510030100 As a guideline, the servo bandwidth of the system is: Generally limited by the frequency the servo can drive thesystem at without exciting structural modes. Without special control techniques can be no higher than thefrequency: Found by drawing a horizontal line 3 dB above the resonantpeak to intersect the response curve. This method is used only to initially size components. A detailed controls simulation must be done to verify performance,and guide further system optimization.11-66

1994 by Alexander H. Slocum The response of the ballscrew driven carriage supported by rollingelement linear bearings will be:Transfer Function x2/f-71. 10-81. 10-91. 10-101. 10-111. 10Hz20.50.100.200.500.1000.2000. In this case, since preloaded linear guides and a ballnut are used,damping to ground will be high. The inertia of the screw will lower the system frequency considerably(note the m1m2s4 term in the TF) The system bandwidth will be limited to about 25 Hz. The Ballscrew was inertia matched to the carriage:DiameterLeadLengthAxial K (N/µm)JReflected inertia 4p2J/l20.0250.0030.52039.6E-064211-77

1994 by Alexander H. Slocum External disturbance force effects on required servo bandwidthk2Fm1m2c1F disturbancec2 Difficult to determine the effects of system parameters without acomplete dynamic simulation including the controller. A high degree of structural damping is required as before. Use the previous analysis method to determine the degree ofstructural damping required. Either a very high static and dynamic stiffness actuator isrequired (e.g., a ballscrew) or: A modest stiffness actuator (linear motor) with a high degree ofdamping to ground is required. This topic is discussed in greater detail in the context of linearpower transmission system requirements.11-88

1994 by Alexander H. SlocumMaterial damping Hysteresis losses from the motion of dislocations in a material understress are typically 2-3%/cycle. Quantifiers of the amount of damping include:hLoss factor of material (%)hsLoss factor of material (geometry and load dependent)QAmplification at resonance factor (Ar)fPhase angle f between stress and strain (hysteresis factor)dLogarithmic decrement (dLd) 1DUThe energy dissipated during one cyclezThe damping factor associated with second order systemskdynamic 1 h 1 d f DUkstaticQAr p2pU1 Most texts on vibration refer to the log decrement as d; however, to avoid confusionwith discussions on displacement termed d, the log decrement will be referred here to asdLd.11-99

1994 by Alexander H. Slocum The logarithmic decrement d Ld is used to relate impulse responsedata to system parameters: dLd is a measure of the relative amplitude between N successiveoscillations of a freely vibrating system:dLd -1 loge aNa1N The logarithmic decrement can also be related to: The damping factor z. Velocity damping factor b. Mass m. Natural frequency w n of a second order system model.z dLd4p2 d2Ldb 2mzw n The peak amplification at resonance of a second order system isgiven by1Q Ar (z 0.707)22z 1 - z21.510.51234t-0.5-1-1.5 Here, n 4, a5 0.5, a1 1.5, dld 0.275, z 0.44, and Q 11.511-1010

1994 by Alexander H. SlocumDamping from joints Microslip in the joints dissipates energy by friction. Contact between the machine bed and the ground, and jointsbetween components creates the total 02Cast BedBed CarriageBed SpindleBed CarriageSpindleMachineComplete2This historical figure (from data from the 1800's) was provided by Dr. RichardKegg of Cincinnati Milacron.11-1111

1994 by Alexander H. SlocumCase Study An old sliding contact bearing machine was rebuilt with linearmotion ball bearings and more range of motion. Rolling element bearings have 1/10th the friction (damping) ofsliding contact bearings. Rolling element bearings allow for 10x better positioningaccuracy than sliding contact bearings. The structural loop static stiffness was maintained. The structural loop length (distance from the bearings to the tool)was greatly increased.11-1212

1994 by Alexander H. SlocumCutting tests The new machine made very accurate parts. When making heavy cuts, the surface finish was very poor, eventhough the same tooling was used as with the old machine! The bearing vendor suggested using a bigger stiffer (moreexpensive) linear motion guide. The Nerd consultant noticed, that when cutting, there was a highpitch squeal. Squealing sounds are in the kHz range. Most machine tool structural vibration s are in the 100's Hzrange. kHz frequencies are caused by short stiff structures (thetooling). The Nerd wrapped the tool shank in electrical tape, and a mirrorsurface finish was obtained! The tool was unwrapped, and tape was place between the toolingblock and the crosslide, and good surface finish was also obtained. Dowel pins can keep establish the planar position of thetooling block. The damping tape (e.g., a 1/4 mm layer of ScotchDamp from 3M) provides enhanced joint damping.11-1313

1994 by Alexander H. SlocumWhat was the difference between the new and oldmachines? The old machine had strong dampers (sliding bearings) closer to thetool. The new machine structure was larger and although it was staticallystiff, its frequency was far lower than the tool. When the tool was vibrating, it coupled with a mode of thecrosslide which was damped by the bearings.The tool acted independently and chattered.Morals of the story: All modes (machine elements) in the structural loop should bedamped. Any element left undamped can become the resonance source. Keep a supply of viscoelastic damping tape handy! Be prepared to do more dynamic analysis before and after themachine is built!11-1414

1994 by Alexander H. SlocumMaterial damping: Typical data shows wide variations because damping is so sensitive toboundary conditions:3MaterialLoadAluminaAluminum (6063-T6)Aluminum (pure annealed)Beryillium (18.6%Be)Copper (brass)Copper (pure annealed)GlassGranite (Quincy)Iron (cast, annealed)Iron (mild steel)LeadPolymer concretePortland cement concreteQuartz (ground, piezo)Sand (loose on an Al beam)beam alone50% wt. layer of sand100% wt. layer of sandSilica (fused, annealed)Silicon nitride (n)Soil ingbendingbendingaxialunspec.unspec.T1 T2 s 1 s 2 f 1( o K) ( o K) (ksi) (ksi) 020002016065k73 0000050012.55.15.11.31000000100004000010.0 Note that the greatest degree of damping is obtained when sand isloaded on top of the beam. Material damping is very low compared to the damping from adamping mechanism. "Old timers" knew that a machine could be damped by filling itwith fine sand or lead shot. One had to be sure the added weight did not deform themachine.Viscous dampers (discussed in detail later) can be designed to yieldan 10x more damping than that of structural materials.3Data from sources in B. J. Lazan, Damping of Materials and Members inStructural Mechanics, Pergamon Press, London, 1968.11-1515

1994 by Alexander H. SlocumTuned mass dampers In a machine with a rotating component (e.g., a grinding wheel): There is often enough energy at multiples of the rotationalfrequency (harmonics) to cause resonant vibrations. Some of the machine's components are usually affected. A tuned mass damper is simply a mass, spring, and damper attachedto a structure at the point where vibration motion is to be decreased. The size of the mass, spring, and damper are chosen so they oscillateout of phase with the structure. They help to reduce the structure's vibration amplitude:k2m2c2m1k1c1BeamBeam model11-1616Beam model with damper

1994 by Alexander H. Slocum The equations of motion of the system aremx1(t) c1 c2 x1(t) - c2x2(t) ( k1 k2) x1(t) - k2x2(t) F(t)m2x2(t) - c2x1(t) c2x2(t) - k2x1(t) - k2x2(t) 0 m100m2k1 k2 - k2x(t) c1 c2 - c2 x(t) x(t)- c2c2- k2k2In the frequency domain, in order to present a solution for themotion of the system, the following notation is introduced:Z ij(w) - w 2mij iwcij kij i, j 1, 2The amplitudes of the motions of the component and the damper asa function of frequency are given byX1(w) Z 22 (w) F1Z 11(w) Z 22(w) - Z 212(w)X2(w) - Z 12 (w) F1Z 11(w) Z 22(w) - Z 212(w)11-1717

1994 by Alexander H. Slocum The design of a tuned mass damper system for a machinecomponent may involve the following steps: Determine the space available for the damper and calculate themass (m2) that can fit into this space. Determine the spring size (k2) that makes the natural frequencyof the damper equal to the natural frequency of the component. Use a spreadsheet to generate plots of component amplitude as afunction of frequency and damper damping magnitude (c2). Note that tuned mass dampers work well at specific frequencies, butthe structural loop changes with cutting loads. Example: Portion of a spreadsheet for the design of a tuned massdamper design:11-1818

1994 by Alexander H. SlocumTMDdes.xlsTuned mass damper design for a cantilever beamWritten by Alex Slocum. Last modified 9/3/95 by Alex SlocumEnter numbers in boldCantilever beam characteristics (input)Modulus (N/m 2)2.07E 11Density (Kg/m 3)7800Length (m)0.25The beam to be damped:For a circular beamTRUEOutside Diameter (m)0.1Inside Diameter (m)0.05For a rectangular beamHeight (m)0.2Width (m)0.5Max. static deflection (microns)0.25Applied dynamic force (N)25Beam mass11.49Added mass on the end5Calculated beam propertiesArea A (m 2)5.89E-03Inertia I4.60E-06Est. first natural frequency (rad/s, Hz)3606Stiffness (N/m, N/micron)182899597Equivelant mass (kg)14Static deflection (microns)0.14Damping coefficient (for steel) (N/(m/s))161.47Cylindrical damper characteristics (input)Cylinder diameter (m)0.035Cylinder length (m)0.06Outer core density7800Inner core density7800% size of core (IDcore %OD)0.75Damper fluid viscosity (N-sec/m 2)10Bore radial clearance (microns)10Number of damping cylinders1maximum dynamic displacement (µm)0.511Calculated damper propertiesDamper mass (kg)0.62Damper damping (N/(m/s))6597Damper stiffness (N/m)8048991Unit spring stiffness (N/m, lbf/in)4024496Maximum damper displacement (microns)0.5411-1919574182.9022997

1994 by Alexander H. Slocum Simulated response of the above-modeled 855750645540225120150.0004350.100330Beam displacement0.500Frequency (Hz) Simulated response of an 80-mm diameter, 400-mm-long steelcantilever beam equipped with a tuned mass damper.Displacement (microns)10Undamped beamTMD with ISO 10 oilTMD with ISO 20 oilTMD with ISO 30 oil1.1.0150100150Frequency (Hz)11-2020200250300

1994 by Alexander H. Slocum Cross section of a tuned mass damper design for an 80-mmdiameter, 400-mm-long steel cantilever beam. There are many different tuned mass damper designs:O rings seal in highviscosity NewtonianfluidDiaphragm springShear damper gapMassLow cost tuned mass damper11-2121

1994 by Alexander H. Slocum The spring and the damper can be combined in a high-losselastomer:TMD massViscolastomer(high-loss rubber)Structure One can also use a mass on a beam damped with a constrained layerdamper, and even make it adjustable:11-2222

1994 by Alexander H. SlocumConstrained Layer Dampers Damping is achieved by viscoelastic shear. Viscoelastic shear dampers work well at all frequencies and can beanalytically modeled.Z axisViscous materialStructural materialZF(t)Effective viscosity mYXxI , c , E111X-Y tablehWidth b (into page)I 2, c , E 22 Delamination can occur with time unless surfaces and adhesives arevery carefully prepared. Exterior surfaces subject to impact etc. are not viablecandidates. Replication can be used to obtain smooth flat surfaces for thedamping mechanism. Machine tool structures often have other components mounted totheir surfaces. Cast iron (and rough surface) structures require the layers to beepoxied together.11-2323

1994 by Alexander H. SlocumDesign theory4 Motion of a structure is greatest far from the neutral axis. Consider dynamic stiffness of other parts of the structure. Abalanced design must be obtained! Determine the moments of inertia of the system: Structure by itself: (EIs) about its own respective neutral axis. Constraining layers (EIcli) about their own respective neutral axes. The system as if the constrained layer had an infinite modulus: (I )about the system nuetral axis. The system as if the constrained layer had a zero modulus:I o I structure N Iclii 1about the system nuetral axis. The maximum damping that can be obtained with this system (giventhe ideal damping material) is:Qmax 1h effective for the systemI -1Ihmax 04constraininglayerStructure I0I 4This theory was developed by Layton Hale. It builds upon work done by EricMarsh as part of his Ph.D. thesis.11-2424

1994 by Alexander H. Slocum Calculate the stiffness ratio:r EI - EI 0EI0 Calculate the optimal damping parameter to maximize dynamicstiffness:a optimal 11 h2 Properties of a typical viscoelastic damping material:11-2525

1994 by Alexander H. Slocum Calculate optimal damping layer thicknessNG damping materialhoptimal w 1w i c 2ia optimal Estructure I - I 0Leff 2 The constraining layer should be attached at the point of zero shearin the beam. The effective length is thus dependent on the beam mounting:End ConditionZero Shear locationLeffFixed-freeFixed end0.613LFree FixedCenter0.160LFree-FreeCenter0.314L11-2626

1994 by Alexander H. Slocum Calculate the dynamic compliance ratio:1 2 r a 1 r a2 1 h2Q hra Often, the damping material is only available in incrementalthicknesses, so calculate a and then calculate Q:Na w i c 2ii 1 hi LG damping material Estructure I - I 0eff2 The stiffness and damping factor of the constrained layer (dampingmaterial) as a function of frequency. This theory is a starting point only. The final design should bechecked using FEA.11-2727

1994 by Alexander H. SlocumSpreadsheet CLDdes.XLS for the design of constrainedlayer dampers The primary issue is that the damping material data (modulus inparticular) is frequency dependent.CLDdes.XLSTo design constrained layer dampers for a rectangular beam with plate CLDsWritten by Alex Slocum. Theory by Layton Hale. Last modified 12/19/95 by ASOnly change cells with boldface numbers.Structural beamOutside height (m)Outside width (m)Inside height (m)Inside width (m)Length (m) [L]Modulus of elasticity (Pa) EMoment of inertia (m 4)Cross section area (m 2)Distance: structure nuetral axis and I nuetral axis (m)0.010.025000.252.07E 112.08E-092.50E-040.0051Beam constraintsCantilever [cant]Simply supported [simple]Free-free [free]Cantilever-simple [other]Fundemental mode shape [mode]FALSETRUEFALSEFALSE0.1013Viscoelastic damping layer propertiesRe(Gv) (Elastic storage shear modulus) GvLoss factor n [eta]Optimal thickness (calculated below) (mm)Desired thickness to use (available damping tape thickness) (mm) [htape]11-28289.00E 0510.020.125

1994 by Alexander H. SlocumTop surface constraining layer (may be 0)Height (m)Width (m)Width constraining layer covers (m) [wt]Moment of inertia (m 4)Cross section area (m 2)Distance: constraining layer and structure's nuetral axes (m) [ct]Distance: constraining layer nuetral axis and I nuetral axis (m)00.0250.0250.00E 000.00E 000.00510.0102Bottom surface constraining layer (must exist)Height (m)Width (m)Width constraining layer covers (m) [wb]Moment of inertia (m 4)Cross section area (m 2)Distance: constraining layer and structure's nuetral axes (m) [cb]Distance: constraining layer nuetral axis and I nuetral axis m cross section propertiesLocation of I nuetral axis from bottom of bottom constraining layerI (m 4) [Iinfinity]Io (m 4) [Io]Stiffness factor r (I /Io-1) [rr]0.01011.70E-084.17E-093.075Damping calculationsMinimum Q with the viscoelastic material selected & hoptTheoretical minimum possible QQ obtained wih the damping tape thickness [htape] availableKviscolayer/kconstraining layer alpha optimal [alphaopt]Optimal damping layer thickness (mm) [hopt]alpha for given damping tape thickness htape [alpha]11-29293.51.37.70.3500.020.055

1994 by Alexander H. SlocumHow much damping and how much static stiffness?Qinitial20Structure h Damper h 200.1460.7300.104 The error budget should tell you how much static stiffness you need,then match the static and dynamic stidffness.11-3030

1994 by Alexander H. SlocumPredicted responses of damped free-free5 beamsFor a 25 mm wide, 250 mm long, cold rolled steel beam:Plain steelbeam3MIsoDamp 112EAR C1002SoundcoatGP3Beam height (mm)20101010Constrained layerheight (mm)NA.1251.51.5Constraining layerheight (mm)NA101010Beam or dampingmaterial modulus(Pa)E 2.0 x 1011G 9.0 x 105G 1.0 x 107G 2.2 x 107FEA w1 (Hz)1678902908971Measured w1 (Hz)61638902910970FEA Q (includesmaterial damping)565.95.23.3Measured Q656.35.13.1CLDdes.XLSSpreadsheetpredicted Q (doesnot includematerial damping)NA7.86.44.05In order to obtain the Q, the free-free case is modeled as a beam supported at itsminimum deflection points (0.225L from the ends) by very soft springs. This results inless than a 0.1% difference in natural frequency calculations (1678 Hz vs 1676.6 Hz).6The predicted first natural frequency using fundemental theory is 1666 Hz11-3131

1994 by Alexander H. SlocumPredicted responses of damped simply supported beamsFor a 25 mm wide, 250 mm long, cold rolled steel beam:Plain steelbeam3MIsoDamp 112EAR C1002SoundcoatGP3Beam height (mm)20101010Constrained layerheight (mm)0.1251.51.5Constraining layerheight (mm)0101010Beam or dampingmaterial modulus(Pa)E 2.0 x 1011G 9.0 x 105G 1.0 x 107G 2.2 x 1070.015111730331375421ANSYS FEASOLID45'sBEATAD h/2pwsteel/damping3.27 x 10-64.26 x 10-44.24 x 10-43.87 x 10-46.38 x 10-66.37 x 10-65.81 x 10-6FEA d static (m)9.8 x 10-83.7 x 10-73.6 x 10-73.0 x 10-7FEA d dynamic (m)6.4 x 10-62.1 x 10-61.8 x 10-61.1 x 10-6655.75.03.76.34.83.47.76.33.9Material hFEA w1 (Hz)FEA Q (includesmaterial damping)Measured QCLDdes.XLSSpreadsheetpredicted Q (doesnot includematerial damping)NA11-3232

1994 by Alexander H. SlocumUsing finite element models to design damped systems Now consider the finite element method, which will be required foranalysis of more complex structures. A designer should be able to digitally design different structures withdifferent damping treatments to compare performance. Using FEA, you can model a beam as an 8 node solid element(e.g., SOLID45 element in Ansys ) with 3 DoF per node.4312867 Most machine tool structures can be modeled with theseelements. For the beam tested above, going from one 8 node element for thecross-section to 4 elements, to 16 elements changes the results byabout 3% The computed first frequency is 1672 Hz. The theory, experiment, and FEA results match very well!11-3333

1994 by Alexander H. SlocumHow can FEA be used to compute the damped vibrationresponse of a structure? Bolted joints can only be modeled as “solid” if the bolt stress conesoverlap! “Bulk” machine damping factor, h, can be applied to all structuralelements. ANSYS’ SOLIDS45 element, for example, allows you to input a valuefor the damping (DAMP g) This is based on a certain amount of damping occurring ineach mode, so it is linked to the stiffness matrix. The damping is the Imaginary part of the response, so it isgiven by g in the response of a classic second order system:mx(t) k 1 i g x(t) Ake iwt In terms of the modal damping coefficient h (e.g., from themodal analyses or material property data, remember, f is inHz!):g h2pfE structureE constrained layerEconstraining layer11-3434

1994 by Alexander H. SlocumGeneral procedure Design the structure for the desired static stiffness Deflections due to gravity and axis force loads should bewithin budgeted values. Use the spreadsheet to design a constrained layer damper. Use FEA to determine the dynamic performance of the machine: DAMP of the structure’s material set to that of a typicalsimilar machine (obtained for example from the LogDecrement). Use FEA to determine the dynamic performance of the machinewith the constrained layer damper. Use FEA to determine the dynamic performance of the machinewere the constrained layer damper material is removed, and theconstraining layer is added directly to the structure. This will determine the most efficient use of added material to thesystem.11-3535

1994 by Alexander H. Slocum Example: Bonding a bottom damping plate to a structure (e.g., asurface plate) allows the weight of the structure to make sure it willnot delaminate:8" thick top 4'x6' granite1/4" thick viscoelastomerwith adhesive on both sidesto bond to ground granitesurfacesWeight of table keepsconstrained layer incompression so it cannotdelaminate with time.2" thick constraininggranite layer Example: A damper plate on the bottom of a machine tool base: EIo 1.7 x 109 N. m2 I 2.5 x 109 N. m2 hb 0.17 w 380 Hz At 20 oC, properties of the material are G 12 MPa and h 1. 70% of the ribbed cast iron machine base is in contact with thedamper plate. Solve for optimum damper material thickness h to be 2.2 mm.Q 6If the machine structure is ribbed, you may decrease a bendingmore, but miss a local plate mode that may be the dominant errorsource.11-3636

1994 by Alexander H. SlocumReplicated Internal ShearTube ShearDampers 7 An internal constrained layer damper, that will also damp localsurface modes in a structure. A ShearTube damper can highly damp a structure without imposingstrict limits on the structure's geometry or materials. The ShearTube damper can decrease the amplification at resonanceof a metal beam from 500 to 10.20Undamped hollowsteel beam15105000.0050.010.0150.020.0250.030.035-5time (seconds)-10 amplitude (g's)Vibration-15-202015Hollow steel beamwith ChockfastOrange anddamping tape105000.0050.010.0150.020.0250.030.035-5-10 amplitude (g's)Vibrationtime (seconds)-15-207Patents pending. For more information, contact Richard Slocum, Aesop Inc., 200Forest Trail, Nicholasville, KY 40356-9150 Phone (606) 224 4140, fax (606) 224-8080,email [email protected]

1994 by Alexander H. Slocum A ShearTube damper is incorporated into a structure in thefollowing manner:1. The structure has rough holes formed in it (casting, drilling, orwelding in a pipe). The holes may be any shape, but should maximize the crosssection perimeter (e.g., a square). The neutral axes of the holes must be as far away as possiblefrom the neutral axis of the structure. Ideally, the holes almost fill the structure (e.g., four squaresinside of a large square beam.2. Modestly smooth-surfaced tubes (0.5 mm Ra) that are 3-5 mmsmaller than the hole are covered with a high loss dampingmaterial (e.g., 3M Scotchdamp , Soundcoat GP3, or EARC1002)3. The tubes are suspended into the hole, and an epoxy replicant(e.g., Vibradamp from Philadelphia Resins) or grout is injected(poured) around the tubes.4. After the epoxy hardens, the component is ready to be used.5. To achieve precise temperature control of the machine, theShearTubes are used like heat exchanger tubes to channeltemperature controlled fluid inside the machine.11-3838

1994 by Alexander H. Slocum Instead of using multiple shear tubes (not practical for smallerstructures such as CMM beams and tooling : A single inner concentric tube can be used, which has been slitthrough its neutral axes to within one diameter of each end. This can be referred to as a Split Sheartube 8 which typically has50% greater damping, and 50% greater static stiffness. The minimum dynamic stiffness of the system where the innerdamping tube is slit all the way to one end is 20.3 N/µm. On the other hand, the minimum stiffness of the system where thedamping tube is slit only in its center portion is 38.3 N/µm!8ibid.11-3939

1994 by Alexander H. Slocum Frequency Response Functions may show that a machine base's firstmode could be damped using a constrained layer damper on thebottom of the machine. Local diaphragm modes could still cause dominant errormotions near the surface where the part is:acceleration displacement is proportional to acceleration/frequency2Accelerometer 111st bending modeMachine baseLocal diaphragm modeAccelerometer 1.12001000frequency A ShearTube damper or filling the base with concrete will alsodamp these local diaphragm modes. The same effect can occur in columns, which are generallyweight sensitive, so ShearTube dampers are more effective.11-4040

1994 by Alexander H. Slocum ShearDampers and Hydroguide water hydrostatic bearings can be usedto greatly increase part finish and accuracy.11-4141

Sep 03, 1995 · Precision Machine Design Topic 11 Vibration control step 2: Damping Purpose: Damping is one of the most important, yet misunderstood, factors in machine design. Without proper damping, a machine or process can shake itself into ineffectiveness. Outline: The importance of damping Damp