Conversion Factors. Dynamic Measurements. Displacement, Velocity, Acceleration Relationships. Acceleration. Pressure. Sinusoids (only for sinusoids)

Transcription

1 Coversio Factors Pressure Multiply by to obtai atospheres bars feet of H O 9.9 iches of Hg of Hg (torr) N/ ( Pa) pouds/sq. ich bar c of Hg 10 5 N/ (Pa) pouds/sq. ich dye/c N/ (Pa) iches of H O N/ (Pa) iches of Hg g(f)/c 14. pouds/sq. ich g(f)/ N/ (Pa) of Hg (torr) N/ (Pa) pouds/sq. ich of H O Newtos/c pouds/sq. ich N/ (Pascal) x 10-4 pouds/sq. ich pouds/sq. foot iches of H O N/ (Pa) pouds/sq. ich atospheres.036 iches of Hg iches of H O illibars of H O 51.7 of Hg N/c N/ (Pa) x 10-4 g(f)/ Velocity Multiply by to obtai feet/iute /secod feet/secod etres/secod iches/secod etres/secod /hour iles/hour ot etres/secod iles/hour(u.s.) etres/secod feet/secod.37 iles/hour(u.s.) iles/hour 88.0 feet/iute etres/secod /hour ots Acceleratio aplitude Multiply by to obtai acceleratio of gravity(g) etres/secod feet/secod iches/secod c/secod (gal) etres/secod feet/secod etres/secod iches/secod etres/secod Average Level Pea-to- Pea Level Exact Dyaic Measureets Siusoids (oly for siusoids) T Pea Level tie rs value = x pea value rs value = 1.11 x average value pea value = x rs value pea value = 1.57 x average value average value = x pea value average value = 0.90 x rs value pea-to-pea = x pea value crest factor = pea value rs value (applies to ay varyig quatity) Displaceet, Velocity, Acceleratio Relatioships (for siusoidal otio oly) Where: d o = pea displaceet D = pea-to-pea displaceet G = acceleratio i g uits f = frequecy i Hz T = period i secods cotiued o ext page RMS Level

2 Displaceet, Velocity, Acceleratio Relatioships Cotiued g = /s = i./s = ft/s G = f D (where: D = iches pea-to-pea) G =.013f D (where: D = etres pea-to-pea) T = 1/f secods d = d o si πft v = d o πf cos πft a = -d o (πf) si πft G = acceleratio/g v o = 6.8 f d o = 3.14 f D v o = 61.4 G/f i./s pea v o = G/f /s pea d o = G/f iches pea = G/f etres pea d o Motio of a Sigle-Degree-of-Freedo Syste atural frequecy: where: ω 1 1 g π π π δ f = = = δ st ω = static deflectio = agular frequecy i radias st = force/deflectio = a/d = excited ass trasissibility: (udaped) critical dapig: dapig ratio: aplificatio factor: (at resoace) for (at resoace) over daped coditio: > 1.0 critically daped: = 1.0 uderdaped: > 1.0 atural frequecy: dapig ratio: daped frequecy: TR =-ω ω TR =1 1-f f c c = = c c c = c ( ) 0.1, κ=1 ω = / ω d = c {ω } = ω 1 logarithic decreet: δ = π 1 frequecy ratio: r ωω agificatio factor: κ XX o κ 1 (1 r ) ( r) trasissibility TR Mechaical Ipedace Xe jφ F ( ω ) jcω X X ta where: F F (ω ) jcω F (ω ) (cω) 1 ( r) κ F κ cω r ta ω 1 r = excitatio force aplitude (Newtos) ω = excitatio frequecy (radias/sec) = elastic costat (Newtos/etre) c = dapig factor (Newto - sec/etre) = excited ass (ilogras) X = respose aplitude (etres) = respose phase shift (radias)

3 The Eviroet Vibratio Decibels All quatities are expressed i root-ea-square (rs) values. For iterpolatios, see Decibel Ratios sectio. Acceleratio Velocity db /s /s 0 1 x x x x x x x x x x Decibel Ratios Ratio db+ Ratio Ratio db+ Ratio Referece Levels: Acceleratio ao = 1 μ/s Velocity vo = 1 /s Acceleratio Level La 0 log (a/ao) db re 1μ/s Velocity Level Lv 0 log (v/vo) db re 1/s Resoace Frequecy of First Bedig Mode where: C = costat, fuctio of ethod of support E = elastic odulus I = oet of iertia of cross sectio g = acceleratio of gravity L = legth W = weight per uit legth Support Method C Catilever 0.56 Poit support each ed 1.57 Both eds fixed 3.56 Totally usupported 3.56 Gree Alphabet Α, α Alpha Ν, ν Nu Β, β Beta Ξ, ξ Xi Γ, γ Gaa Ο, ο Oicro Δ, δ Delta Π, π Pi Ε, ε Epsilo Ρ, ρ Rho Ζ, ζ Zeta Σ, σ Siga Η, η Eta Τ, τ Tau Θ, θ Theta Υ, υ Upsilo Ι, ι Iota Φ, φ Phi Κ, κ Kappa Χ, χ Chi Λ, λ Labda Ψ, ψ Psi Μ, μ Mu Ω, ω Oega

4 Useful Idetities Acosbt Bsibt A B cos( bt ) cos A A B Acosbt Bsibt A B si( bt ) si B A B j e si( ) si cos cos si cos( ) cos si si cos si (1 cos ) 1 si 1 si 1 si cos (1 cos ) 1 cos 1 si 1 si si cos cos( ) cos( ) cos cos cos( ) cos( ) 1 si (1 cos ) 1 cos (1 cos ) j r r(cos jsi ) re j0 j j e 1 e j e 1 e j3 j where j 1 1

5 Glossary of Vibratio Ters Acceleratio A vector quatity that specifies rate of chage of velocity. Acceleroeter A sesor whose electrical output is proportioal to acceleratio. Charge aplifier A aplifier whose output voltage is proportioal to the output charge fro a piezoelectric trasducer. It has the advatage that voltage output is ot affected by the legth of coectig cable fro the trasducer. Copliace The ease with which a syste ay be displaced or copressed for a give force. The reciprocal of stiffess. Critical dapig The iiu viscous dapig that will allow a displaced syste to retur to its origial positio without oscillatio. Cyclic frequecy The easureet, usually i cycles per secod or Hertz (Hz) of the vibratioal otio of a vibratioal syste. Dapig Ay eas of dissipatig vibratio eergy withi a vibratig syste. Dapig ratio Ratio of actual dapig to critical dapig, at a resoace frequecy. Degree of freedo I a echaical syste, equals the iiu uber of idepedet coordiates required to copletely defie the positio of all parts of the syste at ay istat of tie. Displaceet A vector quatity that specifies the chage of positio of a body. Usually easured fro the rest positio. Dyaic ass Ratio of applied force to resultig acceleratio durig siple haroic otio. Dyaic odulus Ratio of stress to strai uder vibratory coditios. Excitatio A exteral force or otio applied to a syste that causes the syste to respod i soe way Free Vibratio The oscillatio characteristics of a vibratioal syste whe there are o exteral forces, such as dapig, actig o it. Force Retardatio Agecy which gives a ass a acceleratio. Ipact Excitatio of a structure with a force pulse e.g. usig a ipact haer. Ipulse Well defied pulse. Periodic ipulse is repeated pulses. Itegrator A electrical frequecy filter used to covert a vibratory acceleratio sigal to oe whose aplitude is proportioal to velocity or displaceet. Jer A vector quatity that specifies the tie rate of chage of acceleratio. Mechaical ipedace Ratio of applied force to resultig velocity durig siple haroic excitatio. Called drivig poit ipedace if force ad velocity are easured at the sae poit, otherwise called trasfer ipedace. Mobility Mechaical adittace. ipedace. Iverse of echaical Modal aalysis A process of deteriig the ode shapes ad associated paraeters, atural frequecy ad dapig of a syste. Natural frequecy The frequecy at which a resilietly outed ass will vibrate whe set ito free vibratio.

6 Periodic vibratio A oscillatory otio whose aplitude patter repeats after fixed icreets i tie. Rado vibratio A vibratio whose istataeous aplitude is ot specified at ay istat of tie. Istataeous aplitude ca oly be defied statistically by a probability distributio fuctio which gives the fractio of the total tie that the aplitude lies withi specified aplitude itervals. Resoace Coditios of pea vibratory respose where a sall chage i excitatio frequecy causes a decrease i syste respose. Resoace Coditios of pea vibratory respose where a sall chage i excitatio frequecy causes a decrease i syste respose. Voltage aplifier A preaplifier which produces a output voltage proportioal to the iput voltage fro a piezoelectric acceleroeter. Iput voltage depeds upo cable capacitace. White figers A disorder of the hads caused by usig had-held tools, such as chai saws ad jac haers. Results i reductio of the had's ability to feel or regulate its teperature. May also result i ubess ad excessive sesitivity to low teperatures. Called Rayaud's disease. Whole body vibratio Vibratio of the hua body as a result of stadig o a vibratig floor or sittig o a vibratig seat. Ofte ecoutered ear heavy achiery ad o costructio equipet, trucs ad buses. Respose Motio or other output resultig fro a excitatio, uder specified coditios. Shoc Rapid trasiet trasissio of echaical eergy. Siple haroic otio A periodic otio whose displaceet varies as a siusoidal fuctio of tie. Stiffess Ratio of the chage i force to the correspodig chage i displaceet of a elastic eleet. Trasissibility Ratio of the aplitude respose of a syste i steady state vibratio to the excitatio aplitude. Velocity A vector quatity that specifies the tie rate of chage of displaceet. Vibratio isolator A resiliet support that reduces trasissibility. Vibratio eter A istruet for easurig oscillatory displaceet, velocity or acceleratio. Vibratio severity A criteria for predictig the hazard of daage related to specific achie vibratio levels

7 Syste Equatio of Motio Natural Frequecy x dx x 0 dt dy y 0 dt y θ L d L ( gl) 0 dt g L G θ L/ L/ 1 d L L g 0 dt 3 g L bar has ass, cetre of gravity G a L/-a O G L/ θ 1 d I o 1a ( L a) 0 dt 1 L Io L a 1 a L a L al a 3 R θ r 3 r R d 1 gr 0 r dt 3 g ( R r) R θ= r φ φ r radius of ass

8 Figure Courtesy of Brüel & Kjær Caada Liited