Analysis of friction-induced vibration leading to EEK noise in a dry friction clutch

Transcription

1 Analsis o riction-induced vibration leading to EEK noise in a dr riction clutch Pierre Wicramarachi a), Rajendra Singh a), and George aile b) (Received 24 March 29; revised 25 Ma 9; accepted 25 August 19) This article deals with the EEK sound that ma occur during engagement o a dr riction clutch in vehicles with manual transmissions Eperimental data showed that near the ull engagement point o the clutch, the pressure plate suddenl starts to vibrate in the rigid-bod wobbling mode with a requenc close to the irst natural requenc o the pressure plate and clutch dis cushion The sel-ecited vibration ehibits tpical signs o a dnamic instabilit associated with a constant riction coeicient A linearied lumped-parameter model o the clutch was developed to eplain the phsical phenomenon The eect o e parameters on sstem stabilit was eamined b calculating the comple eigensolutions Results o the analtical stud were in agreement with eperimental observations or instance, it was observed that the instabilit o the rigid-bod wobbling mode was controlled b riction orces This mode ma, however, be also aected b the irst bending mode o the pressure plate A stier plate could lead to an improved design with a reduced tendenc to produce the EEK sound 25 Institute o Noise Control Engineering Primar subject classiication: 756; secondar subject classiication: Introduction A squealing sound ma be produced during the last part o the engagement o a dr riction clutch in vehicles with manual transmissions The strongl annoing sound o the transient event is nown as EEK noise, which ma dominate an overall perception o vehicle sound qualit Some consumers might even prematurel change the clutch in an eort to eliminate or reduce the disturbing noise igure 1 illustrates a tpical arrangement o a pressure plate and a clutch dis used to transmit torque rom the engine to the transmission and ultimatel to the vehicle s driven wheels Depressing the clutch pedal (not shown) moves a throw-out bearing (not shown) toward a diaphragm and, in turn, causes Engaged Disengaged Cover Tab Cam Pressure plate Pivot rings Diaphragm lwheel Dis Lito earing orce ig 1 Sections o a pressure-plate clutch-dis sstem in engaged and disengaged stages a) Acoustics and Dnamics Laborator, Center or Automotive Research, The Ohio State Universit, Columbus, Ohio, 4321, USA; pierre@dataphsicscom, singh3@osuedu b) LuK, Inc, 341 Old Airport Road, Wooster, Ohio 44691, USA; Georgeaile@lu-uscom the pressure plate to move awa rom the clutch dis into the disengaged position where the engine is uncoupled rom the transmission Letting up on the clutch pedal allows the pressure plate to squeee the clutch dis against the lwheel mounted on the engine s cranshat in the engaged position A critical position is achieved at the point o lito where, in reaction to the orce applied b the throw-out bearing, the pressure plate is just disengaged rom the clutch dis Despite man eperimental studies, this riction-induced EEK sound (lie man other riction problems [1]) remained poorl understood One hpothesis was that the EEK sound was triggered b a dnamic instabilit o the subsstem composed o the clutch pressure plate and the clutch dis cushion It had been observed eperimentall [2] that, during the EEK event, the pressure plate vibrated in a rigidbod wobbling (out-o-plane) motion corresponding to the natural requenc o the pressure-plate/dis-cushion sstem Eperimental studies showed that the modal properties o the pressure plate, as a result o the abrication process, seemed to pla a signiicant role in the mechanism(s) that cause the EEK sound To clari some o these issues, the analtical model described in this article was developed and used to identi e parameters aecting the stabilit o a dr-rictionclutch sstem 2 EXPERIMENTAL MEASUREMENTS AND PROLEM ORMULATION Two conditions are tpicall necessar beore the transient EEK sound (igure 2) can be induced irst, the engine speed should be within the 15 to 25 rev/min range The transmission speed does not seem to have a signiicant eect Since the slip speed is relativel high, a constant coeicient o riction µ at the threshold o EEK ma be assumed These conditions suggest that the EEK sound ma not ollow the smptoms o classical stic-slip phenomenon [1] 122 Noise Control Eng J 53 (4), 25 Jul Aug

2 Engagement Disengagement 11 1 (a) t 1 t 2 ull engagement 9 Sound pressure Engine speed requenc (H) Dominant EEK requenc ƒ w earing travel 5 EEK threshold Transmission speed Elapsed time (s) 4 7 EEK 6 (b) ƒ w 2ƒw 3ƒ w ig 2 EEK sound as measured in the interior o a vehicle as a clutch is being engaged and then disengaged as correlated with the variation o engine speed and the position o the clutch throw-out bearing Magnitude (V) ƒ b Second, the clutch pedal motion (or throw-out bearing travel) has to be such that the clutch is close to ull engagement at the onset o the EEK sound igure 2 shows this particular position (where the EEK sound begins to occur) where the pressure plate and clutch dis cushion are alread in contact, but not et ull engaged The two vertical dashed lines in igure 2 indicate the times t 1 and t 2 at the onset and cessation o the strong EEK sound as noted b the rapid increase and decrease o the sound pressure Measurements o the spectra o the EEK sound ehibit a dominant requenc w, related to the bearing travel position, o approimatel 45 H to 5 H, as shown at various relative times in igure 3(a) This requenc has been correlated to requenc (H) 7 (c) 6 ƒ w 2ƒ w 3ƒ w 5 ig 3 Spectra o the EEK sound; (a) Principal requenc components as the clutch is engaged; (b) Magnitude o the spectral components o EEK sound as measured b a spectrum analer beore the ull engagement o the clutch at relative time t 1, where the component at the undamental requenc b o the bending mode was dominant at approimatel 95 H; (c) at time t 2, where the component at the undamental requenc w o the wobbling mode was dominant at approimatel 5 H [Vertical lines indicate the undamental, second harmonic, and third harmonic o the wobbling-mode requenc in (b) and (c)] Magnitude (V) ƒ b requenc (H) Noise Control Eng J 53 (4), 25 Jul Aug 123

3 the wobbling rigid-bod motions o the pressure plate (in both out-o-plane rotations) rom dnamometer tests [2] and rom a single-degree-o-reedom (SDO) model that included the inertia o the pressure plate and the stiness o the clutch diaphragm coupled with the stiness o the clutch cushion The pressure plate and clutch dis cushion were assumed to be the main components that control the EEK phenomenon This assumption was reinorced b man empirical eperiments that showed that elements eternal to the clutch (gears, release sstem, engine pulsations, etc) as well as internal to the clutch (diaphragm and cover) do not signiicantl inluence the tendenc to produce the EEK sound [2] urther, a change in the pressure plate material rom grairon (Pressure ) to vermicular iron (Pressure ) seemed to reduce the occurrence o EEK Such a change o material could alter the modal properties o the pressure plate, as ound in some brae-squeal studies [3,4] Eperimental modal studies showed that a pressure plate made rom material is essentiall stier than a pressure plate made rom material Thus, the inluence o pressure-plate elastic deormations needed to be investigated rom eperimental modal analses, the second requenc b, between 9 H and 1 H as shown in igure 3(a), could be lined to the irst bending mode o the plate igure 3(b) shows that the prominence o this bending mode (at requenc b ) at relative time t 1 is quicl replaced b the dominance o the wobbling mode (at requenc w and harmonics) 3 s later at relative time t 2 in igure 3(c) This article develops a preliminar simulation model or the clutch assembl At the threshold o the EEK sound, vibration amplitudes were considered suicientl small to build a linearied model that would reproduce the trends o the observed dnamic instabilities An analtical lumped parameter approach was preerred over the structural initeelement method The analtical model eamines a sel-ecited sstem without an eternal torque ecitations The pressure plate was assigned an initial angle in order to eamine the growth o vibration amplitude with time and demonstrate the eistence o dnamic instabilit 3 Analtical Model The lumped parameter model o igure 4 incorporates the inertia o a deormable pressure plate along with the clutch cushion stiness c that was divided into our springs o stinesses, r,, and r, where subscripts and indicate coordinate aes and and r indicate the direction o the motion toward the orward and rear o the power-transmission ais, respectivel igure 4(a) shows the model or the ied-base lwheel and the clutch dis The +-ais points toward the engine and is aligned with the ais o the cranshat The clutch dis, igure 4(b), was modeled as our masses, m, at segments A,, C, and D and connected b our springs o stiness In order to consider the nonlinear characteristic o the clutch-dis cushion, the stinesses and r were respectivel divided and multiplied b a non-dimensional amplitude ratio λ, ied-base lwheel = orward r = rear C a) m a)b) m r r riction surace (rom dis) A r r ããã m as shown in igure 5 and in the ollowing, where the stiness o an individual spring was assumed to equal one ourth o the total clutch stiness c Assume that the bearing travel is such that the EEK threshold point (P in igure 5) is reached This instant would correspond to a constant plate lito υ = υ EEK Lito corresponds to the displacement o the plate rom its engaged position to a disengaged position Now suppose that the plate is alread vibrating about the -ais with amplitude θ This Pressure plate m r ig 4 Schematic o the analtical model or a clutch-dis/pressure-plate assembl; (a) two rotational degrees-oreedom θ and θ about the and aes, respectivel, stinesses shown or the orward and rear directions, pressure-plate masses at points A,, C, and D; (b) our translational degrees-o-reedom in the direction or the pressure-plate masses m coupled b stinesses r D 124 Noise Control Eng J 53 (4), 25 Jul Aug

4 A vibration will change the normal spring orces at locations A and as shown in igure 5 Consequentl, the stinesses and r were obtained b assuming a constant stiness slope around point P The dierent spring orces are used in Equations (1) and (2) c r = (1) 4λ C 4 D c = λ (2) The ratio λ could be used to incorporate an asmmetr into the resulting stiness matri or instance, λ = 9 in Equations (1) and (2) allows a small degree o asmmetr riction orces rom the clutch dis cushion were also included b assuming a constant coeicient o riction µ due to a high slip speed (>7 rev/min) or the si degree-oreedom (DO) model o igure 4, two DOs describe the rigid-bod out-o-plane rotations (wobbling mode) and our additional translational DOs (normal to the pressure plate) depict the irst two nodal-diameter bending modes o the pressure plate choosing an appropriate lumped bending stinesses, this bending mode was created in our model with a requenc close to the observed requenc b Setting one o the modal masses, m in igure 4(b) to correspond to a quarter o the total plate mass was believed to be a reasonable approimation o the modal mass Net, the ree-bod diagrams are drawn as shown in igure 6 Here, even though it is represented as a rigid bod or the sae o clarit, the pressure plate can also elasticall deorm as eplained beore The normal spring orces (N) and the corresponding riction orces () are thereore epressed as ollows along the and aes and in the orward and rearward directions: N = ( rθ ) (3) N = ( + rθ ) (4) r r r N = ( + rθ ) (5) N = ( rθ ) (6) r r r θ o c/4 c/4λ λ c/4 A P υ EEK ig 5 Nonlinear model o the stiness o the clutch-dis cushion as a unction o the lito position where the EEK sound begins to occur υ View on YZ plane θ View on XZ plane θ r A N C N r ó ó r ο r 1 ï í ο ï í ì ì N r D r r ig 6 ree-bod diagrams or the vibration modes o the pressure plate r r (7) (8) r (9) (1) r where r is the radius o the pressure plate, θ is a rotation about the or ais, and µ is the coeicient o riction The resulting governing equations or a linear, undamped and unorced sstem were obtained in a matri orm in terms o the mass [M] and stiness [K] matrices and the generalied coordinate vector {X} [ M ]{ X&& } + [ K]{ X} = {} (11) where T X = [ θ θ ] (12) and r r M = diag([ I I m m m m ]) (13) 2 ( + r) µ ( + r ) Γ Γ r ( 2 + ) ( r 2 ) 2 lr( r ) r ( r ) r( 2 ) r( 2 r) r r lr r r µ Γ Γ K = r 2 + rr 2 r + r 2 + rr 2 + r (14) with Γ = 2r + µ l 2 + (15) ( ) ( ) Γ = 2r µ l 2 + (16) r r N 2 Noise Control Eng J 53 (4), 25 Jul Aug 125

5 ( ) ( ) Γ = 2r + µ l 2 + (17) Γ = 2r µ l 2 + (18) r r 4 Stabilit Studies and Design Guidelines The asmmetric nature o [K] is controlled b the coeicient o riction µ and amplitude ratio λ and ields comple eigenvalues ~ λ s = σ s ± ω s, where the imaginar part ω s is the damped natural requenc (in rad/s) o mode inde s and the real part σ s is an inde o dnamic stabilit When σ s is positive, the amplitude o vibration grows eponentiall in time The eect o µ on ~ λ s is illustrated in igure 7 Two distinct wobbling modes with requencies 1 and 2 (in H) can be seen, where the dierence between the two requencies was ound to be related to the ratio λ or low values o µ Nevertheless, as µ is increased, the coupling between the two modes is enhanced It results in two modes (one stable and one unstable) at µ = 35 (a tpical value or clutch dis cushions or linings) Essentiall, requencies 1 and 2 merge to become the same requenc c The eect o the pressure-plate structural stiness is investigated in igure 8, which diagrams the natural requencies and real parts o the wobbling modes As is increased, one passes rom an unstable region (or ) to a stable region (or ) These results are in agreement with eperimental observations [2] Thereore, Young s modulus does have a signiicant impact on the stabilit o a pressureplate clutch-dis sstem and consequentl on the generation o the EEK sound igure 9 shows an animation o the comple wobbling modes that was developed to visualie the phase dierences As the pressure plate wobbles, a circle indicates the location along the edge that has the maimum positive amplitude (in the -direction) At µ = 35, this circle actuall moves along the edge o the plate in the direction o the riction orces a) Real part σ requenc (H) or the stable mode (represented b the eigenvector ψ 1 ) and in the opposite direction or an unstable mode (denoted b eigenvector ψ 2 ) This result means that the rotation about the -ais (denoted as dnamic motion in igure 9) actuall rotates as a unction o time and in a dierent direction Hence, the riction orces ma enhance the energ o an unstable mode; ωc Modes are decoupled 31 b) Static equilibrium Pressure plate stiness Dnamic motion ωb ωa ig 8 Components o the predicted eigenvalues or the wobbling modes o the pressure plate; (a) Inde o dnamic stabilit σ or real part o the eigenvalues or and, (b) natural requenc ω s o the modes (in hert), which ehibits two distinct values ω a and ω b or high pressureplate stinesses and a single value ω c or low pressureplate stinesses /d ψ ψ 1 2 σ < µ c 2 1 UN σ > ig 7 Two eigenvalues o a pressure plate that could be coupled b varing the coeicient o riction µ The inde o dnamic stabilit σ (real part o the eigenvalues) becomes negative or the stable wobbling mode (dashed line) and positive or the unstable wobbling mode (solid line) riction orces Plate rotation /d /d ig 9 Visualiation o the comple wobbling modes o the pressure plate or a coeicient o riction µ = 35 These modes occurred at the natural requenc c o the clutchdis cushion and illustrate the directions o the traveling waves induced b modes ψ 1 and ψ 2, moving with the ais o rotation indicated b the dnamic-motion line Mode ψ 1 is a stable mode associated with waves that move in the direction o plate rotation; mode ψ 2 is an unstable mode associated with waves that move in the direction o the riction orces The aes were normalied or this setch 126 Noise Control Eng J 53 (4), 25 Jul Aug

6 conversel, the ma dissipate the energ o a stable mode or coeicients o riction less than 35, the ais o rotation remains stationar, showing the absence o an coupling between θ and θ Stabilit diagrams are presented net to summarie the eects o pressure plate geometr (inner and outer radii r i and r o, and thicness 2l ), pressure plate structural stiness ( ) and dis cushion characteristics (µ and c ) irst, a diagram in terms o r i and r o is displaed in igure 1 Deining δ = 5(r o - r i ), the radii were varied rom their baseline value minus δ to their baseline value plus δ The increasing degrees o instabilit (described b the real parts σ s o the unstable eigenvalues) are represented graphicall and grouped rom a low to a medium to a high degree o instabilit Two straight lines indicate the baseline radii It was ound that larger radii would result in increased stabilit However, outer radius r seemed to have a greater inluence than the inner radius r i or practical purposes, it would be more convenient to maintain the same contact area between the pressure plate and the dis A smaller surace is not recommended since it would produce more heat and reduce the lie o the clutch dis Moreover, the heat capacit o the clutch is also aected b the pressure plate mass ased on these considerations, it seemed that r should be increased, since a 15% increase would theoreticall result in a more stable sstem In addition, this change would increase the torque capacit o the clutch Second, the stabilit diagram o igure 11 shows that a thicer pressure plate would result in reduced stabilit This is conceivable since plate thicness 2l controls the torque generated b the riction orces This torque is responsible or r o (mm) r i (mm) ig 1 Regions o stable and unstable wobbling modes o the pressure plate or a range o the inner radius, r i, and outer radius, r o Plate thicness, structural stiness, and coeicient o riction were held constant The vertical and horiontal lines indicate baseline radii The indices o dnamic stabilit (the real part o the eigenvalue or the wobbling modes) were organied in three categories: Low to Medium to High Thicness 2l (mm) Plate stiness ig 11 Regions o stable and unstable wobbling modes o the pressure plate or a range o plate thicness, 2l, and plate stiness, aseline inner and outer radii and coeicient o riction were held constant The horiontal line represents the baseline plate thicness The indices o dnamic stabilit (the real part o the eigenvalue or the wobbling modes) were organied in three categories: Low to Medium to High the wobbling mode, because it couples angular displacement θ with angular displacement θ Interestingl, a 1% decrease in plate thicness would mae the sstem stable As with the previous design change proposed or the outer plate radius r o, one needs to consider the consequences o a thinner plate in terms o clutch lie and perormance or instance, a change in plate thicness would aect the stiness, which is related to the bending mode o the pressure plate igure 12 compares the inluence o the coeicient o riction µ on the stiness o Plates G and V The pressure plate o the plate V material was stable or µ < 45 or the plate made rom material, decreasing µ b 1% (rom 35 to 31) would mae the sstem stable Once again, this change ma cause problems in terms o clutch perormance because the transmitted torque would be also reduced To compensate or this eect, the clamp load (normal load at ull engagement) would have to be increased accordingl inall, the stabilit diagram o igure 13 was obtained in terms o pressure-plate stiness and clutch-dis cushion stiness c The latter stiness was varied up to its maimum value at ull engagement In parallel, the eigenvalues were computed via an iterative process to determine the corresponding values or r and at each point on the plot igure 1 shows the loss o stabilit as the clutch is being engaged Here it occurs around c 26 MN/m or plate G, whereas the instabilit region is avoided with plate V at the same cushion stiness Such predictions match empirical observations [2] airl well Noise Control Eng J 53 (4), 25 Jul Aug 127

7 45 55 Coeicient o riction µ Plate stiness ig 12 Regions o stable and unstable wobbling modes o the pressure plate or a range o the coeicient o riction, µ and plate stiness, aseline inner and outer radii and plate thicness were held constant The horiontal line represents the baseline plate thicness The vertical lines represent the structural stiness o and The indices o dnamic stabilit (the real part o the eigenvalue or the wobbling modes) were organied in three categories: Low to Medium to High Cushion stiness c c at point P Plate stiness ig 13 Regions o stable and unstable wobbling modes o the pressure plate in an analsis that simulated clutch engagement or a range o the stiness, c, o the clutch-dis cushion and plate stiness, aseline inner and outer radii, coeicient o riction, and plate thicness were held constant The horiontal line represents the clutch-dis stiness at Point P, as shown in igure 5 The vertical lines represent the structural stiness o and The indices o dnamic stabilit (the real part o the eigenvalue or the wobbling modes) are organied in three categories: Low to Medium to High 5 Conclusions The analtical stud reported in this paper ielded much insight into the mechanism(s) o EEK noise in dr riction clutches Speciicall, the riction-induced vibration o the pressure-plate dis-cushion sstem was correlated with a loss o dnamic stabilit The analtical model includes a si degreeo-reedom lumped-parameter sstem that describes rigid-bod wobbling modes and the irst elastic deormation mode o the pressure plate The comple eigenvalue method was utilied to stud the sstem stabilit in terms o the coeicient o riction between the pressure plate and the cushion or lining o the clutch dis, pressure-plate geometr, and the structural stiness o the pressure plate The latter was ound to be a e parameter controlling the requenc o the irst elastic deormation mode, the coupling with the wobbling mode could be altered This instabilit mechanism and its eect seemed to correlate well with empirical observations uture wor should ocus on developing an enhanced analtical basis (including nonlinear models) to better understand the EEK phenomena 6 Acnowledgments We than Todd Roo o Goodrich Corp and the engineering team at LuK, Inc, or their valuable help in solving parts o the EEK mster 7 Reerences [1] A J McMillan, A Non-linear riction Model or Sel-ecited Vibrations, J Sound Vib 25(3), (1997) [2] Review o eperimental studies with the LuK, Inc engineers (2-21) [3] S W Kung, K Dunlap, and R S allinger, Comple Eigenvalue Analsis or Reducing Low requenc rae Squeal, Societ o Automotive Engineers, SAE Paper (2) [4] D J eld and D J ehr, Comple Eigenvalue Analsis Applied to an Aircrat rae Vibration Problem, American Societ o Mechanical Engineers, ASME Design Engineering Technical Conerences, DE-Vol 84-1, Volume 3, Part A (1995) 128 Noise Control Eng J 53 (4), 25 Jul Aug