Dynamics

Powertrain induced NVH

Stephanos Theodossiades email: [email protected]

Wolfson School of Mechanical and Manufacturing Engineering Loughborough University, Loughborough United Kingdom Any public or commercial use requires the agreement of the author.

- Overview

- Investigation Strategy

- Transmission Rattle

- Axle Whine

- Driveline Clonk

Any public or commercial use requires the agreement of the author.

Powertrain All the components in a vehicle that contribute to the generation, transmission, and distribution of drive torque to the wheels Drivertrain All the components required to deliver engine power to the road surface Driveline Assembly of the parts that transmit torque from the transmission to the wheels

How NVH issues initiate? The continuous trend for increased engine power, reduced vehicle weight and lower costs have driven developments towards lighter, thinner components -> increased vibration levels in powertrains The significant advances in the reduction of engine/aerodynamic/tyre noises have brought to the forefront other powertrain noise sources, previously masked Any public or commercial use requires the agreement of the author.

Powertrain induced NVH Phenomena Vehicle shunt, boom

Clutch whoop, judder

Drivetrain/Transmission shuffle, clonk, rattle, whine Any public or commercial use requires the agreement of the author.

Axle Drive whine

The Plethora of NVH Concerns Clutch whoop (200-500Hz) – knocking effect on clutch pedal during engagement/disengagement and radiated noise in the driver foot area judder (7-20Hz) – torsional rigid body mode of powertrain at low engine speeds due to stick-slip motion between flywheel/friction disk and friction disk/pressure plate

Gearbox rattle (below 2000Hz) – result of impacts between meshing gear teeth under various loaded or unloaded conditions whine (400-4000Hz) – tonal noise excited by meshing gears in the gear meshing frequency or/and its multiples Differential whine (200-800Hz) – same mechanism as in gearbox Drivetrain shuffle/shunt (2-7Hz) – coupled rigid body torsional and axial low frequency oscillations of the drivetrain system, clonk-thud (500-5000Hz) – short duration transient response of metallic nature, usually the result of a load reversal in the presence of backlash Vehicle Cabin boom (20-160Hz) – drumming noise, excited by engine orders due to coincidence or commercial requires agreement of the author. modes between structural modesAny of public vehicle bodyuseand itstheacoustic cavity

Investigation Strategy

System testing

Any public or commercial use requires the agreement of the author.

Experimentation (Down-cascading)

Vehicle test in the semi-anechoic chamber

Engine-transmission test bed

Single gear Any pairpublic rigor commercial use requiresElectrically the agreement of driven the author.transmission-based rig

Gear teeth impact-induced oscillations in manual transmissions promoting Gear Rattle

Any public or commercial use requires the agreement of the author.

Problem definition - what is gear rattle? 

Noise generated due to impacts between manual transmissions’ meshing gear teeth in the presence of backlash and induced engine order vibrations

Mechanism of rattle

Types of rattle - Idle rattle (clutch engaged, transmission in neutral, engine at idle rpm). - Drive/Creep rattle (clutch engaged, any gear, 1200 - 2000 rpm). - Coast/Over-run rattle (clutch engaged, high engine loads, 1500 Any public or commercial use requires the agreement of the author. - 4000 rpm).

Experimentation: High and low rattle measurements Spectral content:

Low rattle condition

High rattle condition 

High, medium and lowAnymeasured rattle inputtheconditions from vehicle tests public or commercial use requires agreement of the author.

Regime of Lubrication





Ff N

N – normal applied load [N] Ff – friction force [N]

1

3 5

10

100

Stribeck Curve Boundary lubrication (λ < 1) Mixed (1 ≤ λ ≤ 3) Elastohydrodynamic (3 ≤ λ < 5) Hydrodynamic (5 ≤ λ < 100)



h  Ra h – film thickness Ra – RMS surface roughness

Any public or commercial use requires the agreement of the author.

Mathematical Formulation of Conjunctions: (a)- Loose gear pairs • Forcing elements for loose gears (analytical solution)

Petrov friction: F 

Lubricant film thickness:

Shaft

Lubricant

πη0 v l1ros C

Flank friction:

h  Cb  rp φp  rwφw

ros

Loose Wheel

Ff 

F

rcw

πη0 L us

req

2h

W W

h

Hydrodynamic impact load:

rcp

Lubricant between gear teeth surfaces Pinion

    Lη0 req  3π h  h W 2u  , 0 h  t  t 2 h     req   Lη0 req h W  2u  ,  0 h t

Any public or commercial use requires the agreement of the author.

Mathematical Formulation of Conjunctions: (b)- Engaged gear pair • Forcing elements for engaged gear (analytical solution) Grubin’s relationship for load (W) and lubricant film thickness (ho):  αηu  ho  rx  2.076     rx 

8

11

 E * lrx   W   

1 11

Shaft

Lubricant

ros

Loose Wheel

Since there is no relative speed between shaft and gear, no Petrov friction

F f  Fv  Fa Fv  Visous friction

F

rcw

Fa  Adhesive fricion

W W

h

   2l 1  2    2  ln    mv p    b 2  δ    πLE *    

rcp

Lubricant between gear teeth surfaces Pinion

    πlE *  δ W    2l 1     2 ln      Any public or commercial use requires the agreement of the author.    b 2   

1 2

Mathematical Formulation of Conjunctions: (c)- Reynolds’ solution  h   h3 p    h3 p  h h     6 u  v  2     x   x  y   y  y t   x Transient 1-D solution assumes no side leakage (terms in y-direction are disregarded) h  Converged shape from Reynolds' 1-D solution

Shaft

Lubricant

ros

Loose Wheel

F

F f  Fv  Fa

rcw

Fv  Visous friction

W W

h Lubricant between gear teeth surfaces

No Petrov friction for engaged gear and analytical solution for loose wheels

Fa  Adhesive fricion

rcp

W  Integrated pressure from Reynolds' solution Any public or commercial use requires thePinion agreement of the author.

Mathematical Formulation of Conjunctions: (d)- Energy equation  v   p  ve vx θ    η  x   x   z  compressive heating

2

viscous heating

 θ   ρvx C p     x 

  2θ  kc  2   z 

convection cooling

conduction cooling

Hydrodynamic conjunctions

EHL conjunction • In elastohydrodynamic films, the heat is generated by compressive and viscous heating • Due to thin film thickness and a low Peclet number, convective cooling can be neglected

• In flank conjunctions, because of low generated pressures, the effect of compressive heating is neglected • Due to relatively high film thicknesses and a high Peclet number, conduction is assumed to be insignificant θ 

  2bηu 2    uθi α ' ho pmax   ho      θ    bk     ho  uα ' ho pmax    

8ηus b h2 ρC p

• Lubricant temperature rise in Petrov bearings’ can be estimated as in journal bearings

θ  Any public or commercial use requires the agreement of the author.

2kπηuentr R c2Qs*

Mathematical Formulation of Conjunctions: (e)- Effective viscosity EHL conjunction

Hydrodynamic conjunctions

• The effective temperature in the contact is given by:

• Low generated pressures in hydrodynamic contacts (flank and Petrov bearing) do not cause a change in viscosity, hence:

bulk  θbulk  273 , contact  θcontact  273 contact  bulk  contact

• The mean Hertizan pressure is: pm 

  P'E    4   rx  *

1

η  0.0001e

2

• The effective viscosity in the contact is a function of pressure and temperature, as proposed by Houpert:  So  1    138  α  ln  ηo   9.67    p  o  138   *

η  ηo e

Z   pm   1   1   8   1.98  10    

α* p Any public or commercial use requires the agreement of the author.

 1050.6     θ 129 

Shaft and Bearing Dynamics – Coupled to Gear Dynamics

Any public or commercial use requires the agreement of the author.

CAE Numerical Model

Rev.

6th

F fd 2

2nd Output shaft

F6

2nd

Differential

F5 3rd

1st

Frev

Input shaft

F3

F4

F1

5th

F2

F fd 1

1st Output shaft 4th

Diagrammatic view of the gearbox under investigation

  

All the numerical models were created following Newton-Euler’s formulation The gear bodies are assumed to be rigid (except for local contact deformation) The transmission casing is a deformable body

Any public or commercial use requires the agreement of the author.

Natural Frequencies of the Torsional Linear System K  i  

Lubricant Stiffness

Wi 1 ~ 2 hi h

K  i   K 0i 



K

cp

cos  pni  i   K sp sin pni  i 

p 1

Linearised Equations of Motion I inin 

6

K i 1



rpiin  rwii   0

0i r pi







( I1  I prev )1, prev  K 01rw1 rw11, prev  r p1 in  K 0(rev) r prev r prev1, prev  rwrev wrev  0

  M x   K   K   K  K x  K y  0 I 33  K 03rw3 rw33  rp3in   0 M y   K   K   K  K x  K y  0 I 44  K 04rw4 rw4 4  rp 4 in   0 M x  K    K   K   K  K x  K I 55  K 05rw5 rw55  rp5in   0 I 66  K 06rw6 rw6 6  rp6 in   0 M y  K    K   K   K  K x  K I wrevwrev  K 0rev rwrev rwrev wrev  rprev1, prev   0 I 22  K 02rw2 rw2 2  rp 2 in  0

4

1 1

i 1

x1i

i

x1rev

rev

x1in

in

x1 1

x1 y1 1

4

1 1

i 1

y1i

i

y1rev

rev

y1in

in

y1x1 1

y1 1

6

2

2

x 21 1

i 5

x 2i

i

x 2 rev

rev

y 2i

i

y 2 rev

rev

x 2in

in

x 2 x1 1

6

2

2

y 21 1

i 5

Any public or commercial use requires the agreement of the author.

y 2 in

in

y 2 x1 1

y 0

x 2 y1 1

y 0

y 2 y1 1

4th Gear

10 2

3

4

5

6

2

7

3

4

5

6

7

-5 -10

1st Gear

-10

2

-15 -20

ωn = 138Hz

-35

-40

2

3

4

5

6

2nd Gear

-30

Reverse Gear

7

2

-30

3

4

5

5

6

7

ωn = 225Hz

-20

-25 -30

4

-10

ωn = 193Hz

-20

3

Reverse Gear

6

1st Gear

7

2

3

4

5

6

7

-10

-10

-20

-20 -30

ωn = 258Hz

-40 -50

-20

-30

4th

Gear

ωn = 359Hz -40

3rd Gear

ωn = 438Hz

-60

6th Gear

-40 -80

Natural Frequencies and Mode Shapes of the Linearised System (1)

Any public or commercial use requires the agreement of the author.

2

3

4

5

6

7

-20

ωn = 1080Hz

-40

-60

5th Gear -80

n  1800 Hz

n  1775 Hz

X1

Y1

5th Gear

n  1989 Hz

n  2146 Hz X2

Natural Frequencies and Mode Shapes of the Linearised System (2) Any public or commercial use requires the agreement of the author.

Y2

50

90

(a)

(b)

Rad/s2

Rad/s

2

40

60

30

35

(c)

Rad/s2

20

30 20

30

40

50

C

60

20

30

40

50

25

15 20

30

40

50

C

60

RMS Values of the Idle Gears’ Rotational Accelerations with respect to Temperature: (a) 1st, (b) 2nd and (c) 6th gear

When the ratio (Rattle Ratio) RR  Inertia Torque Drag Torque exceeds unity, rattle occurs Any public or commercial use requires the agreement of the author.

C

60

Model predictions – creep rattle conditions Engaged gear wheel:

• Meshing frequency dominates

Loose gear wheel:

• Improper meshing

• Input energy converted to rattling at engine Any public or commercial use requires the agreement of the author. order harmonics

Grubin at 50C Grubin at 60C Transient at 50C

Numerical transient Transient at 60C

Analytical (Grubin)

Comparison of load per EHL conjunction under transient and analytical quasi-static conditions (60oC)

Transient history of central oil film thickness of typical loaded gear teeth pair

Any public or use requires the agreement of of the loose author. gear pair ( Fluctuations in film thickness incommercial lightly loaded conjunctions

and

80 C

)

EHL of an engaged gear Shaft/Gear Wheel conjunction (inlet temperature of 60C)

EHL (inlet temperature of 20C)

Hydrodynamic (inlet temperature of 60C)

Temperature variation for one meshing cycle (EHL - Hydrodynamic conditions) Any public or commercial use requires the agreement of the author.

Impulsion ratio 

Impulsion ratio (I m )  If < 1  Decelerative motion of loose gears  If = 1  Uniform motion  If > 1  Accelerative motion 

Im 

Tdrive C pet f  Tdrag h pet

Three aspects may be controlled  Clearance between loose wheel and retaining shaft  Viscosity ratio (in the flank and Petrov bearing conjunctions)  Inertia is a controllable parameter (however it should not affect torque transmission when engaged)

or commercial use of requires the agreement the author. Fluctuations inAny thepublic impulsion ratio lightly loadedofloose gear pairs (

and

80 C

)

Measured response with medium rattle input (DMF)

• Wavelet response of accelerometer output from transmission casing (lower shaft bearing cap) • Low-medium spectral content agrees with numerical predictions

• High spectral content is due to modal behaviour of casing

• Wavelet response of microphone output positioned 1 metre from bearing cap •Structure-borne noise identified, commensurate with wave propagation through solid and air • Noise response at point (B) in microphone signal Any public or commercial use corresponds requires the agreement the author. vibration at point (A) to ofstructural

Literature - M. De la Cruz, W.W.F. Chong, M. Teodorescu, S. Theodossiades and H. Rahnejat. Transient mixed thermo-elastohydrodynamic lubrication in multi-speed transmissions. Tribology International, 2012, 49, 17-29. - M. De la Cruz, S. Theodossiades, P. King and H. Rahnejat. Transmission drive rattle with thermo-elastohydrodynamic impacts: Numerical and experimental investigations. International Journal of Powertrains, 2011, 1(2), 137-161. - De la Cruz, M., Theodossiades, S. and Rahnejat, H. An investigation of manual transmission drive rattle. Proceedings of the Institution of Mechanical Engineers Part K: Journal of Multibody Dynamics, 2010, 224(2), 167-181. - Tangasawi, O., Theodossiades, S., Rahnejat, H. and Kelly, P. Non-linear vibro-impact phenomenon belying transmission idle rattle. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 2008, 222(10), 1909-1923. - Tangasawi, O., Theodossiades, S. and Rahnejat, H. Lightly loaded lubricated impacts: idle gear rattle. Journal of Sound and Vibration, 2007, 308(3-5), 418-430. - Theodossiades, S., Tangasawi, O. and Rahnejat, H. Gear teeth impacts in hydrodynamic conjunctions promoting idle gear rattle. Journal of Sound and Vibration, 2007, 303(3-5), 632-658. - Grubin, A. N. Contact stresses in toothed gears and worm gears. Book 30 CSRI for Technology and Mechanical Engineering, Moscow DSRI Trans. 1949;337 - Snidle, R.W. and Evans, H.P. Elastohydrodynamics of gears. Trib. Series (Elsevier Sci.). 1997;32:271-280 - Evans, C. R. and Johnson, K. L. Regimes of traction in EHD lubrication. Proc. IMechE, Part C: J. Mech. Engng. Sci. 1986;200:313-324 - Gohar, R. and Rahnejat, H. Fundamentals of tribology, Imperial College Press, London. 2008 - Greenwood, J. A. and Tripp, J. The contact of two nominally flat rough surfaces. Proc. IMechE, J. Mech. Engng. Sci. 1970-71;185:625-633 - Li, S and Kahraman, A. A transient mixed elastohydrodynamic lubrication model for spur gear pairs. Trans. ASME, J. Trib. 2010;132 - Wang, K. L. and Cheng, H. S. A numerical solution to the dynamic load, film thickness and surface temperatures in spur gears, Part I – Analysis and Part II – Results. ASME Journal of Mechanical Design. 1981a;103:177-187, 1981b;103:188-194 - Hua, D. Y. and Khonsari, M. Application of transient elastohydrodynamic lubrication analysis for gear transmissions. STLE Trib. Trans. 1995;38:905-913 - Brancati, R., Rocca, E. and Russo, R. A gear rattle model accounting for oil squeeze between the meshing gear teeth. Proc. IMechE , Part D: J. Automobile Engng. 2005;219:1075-1083 - Houpert, L. New results of traction force calculations in elastohydrodynamic contacts. Tran. ASME, J. Trib. 1985;185:241-248 - Stribeck, R. Die Wesentliechen Eigenschaften der Gleit und Rollenlager. Z. Ver. Dt. Ing. 1902;46;38:1341-1348,1432-1438 and 1902;46;39:1463-1470. - Rahnejat, H. Computational modelling of problems in contact dynamics. Engineering analysis. 1985;2:192-197 - Rahnejat, H. Multi-body Dynamics: Vehicles, Machines and Mechanisms, Professional Engng. Publ. (IMechE) and SAE (Joint publishers), London, UK and Warrendale, PA, USA. 1998. - Gohar, R. Elastohydrodynamics. Imperial College Press, London. 2001 - M. Perera, S. Theodossiades, H. Rahnejat and P. Kelly, Drive rattle elastodynamic response of manual automotive transmissions. SAE 2011 Noise and Vibration Conference and Exhibition, 2011, Grand Rapids, Michigan, USA. - De la Cruz, M., Theodossiades, S., Rahnejat, H. and Kelly, P. Numerical and experimental analysis of manual transmissions - gear rattle. SAE Proceedings, SAE 2009 World Congress, Detroit, USA. use requires the agreement of the author. Any public or commercial

Gear vibrations in automotive differentials promoting Axle Whine

Any public or commercial use requires the agreement of the author.

Vehicle tests

Mic 1

Mic 2 Mic 3

Mic1: Driver’s ear Mic2: Back of the cabin Mic3: Underbody of vehicle

Z Nose Acceleration Z

Wheels

front of Vehicle Y Y Nose Acceleration

X

Any public or commercial use requires the agreement of the author.

Measurements

Wavelet of signal from the rear cabin microphone

Wavelet of microphone data from differential nose

Vibration Intensity Znose - Temperature 3.5

Integrated Power

3 2.5

Test 14 - 49C

2

Test 16 - 51C Test 20 - 61C

1.5

Test 26 - 68C

1 0.5 0 0

200

400 Frequency (Hz)

600

800

Any public or commercial use requires the agreement of the author.

Methods of investigation MDOF rear axle multibody model (ADAMS) - Large Scale Contact ellipse at mesh point of gear pair - Micro Scale

Any public or commercial use requires the agreement of the author.

RWD Driveline Model

S-bend of leaf springs with twist of the rear axle (at 356 Hz)

Butterfly mode with multiple leaf spring bending (at 772 Hz)

Any public or commercial use requires the agreement of the author.

Gear pair model Rp  p km  p  f g (x)

p pinion

Free body diagram

Rp  p cm x

Tp Rg  p cm x

Tg gear

Equations of motion

g

I pp  R p  p c m x  R p  p k m  p  f g x   T p

Rg  p km  p  f g (x)

I gg  Rg  p cm x  Rg  p k m  p  f g x   Tg

t

t

t0

t0

x(t )   R p ( p )p (t )dt   Rg ( p )g (t )dt  e(t )

…or 1 DOF!

 x  b,  f g ( x)  0,  x  b, 

  R   0 R p  R g  R p g

Any public or commercial use requires the agreement of the author.

xb b xb x  b

Contact Properties

Numerical Simulation of Gear Mesh – Tooth Contact Analysis (TCA) Geometrical Data

Any public or commercial use requires the agreement of the author.

Load distribution Contact area Rigid body deflection

Meshing properties (1) Mesh Stiffness km

Static Transmission Error

Any public or commercial use requires the agreement of the author.

Meshing properties (2) Pinion Contact Radius

Gear Contact Radius

Any public or commercial use requires the agreement of the author.

Gear pair dynamics 140

maximum displacement (m )

single DOF - reduced order system double dof system 130

120

110

100

90

80

0

0.2

0.4

0.6 mesh/n

0.8

1

1.2

Any public or commercial use requires the agreement of the author.

Effect of sliding – frictional properties Friction coefficient and corresponding Torque

Pinion speed 1800 RPM (continuous contact)

Pinion speed 3600 RPM (loss of contact)

Any public or commercial use requires the agreement of the author.

Thermal effects Lubricant Temperature and viscosity variation

Pinion speed 1800 RPM (continuous contact)

Pinion speed 3600 RPM (loss of contact)

Any public or commercial use requires the agreement of the author.

Elasto-hydrodynamic lubrication Flank data, Machine setting and assembly parameters

Tooth Contact Analysis (TCA)

Surface velocities, applied load and surface radii

Elastohydrodynamic Lubrication (EHL)

Film thickness, friction force, efficiency, extrapolated equation

Any public or commercial use requires the agreement of the author.

Tribo-dynamic behaviour of engaged gears

Direction of lubricant flow and contact

Contact footprint and direction of angled flow

Instantaneous contact footprint orientation with respect to direction of lubricant entrainment Any public or commercial use requires the agreement of the author.

Pressure Distribution and Film Thickness pinion angle

Load [N]

Magnitude of Velocity [m/s]

0.5027

744.5161

18.0398

pinion angle

Load [N]

Magnitude of Velocity [m/s]

0.9582

5764.1

15.7962

Velocity Along Minor Axis [m/s]

Velocity Along Major Axis [m/s]

Surface Radius in Minor Axis [m]

Surface Radius in Major Axis [m]

7.9751

16.1813

0.0157

1.0067

Velocity Along Minor Axis [m/s]

Velocity Along Major Axis [m/s]

Surface Radius in Minor Axis [m]

Surface Radius in Major Axis [m]

8.9823

12.9938

0.0180

1.2578

Any public or commercial use requires the agreement of the author.

Film thickness comparison to other known methods

Friction coefficient variation during the meshing cycle

Any public or commercial use requires the agreement of the author.

Literature - Cheng, Y., Lim, T.C. (2001), Vibration analysis of hypoid transmission applying an exact geometry based gear mesh theory, Journal of Sound and Vibration, 240(3), pp. 519-543 - Cheng, Y, Lim, T.C. (2003), Dynamics of hypoid gear transmission with non-linear time-varying mesh characteristics, Trans. ASME, Journal of Mechanical Design 125, pp.373-382. - Wang, J., Lim, T.C., Li, M. (2007), Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity, Journal of Sound and Vibration, 229(2), pp.287-310. - Vaishya, M., Singh, R. (2003), Strategies for modelling friction in gear dynamics, Trans. ASME, J of Mech Design, 125, pp. 383-393 - Kar, C. and Mohanty, A.R. (2007), An algorithm for determination of time-varying frictional force and torque in a helical gear system, Mechanism and Machine Theory, 42, pp. 482-496 - Xu, H. and Kahraman, A. (2007), Prediction of friction-related power losses of hypoid gear pairs, Proc, IMechE, J. Multibody Dyn. 221, 387-400 - Vijayakar, S. 1998, Tooth Contact Analysis Software: CALYX, Advanced Numerical Solutions, Hilliard, OH - Gosselin, G., Guertin T., Remond, D., and Jean, Y. 2000, Simulation and experimental measurement of the transmission error of real hypoid gears under load, Journal of Mechanical Design, 122, pp.109-122 - Borner, J., Houser, D., 1996, Friction and Bending Moments as Gear Noise Excitations, SAE paper 961816 - M. Mohammadpour, S. Theodossiades and H. Rahnejat. Elastohydrodynamic lubrication of hypoid gear pairs at high loads. Proc. of the Inst. of Mech. Eng. Part J: Journal of engineering Tribology, 2012, 226(3), 183-198. - I. Karagiannis, S. Theodossiades and H. Rahnejat. On the dynamics of lubricated hypoid gears. Mech. and Mach. Theory, 2012, 48, 94-120. - G. Koronias, S. Theodossiades, H. Rahnejat and T. Saunders. Axle whine phenomenon in light trucks: a combined numerical and experimental investigation. Proc. of the Inst. of Mech. Eng. Part D: Journal of Automobile Engineering, 2011, 225 (7), 885-894. - Rahnejat, H. (Ed.) Tribology and dynamics of engine and powertrain, Woodhead Publishing Ltd., Cambridge, UK, 2010 - Denny, C.M., “Mesh friction in gearing”, AGMA, Technical Paper No. 98FTM2, 1998 - Michlin, Y. and Myunster, V., “Determination of power losses in gear transmissions with rolling and sliding friction incorporated”, Mech.Mach. Theory, 37, 2002, pp. 167-174 - Benedict, G.H. and Kelly, B.W., “Instantaneous coefficients of gear tooth friction”, Trans. ASLE, 4, 1960, pp. 59–70 - Velex, P. and Cahouet, V.“Experimental and numerical investigations on the influence of tooth friction in spur and helical gear dynamics”, Trans. ASME, J. Mechanical Design, 122, 2000, pp. 515–522. - Velex, P. and Sainsot, P. “An analytical study of tooth friction excitations in errorless spur and helical gears”, Mechanism and Machine Theory, 37, 2002, pp. 641–658. - Litvin, F. L., Fuentes, A., Fan, Q. and Handschuh, R. F. “Computerized design, simulation of meshing, and contact and stress analysis of facemilled formate generated spiral bevel gears”, Mech. & Mach. Theory, 37, 2002, pp. 441–459 - Kolivand, M., Li, S. and Kahraman, A. “Prediction of mechanical gear mesh efficiency of hypoid gear pairs”, Mech. & Mach. Theory,45, 2010, pp. 1568–1582 - Simon, V., Influence of machine tool setting parameters on EHD lubrication in hypoid gears, Mech. & Mach. Theory, 44, 2009, pp. 923–937 - Vaishya, M. and Singh, R. “Analysis of periodically varying gear mesh systems with Coulomb friction using Floquet theory”, JSV., 243, 2001, pp. 525-545 - Akin, L. S., “EHD lubricant film thickness formulae for power transmission gears”, Trans. ASME, J. Lubn.Tech., 1974, pp.426-431 - Naruse, C., Haizuka, S., Nemoto, R., and Umezu, T.,“Limiting loads for scoring and frictinal loss of hypoid gear”, Bull. JSME, 29(253), 1986, pp. 2271-2280 public commercial requires the agreement of the author. - Xu, H., Kahraman, A. and Houser, D.R., “AAny model to or predict frictionuse losses of hypoid gears”, AGMA Tech. Pap.: 05FTM06, 2005

Impact induced vibrations in vehicular drivelines promoting Clonk (or Clunk!) Noise

Any public or commercial use requires the agreement of the author.

Shuffle and Shunt Shuffle is the first rigid body torsional vibration mode of the entire powertrain system. It is in the range 3-7 Hz. It can be noted with sudden throttle tip-in from coast to drive condition, or conversely in back-out by sudden release of throttle (tip-out) from drive to coast.

It is usually noted by the coupled fore and aft motion of the vehicle, referred to as shunt (a translational motion at the same frequency as the shuffle response). Shuffle can also be induced by sudden clutch engagement or release. It also manifests itself when negotiating a speed breaking bump. It is most prominent at low road speeds and in low gear. Any public or commercial use requires the agreement of the author.

Clonk accompanies shuffle with sudden demands in throttle tip-in/tip out or with abrupt clutch in low gear and at low engine speed actuation (1.5-5KHz). Clonk is the high frequency elasto-acoustic coupling response of driveline system.

Torque

1st clonk

2nd clonk

shuffle frequency 3-7 Hz

3rd clonk

Time

The shuffle action of the drivetrain leads to torque reversals as impact action takes place in transmission and differential meshing teeth, as well as in the propshaft joints, which in turn can lead to propagation of high frequency structural waves (clonk). Any public or commercial use requires the agreement of the author.

Clonk is an audible and tactile response from the driveline, which may occur under several different driving conditions, as follows: Tip-in clonk, when the throttle is rapidly applied from coast. Tip-out clonk, when the throttle is abruptly released from drive. Clutch engagement clonk may occur after gear selection, if the clutch is rapidly engaged. It is more noticeable during low speed creep manoeuvres and low gear. Shift clonk may occur during a gear up-shift. The resulting torsional impulse delivered to the driveline gives rise to a short duration vehicle jerk and an accompanying metallic clonk or thud noise. Important parameters affecting shuffle and clonk are: - Lash zones in the drivetrain: transmission gear pairs, differential unit gears and splined joints. - Sources of compliance in the system, such as the dual mass flywheel torsional stiffness, the torsional stiffness of the clutch, the presence of any clutch system predamper, the stiffness of the rear-axle half-shafts and driveshafts in rear wheel drives, the longitudinal stiffness of the tyre. - The clonk response refers to coincidence of structural waves with modes of acoustic cavities, such as in the transmission bell housing, the hollow driveshaft tubes and the differential unit cavity. Any public or commercial use requires the agreement of the author.

Driveline experimental rig (“static”)

Any public or commercial use requires the agreement of the author.

Experimental results 100

T o rque 1 - 2 m s im pa c t

50

A c c e le ra tio n

0 T im e -5 0

A p p lie d to rq u e

5 0 m s de c a y tra ns ie nt

-1 0 0

-1 5 0 Any public or commercial use requires the agreement of the author.

The three-piece driveline experimental rig

Positions of all monitoring equipment

Clutch Pedal

A A

L

L

L A

Motor

Transmission

Driveshaft(1)

A Driveshaft(2)

Centre Bearing(2)

Centre Bearing(1)

A: Accelerometer Location L: Laser Location M: Microphone Location

M

Driveshaft(3)

M

Any public or commercial use requires the agreement of the author.

M

Differential

Clonk accelerative noise (impact)

(a) Clonk accelerative noise (impact)

(b) Clonk accelerative noise (impact) Ringing noise

(c) Any public orof commercial use noise requiressignal the agreement of the Solid flywheel configuration – Wavelets the clonk for the (a)author. front, (b) middle and (c) rear shafts

Clonk accelerative noise (impact)

(a) Clonk accelerative noise (impact)

Ringing noise

(b) Clonk accelerative noise (impact)

(c) Any public or commercial use requires agreement the author. DMF configuration – Wavelets of the clonk noise signalthefor the (a)offront, (b) middle and (c) rear shafts

Clonk Investigation in a light truck Rear Wheel Axles

Input-Output Shafts Driveline Tubes

Flexible Components Introduced by FEA Techniques and applying the component mode synthesis method Any public or commercial use requires the agreement of the author.

Transmission (Helical Gears)

Calculation of the developed forces between mating teeth pairs during the meshing cycle through external code and introduction in the model in real time (elastodynamics, elastohydrodynamics)

Differential (Hypoid Gears)

4.2E+008

k(t)

3.9E+008

3.6E+008 0

0.125



0.25

Any public or commercial use requires the agreement of the author.

φ1(t), ω1

452

450

pinion 448

R1

446

444

φ2(t), ω2

k(t)

442

440

gear 0.05

R2

pinion

0.1

0.15

0.2

Gear Meshing Stiffness (N/μm) Variation with Respect to the Roll Angle (rad) (Second Gear Set - One Cycle, Unmodified Gears). 445

Line of Action

440

435

b

b

430

425

420

gear 0.05

0.1

0.15

0.2

0.25

Gear Meshing Stiffness (N/μm) Variation with Respect to the Roll Angle (rad) (Second Gear Set - One Cycle, Modified Gears).

Any public or commercial use requires the agreement of the author.

Any public or commercial use requires the agreement of the author.

1830 Hz

1838 Hz

2312 Hz

2338 Hz

2454 Hz

2457 Hz

2502 Hz

2718 Hz

2678 Hz

2857 Hz

2871 Hz

3540 Hz

3348 Hz

3634 Hz

Any public or commercial use requires agreement the author. Mode shapes of the main breathing modes observed in the clonk noiseofmeasurements and numerical results

Literature - R. Krenz, Vehicle response to throttle tip-in/tip-out. SAE Technical Paper Series 850967 (1985). - A. Laschet, Computer simulation of vibrations in vehicle powertrains considering nonlinear effects in clutches and manual transmissions. SAE Technical Paper Series 941011 (1994). - S. J. Hwang, J. L. Stout and C. C. Ling, Modeling and analysis of powertrain torsion response. SAE Technical Paper Series 980276 (1998). - M. Menday, H. Rahnejat and M. Ebrahimi, Clonk: an onomatopoeic response in torsional impact of automotive drivelines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 213 (1999) 349-357. - S. Vafaei, M. Menday and H. Rahnejat, Transient high-frequency elasto-acoustic response of a vehicular drivetrain to sudden throttle demand. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 215 (2001) 35-52. - A. Farshindiafar, M. Ebrahimi, H. Rahnejat and M. Menday, High frequency torsional vibration of vehicular driveline systems in clonk. International Journal of Vehicle Design 9 (2002) 127-149. - J. W. Biermann and B. Hagerodt, Investigation into the clonk phenomenon in vehicle transmission-measurement, modelling and simulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 213 (1999) 53-60. - F. Petrone, G. Fichera and M. Lacagnina, A numerical model to analyze the dynamic response of a vehicle to variations in torque transmitted by the driveline. SAE Technical Paper Series 2001-01-3334 (2001). - C. K. Chae, Y. W. Lee, K. M. Won and K. T. Kang, Experimental and analytical approach for identification of driveline clunk source and transfer path. SAE Technical Paper Series 2004-01-1231 (2004). - Theodossiades, S., Gnanakumarr, M., Rahnejat, H. and Kelly, P. On the effect of dual mass flywheel upon impact induced noise in vehicular powertrain systems. Proc. of the Inst. of Mech. Eng. Part D: Journal of Automobile Engineering, 2006, 220 (6), 747-761. - Theodossiades, S., Gnanakumarr, M. and Rahnejat, H. Root cause identification and physics of impact induced driveline noise in vehicular powertrain systems. Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2005, 219, 1303-1319. - Gnanakumarr, M., Theodossiades, S., Rahnejat, H. and Menday, M. Impact Induced Vibration in Vehicular Driveline Systems: Theoretical and Experimental Investigations. Proc. of the Inst. of Mech. Engineers Part K: Journal of Multi-body Dynamics, 2005, 219, 1-12. - M. Gnanakumarr, S. Theodossiades, H. Rahnejat and M. Menday, Elasto-multibody dynamic simulation of impact induced high frequency vehicular driveline vibrations. Proceedings of the ASME IMECE 2003, Washington, USA, 2003. - S. Theodossiades, M. Gnanakumarr, H. Rahnejat and M. Menday, Mode identification in impact-induced high-frequency vehicular driveline vibrations using an elasto-multibody dynamics approach. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 218 (2004) 81-94. - K. R. Fyfe and F. Ismail, An investigation of the acoustic properties of vibrating finite cylinders. JSV, 128(3) (1989) 361-375. - Moetakef, M., Bresky, A., Zilberman, M., Pham, T. et al., "Reducing High Frequency Driveshaft Radiated Noise by Polymer Liners“, SAE Technical Paper 2005-01-3554, 2005, doi:10.4271/2005-01-3554. - Nitin Y. Wani, Vinod K. Singh, Greg Falbo and Vincent D. Monkaba, “Finite Element Model Correlation of an Automotive Propshaft with Internal and External Dampers”, SAE Technical Paper 2004-01-0862 - Martin G. Foulkes, James P. De Clerck and Rajendra Singh, “Vibration Characteristics of Cardboard Inserts in Shells”, SAE Technical Paper 2003-01-1489 Any public or commercial use requires the agreement of the author.