1

1

University of Cincinnati

Modeling, Analysis and Control of High-Speed Precision Gear Dynamics

August 10, 2015

Teik C. Lim, Ph.D., P.E., Fellows(ASME,SAE)Dean, College of Engineering and Applied Science

Herman Schneider Professor of Mechanical Engineering

ASME/NCAD Tutorial

2

Presentation Outline

Problems in geared transmissionsVibration, Noise, Durability, Precision

Physics of gear pair dynamicsOut-of-phase gear pair torsion modeDynamic mesh force generationTime-varying and nonlinear response

Quiet gear design approaches Active control of gear pair dynamics

2

3

High-Speed, High-Power Density, Precision Gears

Hypoid

Pinion

GearSpur

Function: to transmit motion and torque in a controlled manner

Applications: automotive, aerospace, industrial, manufacturing, etc.

Basic Types: spur, helical, epicyclic, bevel, hypoid

Problems: vibration, noise, fatigue, durability, precision

Simple to Complex Geometry and

Tooth Form

Pinion

Gear

4

Geared System Dynamic Characteristics

02000

40006000

800010000

12000

0

1000

2000

3000

4000

Shaft speed (rpm)Frequency

1x

2x

Res

po

nse

TransmissionError

Excitation

DynamicMesh Force

Sensitivity to System

Dynamics

VibrationTransmission Gear Noise

Gear noise & vibration generation.

Mesh harmonics = N j where j=1,2,3,…

Teeth Speed

3

5

Gear Excitation Sources Transmission error (TE) arises from deviation of gear rotations from the ideal

motion defined by the gear ratio. This deviation is from profile errors, elastic deformation and misalignment.

N = # teeth (p=pinion, g=gear) = angular displacement = deviation from ideal motion

Other possible excitation sources:

Mesh stiffness variationsShuttling forces and bearing forcesFriction forcesAir and lubricant entrainment

p g

g p

N

N

g

p

kmp

kmg

TE

(TE)

Tra

nsm

issi

on

Err

or

mesh cycle t

j

6

Parallel Axis Gear Pair Torsional Vibration

Km

Cm

p

g

rg

rp Pinion

GearDamped mesh stiffness

Typically rigid body rotation is ignored. Only interested in perturbation about the mean speed as that relates to gear noise

In pure torsion vibration model, all forms of gear system basically behaves like a parallel axis gear pair

4

7

Hypoid Gear Pair Torsion Dynamics

Gear shaft

Pinion shaftpmpmppp TefkecI )()(

gmgmggg TefkecI )()(

2-DOF gear pair torsion, semi-definite, dynamical equations

)()( eI

T

I

Tmpfkpcpm

g

gg

p

ppemme

ggpp

Out-of-phase gear pair torsion mode

bp

bpb

bp

bp

bp

pf

,

,0

,

)(

ep

)///(1 22ggppe IIm

Transmission Error (TE)

Hypoidmodel

No impact

Single-sided impact

Double-sided impact

)( pf

p-b b

p gg

8

Gear Pair Torsion Modes

In-phase gear pair torsion mode

Out-of-phase gear pair torsion mode

The out-of-phase gear pair torsion mode is the primary cause of gear whine response due to TE

emn mK0n

Pinion

Gear

Pinion

Gear

5

9

Gear Pair Torsion Modes in Larger System

Mode number, r Tr r (Hz)

Mode descriptionsClass of out-of-phase gear pair torsion modes

2 2.97E-4 229 Out-of-phase torsion, pinion and gear axial motion

4 3.60E-4 441 Out-of-phase torsion, gear transverse motion

6 1.83E-2 589 Out-of-phase torsion, pinion yaw and pitch motion

7 5.77E-2 770 Pinion torsion and pitch motion, gear pitch

8 5.83E-3 880 Out-of-phase torsion, gear yaw and pitch motion

11 1.53E-1 1210 Pinion torsion and pitch motion

12 1.70E-1 1960 Out-of-phase torsion, pinion bounce

13 2.97E-2 2490 Out-of-phase torsion, pinion yaw motion

14 4.70E-1 3670 Out-of-phase torsion, pinion pitch motion

Tr m r mT { } { } Modal index for mesh action:

Mesh component of mode shape

LOA vector

10

Out-of-phase torsion with pinion bounce

X1

Z1

1

Hypoid Gear

Z2

2

Y1

Z1

Deflected position

Original position

Out-of-phase torsion

Pinion bounce

Hypoid Pinion

Hypoid Gear Pair

Worsen mesh deformation

6

11

Dynamic Mesh Force

Dynamic forces developed at the tooth contact surface due to interaction between TE and system dynamics.

Fm = Net dynamic mesh forceDm = Dynamic mesh stiffness

Dynamic mesh force is a measure of the sensitivity of the drive train system to transmission error excitation.

Dynamic mesh force is theorized to be the main cause of gear whine response.

m mF D * (TE)

g

p

kmp

kmg

Fm

12

500 1000 1500 2000 2500 3000 3500 400010

-1

100

101

102

103

104

Me

sh F

orc

e (l

b)

Frequency (Hz)

Geared System Response Function

3-D Geared System Model

pTpg

Tgd qhqh

dmdm ckF

Dynamic mesh force

Dynamic transmission error

Out-of-phase gear pair torsion modes

7

Gear Whine M&S Methodology

Driveline design parameters

Gear design & mfg parameters

Contact analysis

Mesh model (STE, Km)

Driveline substructures

Gear geometry

Driveline system model

Forced response analysis

Operating response

Inputload & speed

Bearing stiffness analysis

Dynamic characteristics

Modal & FRF analysis

DMF, DTE,

modes

Driveline components

Mean torque

Parametric Analysis

Scope of this Example

13

Gear Mesh and Vibration Modeling

Load, STE, Kmesh

Tooth contact analysis

1

2

Gear

Pinionu-1 uu+1

Spatial/time-varying gear mesh model

Contact cells & mesh properties

Friction loads

Normal loads

Vibratory response

Fmesh DTE

Non-linear system dynamic model

Pinion

Gear

Plane of action

Driver

Load

Gear geometry

Yg

Yp

Xp

E

14

8

Gear Tooth Contact Analysis

Finite Element Mesh

Contact Pattern

KmTEGear

Pinion

Lm

Om

Lm

Om

Om

Fundamental Gear Mesh Parameters: (1) mesh point, (2) mesh stiffness, (3) TE, and (4) line-of-action

15

km

ks

kp

klka

kg

θg

Il

mp

mg

Ia

θp kdIdIs

θa

θs

θl

θd

Ωl

Ωd

E

Ip

Igxg

xp

Inertia: Ip= 0.004 kg.m2 Ig= 0.008 kg.m2

Ia= 0.01 kg.m2 Il = 0.042 kg.m2

Is=0.012 kg.m2 Id=0.044 kg.m2

Mass:mp = 1.0 kg mg= 1.5 kg

Translational Stiffness:kp= 5e7 N/mkg= 4e7 N/mkmo= 1e7 N/m

Rotational Stiffness:ka= ks=6e3 Nm/radkl= kd=8e3 Nm/rad

Radius of Pinion & Gear:Rp= 0.03 m Rg= 0.06 m

Example Driveline Model

Driver speed =

Driven speed =

Input torque = T(t) = Td(t) + Tm

p p

j t

N

E( t ) E e

dj t

d dT ( t ) T e

16

9

)}({}]{[}]{[}]{[ tfqKqCqM

Equations of Motion (LTI model)

Tq } x x {}{ laggppsd

ll

llaa

mggmmpm

agmgmagmgpm

mgmpmpm

pmgpmpmpmss

ssdd

dd

kk

kkkk

kkrkkrk

krkrkkrkrrk

krkkkrk

rkrrkrkrkkk

kkkk

kk

K

000000

00000

0000

000

0000

000

00000

000000

][ 2

2

]I I M I M I I I[][ laggppsddiagM

Mean Torque, Tm

Tmo

Me

sh

Sti

ffn

es

s, k

m

kmo

Tmo = 100 Nmkmo = 1e7 N/m

0 0 Td m p m m g m l{ f ( t )} { T , ,k r E , k E , k r E ,k E , , T } Tl(t) and E(t) are harmonic

= 0.01 (assuming uniform modal damping ratio of 1% for the baseline model)

11 ])([2)]([][

iTC ][ is modal matrix,

17

System Modes

Out-of-phase gear pair torsion, pinion translation1272.1 8

Out-of-phase gear pair torsion, gear translation895.47

Out-of-phase gear pair torsion366.36

In-phase gear pair torsion, driver and driven are in-phase (2nd mode)228.75

In-phase gear pair torsion, driver and driven are out-of-phase182.74

In-phase gear pair torsion, driver and driven are in-phase (1st mode)120.33

Driver, load, inertia Is and inertia Ia torsion40.82

Rigid body torsional motion0.01

Mode shape descriptionsNatural freq (Hz)Mode #

Out-of-phase gear pair torsion, pinion translation1272.1 8

Out-of-phase gear pair torsion, gear translation895.47

Out-of-phase gear pair torsion366.36

In-phase gear pair torsion, driver and driven are in-phase (2nd mode)228.75

In-phase gear pair torsion, driver and driven are out-of-phase182.74

In-phase gear pair torsion, driver and driven are in-phase (1st mode)120.33

Driver, load, inertia Is and inertia Ia torsion40.82

Rigid body torsional motion0.01

Mode shape descriptionsNatural freq (Hz)Mode #

-3.6515 -1.9876 -2.1559 0.7620 -0.4619 0.0430 -0.0001 -0.0000-3.6515 -1.2688 4.6221 -4.7636 4 .7826 -1.2087 0.0226 0 .0122-3.6515 -0.1436 8.3751 0 .4304 -7.9723 9.9263 -1.3800 -1.5248-0.0000 -0.0047 -0.0023 -0.0204 0.0077 0 .1105 -0.3120 0.9434-1.8257 0.5120 4.4786 2 .7300 -4.9239 -8.0974 1.3460 1.5066

0 .0000 0.0059 0 .0030 0.0262 -0.0100 -0.1541 -0.7662 -0.2346-1.8257 2.7301 2.1880 7 .5621 5.0657 1.2565 -0.0267 -0.0145-1.8257 4.1693 -1.0934 -1.2769 -0.5149 -0.0469 0.0002 0.0000

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8

Mode shapes

d

s

p

p

g

g

a

l

x

x

Primary gear pair (mesh) modes

18

10

Natural Frequencies vs Mean Drive Torque

0 20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

1200

1400

Torque (N-m)

Nat

ural

fre

quen

cies

(H

z)

Mode 1

Mode 2Mode 3

Mode 4

Mode 5

Mode 6Mode 7

Mode 8

Tm

o=

10

0 N

m

Mode 7

Mode 8

Mode 6

Mode 5

Mode 4Mode 3

Mode 2

Mode 1, rigid body rotation

19

Dynamic Transmission Error (DTE – FRF result)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

Pha

se (

degr

ee)

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-3

10-2

10-1

100

101

102

Frequency (Hz)

Dyn

amic

tra

nsm

issi

on e

rror

(m

icro

-m p

er u

nit

TE

) p p g g g pDTE r r x x E

1m

ST

E, |

E|

Assume STE, |E|=1m

Frequency

20

11

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

Pha

se (

degr

ee)

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-2

10-1

100

101

102

103

Frequency (Hz)

Dyn

amic

mes

h fo

rce

(N p

er u

nit

TE

)

Dynamic Mesh Force (DMF – FRF result)

Assume unit STE, |E|=1m

mDMF k DTE

SMF=kmSTE=10

21

Effect of Damping on DMF

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

Pha

se (

degr

ee)

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-2

10-1

100

101

102

103

Frequency (Hz)

Dyn

amic

mes

h fo

rce

(N p

er u

nit

TE

)

Damping ratio = 5%

Damping ratio = 1% (Baseline)

22

12

)}({}]{[}]{[}]{[ tfqKqCqM

2 1 ji tj j j j{ q } ( [ M ] i [ C ] [ K ]) { F } E e

Transmission Error Excitations

6

1

}{}{j

jqq

m 1 sm 2 sm 3

m 24 sm 25 sm 26

6

1 ji t

jj

E( t ) E e

1 2 3 11

E 3 m, E E E2

Tgpm rrkF }0,0,1,,1,,0,0{}{

6

1

2

jjSRSS DMFDMF

4 5 6 41

E 1.5 m, E E E2

jpjgjgjgpjpj ExxrrDTE j m jDMF k DTE

SRSS = square root of sum squares

w1w2 w3 w4w5 w6

E1

E2 E3E4

E5 E6

Frequency

Sta

tic T

ran

smis

sion

Err

or

1st mesh2nd mesh

23

Pinion tooth number = 10, Shaft frequency = 35 Hz, Mesh frequency = 350 Hz

DTE at driver shaft speed = 2100 rpm

0 10 20 30 40 50Shaft order

0 1 2 3 4 5Mesh order

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

14

Frequency (Hz)

Dyn

amic

tra

nsm

issi

on e

rror

(m

icro

-m) 1st mesh

2nd mesh

x

x x xx x

x STE

DTE

24

13

0 10 20 30 40 50Shaft order

0 1 2 3 4 5Mesh order

0 200 400 600 800 1000 1200 1400 1600 1800 20000

20

40

60

80

100

120

140

Frequency (Hz)

Dyn

amic

mes

h fo

rce

(N)

DMF at driver shaft speed = 2100 rpm Pinion tooth number = 10, Shaft frequency = 35 Hz, Mesh frequency = 350 Hz

1st mesh1st mesh

2nd mesh

x

x x xx x

x

DMF=kmDTE

SMF=kmSTE

25

3-D Order Plot of DMF for a Fixed Mean Drive Torque

02000

40006000

800010000

12000

0.5

1

1.5

2

2.50

100

200

300

400

500

Shaft speed (rpm)Mesh order

Dyn

amic

mes

h fo

rce

(N)

26

14

02000

40006000

800010000

12000

0

1000

2000

3000

4000

50000

100

200

300

400

500

Shaft speed (rpm)Frequency

Dyn

amic

mes

h fo

rce

(N)

3-D Freq Plot of DMF for a Fixed Mean Drive Torque

27

3-D Torque-Speed Plot of DMF (1st mesh)

02000

40006000

800010000

12000

0

50

100

150

2000

100

200

300

400

500

Shaft speed (rpm)Torque (N-m)

Dyn

amic

mes

h fo

rce

(N)

1DMF

28

15

3-D Torque-Speed Plot of DMF (SRSS)

02000

40006000

800010000

12000

0

50

100

150

2000

100

200

300

400

500

Shaft speed (rpm)Torque (N-m)

Dyn

amic

mes

h fo

rce

(N)

6

1

2

jjSRSS DMFDMF

SRSS = square root of sum squares

29

DTE for a Fixed Mean Drive TorqueHighly compliant driveline torsional stiffnesses (kd=ks=kl=ka=1 Nm), i.e. Gear Pair Dynamics only

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

Pha

se (

degr

ee)

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-4

10-3

10-2

10-1

100

101

102

Frequency (Hz)

Dyn

amic

tra

nsm

issi

on e

rror

(m

icro

-m p

er u

nit

TE

)

Gear pair dynamics

Driveline dynamics

p p g g g pDTE r r x x E

Assume STE, |E|=1m

Gear pair dynamics

30

16

DMF for a Fixed Mean Drive TorqueHighly compliant driveline torsional stiffnesses (kd=ks=kl=ka=1 Nm), i.e. Gear Pair Dynamics only

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

Pha

se (

degr

ee)

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-3

10-2

10-1

100

101

102

103

Frequency (Hz)

Dyn

amic

mes

h fo

rce

(N p

er u

nit

TE

)

Gear pair dynamics

Driveline dynamics

Assume unit STE, |E|=1m

mDMF k DTE

SMF=kmSTE=10

Gear pair dynamics

31

0 20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

1200

1400

Torque (N-m)

Nat

ural

fre

quen

cies

(H

z)

Mode 1

Mode 2Mode 3

Mode 4

Mode 5

Mode 6Mode 7

Mode 8

Natural Frequencies vs Mean Drive TorqueHighly compliant driveline torsional stiffnesses (kd=ks=kl=ka=1 Nm), i.e. Gear Pair Modes only

Mode 6

Mode 7

Mode 8

Modes 1-5

32

17

0 10 20 30 40 50Shaft order

0 1 2 3 4 5Mesh order

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

14

Frequency (Hz)

Dyn

amic

tra

nsm

issi

on e

rror

(m

icro

-m)

Pinion tooth number = 10, Shaft frequency = 35 Hz, Mesh frequency = 350 Hz(E5=E6=2*E4)

DTE at driver shaft speed = 2100 rpm

1st mesh

2nd meshx

x x x

x x

x STE

DTE

33

0 10 20 30 40 50Shaft order

0 1 2 3 4 5Mesh order

0 200 400 600 800 1000 1200 1400 1600 1800 20000

20

40

60

80

100

120

140

Frequency (Hz)

Dyn

amic

mes

h fo

rce

(N)

Pinion tooth number = 10, Shaft frequency = 35 Hz, Mesh frequency = 350 Hz(E5=E6=2*E4)

DMF at driver shaft speed = 2100 rpm

1st mesh

2nd meshx

x x x

x x

x

DMF=kmDTE

SMF=kmSTE

34

18

02000

40006000

800010000

12000

0.5

1

1.5

2

2.50

100

200

300

400

500

Shaft speed (rpm)Mesh order

Dyn

amic

mes

h fo

rce

(N)

(E5=E6=2*E4)

3-D Order Plot of DMF for a Fixed Mean Drive Torque

35

02000

40006000

800010000

12000

0

1000

2000

3000

4000

50000

100

200

300

400

500

Shaft speed (rpm)Frequency

Dyn

amic

mes

h fo

rce

(N)

(E5=E6=2*E4)

3-D Freq Plot of DMF for a Fixed Mean Drive Torque

36

19

(E5=E6=2*E4)

3-D Torque-Speed Plot of DMF (1st mesh)

1DMF

02000

40006000

800010000

12000

0

50

100

150

2000

100

200

300

400

500

Shaft speed (rpm)Torque (N-m)

Dyn

amic

mes

h fo

rce

(N)

37

(E5=E6=2*E4)

3-D Torque-Speed Plot of DMF (SRSS)

6

1

2

jjSRSS DMFDMF

SRSS = square root of sum squares

02000

40006000

800010000

12000

0

50

100

150

2000

100

200

300

400

500

Shaft speed (rpm)Torque (N-m)

Dyn

amic

mes

h fo

rce

(N)

38

20

Geared Rotor System Models

Multi-body system

Pinion

pinion

shaft

Gear

gear

shaft

Pinion

pinion

shaft

Gear

gear

shaft

g

p

Gear pairMDOF lumped

parameter system

Dynamic finite element model

Engine

Trans

P/S

39

40

Gear Mesh Compliance TheoryPinion

Gear

Kp

Kg

CpCg

Compliance Functions:

Cp = Hpp – Hgp

Cg = Hgg – Hpg

Fm = (Cp + Cg + 1/Km)-1

Design Fm

Cp = -(Cg + 1/Km) Fm is max

|Cp|>>|Cg+1/Km|; high Cp low Fm; low Cp high Fm

21

41

Gear Vibration Transmissibility Model

TE Fm

2)a(c)a(oH

1)a(c)a(oH

p)a(c)a(oH

Vibration transmissibility

Structure response sensitivity

1cT

2cT

pcT

Coupling force

bF

Coupling force

bF NoiseP()

Coupling force

bF

1

2

p

)}({)}({)( rT

m TFP

Design Trade-off

42

Case Study – Rear Axle Whine

Baseline

Improved

Freq. rangeof interest

200 400 600 800Frequency (Hz)

1.0E3

1.0E2

1.0E1

F m

Effect of design changes on dynamic mesh force

Effect of design changes on vehicle interior sound pressure level

Design changes adopted include making the gear train more compliant torsionally, lowering ring gear inertia,

and tuning the final drive carrier mount stiffness

Im proved

B ase line

SP

L

Frequency (Hz)

22

43

Time-Varying Nonlinear Effects

Time/spatial-varying mesh

Mesh stiffness variation

Backlash nonlinearity

eTTpfkpp ggppgp

gp

~~~~~

)~(~

1

~~~)

~~(2~

2222

1~1~1

1~

1~ ,0

,1~

)~(

p

p

p

p

p

pf

Mean load

Non-linear displacement function

Time-varying mesh stiffnessTime-varying directional rotation radius

No impact

Single-sided impact

Double-sided impact

)~( pf

p~-1 1

Harmonic Balance Method for simplified NLTV case, but generally numerical integration is needed

44

Nonlinear Vibration Response

* and denote no tooth impact.x and denote single-sided tooth impact.+ and denote double-sided tooth impact.

This image cannot currently be displayed.

Increasing frequency of excitationDecreasing frequency of excitation

)()( 12 tet pg

1.0 fundamental frequency

=0.60

=1.4

=1.6

23

45

Harmonic Solution – Period One

Elliptic phase plane

Poincare map

One-single point

22

DTE-disp. DTE-disp.

m

Am

plit

ude

60.0

Discrete peaks

46

Harmonic Solution – Period FourPoincare map

4

2

4

3

4 discretepoints

DTE-disp. DTE-disp.

4.1

Frequency spectrum

Discrete peaks

2-sided impact

Am

plit

ude

24

47

Chaotic ResponsePoincare map

~ broadband

DTE-disp. DTE-disp.

Frequency spectrum

6.1

1-sided impact

Am

plit

ude

48

Effect of Torque Load

0 0.5 1 1.5 2 2.5

100

101

102

0 0.5 1 1.5 2 2.5

100

101

102

0 0.5 1 1.5 2 2.5

100

101

102

0 0.5 1 1.5 2 2.5

100

101

102

(200Nm) 0.98~

pT

(1000Nm) .283~

pT(500Nm) .012~

pT

(125Nm) 0.65~

pT

Frequency Frequency

Dyn

amic

Res

pons

e

Dyn

amic

Res

pons

e

Dyn

amic

Res

pons

e

Dyn

amic

Res

pons

e

*, □ no tooth impact•, ○ single-sided tooth impact

+, ▽ double-sided tooth impact

IncreasingFrequency

DecreasingFrequency

25

49

Active Shaft Transverse Vibration Controller

Speed & Torque Sensors

Adjustable Support

Vibration Sensor

Adjustable Support

Piezoelectric Actuator

Stinger Rod

Line of Action

Load Cell Auxiliary Bearing

The active control system exploit the strong coupling between torsional and lateral gear vibration in the

attempt to suppress generation of dynamic mesh force

50

Experimental Gearbox Systems

Open-loop Direct Drive Gearbox Test System

Reconfigurable Gearbox

Drive Motor Load

Vibration Sensor

Actuator

Electronics &Amplifier

Closed-loop Power Re-Circulation Gearbox Test System

TestGearbox

SlaveGearbox

AdjustableSupport

ActuatorClutch

Drive Motor

Vibration Sensor

26

51

Active Gear Vibration Control SetupVibration sensors

FFT Analyzer

Oscilloscope

PC computer

Gearbox system

PowerAmplifier

Signal Conditioner

Load

Driver

Actuator

Digital Signal Processing Board

52

Enhanced Filtered-X Least Mean Square

HhTE(z)

LMS1

Noise Generator

H2(z)

LMS2

+

te(n)

v(n)

u(n)

d(n)yh(n)

+

-

+

+

r(n)

Gearbox System

Frequency Estimator

Controller

W(z)

TE Excitation

Predictive Error Filter

+

Rotation Pulse Train

)(ˆ2 zh

)(ˆ2 zh

27

53

Control of Fundamental Gear Mesh Harmonic

0 100 200 300 400 500 600 700 800 900 1000-55

-50

-45

-40

-35

-30

-25

-20

Acc

y(dB

)

Frequency (Hz)

Control OffControl On

Gea

rbox

vib

rati

on (

dec

ibel

sca

le) Greater than 10dB

reduction at mesh frequency

Gearbox response with and without active vibration control(Experimental Results)

Measured gearboxvibrationresponse

Load

DriverMotor

54

Dual-mesh Vibration Control Result

0 100 200 300 400 500 600 700 800 900 1000Frequency (Hz)

Gea

rbox

Vib

ratio

n

Control OffControl On

10dB

Dual-mesh vibration control

Vibration reduction

Control Algorithm

Vibration Sensors

Actuation Signal

Data Acquisition

Test Gearbox

28

55

Multi-mesh Vibration Control Result

-60

-50

-40

-30

4 x

mes

h

-60

-50

-40

-30

5 x

mes

h

-60

-50

-40

-30

6 x

mes

h

160 180 200 220 240 260-60

-50

-40

-30

Sha ft Speed (RPM)

7 x

mes

h

Acc

y (dB

)

( a)

( b)

( c)

( d)

Control off

Control on

Vibration reduction up to 14dB and averages about 5dB

56

Summary

Modeling/Analysis of Gear Pair Dynamics

Out-of-phase Gear Pair Torsion Modes

Mesh Force Generation and Transmissibility

Design Strategies

Time-varying and Nonlinear Effects

Active Gearbox Vibration Control

29

57

Thank you!Questions?

Acknowledgements: Gear Consortium (since 1997) NSF, ARO Graduate Students:

Y.Cheng(PhD), H.Wang(PhD), C.Moon(MS), Y.H.Guan(PhD), M.Li(MS,PhD), R.Tanna(PhD), J.Wang(PhD), P.Sondkar(PhD), T.Peng(PhD), J.Yang(PhD), J.Duan(PhD), G.Sun(PhD)