vehicle ride. dynamic system & excitations vehicle excitations: 1.road profile & roughness...
TRANSCRIPT
![Page 1: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/1.jpg)
Vehicle Ride
![Page 2: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/2.jpg)
Dynamic System & Excitations
Vehicle Excitations:
1. Road profile & roughness2. Tire & wheel excitation3. Driveline excitation4. Engine excitation
![Page 3: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/3.jpg)
Road Excitation
• Road excitation is the road profile or the road elevation along the road and includes everything from smooth roads, potholes to “kurangkan laju”
• Road elevation profiles are measured using high speed profilometers
V
X – distance (m)
Roa
d E
leva
tion
(mm
)
![Page 4: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/4.jpg)
Statistical Road Profile
Gz(ν ) = G0[1+(ν0/ν)2]/(2πν)2
Where
Gz(ν) = PSD amplitude (feet2/cycle/foot)
= wave number (cycle/ft)
G0 = roughness parameter
= 1.25 x 105 – rough roads = 1.25 x 106 – smooth roads
ν0 = cut-off wave number
= 0.05 cycle/foot – asphalt road = 0.02 cycle/foot - concrete road
![Page 5: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/5.jpg)
Road Surface Power Spectral Density PSD
![Page 6: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/6.jpg)
Tire&Wheel Assembly Excitation
• Mass imbalance = m r ω2
• Tire/wheel dimensional variation
• Tire radial stiffness variation
![Page 7: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/7.jpg)
Driveline Excitation
• Mass imbalance– Asymmetry of rotating parts– Shaft may be off-center on its supporting flange– Shaft may not be straight– Shaft is not rigid and may deflect
![Page 8: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/8.jpg)
Engine Excitation
• Torque output to the drive shaft from the piston engine is not uniform. It has 2 components– Steady state component– Superimposed torque variations
![Page 9: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/9.jpg)
Ride Isolation
Road roughnessexcitation
Wheel/tire,Driveline excitation
Engine excitation
![Page 10: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/10.jpg)
Suspension Parameters
M – Sprung mass, kg (body, frame, engine, transmission, etc.)m – Unsprung mass, kg (driveline, wheel assembly, chassis, etc.)
Ks – Suspension stiffness, N/mm (spring stiffness)
Kt - Tire Stiffness, N/mm (tire stiffness)
Cs - Suspension damping, N.sec/m (damper)
Z – sprung mass displacement
Zu – unsprung mass displacement
Zr - road elevation
Fb – Force on the sprung mass (engine excitation)
Fw – Force on the unsprung mass (wheel/tire or driveline excitation)
![Page 11: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/11.jpg)
Ride Properties
Ride Rate, RR = Ks*Kt/(Ks + Kt) N/mm
Ride Frequency fn = √RR/M/(2*π) Hz
Damped Frequency, fd = fn √1-ξ2 Hz
Where
ξ = damping ratio = Cs/√4KsM %
![Page 12: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/12.jpg)
Suspension Travel
Static suspension deflection = W/Ks = Mg/Ks (mm)Ride Frequency = 0.159√Ks/M
Hence,
Ride frequency = 0.159√g/static deflection (Hz)
![Page 13: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/13.jpg)
Vehicle ResponseEquations of Motion
M*Z” + Cs*Z’ + Ks*Z = Cs*Z’u + Ks*Zu + Fb --------------------- (1)
m*Z”u + Cs*Z’u +(Ks+Kt)*Zu = Cs*Z’ + Ks*Z + Kt*Zr + Fw- --- (2)
Dynamic Frequency Responses:
Z”/Z”r = Hr(f) = (Ar + j Br)/(D + j E) ---------------------------- (3)
MZ”/Fw = Hw(f) = (Aw + j Bw)/(D + j E) ----------------------- (4)
MZ”/Fb = Hb(f) = (Ab + j Bb)/(D + j E) ----------------------- (5)
Where j = √-1 - complex operator
![Page 14: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/14.jpg)
Vehicle Response
Ar = K1*K2 Br = K1*C*2πf
Aw = K2*(2πf)2 Bw = C*(2πf)3
Ab = μ*(2πf)4 – (K1+K2)*(2πf)2 Bb = C*(2πf)3
D = μ*(2πf)4 – (K1+K2*μ+K2)* (2πf)2 + K1*K2
E = K1*C*(2πf) – (1+μ)*C*(2πf)3
And μ = m/M, C = Cs/M, K1 = Kt/M, K2 = Ks/M
![Page 15: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/15.jpg)
Vehicle Response
|H(f
)|
![Page 16: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/16.jpg)
Observations• At low frequency, gain is unity. Sprung mass moves as the road input• At about 1 Hz, sprung mass resonates on suspension with amplification• Amplitude depends on damping, 1.5 to 3 for cars, up to 5 for trucks• Above resonant frequency, response is attenuated• At 10-12 Hz, un-sprung mass goes into resonance (wheel hop)• Sprung mass response gain to wheel excitation is 0 at 0 frequency as
the force on the axle is absorbed by the tire• Resonance occurs at wheel hop frequency, gain is 1 and axle force
variation is directly transferred to sprung mass• Sprung mass response gain to engine excitation reaches maximum at
sprung mass resonance• At higher frequencies gain becomes unity as displacements become
small, suspension forces do not change and engine force is absorbed by sprung mass acceleration
![Page 17: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/17.jpg)
Isolation of Road Acceleration
Gz(f) = |Hr(f)|2*Gzr(f)
Where: Gz(f) = acceleration PSD of the sprung mass
H(f) = response gain for road input
Gzr(f)= acceleration PSD for the road input
RMS acceleration = sqrt [area under Gz(f) vs f curve]
![Page 18: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/18.jpg)
RMS Acceleration CalculationRoad profile acceleration power spectral density PSD
LOG Gzr(f) = -3.523 when LOG(f) <= 0
LOG Gzr(f) = -3.523 + LOG(f) when LOG(f) >= 0
Frequency Response Function |H(f)|
Sprung mass acceleration power spectral density PSD
Gzs (f) = |H(f)|2 Gzr(f)
RMS acceleration = area under the curve
Gzr
Gzs
|H(f
)|
f
f
f
![Page 19: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/19.jpg)
RMS Acceleration Calculation
Step 1 : Calculate road surface PSD for each frequency from 0.1 Hz to 20 Hz
Step 2 : Frequency response function for each frequency from 0.1 Hz to 20 Hz
Step 3 : Calculate vehicle acceleration PSD for each frequency from 0.1 Hz to 20 Hz
Step 4: Calculate area under the curve found in Step 3.
Step 5: That is RMS acceleration. 99% confidence that the vehicle acceleration will not exceed 3*RMS
![Page 20: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/20.jpg)
Allowable vibration levels
![Page 21: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/21.jpg)
Suspension Stiffness
Acc
eler
atio
n P
SD
Note: softer suspension reduces acceleration level
![Page 22: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/22.jpg)
Suspension Damping
Note: higher damping ratio reduces resonance peak, but increases gain at higher frequencies
![Page 23: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/23.jpg)
Suspension Design
![Page 24: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/24.jpg)
Wheel Hop Resonance
Wheel hop resonant frequency
fa = 0.159√(Kt+Ks)/m
![Page 25: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/25.jpg)
Bounce/Pitch Frequencies
Equations of Motion
Z” + αZ + βθ = 0
θ” + βZ/κ2 + γθ = 0
Where, α = (Kf+Kr)/M
β = (Kr*c-Kf*b)/M
γ = (Kf*b2+Kr*c
2)/Mκ2
Kf = front ride rate
Kr = rear ride rate
b = as shownc = as shown
Iy = pitch inertia
κ = radius of gyration
sqrt(Iy/M)
![Page 26: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/26.jpg)
Bounce/Pitch Frequencies
ω12 = (α+γ)/2 + (α-γ)2/4+ β2κ2
ω22 = (α+γ)/2 - (α-γ)2/4+ β2κ2
f1 = ω1/2π Hz
f2 = ω2/2π Hz
![Page 27: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/27.jpg)
Uncoupled FrequenciesFront Ride Frequency = √Kf/M /(2π) Hz
Rear Ride Frequency = √Kr/M /(2π) Hz
Pitch Frequency = √Kθ/Iy /(2π) Hz
Roll Frequency = √Kφ/Ix /(2π) Hz
Where
Kθ = (Kf*b2+Kr*c
2) = pitch stiffness
Kφ = (Kf+Kr)*t2/2 = roll stiffness
Iy = 0.2154ML2 = pitch moment of inertia
Ix = 0.1475Mt2 = roll moment of inertia
t = tread width and L = wheel base
![Page 28: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/28.jpg)
Olley’s criteria for good ride
• Spring center should be at least 6.5% of the wheelbase behind C.G.• Rear ride frequency should be higher than the front• Pitch and bounce frequencies should be close to each other• Bounce frequency < 1.2 * pitch frequency• Neither frequency should be greater than 1.3 Hz• Roll frequency should be close to bounce and pitch frequencies• Avoid spring center at C.G., poor ride due to uncoupled motion
• DI = κ2/bc >= 1, happens for cars with substantial overhang. Pitch frequency < bounce frequency, front ride frequency < rear ride frequency, good ride
![Page 29: Vehicle Ride. Dynamic System & Excitations Vehicle Excitations: 1.Road profile & roughness 2.Tire & wheel excitation 3.Driveline excitation 4.Engine excitation](https://reader036.vdocuments.net/reader036/viewer/2022081501/56649ccb5503460f94994e0b/html5/thumbnails/29.jpg)
Suspension System Design
Vehicle
•Spring Rate•Tire Rate•Jounce/Rebound Clearance•Shock Rate•Unsprung Mass
Mass, C.G.Roll Inertia
Pitch InertiaWheelbase, Tread
RMS AccelerationRMS Susp TravelFrequenciesOlley’s Criteria
Road PSD