Handling Lowspeed turning Highspeed turning Understeer.

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Transcript of Handling Lowspeed turning Highspeed turning Understeer.
Handling
• Lowspeed turning
• Highspeed turning
• Understeer
Lowspeed Turning
o i
RL
t Inboard offtracking
L2 R
2
R+t/2
TurnCenter
R+t/2tan1L
o L
tan1Rt/2
Li Rt/2
L
For large radii, R >> t/2
AckLR
High Speed Turning
V
RRR
RR
R0
Original Path/Neutral Steer Path
Under Steer Path
R > R0
Over Steer Path
R < R0
Tire Slip Angle
Direction of Heading
Direction of TravelContact Patch
Slip Angle,
Fy Mz
Pneumatic Trail, P
Slip Region
Tire Cornering Stiffness
Slip Angle, (deg)
C
Fy
Slip Angle ()
La
tera
l Fo
rce
, F
(
lb)
y
Direction of Travel
0
0
200
400
600
800
2 4 6 8 10 12
positive is
0
Cd
dFC
CF
y
y
Factors affecting cornering stiffness
• NSL for force and moment analysis
• Geometry for steer angle vs. radius
2
y f rc
W VF F F
g R
R
b
c
f
r
f
r
L/R
Ff
Fr
V
W Vg R
2From Newton’s Second Law
From tire properties
0cg f rT F b F c
Ff Wfs
V 2
Rgc
f FfC f
Wfs
Cf
V 2
Rgc
r FrCr
WrsCr
V2
Rgc
57.3L
R f r
From the geometry: 57.3L
RWfs
Cf
V 2
RgcWrsCr
V2
Rgc
57.3L
R (Wfs
Cf
WrsCr
)V2
RgcUndersteer Gradient
Fr WrsV 2
Rgc
Highspeed Turning
ry f
f
rfz
f
r
rr
f αf
αr
αf
αr
• Positive – understeer
• Zero – neutral steer
• Negative – oversteer
– Has a critical speed
– Vehicle is unstable
• Oscillatory
• Divergent
57.3L
R (Wfs
Cf
WrsCr
)V2
RgcUndersteer Gradient, K
Understeer Gradient
Steer Angle vs. Speed
Speeds & Gains
Characteristic speed = speed at which steer angle required to negotiate a turn is 2 times Ackerman angle
Vchar = √57.3Lg/K
Critical speed = speed at which steer angle required to negotiate a turn is 0
Vcrit = √57.3LgK
Lateral acceleration gain ay/δ = V2/57.3Lg(1+ KV2/57.3Lg)
Yaw velocity gain r/δ = V/L(1+ KV2/57.3Lg)
• Understeer – Very controlled gain with speed• Neutral steer – Increasing gain with speed
• Oversteer – Increases dramatically with speed
0
1
2
3
4
5
6
0 20 40 60 80 100 120
Speed (mph)
Lat
eral
Acc
. Gai
n (
g/d
eg)
Understeer (5 Deg/g)
Neutral Steer
Oversteer (1 Deg/g)
Understeer (2 Deg/g)
108 in wheelbase
Stability limit88 mph
SW Angle/g5 deg
6 deg
10 deg
20 deg40 deg
Effect on Lateral Acceleration Gain
Effect on Yaw velocity gain
Slip Angle Calculation (primary tire effect)
1. Calculate front and rear vertical wheel loads Wf and Wr
2. Assume lateral acceleration ay/g as % (g).
3. Lateral tire force (front & rear) Fyf = Wf*ay and Fyr = Wr*ay
4. From tire data find slip angles for all 4 tires, use extrapolation
5. Find average slip angle for front and rear αf and αr
6. Calculate under steer αf – αr
7. Do calculations for ay/g from 0.1 to 1.0
Effect of Body Roll
W
Fz0 > Fzi
Effect of Body Roll
No roll: For 800 lb load on each wheel 760 lb of lateral force at 5 deg slip angle
Body Roll: In hard cornering inside & outside wheel loads can be 400 & 1200 lbwith average lateral force of 680 lb, requiring more slip angle to maintain the turn
Effect of Body RollOverturning moment Mφ = Wh1 [ V2/(Rg) + φ]
Mφ = Mφf + Mφr = (Kφf+Kφr) φ
Hence, φ = Wh1V2/[Rg(Kφf+KφrWh1)]
Roll rate Rφ = dφ/day = Wh1/[Kφf+KφrWh1]
Where φ = roll angle, Kφ = roll stiffness, h1 = distance between C.G. & roll
ctr.
Vertical load difference between outside and inside wheel
(Fzof –Fzif)tf = Kφf*φ + WfhfV2/Rg and (Fzof +Fzif) = Wf
(Fzor –Fzir)tr = Kφr*φ + WrhrV2/Rg and (Fzor +Fzir) = Wr
Where hf and hr = roll center height front and rear
Slip Angle Calculation (roll effect)
1. Calculate front and rear vertical wheel loads Wf and Wr
2. Assume lateral acceleration ay/g as % (g).
3. Lateral tire force (front & rear) Fyf = Wf*ay and Fyr = Wr*ay
4. Calculate roll rate and find roll angle φ
5. Calculate Fzi and Fzo for front and rear
6. From tire data find slip angles for all 4 tires, use extrapolation
7. Find average slip angle for front and rear αf and αr
8. Calculate under steer αf – αr
9. Do calculations for ay/g from 0.1 to 1.0
0 1 2 3 4 5 6 7 8 9
Camber Angle (deg)
0
50
100
150
200
Late
ral F
orce
(lb
) F = 1000 lb
Zero Slip Anglez
C
• Tires produce a lateral force (camber thrust) when inclined• Characterized by camber stiffness, C
Camber Thrust
• Camber coefficient– Radials are lower
– Biasply are higher
.01 0.02 0.03
Camber Coefficient, C /F (lb/lb/deg)z
20
15
10
5
0R
ela
tive
Fre
qu
en
cy (
%)
BiasPly
Radial
Camber Coefficient, C/Fz (lb/lb/deg)
Camber Thrust
γg = γb + φ
Where
γg = camber w.r.t. ground
γb = camber w.r.t. body
φ = roll angle
Lateral Tire load due to camber
Fyc = Cγ*γ
= Cγ*(dγ/dφ)*(dφ/day)*ay
= Cγ*(dγ/dφ)*roll rate*ayγφ relationship
Lateral tire force causing tire slip = W*ay  Fyc
Slip Angle Calculation (roll/camber effect)
1. Calculate front and rear vertical wheel loads Wf and Wr
2. Assume lateral acceleration ay/g as % (g).
3. Calculate roll rate and find roll angle φ
4. Calculate Fzi and Fzo for front and rear
5. Calculate γφ relationship from suspension data6. Calculate lateral tire force due to camber for each tire
7. Lateral tire force for slip (front & rear) Fyf = Wf*ayFycf and
Fyr = Wr*ayFycr
8. From tire data find slip angles for all 4 tires, use extrapolation
9. Find average slip angle for front and rear αf and αr
10. Calculate under steer αf – αr
11. Do calculations for ay/g from 0.1 to 1.0
Roll Steer• All suspensions steer with roll• Steer to the outside is:
– Understeer on front– Oversteer on rear
• Solid axle on a trailing arm:– Arm angle determines
understeer– Angled down is oversteer– Angled upward is understeer
Roll Center Inclination of Suspension Roll Axis
Neutral Steer
Oversteer
Understeer
Front of Vehicle
yrf da
dK
)(steer roll
Lateral Force Compliance Steer
• All suspensions steer due to a lateral force
• Minimize compliance steer
Yaw center
CorneringForce
Deflection Understeer
Turn
CorneringForce
Deflection Oversteer
Turn
y
cFA
rrfflfcs WAWAK
Yaw center
Constant Radius Understeer TestS
tee
r A
ng
le/S
tee
rin
g R
atio
(d
eg
)
Lateral Acceleration (g)
Understeer
Neutral Steer
Oversteer
Limit Understeer
Limit Oversteer
CONSTANT RADIUS
K (deg/g)
Constant Speed Understeer Test
Process for Calculating Cornering Response• Decide on the lateral acceleration requirement• Calculate rollstiffness based on the suspension properties• Calculate roll rate• Calculate left and right tire vertical loads for the max lateral acceleration• Choose tire to minimize understeer or oversteer• Determine camber vs roll angle relationship for your suspension• Make adjustments to understeer/oversteer• Calculate critical speed• Calculate yaw velocity and lateral acceleration gains
Suspension Design for Handling
Vehicle
•Roll Stiffness•Roll Stiffness Distribution•Roll Center Height•Tire Capacity•Steering Geometry•Camber
Mass, C.G.Roll Inertia
Tread
UndersteerOverSteerStability
LateralAcceleration
Vehicle Rollover Safety
Rollover Forces
M*ay*h  M*g*θ*h + Fzi*t – M*g*t/2 = 0
ay/g = (t/2 + θ*h – Fzit/Mg)/h
When θ=0 and ay=0, Fzi = M*g/2
When θ=ay/g, Fzi = M*g/2
Rollover condition ay/g = t/2h + θ
Where θ is the crossslope
Road superelevation angle θ
Mgθ
Rollover Threshold t/2h
Rollover Forces
M*ay*h + M*g*φ*h + Fzi*t – M*g*t/2 = 0
ay/g = (t/2  φ*h – Fzit/Mg)/h
When φ=0 and ay=0, Fzi = M*g/2
When φ=ay/g, Fzi = M*g/2
Rollover condition ay/g = t/2h  φ
Where φ is the vehicle roll angle
Vehicle roll angle φ
Mgφ
Rollover Threshold
Rollover Forces on a Suspended Vehicle
M0=0= MsayhMsg[t/2  φ(hhr)]
φ = Rφ*ay
Hence, max acceleration
ay/g = t/{2h[1+Rφ(1hr/h)]}
Rollover Threshold for Suspended Vehicle
Transient Rollover in Step Steer
Iφφ”+ Cφφ’ + [KφMg(hhr)] φ=W ay(hhr)/g
Where
Iφ = Roll moment of inertia
Cφ= Roll damping
Kφ= Roll stiffness
h = C.G. height
hr = roll center height
W = vehicle weight
ay = lateral accelerationRollover condition
ay/g = t/{2h[1+Rφ(1hr/h)]}
where
Rφ = φmax/(ay/g)
Step Steer
L
R
V
time
Late
ral A
ccel
erat
ion
L / V
V2/R
Roll Response to Step Steer
Effect of Damping
Transient Rollover in Sinusoidal Steer
Iφφ”+Cφφ’+[KφMg(hhr)]φ=Way(hhr)sinωt/g
Where
Iφ = Roll moment of inertia
Cφ= Roll damping
Kφ= Roll stiffness
h = C.G. height
hr = roll center height
W = vehicle weight
ay = lateral accelerationRollover condition
ay/g = t/{2h[1+Rφ(1hr/h)]}
where
Rφ = φmax/(ay/g)
Sinusoidal Steer
V
Y0
2L
Y = Y0 sin (π*V*t/L) and lateral accn Y” = (π*V/L)2Y0 sin (π*V*t/L)
Sinusoidal Steer
Suspension Design to Prevent Rollover
Vehicle
•Roll Stiffness/stabilize bar•Roll Stiffness Distribution•Roll Center Height•Tire Capacity
Mass, C.G.Roll Inertia
Tread
Roll AngleRollover Threshold
Step &SinusoidalSteer