mech3100_suspension3
TRANSCRIPT
MECH3100Engineering Design
Lecture 6Roll centers for independent suspensions
Suspension Dynamics - simple modelsEstimating Design loads
In the last lecture we ...
• … looked at the roles the control arms serve in acceleration and braking.
• … developed design guidelines for control arm geometry based on anti-squat and anti-dive and saw there’s a design compromise to make - you can’t simultaneously realize both.
This final lecture on suspections
• … looks at how the suspension geometry determines suspension roll centers and the vehicle roll-axis.
• … introduces simple models for the dynamics of suspensions.
• … looks at how we might use Newton’s 2nd Law to estimate loads acting on the suspension
Vehicle roll axis
• Roll axis: instantaneous axis is about which the unsprung mass rotates with respect to the sprung mass when a pure couple is applied to the unsprung mass.
Based on Fig 7.14 of T. Gillespie,Fundamentals of vehicle dynamics, SAE Press,1992, pp 258.
Suspension roll centers
• Suspension roll center: point in the transverse vertical plane through the wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll.
• Both front and rear suspensions will have role centres
Role center for a solid axle
• In a plan view of the suspension, find the linkages that react the side force. Then find where the projection of the linkages crosses the vehicle centerline.
• In a side view, find the same two points and connect them. That’s the suspension roll axis.
• The roll center is the point where the roll axis is over the wheel center.
Note that this is an instantaneous roll center.It changes as the body rolls.
Solid Axle Roll CenterRef. T. Gillespie, Fundamentals of Vehicle Dynamics, SAE Press, pp 260
Plan view
Side view
Roll center analysis of a four-link rear suspension.
SLA suspension - equivalent four-bar mechanism
A
B C
D
E
ICDE
Instantaneous point about which C, D, & E rotaterelative to the body of the car
Instantaneous Center
• Fictitious point about which the wheel (instantaneously) rotates under constraints provided control links
Independent suspension
AR
BRCR
DR
ER
AL
BLCL
DL
EL
IL IR
CL
Independent Suspension Roll Centers
• In a front view, locate the point about which the wheel rotates (Virtual Reaction point or Instantaneous Center). For double-A arms, this is the intersection of the projection of the arms.
• Draw a line from the tire-ground contact point to the virtual reaction pt. (A)
• Where the line crosses the centerline of the body is the suspension roll center.
Independent Suspension
Positive swing arm independent suspension.Called (+) because roll ctr is above ground
Ref. T. Gillespie, Fundamentals of Vehicle Dynamics, SAE Press
Recap - vehicle roll axis
• We construct the roll axis by drawing a line through the front and rear suspension roll centres.
Based on Fig 7.14 of T. Gillespie,Fundamentals of vehicle dynamics, SAE Press,1992, pp 258.
AR
BRCR
DR
ER
AL
BLCL
DL
EL
IL IR
Relationship between suspension motion and chassismotion
As wheelmoves down
This point moves up and chassis rolls
Imagine this link is fixed
CL
AR
BRCR
DR
ER
AL
BLCL
DL
EL
IL IR
Suspension motion from cornering
COG2m rω
Right tyre move down and point inwards
Left tyre moves up and out
Suspension geometry chassis roll
• The suspension geometry controls the vehicles roll axis.
• Desire your suspension keep tyres close to vertical during cornering
• Some designs seek to have the roll axis pass as near as possible to the centre of gravity of the vehicle to minimize the roll moment.
• But this is not a universal design objective!
Negative roll centre
(-) because roll ctr lies below ground
Negative swing arm independent suspension.
Zero roll centre
Parallel horizontal link independent suspension.
Positive roll centre
Inclined parallel link independent suspension.
Independent Suspension
• Roll center can change if there is body roll
no body roll
with body roll
Ref. Milliken &Milliken, Race Car Vehicle Dynamics, SAE Press
Dynamics: 1/4 Car Suspension• First approximation: consider the 1/4
car, single DOF system:independent suspensionmCar body
(sprung mass)z
k b
M = 1/4 of total car massk = combined tyre and suspension stiffness b = combined tyre and suspension damping
Ride comfort• One function of the suspension is to isolate the
chassis from the road. • Ride comfort is a measure of this and is affected
by – high frequency vibrations – body roll and pitch– vertical spring action
• Ride quality normally associated with the vehicles response to bumps is a function of the bounce and rebound movements of the suspension.
• Following a bump the undamped vehicle with experience oscillations that cycle at the natural frequency of the ride.
Ride comfort• Ride is perceived as most comfortable when the
natural frequency is in range of 1 to 1.5 Hz. • A high performance car will typically have a stiffer
suspension with a natural frequency of 2 to 2.5 Hz. • Sensitivity to frequency was at one time thought to
be associated with the natural oscillations of the body during walking (70 to 90 steps per minute with 5 cm vertical oscillation.)
• Early suspension design tried to mimic this.
Human sensitivity to vibration
• 0.5 to 0.8 Hz produces motion sickness• 5 to 6 Hz adversely affects the visceral
regions• 18 to 20 Hz is bad for the head and neck. • Humans are most uncomfortable with
longitudinal vibrations in range 1-2 Hz. The frequency at which most comfortable with vertical vibrations
Vibrational Characteristics• The unforced equations of motion of this system
are
• Which has natural frequency and damping
0=++ kzzbzm ⋅
2nk b
m mkω ζ= =
Vibrational Characteristics of Suspensions
• For the suspension that we’re modeling, the input usually comes from a road disturbance, not a force on the car body.
m Zc sprung massdisplacement
b kZr road displacement
Vibrational Characteristics of Suspensions
• We can look at the relative motion of the car with respect to the the road for a range of frequencies.
transmissibilityplot
System Dynamics• What do the system dynamics tell us?• If we known m we can choose k and b to satisfy
various goals based on requirements for natural frequency and damping.
• Natural frequency is 2 to 2.5 Hz. • ζ ≈ .2 to .4 for most cars.• This analysis is much simplified
– Damping in jounce and rebound are not usually equal.
– Usual to have lower damping on jounce than rebound.
½ Car Model and Coupling Effect
forward velocity
ms, I θzsr
za b
mur muf
zsf
ksr bsr ksf bsf
zur zuf
ktfktr zrr zrf
Equations of Motion
rfs ffzm +=
bfafI rf ⋅−⋅=θ
)( rfuftffufuf zzkfzm −−−=
)( rrurtrrurur zzkfzm −−−=
Bounce and Pitch
• If the road wavelength is equal to the vehicle wheelbase, or has an integer multiple equal to the wheelbase, then the ½ car model will experience pure bounce.
• If the road wavelength is equal to twice the wheelbase, or has an odd integer multiple equal to twice the wheelbase, then the ½ car will experience pitch.
Bounce and Pitch
⇒
Estimating design loads• We’ve been concentrating on roles of a suspension • Remember the suspension acts as the interface
between car and road and sees various loads– React the drive and braking forces– React cornering and other lateral loads– React vertical loads, e.g. those due to static
weight and those generated during acceleration.• Suspension has to be strong enough to withstand
these loads - I.e. in addition to basic kinematic issues discussed suspension should be designed for structural integrity under static loads and fatigue
How do we estimate design loads?• Intimately linked with suspension geometry. • In practices advanced modelling packages are used to
estimate loads, e.g. ADAMS • Suggest you make simple estimates using basic physics,
e.g. Newton’s second law.• A strategy might be to identify component ‘loads’ at
wheels under steady state conditions– Static weight– Cornering and other lateral forces– Motive forces– etc.
• Use these with appropriate multi-axis stress failure predictor (Von Mises) and factors of safety.
Estimating design loads • Vertical forces
– Static weight - mass of vehicle and centre of mass
– Acceleration forces - How quickly can vehicle accelerate/decelerate
• Identify component of reaction in each link
Lb a
h
V
FzrFzf
Fx
Force decreasesby m ax h/LForce increases
by m ax h/L
Estimating design loads • Drive forces
– What is the maximum drive torque at the wheels?
– What are the braking torques. – What forces do these generate at the tyres?
• Identify component of reaction in each link? L
b a
V
h
Fx Fz Fzr f
Estimating design loads • Lateral forces, e.g. those due to cornering
– What is the ‘tightest corner the car will take’– How fast will it take turn.– Note interactions with other loads, e.g vertical
loads on tyres• Identify component of reaction in each link
c
Force decreasesby mw2rh/c
Force increasesby mw2rh/c
c
F = mw2r
h