Week 9- suspension Flashcards
Draw the free-body diagram for the sprung mass in a suspension system. Derive the equation
Top mass, should include Fks, Fcs downward forces, and acceleration upwards (d^2 x).
Equation: F= ms (dx^2 (s)) + cs ( vs- vu) + ks (xs- xu)
Draw the free-body diagram for the unsprung mass in a suspension system. Derive the equation
Bottom mass should include Fks, Fcs upwards forces and acceleration upwards, au, should include Fku and Fcu downwards:
Equation:
F= mu (dx^2(u)) - cs (vs-vu) - ks (xs - xu) + ku * xu + cu * vu
Derive the matrix for unsprung and sprung mass
Answer on canvas
What is the displacement, acceleration, and velocity considering the unsprung and sprung masses move with SHM? HINT use differentiation.
displacement, x(t) = A cos (wt- angle)
velocity, v(t) = -Aw sin (wt - angle)
acceleration, a(t) = -Aw^2 cos (wt - angle)
what is the equation for angular velocity with K and M?
W = SQRT (k/m)
Derive the characteristic equation considering it as an undamped, free vibration.
answer should be 𝜔^4 𝑚𝑢𝑚𝑠 + 𝜔^2 −𝑘𝑠𝑚𝑢 − 𝑘𝑡𝑚𝑠 − 𝑘𝑠𝑚𝑠 + 𝑘𝑡𝑘𝑠 = 0
What is the natural frequency?
It is the frequency oscillated at if the system is not subjected to a repeated external force
What happens if a system is exited and left at natural frequency?
It will oscillate indefinitely at this frequency (pendulum clock- think about clock at home)
Define SHM.
If a mass/ body is always accelerating towards a fixed point that is proportional to the displacement from the point the oscillation is SHM.
What is the sprung mass?
Mass of all components supported by the suspension e.g chassis
What is the purpose of suspension?
To isolate the driver and passengers from road shocks and wheel movements as the driver passes over the road
What should a well-designed suspension system be able to do?
3 ones to remember:
-Provide a balance between safety, comfort, and cost
-isolate passengers from road shocks
-Ensure the wheel remains in contact with the ground
What are the equations for Wu, fu, Ws, and fs?
On one note
What is the equation for kr involving tyre stiffness and suspension stiffness?
1/kr = 1/kt + 1/ks
