Past Paper 1 Flashcards
what are the three assumptions made about the tyres in the bicycle model
- small slip angles so creep is linear
- neglect tyre realigning moments
- the spin creep has constant speed
what does it mean if a steady state steer angle is applied
- the motion of the vehicle is circular
- meaning Ω_dot = v_dot = 0
- and Ω = u/R where R is the radius of the turn
what does it mean if there are no external forces on the vehicle
- X = Y = N = 0
how do you work out the inverse of a 2x2 matrix
- inverse = 1/det * adj
- the adjugate is found by swap (top left, bottom right) and negative (other two)
- this is intuitive for me as “swap-negate” while drawing an ‘X’ with my left hand
what is meant by the steady state yaw rate when a steady steer angle is applied
- the yaw rate is the rate of turning which is Ω
- the steady state yaw rate is when Ω_dot = 0 to give Ω_ss
- this is then divided by δ to give Ω_ss / δ
what is the form you would like the denominator (after finding the inverse of the matrix) to be in when solving for the steady state velocity raitos
- C_fC_rl^2 -csmu^2
what is referred to as the sideslip response
- it seems to be β = v/u
if the vehicle forward velocity u tends to 0, what do α_f and α_r tend to
- α_f = α_r = 0
- this is not intuitive from looking at the equations
how do you find the position of the turn center on a vehicle
- there are 3 points with their own velocity and direction: the rear, G and the front
- if you draw dashed lines perpendicular to these directions, their intersection gives the position of the turn center
if you have the turn radius R as a function of speed u, and are told to sketch how it varies with neutral steer, understeer, oversteer and for real vehicles, how would you go about this
- find dR/du and see how its sign changes with s = 0, s > 0 and s < 0
- typically, s = 0 means dR/du = 0 (neutral steer), s > 0 means dR/du < 0 (oversteer) and s < 0 means dR/du > 0 (understeer)
- neutral steer is represented by a straight horizontal line on the plot for what R is when s = 0 (typically l / δ)
- understeer is an x^2 shape starting from the same point
- oversteer is a -x^2 shape starting from the same point
- the point that the oversteer line crosses the x-axis is U_c for instability
- the real vehicle line starts at the same point, is initially understeer then curve to being oversteer
we know that the lateral creep/sideslip α = -tanδ where δ is the yaw/steer angle . but what is α for small oscillations
- α = v/u - δ
- δ is just the steer angle which can be other symbols like θ
when given a ‘wheel system’, how would you derive the equations for small lateral oscillations of the system
- find the resultant force and moment on the wheel system
- the force will be a combo due to any springs, dampers, acceleration of displacements AND lateral creep forces
- the moment will be due to the moment of inertia and any springs, dampers acting parallel to the lateral direction (F*distance)
- you need to remember to use any small oscillation assumptions too (mainly for lateral creep)
- then the equation is the resultant force and moment in matrix form
how do you find the roots of the characteristic equation of an equation of motion on matrix form
- assume the stability condition that generally means the RHS = 0
- assume characteristic solutions of the form v = v_0*e^λt for the ‘main’ variables
- this mans that for any v, v_dot or v_double_dot you write it in terms of v_0
- this allows you to add all the 2x2 matrices together into one
- the roots of the characteristic equation are found by solving for the determinant = 0
what is the routh-hurwitz criterion (generally)
- after you have found the determinant of the characteristic matrix to get the characteristic equation = 0
- the motion is stable if the coefficients of the λ’s of different powers are ALL positive
- the further conditions for different expressions are in the datasheet
