Clarification in Fundamentals of Vehicle Dynamics (Milliken)
Clarification in Fundamentals of Vehicle Dynamics (Milliken)
(OP)
I'm having a problem understanding the terms in Chapter 6 (steady-state cornering)
They start with a free body diagram of a bicycle model (front and rear axles are each represented by a single wheel) turning a corner in equilibrium at velocity V with radius r. With vehicle mass M, wheelbase L, and CG to front axle distance b and CG to rear axle distance c, the cornering forces on the front and rear are given as:
Fyf = M*(c/L)*(V^2/r)
Fyr = M*(b/L)*(V^2/r)
They then make a substitution because M*(c/L) and M*(b/L) "are the portions of the vehicle mass carried on the front/rear axles" and "are equal to" Wf/g and Wr/g. They continue using the terms Wf and Wr throughout the entire chapter.
The problem I'm having is that the list of symbols at the beginning of the book defines Wf as "the dynamic weight on the front axle" and Wr as "the dynamic weight on the rear axle" (and Wfs and Wrs as the respective static weights.) Within the chapter, Wf and Ws are periodically defined as "the load on" the respective axles.
From these definitions, it seems like Wf and Wr are the dynamic axle loads (i.e. affected by longitudinal weight transfer) but everything seems to be derived from the bicycle model sum of the moments around the CG, which to me, implies it should be the static weights because the CG position (and therefore its moment arm lengths to the front and rear axles) don't actually change?
Thanks in advance!
Mark
They start with a free body diagram of a bicycle model (front and rear axles are each represented by a single wheel) turning a corner in equilibrium at velocity V with radius r. With vehicle mass M, wheelbase L, and CG to front axle distance b and CG to rear axle distance c, the cornering forces on the front and rear are given as:
Fyf = M*(c/L)*(V^2/r)
Fyr = M*(b/L)*(V^2/r)
They then make a substitution because M*(c/L) and M*(b/L) "are the portions of the vehicle mass carried on the front/rear axles" and "are equal to" Wf/g and Wr/g. They continue using the terms Wf and Wr throughout the entire chapter.
The problem I'm having is that the list of symbols at the beginning of the book defines Wf as "the dynamic weight on the front axle" and Wr as "the dynamic weight on the rear axle" (and Wfs and Wrs as the respective static weights.) Within the chapter, Wf and Ws are periodically defined as "the load on" the respective axles.
From these definitions, it seems like Wf and Wr are the dynamic axle loads (i.e. affected by longitudinal weight transfer) but everything seems to be derived from the bicycle model sum of the moments around the CG, which to me, implies it should be the static weights because the CG position (and therefore its moment arm lengths to the front and rear axles) don't actually change?
Thanks in advance!
Mark





RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)
I guess the devil is in the details: *steady state* cornering - I assumed that meant they are not considering changes in the radius of the path the vehicle is taking (i.e. corner entry and exit), as opposed to they are also not considering longitudinal weight transfer due to acceleration/braking.
RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)
Could accounting for longitudinal weight transfer due to acceleration and braking in a corner be as straightforward as adjusting for changes in Fz, camber, etc. due to the change in axle loading, or does the fact that the tire is producing larger forces in both the X and Y directions (and therefore experiencing simultaneous sideslip and longditudonal slip) throw a huge proverbial wrench into the analysis?
Thanks again,
Mark
RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)
The devil will be in your tire model, not the vehicle model.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)
This would get you a close approximation, depending on the depth of complication in your tire model. But, you'd still be evaluating a steady-state condition, meaning constant acceleration in all directions. This would be useful only for an instantaneous point, and I don't think very applicable to any real situation.
RE: Clarification in Fundamentals of Vehicle Dynamics (Milliken)