Vehicle Ride 1

Given,

Front sprung mass natural frequency at design = 1.15 Hz

Timelag due to wheelbase (t_lag) = Wheelbase/Speed = 2700mm/60mph = 2700mm/26.82m/s = 0.10066 sec

Then,

1.

i. Recommended rear sprung mass natural frequency = 1/(1/1.15 - t_lag) = 1.30055 Hz

ii. Front sprung mass natural frequency at design = 1.15 Hz

We know,

Ride rate = 4*pi^2*f^2*sprung_mass

Also, ride rate = wheel rate*tire rate/(wheel rate + tire rate)

So, wheel rate = ride rate*tire rate/(tire rate - ride rate)

And, spring rate = wheel rate / motion ratio^2

Then,

Front ride rate = 4*pi^2*1.15^2*456.875 = 23853 N/m = 23.853 N/mm

Front wheel rate = 23.853*245/(245 - 23.853) = 26.426 N/mm

iii. Front spring rate = 26.426/0.97^2 = 28.086 N/mm

Likewise,

Rear ride rate = 4*pi^2*1.30055^2*380.625 = 25416 N/m = 25.416 N/mm

Rear wheel rate = 25.416*245/(245 - 25.416) = 28.358 N/mm

iv. Rear spring rate = 30.875/0.85^2 = 39.250 N/mm

We know, natural frequency for sprung mass = (1/2pi)*sqrt(ride rate/sprung mass)

v.

Front sprung mass natural frequency at curb = (1/2pi)*sqrt(23853/405) = 1.22142 Hz

Front sprung mass natural frequency at GVW = (1/2pi)*sqrt(23853/475) = 1.12783 Hz

vi.

Rear sprung mass natural frequency at curb = (1/2pi)*sqrt(25416/270) = 1.54416 Hz

Rear sprung mass natural frequency at GVW = (1/2pi)*sqrt(25416/450) = 1.19610 Hz

We know, natural frequency for unsprung mass = (1/2pi)*sqrt((wheel rate+tire rate)/unsprung mass)

vii.

Front unsprung mass natural frequency at curb, design, GVW = (1/2pi)*sqrt((26.426+245)*1000/45) = 12.3606 Hz

viii.

Rear unsprung mass natural frequency at curb, design, GVW = (1/2pi)*sqrt((28.358+245)*1000/30) = 15.1924 Hz

ix.

Rear/Front frequency ratio at curb = 1.54416/1.22142 = 1.26423

Rear/Front frequency ratio at design = 1.30055/1.15 = 1.13091

Rear/Front frequency ratio at GVW= 1.19610/1.12783 = 1.06053

2.

At curb

At design

At GVW