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Automotive and Tractor Dept. Vehicle Dynamics.
Faculty of Engineering. 4th Year.
Minia University. Sheet No.4 Code: AT 415
1. Write the equation of motion for bicycle car model as following figure.
2. A passive suspension is used with a minibus of 2650 mm wheelbase. Unladen
sprung mass is 1755 kg. Front axle load is 35 %. Unsprung masses are 85 kg for
front and 110 kg for rear. Axial spring stiffness/each 22.6 N/mm for front and
22.6 N/mm for rear. Stiffness of any tire is 172.4 N/mm. Spring span of front or
rear is 1250 mm. Wheel track is 1780 mm for both axles. Center of gravity and
of oscillation are 960mm and 450mm above road level respectively. Determine
the pitch angle around transverse axle during brake from 120 km/hr. at 3.5 sec to
car stop.
3. A 3300 mm wheelbase 2 axles 6.4 ton (32%on front axle) has front springs of
107 kp/cm each and rear springs 175kp/cm each. Stiffness of any tire 300kp/cm
(rear wheels with double tires). Front and rear unsprung weights are 350 and 650
kg respectively. Determine the angular deflection during speeding up at 3.5 m/s 2
and braking at 5.7 m/s2. Center of gravity is 960mm
Prof.Dr. Ali. M. Abd-El-Tawwb.
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Eng. Ebram Fayez
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4. Write the equation of motion for bounce car model as following figure.
5. A passive suspension is used with a minibus of 2840 mm wheelbase. Laden
sprung mass is 3600 kg, front axle load 40 %. Unsprung masses are 150 kg front
and 240 kg rear. Axial spring stiffness/each 60 N/mm front, 90 N/mm rear. 270
N/mm, 405 N/mm are lateral stiffness of front and rear springs respectively.
Stiffness of any tire is 210 N/mm. Rear wheel with double tire. Spring span front
or rear is 1260 mm. Wheel track 1780 mm for both axles. Center of gravity and
of oscillation 960 mm and 450 mm above road level respectively. Determine
the angle of roll during cornering around a 150 m, at 107Km/hr. and the
stiffness of stabilizer to limit it at 2o 52\.
Prof.Dr. Ali. M. Abd-El-Tawwb.
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Eng. Ebram Fayez
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6. A 2400 mm wheelbase passenger car of 1500 kg sprung mass
equally distributed. Axial front and rear spring stiffness 15 N/mm. Center
of gravity and of oscillation are 600 mm and 400 mm above road level
respectively. Wheel track 1600 mm, spring span 1200mm. Radial tire stiffness
200 N/mm. Determine with consideration of tire elasticity:
a) The stiffness of stabilizer to limit the angle of roll at 3o 30\. At specific
side force V2/R determined by the formula V=18.35 m/sec. where R=75
m the radius of turn.
b) The angle of roll if the stabilizer was not installed.
7. If the sprung mass of 1970 kg passenger car is 1750 kg. Wheelbase 2700 mm.
The distance from c.g. to front axle 1390 mm. Stiffness of each front springs
181.5 N/cm and that of the rear springs 237.4 N/cm. Stiffness of any tire 2138.6
N/cm. Front unsprung mass 80 kg. Wheel track 1800 mm, springs span on right
and rear 1400mm. height of healing is 450 mm and C.G height is 960 mm
Maximum Side force is about 35% of sprung mass. Determine:
a) Angular deflection during speeding up at 3m/s2 and braking at 6.7
m/s2.
b) Stabilizer stiffness to limit healing angle at 4o.
c) Calculate its diameter for a working length 1300 mm of one
stabilizer only is used on either axle. Where modules of rigid
0.8*106kp/cm2.
With my best wishes
Prof.Dr. Ali. M. Abd-El-Tawwb.
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Eng. Ebram Fayez
