Mercedes Benz Manuals - see pdf titles for vehicle systems covered
STEERING GEAR
sistema direccion st1030
Nowadays, road safety is one of the priority of the government to avoid accidents. Road safety adopts those methods that can prevent road users from being seriously injured or killed. Most of the accidents happened during night time when the driver i
Angle B = ARCTAN (king pin center to center distance / 2) Wheelbase Angle B = ARCTAN
56” / 2 68”
Angle B =22.38 °
So the ackerman angle for new design is 22.38
LENGTH OF THE TIE ROD
°
Y SIN Ackerman Angle = Ackerman Arm Radius.
SIN 22.38º = Y/5” Y =1.904”
LT = DKC – 2Y Where: LT is the length of the tie rod and rack rod DKC is the distance between king pins center to center LT = 56” – 2*5”*SIN 22.38º LT =52.193”
TURNING RADIUS From Law of Sin a b c = = sinA sin B sin C turning radius wheel base = sin 90 sin ( θi )
68 } over {sin (θi)} 3000 =¿ sin 90
90 ( 1727.330×sin ) 00
θi=arcsin
θi=35.15
◦
ACKERMANN STEERING GEOMETRY TO DETERMINING INNER AND OUTER WHEEL TURN ANGLE FOR 100% ACKERMAN Cot θo – Cot θi = L/B Where Θo= turn angle of the wheel on the outside of the turn Θi= turn angle of the wheel on the inside of the turn L= track width B= wheel base Wheel base =1727.2mm Track width=1422.4mm Substitute the W and L in above equation Cot θ o – Cot θi = 0.824 As we known the maximum wheel turning angle as 35.15 ° are calculated from ackerman geometry (turning radius).
Cot
θo
Cot
θo = 0.824+1.42
θo
– Cot (35.15) = 0.824
= arccot(2.244)
θo = 24.017
°
TO DETERMINING INNER AND OUTER WHEEL TURN ANGLE FOR ACTUAL DESIGN
Point B’s X coordinate = RAA * COS(AA + SAL)
Point B’s Y coordinate = RAA * SIN(AA + SAL) Assume if a car takes 30º left turn… Point B’s X coordinate = 5” * COS(22.38º + 35.15º) Point B’s X coordinate = 2.684” Point B’s Y coordinate = 5” * SIN(22.38º + 35.15º) Point B’s Y coordinate = 4.218” So, the coordinates of Point B at a 0º left turn are (2.684”, 4.218”)
TO DETERMINE ANGLE α
DE = AD – AE DE = 56”-4.218” DE = 51.78”
Now that we know EB and ED, we can find the length of BD because it is a hypotenuse of the triangle formed. Using Pythagorean Theorem:
BD =
BD =
(EB 2 + (DE)2
(51.78”) 2 + (2.684”)2
BD = 51.85”
we know the sides of the triangle we can determine angle α
TAN
α = EB/ED
ARCTAN (EB/ED) =
α
ARCTAN (2.684”/51.78”) =α
α=2.96” So now that we know angle k and the Ackerman angle TO FIND ANGLE(
γ)
Law of cosines for non-right triangles COS γ = A2 + B2 – C2 2AB ARCCOS A2 + B2 – C2
=γ
2AB ARCCOS (52)2 + (5)2 – (51.78)2
= γ
2(52)(5) γ =84.72°
Now if we add up angle α, γ and the Ackerman angle, we’ll have the tire’s steer angle from the line that connects the two kingpins. To get the steer angle, we have to subtract 90°. The formula is: Steer Angle = α + γ + Ackerman Angle - 90° Steer Angle = 2.96º + 84.72° + 22.38° - 90° Steer Angle = 20°
STEERING RATIO CALCULATION
Steering ratio =
Turn of steering
wheel Turn of wheel Maximum wheel turning angle =35.15
