Design Analysis of Suspension System

Ground clearance	20 cm
Kerb weight	1270 kg
Gross weight	1900 kg
Overall height	1450 mm
Overall length	4505 mm
Overall width	1755 mm
Tires	195/65/R15

Dimension and Force Analysis of the Pedal

Hydraulic system uses positive displacement input and output device require force analysis. Variation in length and points of supports on this vehicle pedal gives various outputs; thus iteration for acceptable range of length will be important.

Case 1: when the pump piston or plunger is at its lowest position

Where piston is the force that the driver applies on the pedal.

R1- reaction force b/n the link and pedal
R2- reaction force b/n the plunger and the pedal

The pedal socket can be at equilibrium when the force and the momentum should be balanced.

(4.1)

Case 2: when the plunger is at its maximum position

• this happens when the operator up strokes or moves the pedal rise up; this can be shown diagrammatically as follows
• this is the maximum height of the plunger and socket

Where h_A – the distance through which the piston in the pump moves.

θ – The maximum angle through which the pedal moves with horizontals.

Now, 

(4.2)

Considering Pascal’s low of the fluid or oil in the cylinder of the vehicle

• When valve 1 is closed then the oil’s route or path is actuating the cylinders
• Valve 2 actuating pipe
• Main cylinder

• Fr this route or path the pressure is constant all over the path(if valve 1 is closed)
• Assuming that the typical oil or fluid is incompressible we can apply Pascal’s law to the system (the pistons and the path of the oil above)

If F is the load acting on the piston and R₂ be the force acting on the plunger actuator (piston) then

Where p- is the pressure require in the fluid require to hold the piston in equilibrium and

A- The area of the main cylinder

The force necessary to keep the actuator piston in equilibrium will be

R₂ = P₂A₂ Where A₂ area of the actuator cylinder

From Pascal’s law    P₂ = P₁ thus from the piston

And from the actuating cylinder P₂ = R₂ / A₂

(4.3)

• Considering volume relation of the cylinders
• In order to bring the piston to its maximum possible position the actuator cylinder must be moved’ times up and down n is in other words called the number of stroke needs to which the maximum lift height volume of cylinder filled to move the piston

= n (volume of cylinder moved by the actuating piston)

Where, V₁ – volume of main cylinder

V₂ – volume of the actuating cylinder when the plunger up to its maximum position

(4.4)

Now we have got four equations containing the unknown parameter of the geometry.

Now we can summarize the equation as follows,

But this holds true when the pedal is a horizontal position; when the pedal is deflected by an angle θ then the reaction force R₂ is given by

R_{2 –} Is actuating vertical reaction
P – Is always perpendicular to the pedal axis

• Now taking summation of moment due to all force at A will be zeroWhen the pedal is at the horizontal position then then the reaction force becomes then θ = 0 then the reaction force becomesWhich is the same with equation (1) derived earlier
• Thus, the reaction force R₂ can more generally be written asLet us summarize the equations,(1)(2)(3)(4)D₁=d_P + 2(lower thickness of piston) + 2(clearance b/n the piston head and cylinder)Where, d₁ – internal diameter of main cylinderFigure 4.10 Connection of piston and cylinder.

• Let the range of the force the driver can apply on the pedal vary from 200–400N
• Length of the pedal and socket
• Let the length of the pedal L be vary from 400–600mm
• Let the length of the socket b/n the hole of the pin joint X vary from 30–40mm

• Now the driver wants to apply a force of 260N on the pedal the iteration will produce as follow with an objective of finding the possible number of strokes to practically raise the piston up to the indicated maximum lift height

As can be seen from Table 4.3, we made five iterations to calculate the unknown over the indicated range of the assumed value, although many designers select a different iterative approach objective. We have selected the optimum and frequently observed number of strokes to be our objective of the iteration process looks the two extremes of the iteration, that is, iteration number 1 and number 2. The first one is too much to be used for 20 KN load and it is mostly stroke number for loads high in magnitude and number 5 is too small to raise the load, thus the 2^nd iteration contains the most practicable number of stocks, that is n = 22.2. Then the processing design analysis of each part will depend on the value of parameters obtained from the 3^rd iteration.

Table 4.3 Iteration.

	Known		Assumption					Calculated value
No iter	H min	H max	P	L	X	d1	θ	d2 = d1√R2/20	hA = xsinθ	R2 = (X+L) p/XCOSθ	n = d12*242/d22*hA
1	270	470	260	400	30	100	30	58.6	13.6	4.3	30
2	270	470	260	450	30	100	35	60	15.67	4.87	22.2
3	270	470	260	480	30	100	40	62.5	17.63	5.46	17.07
4	270	470	260	500	30	100	45	70.6	19.48	6.04	13.65
5	270	470	260	550	30	100	50	75.4	21.2	7.1	10.6

Generally, the geometry analysis of this system can be summarized,

Height of the main cylinder	27cm
Height that the vehicle rises	20cm
The applied force	260N
Diameter of main cylinder	10cm
Angle that the pedal makes with horizontal	35°
Diameter of actuator cylinder	60mm
Maximum rise of the plunger	15.67mm
Vertical plunger pin reaction force	4.87KN
Number of stroke	22.2 ≈ 23

Total Height of the piston = head of the piston + height of piston

                       = 2+20 =22cm