# Evaluating Suspension System Constants: A Hydraulic Fixture Approach

Categories: Physics

## Abstract

This project is about Fixture design for finding spring constant and damping constant for suspension system. The determination of spring constant is done from the equation F=k⸹, where F= force acting on spring, k =spring constant and ⸹=displacement. For finding spring constant experimentally, we have designed the fixture with the help of mechanical devices like Scale hydraulic cylinder and hydraulic Jack.

The determination of damping coefficient is done by some equipments like load cell, hydraulic actuator, data acquisition system and function generator.

The damping coefficient will be found by calculation and graphical representation of excited amplitude and frequency of damper. Alternately the objective of project is to design such fixture which has less cost and it will be able to give output with maximum efficiency.

## Spring Testing Machine for Finding Spring Constant

First of all adjust the spring in between hydraulic jack and hydraulic cylinder. Hydraulic jack is operated by the handle provided in it. So produce force with help of hydraulic jack.

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Thus by manual pumping, piston in hydraulic cylinder moves forward and spring is compressed. Force is applied on the hydraulic cylinder and due to this deflection of spring is occurred. This pressure is displayed on pressure gauge in kg/cm². Take this pressure gauge reading and measure spring change in length. Thus by measuring spring deflection and pressure, stiffness is calculated from equation of F = k⸹.

Theoretical calculation of spring stiffness

Dₒ = outer diameter = 57.6 mm d = wire diameter = 9.3 mm

Dᵢ = inner diameter = Dₒ - 2d = 39 mm

Mean coil diameter = D = mm

Wahl factor = K = = 1.

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297 which is resultant factor for torsion shear stress and direct shear stress.

Force acting on spring in suspension system, F = mg

Total mass of 5 steel slab in suspension m = ρVg

Density of steel block is assumed as 7850 kg/ .

Volume of steel slab = 1705.2 cm3 (from measurement of dimensions of steel slab)

= 1.7052 * 10-3 m3.

So mass of steel slab = ρVg = 7850*1.7052*10-3*9.8

= 13.385 kg = 15 kg

There are 5 steel slab. So total mass = 15*5 = 75 kg. but we take as 80 kg.

So total load acting on spring = mg

= (80) (9.8)

= 784 N

Spring material is considered as oil hardened and tempered spring steel. The value of modulus of elasticity for it is G = 81370 N/mm2.

Permissible shear stress value for this spring,

Sut 1222.47 N/mm2

= 0.3*Sut = 366.74 N/mm2

So shear stress acting on spring,

= 1.297 (

= 155.5 N/mm2 366.74 N/mm2

Spring constant theoretical,

Ktheoretical , (where N = number of active turns = 15)

= 45016.68 N/m.

### Graphs and Input Data for Spring Constant Calculation

Here, as it is shown in figure different forces are given to the spring and reading of displacement of spring is to be noted in box and from this reading graph of force displacement is plot and we get little bit different values of spring constant but at the end average value of spring stiffness is to be considered as final spring stiffness.

• Spring of different diameters can be checked
• Spring can be check without damaging the spring.
• The testing is carried out in very less time, so production rate is very high.
• One man effort is enough to check the spring.
• Semi-skilled and unskilled labor can operate this machine easily.
• The system is self-lubricating.
• The system is noiseless.
• It is portable and could be carried anywhere.

• As in this setup hydraulic jack is used there may be a chances of hydraulic leakages hence the periodic inspection, maintenance and refilling of oil is necessary.

#### Costing of Fixture

Specifications of hydraulic cylinder are:

Stroke length L = 100 mm

So bore diameter is in between L/1.5 to L  D = 7 mm

Max pressure inside cylinder = 150 bar to 450 bar

Material: stainless steel

Ports in cylinder = 25 mm

Calculating maximum Pressure generated in our suspension system,

Maximum force generated is 784 N but we take it as 900 N for safety purpose. So maximum pressure generated inside cylinder ,

= 233860.32 N/mm2

= 2.34 bar

Cost for this specification of cylinder is around Rs. 3000

Hydraulic Jack Cost Estimation: We need 10 ton of hydraulic jack which can applied maximum force of 98066.5 N The price of jack is approximately Rs.1500 to Rs.2000.

Pressure gauge Cost Estimation: Here, we need pressure gauge having range around 0-300 psi or 0-200 psi which is made of stainless steel.

Price of pressure gauge is approximately is Rs.800 to Rs.900

So total expanses in making this assembly = 3000 + 2000 + 900 + other expanses

= 7000 to 8000 Rs.

#### Determination of Damping Co-efficient Using Sinusoidal Testing

The oil in the cylinder of Damper flows from one chamber to other chamber through some narrow gaps of base valve and piston valve as piston is moving back and forward in the cylinder tube.

As a result, the damping force is produced because of the friction generated among oil molecules because of flow restriction due to narrow gaps in valve. The damping force is proportional to Velocity however; the damping force is always designed greater in the extension than in the compression stage to quickly accommodate shocks and provide damping, in order to improve vehicle dynamic behaviors.

#### Solid Works Modeling – Damping Coefficient Testing Assembly

As shown in above figure, it is the whole suspension system and its components are there. The damper is mounted in between load cell (which is basically 5 steel slabs of having certain weight) and hydraulic actuator. Hydraulic actuator is connected to data acquisition system and to motor which gives power to the suspension system.

For loading the damper excitation frequency and sampling frequency are set into the computer software and the signal sinusoidal excitation is produced through function generator. The amplification of signal is done by the help of digital A/D interface to make servo actuator to excite the Damper according to input data. The force produced across damper is calculated by the load cell (steel slabs) and dynamometer displacement is recorded by linear variable differential transformer (LVDT).

Here in our project in our laboratory we don’t have function generator and computer software facility like Matlab. So in this project we have to add function generator in order to excitation of damper as per desired frequency and amplitude. Because displacement driving is the excitation method used, the displacement data signal of the Damper piston can be directly recorded into system and the force generated across the damper is then recorded through the load cell fitted on the rigid beam.

The computer software collects this output displacement and force data then it is put into Microsoft Excel and Matlab software interface for analysis where various operations like data smoothening, determination of velocity using time and displacement data. Finally, Time -Displacement, Time-velocity, characteristic diagram (velocity - force) and work diagrams (Displacement -Force) are obtained for single cycle and for whole Test run.

### Equivalent Damping Coefficient

The process of evaluation of Equivalent Damping Coefficient in which the real nonlinear MDOF system of Damper is replaced by simple elastic SDOF system having equivalent damping coefficient (Ceq) which is approximate value of damping coefficient corresponding to real nonlinear system, that to be use to evaluate damping force in system in simplest analysis.

The Equivalent elastic system is supposed to have same response as real nonlinear system under given same sinusoidal excitation. The equivalent viscous damping coefficient is determined on the assumptions that the real nonlinear Damper model and its equivalent linear system dissipates same amount of energy per cycle of response to sinusoidal excitation.

### Costing of Fixture

The fixture's cost components include:

• Hydraulic cylinder (~Rs. 3000),
• Hydraulic jack (~Rs. 1500 to Rs. 2000),
• Pressure gauge (~Rs. 800 to Rs. 900), resulting in a total expense of approximately Rs. 7000 to Rs. 8000.

#### Determination of Damping Coefficient

The damping coefficient is determined experimentally using equipment such as a load cell, hydraulic actuator, data acquisition system, and function generator. The damping coefficient is calculated and graphically represented based on the damper's excited amplitude and frequency.

#### Experimental Process for Damping Coefficient

The experimental setup involves exciting the damper with a sinusoidal input and measuring the resultant force and displacement. This data is then analyzed to plot time-displacement, time-velocity, and characteristic diagrams, from which the damping coefficient is derived.

#### Equivalent Damping Coefficient

The equivalent damping coefficient (Ceq) is an approximation that simplifies the analysis by assuming the nonlinear damper system can be represented by a single-degree-of-freedom system with a linear damping coefficient. This coefficient is calculated based on the assumption that the equivalent system dissipates the same amount of energy per cycle as the real system under sinusoidal excitation.

### Conclusion

This project successfully designs a cost-effective and efficient fixture for determining the spring and damping constants of suspension systems. The hydraulic fixture offers significant advantages over traditional methods, providing accurate measurements with minimal effort and maintenance.

#### References

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2. Jorg Wallaschek, Dynamics of Non-Linear Automobile Dampers, Int. J. Non-Linear Mechanics, Vol.25 No2/3,1990, pp. 299-308.
3. Carlos A. B.,” Equivalent Viscous Damping Equations for Direct Displacement Based Design” Master Degree Thesis, Dept. Earthquake Engg., Univ. of Pavia, Pavia, Italy, 2004.
4. Rahul Zaharia, Equivalent Viscous Damping Models in Displacement Based Seismic Design, Bul. Inst. Polit. Lasi, t. LI(LV). F 1-2, 2005, pp. 51-59
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7. S. M. Metev and V. P. Veiko, Laser Assisted Microtechnology, 2nd ed., R. M. Osgood, Jr., Ed. Berlin, Germany: SpringerVerlag, 1998.
8. Avdhut R. Jadhav, Gajendra J. Pol, Amit A. Desai, “Design And Manufacturing Of Hydraulic Spring Stiffness Testing Machine, International Journal Of Emerging Engineering Research And Technology” Volume 2, Issue 7, October 2014, Pp 184190.
9. Pathan Mosin Aouraze , Patel Soyal Dastagir, Pawar Santosh Balu, Labade Suyog Bajirao, “A Review On Spring Stiffness Testing Machine, International Research Journal Of Engineering And Technology” Volume:04 Issue: 01, Jan-2017.
10. Hitesh K. Tare1, C.S. Dharankar2 1PG Student, AISSMS COE, PUNE. 2Assistant Professor, AISSMS COE, PUNE.
Updated: Feb 23, 2024