U18PCAU7L1 - Vehicle Dynamics Lab

LAB MANUAL

B.Tech IV Year – 7h semester

DEPARTMENT OF AUTOMOBILE ENGINEERING

BHARATH INSTITUTE OF HIGHER EDUCATION AND RESEARCH

173, AGARAM MAIN ROAD, SELAIYUR,

CHENNAI - 600073

Department of Automobile Engineering

U18PCAU7L1 - Vehicle Dynamics Lab

LIST OF EXPERIMENTS

1. DETERMINE NATURAL FREQUENCY OF TORSIONAL VIBRATION IN SINGLE ROTOR SYSTEM

2. FIND THE DISPLACEMENT, VELOCITY AND ACCELERATION WITH THE USE OF MATHEMATICAL SOFTWARE USING VARIOUS SENSORS

3. DETERMINATION OF WHIRLING SPEED OF SHAFTS

4. CRITICAL SPEED OF SHAFT

5. CAMBER ANGLE MEASUREMENT

6. Study of introduction to MATLAB

DETERMINE NATURAL FREQUENCY OF TORSIONAL VIBRATION IN

SINGLE ROTOR SYSTEM

Exp No. 1 Date:

Aim:

To determine natural frequency of torsional Vibration in single rotor System

Equipment:

1. Vibration machine,

2. Shaft,

3. Chuck,

4. Stop watch.

Formula Used:

T theo =2π√ I/Kt

Procedure

Fix the bracket at convenient position along the tower beam. Grip one end of the shaft at bracket by the chuck. Fix other end of shaft in the rotor. Twist the motor rotor to some angle and then release. Note down the time for no. of oscillations. Repeat the procedure for different length of shaft.

Observation:

Observations are to taken for mild steel brass shafts

Observation Table:

Sr. No Len.

Of

Shaf

No. of

oscillation

Time K Tth Texp Fth Fexp

Result:

The natural frequency of the torsional vibration in single rotor system is--------------------- Hz

Conclusion:

Natural frequency of torsional vibration experimental to theoretical is nearly same.

FIND THE DISPLACEMENT, VELOCITY AND ACCELERATION WITH

THE USE OF MATHEMATICAL SOFTWARE USING VARIOUS

SENSORS

Exp. No:2

Date:

Aim: Find acceleration, velocity & displacement.

we should consider what these measurements are.

Displacement is the measurement of a distance travelled. If an object has moved 10 meters then it has been displaced by 10 meters or 10 m.

Velocity, often incorrectly called speed, is the measurement of a certain displacement in a certain time in a specific direction. For example an object that moves 10 meters in a second is travelling at the velocity of 10 meters per second or 10 m/s.

Velocity can be both negative and positive as it is a vector. The magnitude of a velocity is the speed, this can only be positive.

Acceleration is the rate of change of velocity, it is also a vector as it implies a direction. If we had a stationary object, it would have no acceleration. The rate of change of its velocity is zero. And, it follows, that an object travelling with a constant velocity of 10 m/s is not accelerating, it is not getting any faster or any slower. Therefore the rate of change of its velocity is zero. However, if an object is changing velocity then it is accelerating. Acceleration can be both negative, which is deceleration and positive, which is acceleration.

If an object starts from a stationary position and accelerates up to a velocity of 10 m/s in 1 second then the acceleration is 10 meters per second per second or 10 m/s/s.

If the object started from a stationary position and accelerates up to a velocity of 10 m/s in 50 seconds then the acceleration is 0.2 meters per second per second or 0.2 m/s/s.

Units of acceleration are often shown as , or .

As can be seen from these definitions of displacement, velocity and acceleration, they are all very closely related. In fact, in mathematical terms they are directly

related and simple conversions exist. The mathematical relationship involves calculus, specifically integration and differentiation.

The mathematical integral of the velocity curve against time, is the displacement. That means if you plot the velocity curve f(x) against time and measure the area under the curve you have the total displacement. This relationship is shown in Figure 1.

Figure 1: Integrating velocity to obtain displacement The mathematical differential of the velocity curve f(x) against time, is the acceleration. That means if you plot the velocity curve against time and measure the slope of the curve a at a given point in time T you would have the acceleration at that time. This relationship is shown in Figure 2.

Figure 2: Differentiating velocity to obtain acceleration

In simple terms these curves can be described as functions, a function being a representation of a signal. For example, in Figure 3 below, a simple signal exists.

Figure 3: A simple digital signal The (x,y) co-ordinates for this curve are as follows in Table 1.

X Y

0 1

1 2

2 3

3 4

4 5

Table 1

The pattern is clearly repeating and simple in its nature. To express the contents of Table 1 as a function would be (x, f(x)) rather than (x, y) or more commonly denoted as y = f(x). In this case when x = 1 so then y = x + 1 and so on. Therefore the function is actually ,

So

This explains the concept of a curve or signal being expressed as a function rather than sets of co-ordinates. Returning to our velocity curve, if the velocity curve against time was represented as a function, it would be

Where is the function at a given time the x-axis value, that produces the y-axis value .

But as a displacement curve it would be represented as the function,

Where is the displacement and is the change in displacement with time.

Hence as an acceleration curve it would be represented as the function,

Where is the acceleration and is the change in velocity in time.

Returning from core mathematics and using DATS to visualise these conversions, we have a simple worksheet as shown in Figure 4.

Figure 4 This worksheet takes a vibration signal and performs integration using three different methods and then integrates again on the resulting signals. Thus from one acceleration signal, it is possible to convert to velocity and then to displacement

DETERMINATION OF WHIRLING SPEED OF SHAFTS

Exp. No:3 Date:

Aim:

To determine the whirling speed for various diameter shafts experimentally and compare it with the theoretical values

.Apparatus Required:

1) Shaft – 3 nos.

2) Digital tachometer

3) Chuck key

4) AC voltage regulator

Description of the setup:

The apparatus is used to study the whirling phenomenon of shafts. This consists of a frame in which the driving motor and fixing blocks are fixed. A special design is provided to clear out the effects of bearings of motor spindle from those of testing shafts.

Procedure:

The shaft is to be mounted with the end condition as simply supported. The speed of rotation of the shaft is gradually increased. When the shaft vibrates violent in fundamental mode ( I mode ), the speed is

noted down. The above procedure is repeated for the remaining shafts.

Observation:

Young’s modulus, E (for steel) = 2.06 x 1011 , N / m2

Young’s modulus, E (for copper) = 1.23 x 1011 , N / m2

Length of the shaft, L = , m

Shaft 1 (steel) Shaft 2 (copper) Shaft 3(steel)

m1 = 0.0584 kg m2 = 0.16496 kg m3 = 0.16051 kg

d1 = 0.0031 m

d2 = 0.00484 m

d3 = 0.00511 m

l1 = m l2 = m l3 = m

Formulae

Theoretical whirling speed, Nctheo = {0.4985 / [sqrt (δs / 1.27 )] } x 60 , rpm

Static deflection due to mass of the shaft (UDL), δs = (5wL4) / (384 EI)

Where,

w = weight of the shaft per metre , N/m

L = Length of the shaft, m

E = Young’s modulus for the shaft material, N/m2

I = Mass moment of inertia of the shaft

= ( π / 64 ) d4 , m4

Tabulation:

S.No. Diameter

of shaft (

m )

Mass

moment

of inertia

of the

shaft , I (

m4) x 10-

12

Weight

of the

shaft per

m, w (

N/m )

Whirling speed ( rpm )

Nc exp Ne theo

Result:

The whirling speed for various diameter shafts are determined experimentally and verified with the theoretical values.

CRITICAL SPEED OF SHAFT

Exp. No:4 Date:

Aim:

To, study the whirling phenomenon of a shaft at different end conditions.

Apparatus required:

1. End joining blocks

2. Sliding blocks.

3. Tacho meter

Formulae:

F th = K/L2[(E*I)/(Aρ)]1/2

Where,

F th = torsional frequency (Hz)

K= radius of gyration m=3.58, 2.45

L=length of rod

E=modulus of velocity =2X10N/m2

�= Density =7850kg/m3

W= weight of rod

I=moment of inertia, mm4

Fexp= n/60 Hz where,

F exp=experimental frequency (Hz)

N=speed rpm Raghavendran.P.R | HITS

Procedure:

1. Fix any one of the three shafts, say 4mm dia in the experimental setup.

2. Increase the speed of rotation of shaft till the first mode is obtained using tachometer.

3. Again increase the speed of shaft until next mode of rotation occurs and note down the speed of rotation.

4. Repeat the procedure for various end conditions and various shaft diameter.

5. Using the formula an actual and theoretical frequency are calculated and compared.

Results:

Thus the whirl phenomenon for different end conditions of studied and theoretical, experimental frequencies are compared.

CAMBER ANGLE MEASUREMENT

Exp. No:4 Date:

Aim: To study by using Multi Body dynamics software to solve simple Car model

Model provided by Volvo Cars

Here're some of the highlights for MaxFlex:

Using Adams MaxFlex, an MBD analyst can increase model accuracy by including nonlinear structural behavior

It's a streamlined workflow, similar to Adams Flex Simulation is conducted entirely in Adams There is shared memory parallel (SMP) support to increase simulation

efficiency Easy to set up models and run simulations No third-party tool is needed to generate animations with both rigid and

nonlinear flexible parts, since it can be done in Adams/Postprocessor

Results:

Thus the camber angle measurement for different end conditions of studied and theoretical, experimental frequencies are compared

Study of introduction to MATLAB

Exp. No:6 Date:

AIM:

To study about the introduction to mat lab and to know the analysis of a shaft car model.

Description:

Automotive suspension:

A simplified half car model includes an independent front and rear vertical suspension. The model also includes body pitch and bounce degrees of freedom. To show how simulation can be used to investigate side characteristics .you can use this model with conjunction with a powertrain simulation to investigate longitudinal shuffle resulting from changes in throttle setting.

Contents:

• Analysis and physics

• The model

• Running the simulation

• Closing the model

• Conclusions

Analysis and physics:

A free body diagram of the half car model illustrates the modeled characteristics of the half cart. The front and rear suspension or modeled as spring/ damper systems. A more detail model would include a Tyre module and damper nonlinearities such as velocity- dependent damping. The vehicle body has pitched and bounces degrees of freedom.

They are represented in the model by four states:

• Vertical displacement

• Vertical velocity

• Pitch angular displacement

• Pitch angular velocity

A full model with six degrees of freedom can be implemented using vector algebra blocks to perform access transformations and force /displacement /velocity calculations. The front suspension influences bounce according to the equation 1. Raghavendran.P.R | HITS

Equation 1:

F front = 2 kf (Lf θ-Z) + 2Cf (Lf θ-Z)

F front, Frear = upward force on body from front/rear suspension.

kf, kr = front and rear suspension spring constant.

Cf , Cr = front and rear suspension damping rate.

Lf, Lr = horizontal distance from gravity center to front / rear suspension.

P,θ = pitch ( rotational ) angle and its rate of change.

Z, Z = bounds (vertical) distance and its rate of change.

The pitch contribution to front suspension is given by

Equation2:

M front = L front F front (pitch movement due to front suspension).

The expression for rear suspension is Equation3.

Equation3:

Frear = 2 kr (Lr θ+Z) - 2Cr (Lr θ+Z)

M rear = Lr Frear (pitch movement due to rear suspension).

The forces and movement result in body motion according to newton second in equation 4.

Equation 4:

Mbz = F front + Frear - mbg

Iyy θ = M front + M rear + My

mb = body mass

My = pitch movement included by vehicle acceleration.

Iyy = body movement of inertia about gravity center. Raghavendran.P.R | HITS

The model:

To open this model, type SIdemo - suspn in mat lab command window. It shows the top level diagram of the suspension model.

The suspension model has two inputs and both input blocks are highlighted. The first input is the road height. The second input is a horizontal force acting the center of the wheels that results from braking or acceleration maneuvers. A step input here corresponds to the vehicle driving over a road surface with a step change in height for first input.

This input appears only as a movement about the pitch axis because the longitudinal body motion is not modeled. A spring/damper sub system that models the front and rear suspension, right click on the front/rear suspension block and select “look under name “to see the front/rear suspension sub system. The suspension subsystems are used to model equation1-3. The equation is implemented directly in the Simulink diagram to the straight forward use of gain and simulation blocks.

The difference between front and rear are accounted as follows, because sub system is a masked block, a different data set (L, K and C) can be entered for each instance. Furthermore, L is through as Cartesian coordinate, x being negative or positive with respect to the origin or center of gravity. Thus Kf, Cf and Lf are used for the front suspension block whereas Kr,Cr, and Lr are used for the rear suspension block.

Running the simulation:

To run this model press the play button on the tool bar in the model window. Initial conditions are loaded in to the model work spaces from the Sl demo – sus dat .mfile. To see the contents of the model workspace, go to view menu> model explorer, look under the contents of the Sl demo – suspn model and select “model workspace”. Loading initial conditions in the model workspace prevents any accidental modifications of parameters and keeps MATLAB workspace clean.

Note that the model logs relevant data to MATLAB workspace in a data structure called Sl demo – suspn – output. Type the name of the structure to see what data it contains. Read more about signal logging in simulation help.

Simulink results are displayed and plotted by the Sldemo- Sus graph .m.the default initial conditions are given in table1. Raghavendran.P.R | HITS

Table 1: default initial conditions

Lf, = 0.9: % front hub displacement from body gravity center (m)

, Lr = 1.2:% rear hub displacement from body gravity center (m)

Mb = 1200:% body mass (kg)

Iyy = 2100:% body moment of inertia about Y-axis in (kg m2)

Kf = 28000:% front suspension stiffness in (N/m)

Kr = 21000:% rear suspension stiffness in (N/m)

Cf = 2500:% front suspension damping in (Nsec/m)

Cr = 2000:% rear suspension damping in (Nsec/m)

Closing the model:

Close the model and delete generated data from MATLAB workspace.

Conclusions:

This model allows you to simulate the effect of changing the suspension damping and stiffness, thereby investigating the mode between comfort and performance. Raghavendran.P.R | HITS