The acceleration of a geared system

APPLIED MECHANICS LABORATORY REPORT

Title: The acceleration of a geared system

Aim: To support the theory on the prediction of the motion of rotors connected by gears.

Object:

The main object of the experiment is:

To investigate the theory on the prediction of the motion of rotors connected by the gears.

By the falling weight method to evaluate the inertia on each shaft.

Determine the equivalent inertia of the system at the first shaft, by the falling weight method.

Test rig figure:

The number of teeth on each gear:

N =90, N =30, N =90, N =90

Theory:

In order to evaluate the equivalent inertia on each shaft by the "Falling Weight" method.

The free body diagrams reveal:

P*R=I*a+Tf

Should be a straight line graph of P*R plotted against a. The intercept should give the friction torque. Measure the time taken for the mass to fall through Im then a=2s * m then α= a (rad/sec^2)

t^2 s^2 R

Also P=m*g-m*a=m[9.81-a] Nt

And for the calculation of moment of inertia of the system referred to shaft1 we use:

Ieqv= I1+I2*[Na] ^2+I3 [Na*Nc] ^2

Nb Nb Nd

Procedure:

1. Determine, by the falling weight method the moment 's of inertia associated with each of the individual shafts.

2. Assemble the system so that the gears meshed.

3. Determine by the falling weight method the equivalent inertia of the system at the fist shaft.

4. Compare the equivalent inertia with the theoretical using the equation:

Sample Calculations:

M=F = 1=0.101 Kg

g 9.81

a=2s= 2*1 =0.0154 m/sec^2

t^2 11.38^2

P=m(9,81-a)=0.101*(9.81-0.0154)=0.999 Nt

P*R1= 0.999*0.019=0.0190 Nt*m

α= a = 0.0154 =0.8105 rad/sec^2

R 0.019

Table of results:

Shaft 1

R=0.031 m

S=1 m

W(Nt) t(sec) a(m/sec^2) P(Nt) Pr(N*m) α(rad/sec^2)

1 11.17 0.016 0.999 0.031 0.517

2 6.99 0.041 1.993 0.062 1.322

3 4.51 0.098 2.972 0.092 3.161

4 4.24 0.111 3.957 0.123 3.581

5 3.72 0.144 4.93 0.153 4.645

6 3.42 0.171 5.899 0.183 5.516

Shaft 2

R=0.019 m

S=1 m

W(Nt) t(sec) a(m/sec^2) P(Nt) Pr(N*m) α(rad/sec^2)

1