6.acceleration of Gear System

 

 

ACCLERATION OF GEARED SYSTEM

Experiment No. Date: Aim:

 

To determine the equivalent mass moment moment of inertia of a system of shafts.

  Apparatus Required:   1. Gear system.   2. Stop Wath.

!. "eter sale. #. Different "asses.   Theory:

$t an %e sho&n s ho&n that for a %ody' %ody' &hose mass moment of inertia is $' rotatin( a%out an axis )' then the torque T required to produe an an(ular aeleration  is (iven %y the equation T* $

+onsider t&o shafts , and - onneted %y (earin( as sho&n and onsider the torque T, required at shaft , to aelerate the system. Torque required at shaft , to aelerate shaft , *$,, Torque required at shaft - to aelerate shaft *$-et veloity ratio

  A



G

  B

Then torque required at shaft , to aelerate shafts , and * $,, / $-* $,, /G $-G* , 0$, /G $- or T,*$ , &here $*$, /G2$$ is then the equivalent mass moment of inertia of the system referred to shaft ,.

 

+onsider three shafts ,'-' and + onneted %y (earin( as sho&n and onsider the torque required at shaft , to aelerate the system.   A

et veloity ratios



 

G1  

 B

 

and

C  

 

G2

 D

Then similarly

T  A

   A

0 I  A 



2

 

G1   I  B



2

2

G  1 G2 I C  

)r T,*$,  &here $*0$,/G12 $-/ G12G22 $+

+onsider three shafts ,'-' and + onneted %y (earin( as sho&n and onsider the torque required at shaft to aelerate the system. et veloity ratios  

C  

and

 

  A 

  B

G 2

 D

Then similarly

T  B

  

 B

0 I  B 



2 

2

 G1  I  A   G2 I C  

or T-*$-  &here $*0$-/G12 $,/ G22 $+

G1  

 

Method to determie the mass momet o! iertia o! a system"

,ssumin( the system starts from rest and ne(letin( the ineti ener(y (ained %y the fallin( mass. m(x3mf (x*4.5$ (x*4.5$2 &here $*effetive mass moment of inertia of the system mf * mass required to rotate the system &ith uniform an(ular veloity.i.e veloity.i.e that required ti overome %earin( frition fri tion  * an(ular veloity of the system as mass m reahes the datum

 I  

 m 6 gx 27m   f    

 

2 x 

2

  &here t* time for m to fall throu(h

rt 

distane x

 I  

7m   m f   6 gr 2t 2 2 x

,lternatively . ,ssumin( that the torque produin( the aeleratin of the system *7m3m f 6(r  6(r  2 x Then 7m3mf 6(r*$ 6(r*$  %ut    2 rt    2 2 7m   m f   6 gr  t   I   2 x 8or the experiments su((ested' this assumption is onsidered aepta%le provided that the ma(nitude of the aeleration is relatively small.

 

Sha!t Assem#$y A

F$y/hee$

I %&' m() *"***++

,

*"*+*-

C

*"***+.

Sha!t

Diameter %m)

Mass %&')

&(  %m()

I %0' m()

A

*"+-*

("12

*"**1(1

*"**3.-

,

*"+(*

+"1+

*"**+41

*"**+44

C

*"(**

1"-5

*"**.*1

*"*+4.-

No o! Teeth

Mass %&')

&(  %m()

I %0' m()

5*

*"-1

*"**(.4

*"**+-(

4*

*".*

*"**(*2

*"**+*(

-*

*"(4

*"**++-

*"***1(.

Gears

Torque Drum .*mm diameter

 

Experimental Procedure. For each of the experiments suggested 1. De Dete term rmin ine e a va valu lue eo off mf by adding loads to the load hanger until the system just rotates with uniform angular velocity velocity.. 2. For a serie series s of incre increasing asing lo loads, ads, me measure asure th the e tome for the lload oad to fall th through rough a predetermined height. Note !t is suggested that x is approximately "##$%## mm and the cord length is so arranged that the cord frees itself from the drum when the load reaches the datum. &. 'lo 'lott a gra graph ph o off m a agai gainst nst 1(t2 and use the slope to estimate a value for moment of inertia !.

 

E6perimet !

",SS T,9EN 7(m6

 

T$"E T,9EN T) 8, 7se6

1t2

T$"E T,9EN T) 8, 7se6

1t2

T$"E T,9EN T) 8, 1.5m 7se6

1t2

E6perimet III

",SS T,9EN 7(m6

 

1t2

E6perimet !!

",SS T,9EN 7(m6

 

T$"E T,9EN T) 8, 7se6

E6perimet I7

",SS T,9EN 7(m6

)esults