FORCE MEASUREMENT
INTRODUCTION
•TRANSDUCERS THAT MEASURE FORCE AND TORQUE USUALLY
CONTAIN AN ELASTIC MEMBER THAT CONVERTS THE MECHANICAL
QUANTITY TO A DEFLECTION OR STRAIN (IS CALLED LOAD CELL)
•A DEFLECTION SENSOR (FOR EXAMPLE, STRAIN GAGE) IS THEN USED
TO GIVE AN ELECTRICAL SIGNAL PROPORTIONAL TO THE QUANTITY
OF INTEREST (FORCE OR TORQUE)
•RANGE, LINEARITY AND SENSITIVITY ARE DETERMINED BY THE SIZE
AND SHAPE OF THE ELASTIC MEMBER, THE MATERIAL USED AND
THE SENSOR
The elastic members commonly used in load cells are links, beam, rings,
and shear web
P
Wheatstone bridge
strain gage 3(axial) on
the back face
strain gage 4
(transverse)
strain gage 2
(transverse)
For full bridge arrangement

R3
R4
V o  

 R 2  R 3 R1  R 4
strain gage 1 (axial)
 R1

R1
R2
P
R2
 R3
R3

R4
R4
  GF . a   GF .
 GF . t  GF .
P

V s


Vo 
  R 3  R1  R 2  R 4




( R 2  R 3 )  R 3
R1
R2
R4
V s R2 R3
2
If R1=R2=R3=R4
AE
P
AE
Vo  
GF . P (1   )V s
2 AE




EXAMPLE
A strip of high strength steel has a length of 30 cm and a cross section of
20 mm by 20 mm. The modulus of elasticity is 200 GPa, and Poisson’s ratio
is 0.27. It is subjected to an axial load of 15000 N and it is instrumented with
full bridge arrangement of strain gage with R=120 W and gage factor of 2.10.
Determine output voltage if a supply voltage of 2.5 V is applied.
Solution :
Use equation
Vo  
GF . P (1   )V s
2 AE
where the link type load cell is too stiff to be effective
P
x
 1   2   3   4 
6M
Ebh
2

6 Px
Ebh
2
1
h
3
 R1

R1
R2

R2
 R3

R3
R4
R4

6 GF . Px
Ebh
2
b
Vo 
axial gage 1 and 3
axial gage 2 and 4 on the
bottom surface
  R 3  R1  R 2  R 4




( R 2  R 3 )  R 3
R1
R2
R4
V s R2 R3
2
If all strain gage are identical
Vo 
  R 3  R1  R 2  R 4




( R 2  R 3 )  R 3
R1
R2
R4
V s R2 R3
2
V0 
6 GF . P . x .V s
Ebh
2








TORQUE MEASUREMENT (TORQUE CELLS)
Torque cells are transducers that convert an applied torque to an electrical
output signal.
V
 xy 
1 
TD
2J

16 T
D
3
16 T  1   
16 T  1   

,  2  


3
3
D  E 
D  E 
For circular shaft subjected to pure torsion,
all normal stress are 0, the principal stress s1=s2=xz
Principal strain
 R1
R1

R2
R2

 R3
R3

R4
R4

16 T  1  

3
D  E

.GF

V0 
16 T  1  

3
D  E

 GF .V s

MECHANICAL POWER MEASUREMENT
(DYNAMOMETER)
END OF LECTURE