FORCE & TORQUE MEASUREMENTS

Link type load cell

A simple uniaxial link-type load cell with strain gages as the sensor is a very common load cell configuration. The load P can be either a tensile load or a compressive load.

The four strain gages are bonded to the link such that two are in the axial direction and two are in the transverse direction. The four gages are wired into a Wheat stone bridge with the axial gages in arms 1 and 3 and the transverse gages in arms 2 and 4.

Link type load cell

Link type load cellWhen the load P is applied to the link, axial and

transverse strains and develop in the link and are related to the load by the expressions

Where,A is the cross-sectional area of the link. E is the modulus of elasticity of the link material. ν is Poisson’s ratio of the link material.

AE

vP

AE

Pta

Link type load cell

The output voltage Eo from the Wheatstone bridge can be expressed in terms of the load P. If it is assumed that the four strain gages on the link are identical, then R1 = R2. Therefore,

Or

ooi

CEEEvK

AEP

)1(

2

AE

EvKPE io 2

)1(

Beam type load cell

Beam-type load cells are commonly employed for measuring low-level loads where the link-type load cell is not effective. A simple cantilever beam with two strain gages on the top surface and two strain gages on the bottom surface (all oriented along the axis of the beam) serves as the elastic member and sensor for this type of load cell.

Beam type load cell

Beam type load cell

The load P produces a moment M = Px at the gage location x that results in the following strains:

Where b is the width of the cross section of the beamh is the height of the cross section of the beam

22432166

Ebh

Px

Ebh

M

Beam type load cell

The output voltage Eo from the Wheatstone bridge, resulting from application of the load P, is obtained by assuming the four strain gages on the beam to be identical

or2

6

Ebh

EKPE ixo

ooi

CEEKxE

EbhP 6

2

Ring type load cell

Ring-type load cells incorporate a proving ring as the elastic element. The ring element can be designed to cover a very wide range of loads by varying the diameter D (or radius R), the thickness r, or the depth w of the ring.

Either strain gages or a linear variable-differential transformer (LVDT) can be used as the sensor.

Ring type load cell

Ring type load cell

If an LVDT is used to measure the diametric compression or extension of the ring, the relationship between displacement and load P is given by the following approximate expression:

Equation (6.14) is approximate since the reinforced areas at the top and bottom of the ring that accommodate the loading attachments have not been considered in its development.

3

3

79.1Ewt

PR

Torque CellTorque cells are transducers that convert torque to an electrical signal. The two types of torque cells in common usage include those installed on fixed shafts and those installed on rotating shafts. The latter type is more difficult to utilize, since the electrical signal must be transmitted from the rotating shaft to a stationary assembly of recording instruments. The problem of signal transmission will be considered after design concepts associated with torque cells are discussed.

Torque Cell

Torque Cell

A circular shaft with four strain gages mounted on two perpendicular 45-degree helixes is shown in figure.

Gages 1 and 3, mounted on the right-had helix, sense a positive strain, while gages 2 and 4, mounted on the left-hand helix, sense a negative strain. The two 45-degree helixes define the principal stress and strain directions for a circular shaft subjected to pure torsion.

Torque Cell

The shearing stress in the circular shaft is related to the applied torque T by the equation

Where D is the diameter of the shaft and J is the polar moment of inertia of the circular cross sectionSince the normal stresses x = y =z = 0 for a circular shaft subjected to pure torsion

3

16

2 D

T

J

TDxz

32116

D

Txz

Torque Cell

Principal strain are obtained by using equations and Hooke’s law for the plane state of stress. Thus,

E

v

D

Tv

E

E

v

D

Tv

E

116)(

1

116)(

1

3122

3211

Torque Cell

The response of the strain gages is obtained from the equations above as

If the gages are connected into a Wheatstone bridge, as illustrated, the relationship between output voltage Eo and torque T is obtained as

KE

v

D

T

R

R

R

R

R

R

R

R

116

34

4

3

3

2

2

1

1

io KEE

v

D

TE

116

3

Torque Cell

Or

Equation indicates that the torque T is linearly proportional to the output voltage Eo and that the constant of proportionality or calibration constant C is given by

ooi

CEEKEv

EDT

)1(16

3

iKEv

EDC

)1(16

3

Torque Cells-Data Transmission

Frequently, torque must be measured on a rotating shaft, which necessitates signal transmission between a Wheatstone bridge on the rotating shaft and a stationary instrumentation centre.

Signal transmission under these circumstances is usually accomplished with either slip rings or telemetry.

Slip Rings

The slip-ring assembly contains a series of insulated rings mounted on a shaft and a companion series of insulated brushes mounted in a case. High-speed bearings between the shaft and the case permit the case to remain stationary while the shaft rotates with the torque cell. A commercial slip-ring assembly is shown in the figure

Slip Rings The major problem associated with slip-ring usage is noise (generated by contact resistance variations between the rings and brushes). The contact resistance variations can be kept within acceptable limits if the rings are fabricated from monel metal (a copper-nickel alloy), if the brushes are fabricated from a silver-graphite mixture, and if the ring-brush contact pressure is maintained between 50 and 100 psi. Rotational speed limits of slip-ring assemblies are determined by the concentricity that can be maintained between the shaft and the case and by the quality of the bearings. Slip-ring units with speed ratings of 6000 rpm are available.

Slip Rings

Signal Transmission with Telemetry

In many applications, the end of the shaft is not accessible for mounting of the slip-ring unit and telemetry must be used to transmit the signal from the rotating shaft to the recording instrument. The output from the Wheatstone bridge is used to modulate a radio signal. The strain gages, bridge, power supply, and radio transmitter are mounted on the rotating shaft, while the receiver and recorder are located at a stationary instrumentation centre.

In most applications, the distance over which the signal must be transmitted is only a few feet; therefore, low-power transmitters, which do not need to be licensed, can be used.

Telemetry system