STRAIN MEASUREMENT IN A SHAFT

SUBJECTED TO TORQUE

Introduction

The torque on a shaft can be measured using strain gages by attaching several

strain gages to the shaft in proper orientation to measure torque. Properly installed gages

allow direct measurement of torsional shear strain that can be calibrated to output torque.

The measurement of static and dynamic torque can be a tremendous troubleshooting tool

for evaluating failures of rotating machinery that could relate to torsional loading.

Types of machinery that are commonly tested include:

Synchronous motor driven equipment (transient torsional analysis during startup)

Reciprocating compressors and pumps (harmonic torques)

Turbomachinery shafting with universal joint type couplings

Transmission shafting with universal joint type couplings

Variable frequency drive motors (torsional loading from drive harmonics)

Mounting Gages and Measuring strain

The strain gages are installed on the shaft using rosette type gages that include

two strain gages mounted on the same foil backing. This allows precise positioning of a

pair of gages with exact 90° separation between each portion of the gage. Two rosettes

are used on opposite sides of the shaft with the gage elements oriented 45° away from the

axis of rotation. Alternative gage arrangements can be used to measure other loads such

as bending or axial force. In these situations, other gage wiring and/or gage type and

mounting location would vary.

The gages are attached using a standard Wheatstone bridge arrangement using a

full bridge configuration for torque measurement. When the gages are installed using this

layout, the bridge output is insensitive to temperature variation of the shaft surface and

insensitive to shaft bending stresses. The only significant output on the gages will be

strain related to shaft torque.

An example of a single rosette mounted on a shaft coupling spool is shown below.

This picture shows a single rosette located on one side of the coupling spool. An identical

gage would be located on the opposite side of the shaft.

The strain maxima are under ±45° with reference to the direction of shear plane

(or under ±45° with reference to the shaft axis, which is in fact the same). The strain

gauges must be positioned as shown in the fig., below.

Full Bridge Circuit

For the full bridge, it can in general be assumed that the connections within the

bridge are short and their interferences effects are negligible. The cables Rk2 and Rk3 can

be considered as a lumped resistance in the bridge excitation circuit. The actual bridge

will then be supplied with a voltage UEK according to the voltage drop across the cable

resistance.

From this we can derive:

Wireless Transmission

The strain gage system on the shaft is powered and amplified using an onboard

wireless transmitter. The transmitters used have self contained batteries or induction

power. The wireless signal transmission is accomplished using 2.4 GHz spread spectrum

technology. The current products used function well in industrial environments.

The system requires a wireless receiver to capture the signals for data logging.

This is accomplished using a variety of antennas and receivers depending on the

measurement environment. We have installed the wireless transmitters inside compressor

crankcases, motors, inside coupling guards and a variety of different locations.

Calibration

The system is calibrated using a precision shunt calibration method that provides

for a simulated strain input to the gage installation. When the gages are properly installed

and wired, the shunt calibration provides accurate strain to torque conversion. The output

from the receiving station is recorded using standard data acquisition equipment with the

input signals scaled to report directly in torque units.

Measurements include both static and dynamic torque, as both are necessary for

analysis of most situations. The static torque measurement also provides an additional

reference point to verify the calibration based on known torque using motor amps or

power from another driver.

REFERENCES

1) Karl Hoffmann, “Applying Wheatstone Bridge Circuit”.

2)“Strain Gauges”

Available at http://en.wikipedia.org/wiki/Strain_gauge#Mechanical_types

3) “Torque Measurement Using Strain Gauges”

Available at http://www.kelmengineering.com/torque.html