CONVERTING STRAIN TO A SIGNAL USING STRAIN GAGE
Strain gages are mounted directly on the shaft to measure torque. Strain gages use a 4-arm wheatstone bridge circuit that changes in resistance proportional to the amount of strain (deformation) it experiences. Torque strain gages are specially designed to maximize the amount of deformation of each of the arms. As the arms become longer, the electrical resistance goes up, as they become shorter, the resistance goes down. The change in resistance creates a voltage change on the signal line which then needs to be transferred off the shaft.
Other types of torque transducers (such as in-line load cells) are often less desirable since they require disassembly or modification of the shaft.
TRANSFER OF SIGNAL OFF THE SHAFT - INDUCTIVE
Binsfeld's permanent torque and power monitoring products use induction to transfer torque sensor data. In these systems, a stationary power ring is connected to an external power source, creating a magnetic field that "induces" a current on the shaft collar. The current powers the transmitter, which energizes the strain gage. When torque is applied to the shaft, the torque signal is received by the transmitter and digitized. The digital signal is transferred back to the power coil, and converted to an analog (or digital) output via the master control unit. This output can be converted to a torque value based on shaft mechanical properties.
tRANSFER OF THE SIGNAL OFF THE SHAFT - High Frequency RF
Binsfeld's temporary torque measurement products use high frequency RF to transfer the torque signal off the shaft. In these systems, a battery-powered transmitter energizes the strain gage, receives the torque signal, then converts the torque signal to a radio frequency signal, which is received by a nearby "receiver". The receiver converts the radio frequency signal back to an analog (or digital) output which can be processed and converted to a mechanical torque measurement using the mechanical properties of a shaft.
If the true mechanical torque is known, the only variable that needs to be acquired is the speed (RPM) of the shaft, which can be measured using a tachometer. These two inputs can be combined to give the true mechanical power of the shaft.
For a rotating shaft, the equations for power are as follows
- Power (KW) = Torque (N*m) x shaft speed(rpm) / 9550
- Power (HP) = Torque(in*lb) x shaft speed(rpm) / 5252
The TorqueTrak TPM2 and Revolution have speed sensing built in, while the TorqueTrak temporary system requires an additional speed sensor and a data aqcuisition device (such as the OpDAQ Field Test 2) to "integrate" the signals into a true power output. This is the most accurate way of measuring the power output of a motor. Other methods of power measurement, such as at the motor with an electrical device (i.e. a watt meter) are not as accurate because the measurements include power loss of other system components (i.e. bearings and couplings). Watt meters do not reveal the exact power output of the engine - to do that you must measure the true mechanical horsepower at the shaft.
Below are a list of technical definitions that are fundamental for the understanding of how Binsfeld's wireless torque telemetry works.
Strain is a unitless measurement of how much an object deforms due to an applied force.
- Strain = Change in length / Starting length =
Poisson's Ratio is a material-specific constant that relates the transverse deformation (strain) to axial deformation (strain).
- Poisson Ratio = (axial strain) / (transverse strain) =
- Typical Poisson's Ratio for shafts
- Steel = .3
- Aluminum = .32
Polar Moment of Inertia
The moment of inertia is a measure of an object's ability to resist a change in rotational direction. The Polar Moment of Inertia is used when analyzing the ability of objects to resist torsion (or twisting) specifically.
- The units of the Polar Moment of Inertia is or
- Typical Polar Moment of Inertia for shafts:
- Solid Shaft:
- Hollow Shaft (Tube):
Young's Modulus of Elasticity
Young's Modulus of Elasticity is a material-specific constant that predicts how much a material is going to deform (strain) under a certain stress.
- Young's Modulus is in the same units as stress (Newtons / square meter or Pounds / square inch)
- Typical Young's Modulus Values for shafts:
- Steel = 30,000,000 psi
- Aluminum = 10,000,000 psi
A wheatstone bridge is a circuit with 4 resistors connected in parallel. The bridge is "Excited" with an input voltage (Vex), and the output voltage (Vo) can be sensed to a high degree of accuracy. A typical schematic and equation relating these two voltages are shown below:
Torque transducers convert mechanical energy to electrical energy. Common examples include a load cell and a strain gage.
Torque is the measure of a twisting force that causes an object to rotate about a point. The equation is as follows:
- Torque = Force x (Distance force applied from a point)
- The units of torque measurement are typically Newton-meters or inch-pounds.
Power is the rate in which energy is being expended (or work is being done).
- Power = Work / Time = Force x distance / time = Force x Velocity
- Units are typically in Watts or Horsepower
Stress is the measurement of the amount of force per area:
- Stress = Force / Area
Alternatively, stress can be calculated using "Hooke's Law", which combines strain and modulus into the equation below:
- Stress = Young's Modulus * Strain
The units of stress measurement are Newtons/square meter or lbs/square inch.
For a shaft, it is sometimes desired to calculate the torsional stress caused at the surface of the shaft due to an applied torque. This is found by using the following equation:
- τ = T*R / J
- T = Twisting moment
- R = Radius of shaft
- J = Polar Moment of Inertia of the shaft cross section