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
BINSFELD ENGINEERING INC.
Binsfeld's Torque Measurement Systems measure true mechanical torque and power on rotating shafts. We also offer consultation, strain gaging and installation services.
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