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# TORQUETRAK THEORY

## TORQUETRAK PRODUCTS

Below are a list of technical definitions that are fundamental for the understanding of how Binsfeld’s wireless torque telemetry works.

STRAIN

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

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

WHEATSTONE BRIDGE

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 TRANSDUCER

Torque transducers convert mechanical energy to electrical energy. Common examples include a load cell and a strain gage.

TORQUE

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

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

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.

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Maple City, MI 49664 USA

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