Force Measurements

Force Measurements

What is Force

  • Newton’s 2nd Law of Motion:

    • States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

    • Mathematical representation: F = m * a where:

      • F: Force in Newtons (N)

      • m: Mass in kilograms (kg)

      • a: Acceleration in meters per second squared (m/s²)

  • Force (F): The product of mass and acceleration.

  • Vector Quantity: Force has both magnitude and direction.

  • Unit: Newton (N)

    • 1 N is the force required to accelerate 1 kg of mass at 1 m/s².

Measurement of Force

  • Direct Methods:

    • Comparison between unknown force and known gravitational force on a standard mass.

    • Example tool: Beam balance.

  • Indirect Methods:

    • Involves calibrated transducers sensing gravitational attraction or the deformation of materials.

    • Measures gravitational weight indirectly through elastic deformation.

Devices to Measure Force

  1. Scales and Balances

    • a) Equal Arm Balance

    • b) Unequal Arm Balance

    • c) Pendulum Scale

  2. Elastic Force Meters

    • Operates based on material deformation principles.

  3. Load Cells

    • a) Strain Gauge Load Cells

    • b) Hydraulic Load Cells

    • c) Pneumatic Load Cells

Scale and Balance

Equal Arm Balance

  • A mechanical device to measure mass by comparing an unknown mass to a known mass.

  • Consists of a beam balanced on a pivot with two pans to hold masses.

Operating Principle

  • Principle of Moments:

    • The balance remains horizontal when equal moments are applied on both sides.

    • Both sides have equal distances from the fulcrum for direct mass comparison.

Unequal Arm Balance

  • Measures mass/force using a beam with arms of different lengths.

  • Operates on the principle of moment comparison to balance an unknown weight against a known one.

Operating Principle

  • The equilibrium condition involves balancing forces based on lengths of the arms.

Pendulum Scale

  • Measures weight/force using a pendulum's deflection under load.

  • Operates on the principle of torque: force applied generates torque that deflects the pendulum or lever arm.

Torque Equilibrium

  • Deflection degree is proportional to the force applied.

Elastic Force Meter

  • Measures force through the elastic deformation of materials like springs.

  • Also called a proving ring.

  • Deformation follows Hooke's Law: proportional to applied force.

  • Standard uses include material testing calibration, capable of measuring forces from 1000 N to 1000 kN.

Load Cells

a) Strain Gauge Load Cells

  • Highly accurate devices converting material deformation into electrical signals.

  • Common in industrial weighing, force measurement, and structural monitoring.

Operating Principle

  • Deformation causes strain gauges to change resistance, generating a voltage signal related to the applied force.

Wheatstone Bridge Circuit

  • Converts resistance changes into electrical signals:

    • Consists of four resistive elements.

    • Excitation voltage is applied across the bridge; output voltage is measured.

Output Voltage Calculation

  • Calculated based on balanced resistances in the Wheatstone bridge, relating output to resistance changes.

Example Calculations

Example 1

  • Given data for a strain gauge load cell (Gauge factor, Nominal resistance, Input voltage, etc.) to find:

    1. Strain induced

    2. Change in resistance

    3. Output voltage of Wheatstone bridge.

Example 2

  • During tensile test, a load cell measures applied force with steps to calculate:

    1. Output voltage at full-scale force.

    2. Actual force with given output voltage.

    3. Displacement under applied force.

    4. Error comparison based on voltage measurement assumption.

Load Cells

b) Hydraulic Load Cells

  • Measure force using fluid pressure based on Pascal’s Principle.

  • When pressure is applied to a confined fluid, it’s transmitted uniformly.

  • Applied force compresses fluid, creating pressure proportional to the force.

Construction

  • Includes piston, diaphragm, and pressure gauge; pressure gauge measures force calibration.

c) Pneumatic Load Cells

  • Use compressed air to measure force based on equilibrium pressure.

  • Applied force on a diaphragm leads to back pressure that is regulated until equilibrium is achieved.

  • Air pressure indications correspond to measures of applied force when calibrated.