Measuring bending involves quantifying the amount of deformation a material undergoes when subjected to a bending force. The specific method depends on the context, the material being bent, and the desired accuracy. Here's a breakdown of common approaches:
1. Measuring Bend Angle
The bend angle is the most straightforward measure of bending. It quantifies how much the material has deviated from its original straight line.
- Protractor or Angle Finder: For simple bends and rough estimations, a protractor or angle finder can be used directly on the bent object.
- Goniometer: A goniometer is a more precise instrument specifically designed for measuring angles, often used in medical or engineering contexts.
- Coordinate Measuring Machine (CMM): CMMs use touch probes or laser scanners to precisely measure the geometry of a bent object, allowing for accurate determination of the bend angle.
- Optical Comparators: These project a magnified image of the bent object onto a screen with angular scales, allowing for precise angle measurement.
2. Measuring Bend Radius
The bend radius is the radius of the arc formed by the bend.
- Radius Gauges: These are physical templates with different radii that can be compared to the bend to find the closest match.
- CMM or Laser Scanning: As with bend angle, CMMs and laser scanners can accurately measure the geometry of the bend and calculate the radius.
- Mathematical Calculation (for circular bends): If the bend is a circular arc, the radius can be calculated from the chord length (straight line distance between the endpoints of the arc) and the height (distance from the midpoint of the chord to the arc).
3. Measuring Bending Strain
Bending strain quantifies the amount of deformation within the material itself.
- Strain Gauges: These are small sensors that are bonded to the surface of the material. As the material bends, the strain gauge deforms, changing its electrical resistance. This change is measured and converted to a strain value. Strain gauges are typically used to measure strain during bending.
- Digital Image Correlation (DIC): This non-contact technique involves tracking the movement of a pattern on the surface of the material using cameras. By analyzing the changes in the pattern, the strain field can be calculated.
4. Measuring Bending Stress
Bending stress is the internal stress within the material caused by the bending moment. While stress cannot be directly measured, it can be calculated.
- Calculation from Bending Moment and Section Properties: Bending stress is typically calculated using beam bending theory, which relates the bending moment, the material's section properties (e.g., moment of inertia), and the distance from the neutral axis to the point of interest. The formula is often expressed as: σ = My/I, where σ is bending stress, M is bending moment, y is the distance from the neutral axis, and I is the area moment of inertia.
Considerations for Accurate Measurement
- Material Properties: The material's ability to bend without breaking, and its springback characteristics (tendency to return to its original shape after bending) must be considered.
- Accuracy Requirements: The required accuracy will determine the appropriate measurement method.
- Calibration: Ensure that any measuring instruments are properly calibrated.
- Measurement Environment: Environmental factors like temperature can affect the accuracy of measurements.
Example Formula for Estimating Circumference of a 90-degree Bend:
As referenced, estimating material needed for a 90-degree bend can be found with:
Circumference = (π 2 r) / (360/90)
Where:
- π (pi) ≈ 3.14159
- r = bend radius
This formula calculates the arc length (circumference) of a quarter-circle (90-degree bend) with radius r. It's useful for estimating the material needed for bending operations.
