Load Cells, Force Measurement & Load Calibration

The measurement chain

A force measurement is a chain: a physical load deforms a transducer, the transducer converts deformation into an electrical signal, signal conditioning amplifies and filters that signal, a data acquisition system samples and digitises it, and software converts the digitised value into engineering units using a calibration. Each stage has a transfer function and each stage can introduce error. The load cell is the most visible element, but the accuracy of the force reading depends on every stage: a perfectly calibrated load cell with a noisy amplifier, an out-of-range DAQ, or a stale calibration factor will produce a wrong number. Understanding the chain is the first step in diagnosing a force measurement that does not agree with expectation.

The measurement chain visualised

The diagram below shows the chain from physical load to engineering units. The load cell is a transducer that converts force into a small electrical signal — typically millivolts — via a strain-gauge bridge. Signal conditioning amplifies the bridge output, excites the bridge with a stable voltage, and may filter noise. The DAQ samples the conditioned signal, digitises it, and records it. Software applies the calibration factor to convert the digitised value into force in engineering units. Each arrow is a potential source of error, and each must be understood to diagnose a discrepancy.

FORCE MEASUREMENT CHAIN

  PHYSICAL LOAD
  (force on the specimen / rig)
         │
         ▼
  TRANSDUCER
  (load cell: strain-gauge bridge
   deforms with the cell body)
         │  millivolts (mV/V)
         ▼
  SIGNAL CONDITIONING
  (bridge excitation, amplification,
   filtering)
         │  volts
         ▼
  DATA ACQUISITION (DAQ)
  (sample, digitise, record)
         │  digital counts
         ▼
  ENGINEERING UNITS
  (calibration factor applied;
   force in N, kN, lbf)

  Each stage has a transfer function.
  Each stage can introduce error.
  Calibration ties the digital value
  back to a known physical force.

Load cell types and their characteristics

Load cells come in several configurations, each suited to a different loading arrangement and each with different alignment sensitivities. A tension/compression load cell measures axial load in one direction and is the most common cell for uniaxial tests. A multi-axis load cell measures forces and moments in several directions simultaneously, which is valuable when off-axis components must be monitored but requires more complex calibration. An inline load cell is placed in series with the load path and measures the load passing through it. A load washer is a ring-shaped cell that measures compressive load through a central bolt or ram. A through-hole load cell is similar but allows a bolt or rod to pass through the centre. The choice depends on the load path, the space available, and whether off-axis components must be measured.

The Wheatstone bridge concept

Most strain-gauge-based load cells use a Wheatstone bridge to convert the small resistance change of the strain gauges into a measurable voltage. The bridge consists of four resistive arms; in a load cell, one or more arms are strain gauges bonded to the cell body, and the others are either matching gauges or completion resistors. When the cell is loaded, the gauges deform, their resistances change, and the bridge becomes unbalanced, producing an output voltage proportional to the load. A full bridge — with gauges on all four arms, arranged so that tension and compression gauges respond oppositely — gives the highest sensitivity and the best temperature compensation, because temperature-induced resistance changes cancel between adjacent arms. The bridge is excited by a stable voltage, and the output is a small signal, typically in millivolts per volt of excitation.

Wheatstone bridge output:

  V_out = (V_ex / 4) · (ΔR1/R1 − ΔR2/R2 + ΔR3/R3 − ΔR4/R4)

For a full-bridge load cell with gauges arranged so that
axial load produces equal and opposite strain in the arms:

  V_out ≈ (V_ex / 4) · K · ε · n

where:
  V_ex   = bridge excitation voltage
  ΔR_i   = resistance change of arm i
  K      = gauge factor of the strain gauges
  ε      = strain in the gauges (proportional to applied force)
  n      = number of active gauges (1, 2, or 4)

A full bridge (n = 4) gives the highest sensitivity and
inherently compensates for temperature-induced resistance
changes, because those changes cancel between adjacent arms.

Calibration, zero and drift

Calibration is the process of establishing the relationship between the load cell output and a known applied force, traceable to a reference standard. A calibration is performed at defined load points, typically including zero and several points across the cell's range, and the result is a calibration factor — or a calibration curve, if the relationship is not perfectly linear — that converts the measured signal into force. Calibration is not permanent: load cells drift, they can be affected by overload, temperature and handling, and their calibration must be re-verified at intervals appropriate to the cell, the usage and the programme requirements. Zero is a special calibration point: the reading at zero load defines the reference from which all subsequent loads are measured, and zero drift — a change in the zero reading over time — directly biases every load measurement. Zero should be checked at the start of a test, monitored during the test, and re-checked at the end.

Cross-axis sensitivity and off-axis loading

A uniaxial load cell is designed to measure load along one axis. When load is applied along a different axis — because of misalignment, eccentricity, or a side load — the cell produces a reading that includes a component due to the off-axis load. This is cross-axis sensitivity: the cell responds, undesirably, to loads it was not designed to measure. The magnitude of the error depends on the cell design and the amount of off-axis load; for some cells it is small, for others it is significant. The defence is to ensure the load line is aligned with the cell axis, to monitor for off-axis components (using a multi-axis cell or by measuring the structural response for asymmetry), and to account for cross-axis sensitivity in the uncertainty budget when it cannot be eliminated. The load cell reads what it feels, not necessarily what you intend to apply.

USING A LOAD CELL IN AN ALIGNMENT THAT INTRODUCES OFF-AXIS LOADING WITHOUT ACCOUNTING FOR CROSS-AXIS SENSITIVITY CAN PRODUCE A FORCE READING THAT INCLUDES COMPONENTS THE CELL WAS NOT DESIGNED TO MEASURE. The load cell reads what it feels, not necessarily what you intend to apply.

Preload and seating

Many load cells and loading arrangements require a small preload to seat the contacts, remove play and establish a stable zero. The preload is applied, the zero is taken at the preload, and the test load is measured relative to that zero. The preload must be large enough to seat the contacts but not so large that it pre-damages the specimen or consumes a significant fraction of the cell range. The preload also establishes the contact condition at interfaces — bolted, clamped or pinned — and for tests where the contact condition matters, the preload is part of the test definition, not a rig detail.

What to check before trusting the force reading

Before a force measurement is used as evidence, the measurement chain should be checked. Is the load cell calibrated and in date? Is the zero stable? Is the load line aligned with the cell axis? Is the cell in the correct range — not overloaded, not operating at a tiny fraction of its range where resolution and signal-to-noise suffer? Is the signal conditioning configured correctly — excitation voltage, gain, filter? Is the DAQ sampling at an adequate rate for the test, and is the calibration factor correct in the software? Each of these is a link in the chain, and a discrepancy in any one will bias the force reading. A force measurement that agrees with expectation is not, by itself, evidence that the chain is correct; it may be that two errors have cancelled.