Load cell linearity, hysteresis and deflection in force control

01 / ENGINEERING DECISION

State the error definition before comparing percentages.

A practical load cell linearity definition is the largest departure of an increasing-load calibration response from a specified straight reference over the stated range. Endpoint and best-fit references need not produce the same value. Identify the reference and range before comparing two nonlinearity specifications.

Nonlinearity is one contribution to measurement error. It does not include every effect of temperature, creep, installation, conditioning or the reference itself. Hysteresis and repeatability describe different comparisons and should not be substituted for one another.

Supporting scope: FUTEK: resolution, accuracy and repeatability ↗ · FUTEK: load cell calibration variables ↗ · NIST: metrological traceability ↗

02 / ENGINEERING DECISION

A percentage needs a denominator.

For an illustrative 500 N calibrated force span, a 0.1% full-span force-equivalent bound is 0.5 N. It is not 0.1% of every reading: at a 10 N reading the same 0.5 N corresponds to 5% of that reading. Signed tension/compression spans and rated-output conventions must be defined explicitly.

The examples below use a single 0–500 N direction, zeroed output and an endpoint line from 0 to 100% normalized span. They do not establish a vendor’s accuracy or combine errors into a system uncertainty.

Supporting scope: FUTEK: resolution, accuracy and repeatability ↗

03 / ENGINEERING DECISION

Worked example A: separate nonlinearity from hysteresis.

This synthetic one-cycle dataset is authored to show the calculations. It is not a calibration certificate or an instrument capture. Against the endpoint reference, the largest increasing-load deviation is 1 N, or 0.2% of the 500 N span. The largest loading/unloading difference is 1.5 N, or 0.3% of span.

One increasing/decreasing cycle cannot establish repeatability. A best-fit calculation would use a separately defined fitting rule and could change the reported nonlinearity. The residual diagram plots percent-of-span errors directly; it does not exaggerate an unlabeled force axis.

04 / ENGINEERING DECISION

Retain the conditions that make the comparison reproducible.

Zero and loading sequence affect the interpretation. Record mounting, excitation, cable/conditioner, force direction, dwell and temperature. If zero is removed, retain how it was established; a changing mechanical preload may otherwise disappear into a tare operation.

Choose repetitions and reference points that address the intended measurement. A shunt check exercises an electrical response; it does not impose reference force on the structure. A static calibration does not by itself characterize dynamic force response.

Supporting scope: FUTEK: load cell calibration variables ↗ · NIST: metrological traceability ↗

05 / ENGINEERING DECISION

Worked example B: include fixture compliance.

Assume a sensor has a 500 N nominal force and 0.025 mm displacement at that force. A linearized stiffness estimate is 500/0.025 = 20,000 N/mm. If the rest of the axial load path contributes a 10,000 N/mm series stiffness, the combined value is about 6,667 N/mm, not 30,000 N/mm.

At 500 N, the assumed total elastic displacement is 0.075 mm: 0.025 mm in the sensor and 0.050 mm in the rest of the modeled path. These values illustrate a linear series model. Contact changes, backlash, joints, bending and nonlinear specimen behavior can invalidate that simplification.

Supporting scope: HBK force glossary ↗

06 / ENGINEERING DECISION

Attached mass changes the dynamic question.

In a single-degree-of-freedom linear screen, f_n = sqrt(k/m)/(2 × pi), with k in N/m and m in kg. Using the example combined stiffness of about 6.667 million N/m, an assumed effective mass of 1 kg gives about 411 Hz; 4 kg gives about 205 Hz.

These are illustrative model frequencies, not measured sensor frequencies or approved controller bandwidths. Real installations can have multiple modes, damping and changing contact stiffness. Include acquisition/conditioner filtering and transport delay, and identify the installed response before selecting loop gains.

Supporting scope: HBK force glossary ↗

07 / ENGINEERING DECISION

Do not turn unrelated specification limits into a total accuracy claim.

A sum of applicable worst-case bounds and a root-sum-square of standard uncertainties answer different questions. Datasheet maximum errors are not automatically independent standard uncertainties. Temperature, loading history and reference conditions determine which terms apply and how they relate.

For a procurement decision, state the allowed error at the operating forces and environment, then request a documented evaluation of the complete chain. Prefer residuals against a traceable reference under relevant conditions over a single unqualified “accuracy” number.

Supporting scope: NIST: metrological traceability ↗ · NIST Technical Note 1297 ↗

08 / ENGINEERING DECISION

Request both the static record and the installed-response evidence.

Include working/peak force, the smallest useful increment, mounting stiffness or specimen information, moving mass and relevant frequency content. Specify desired calibration direction/range, reference-line definition, repeated loading and any dynamic acceptance test.

Download the synthetic CSV to reproduce the error calculation. Use the calibration/quality page to define a real serial-linked record; the example CSV and diagrams are educational aids rather than evidence of supplied sensor performance.