Main Menu

See All Software See All Instruments See All Transducers See All Vibration Testing Equipment See All Electroacoustics See All Acoustic End-of-Line Test Systems See All Academy See All Resource Center See All Applications See All Industries See All Services See All Support See All Our Business See All Our History See All Global Presence

Main Menu

See All nCode - Durability and Fatigue Analysis See All ReliaSoft - Reliability Analysis and Management See All Test Data Management See All DAQ Software See All Drivers & API See All Utility See All Vibration Control See All High Precision and Calibration Systems See All DAQ Systems See All S&V Hand-held Devices See All Industrial Electronics See All Power Analyzer See All S&V Signal Conditioner See All Acoustic Transducers See All Current and Voltage Sensors See All Displacement Sensors See All Force Sensors See All Load Cells See All Multi Component Sensors See All Pressure Sensors See All Strain Sensors See All Strain Gauges See All Temperature Sensors See All Tilt Sensors See All Torque Sensors See All Vibration See All Accessories for Vibration Testing Equipment See All Vibration Controllers See All Measurement Exciters See All Modal Exciters See All Power Amplifiers See All LDS Shaker Systems See All Test Solutions See All Actuators See All Combustion Engines See All Durability See All eDrive See All Production Testing Sensors See All Transmission & Gearboxes See All Turbo Charger See All Training Courses See All Acoustics See All Asset & Process Monitoring See All Custom Sensors See All Data Acquisition & Analysis See All Durability & Fatigue See All Electric Power Testing See All NVH See All Reliability See All Vibration See All Weighing See All Automotive & Ground Transportation See All Calibration See All Installation, Maintenance & Repair See All Support Brüel & Kjær See All Release Notes See All Compliance

Main Menu

See All API See All Experimental Testing See All Electroacoustics See All Noise Source Identification See All Environmental Noise See All Sound Power and Sound Pressure See All Noise Certification See All Industrial Process Control See All Structural Health Monitoring See All Electrical Devices Testing See All Electrical Systems Testing See All Grid Testing See All High-Voltage Testing See All Vibration Testing with Electrodynamic Shakers See All Structural Dynamics See All Machine Analysis and Diagnostics See All Dynamic Weighing See All Vehicle Electrification See All Calibration Services for Transducers See All Calibration Services for Handheld Instruments See All Calibration Services for Instruments & DAQ See All On-Site Calibration See All Resources See All Software License Management

Uncertainty of Force Measurements

Learn which factors influence the accuracy of force measurements. This webinar will present an easy-to-use mathematical method to estimate the measurement uncertainty of a force measurement. We will also show some practical ways to improve the measurement uncertainty if required.

The following topics will be addressed:

  • What is measurement uncertainty? 
  • What influences the uncertainty of measurement? How to assess the measurement uncertainty of your force measurement?
  • What does the datasheet mean to me?
  • Reducing the uncertainty of measurement: What are your options?

Date: 2021 October 06th

Instructors: Thomas Kleckers (EU webinar) and Chris Novak (US webinar) 

Duration: 40 minutes

Language: English

knowledge, resource center, recorded webinars, webinar is a newton always a newton, contact presenter thomas kleckers chris novak
Thomas Kleckers

Product Manager 

knowledge, resource center, recorded webinars, lower production costs using smart industrial electronics
Chris Novak

Field Sales Engineer

Questions from participants of previous "Uncertainty of Force Measurement" webinars answered by the presenters

In general, every force transducer (that is, if we are talking about strain gauge-based sensors) works with every bridge amplifier. As well as the requirements for accuracy, the following points are also important:

  • Fast measurement => High sampling rate
  • Force measurement in production => Consider the right interface
  • Force measurement in testing => Flexible amplifier solutions

TIP: An amplifier is usually an investment for more than a decade, so I would again recommend talking to the sales team.

We definitely recommend doing a rough uncertainty calculation before ordering the sensor to check which model fulfils the accuracy requirements. Contact the sales team if you are in doubt.

TIP: Load cells with high-end performance are not always expensive. HBK offers ‘S-type’ load cells (S2M and S9M) with outstanding accuracy at affordable prices.

Yes. Instruments have a linearity error, which is mostly very low. But there is a temperature dependence of the zero point and the amplification. The noise of the amplifiers also has an impact on the uncertainty of the measurement.

The resolution of the measurement chain is determined by the instrument. It only depends on the load cell in terms of the output signal it provides. If the signal is 100%, the whole resolution of the instrument is available. The limit of resolution of a load cell is given simply by the resistor noise of the load cell. In general, the higher the output of the load cell, the higher the resolution. The nearer the output signal of the load cell and the input range of the amplifier, the better the resolution.

TIP: HBK offers U15 and C15 load cells with a high output signal >4 mV/V and an amplifier system (QuantumX MX430B/MX238B) with matching input ranges. Ask your local sales engineer.

The result of our calculation is a range of force. In our first example we found out that if the measurement is 1000 N and the surroundings are as explained, the result is between 989 N and 1011 N. The probability that our real force is in this range is 68.27 %. That means that 31.77 % are outside this range.

In many cases this is not acceptable, and the target is to have a higher probability. So, we can double our force range from 1000 N ± 11 N to 1000 N ± 22 N. This means that more than 68.27 % of our measurements results are inside the new and larger interval. In our example 11 N is equal to k=1 and this is the first result. When doubling the range, this is k=2 and 95.45% of all measurements are in the new range. Tripling our 11 N will lead to a range from 967 N to 1033 N, and 99.73 % of all measurements show a reading inside this range. We call this k=3.

TIP: This principle is a consequence of the Gaussian function.

The calculation in the webinar was done based on the data sheet, which is a conservative approach, as the deviations (linearity, hysteresis…) are guaranteed to stay within the values specified there (at HBK, the sensors actually perform better than the values specified in the data sheet as these are the extremes). However, for a more precise calculation, a calibration certificate is preferable. It gives specific information about the linearity, repeatability, and hysteresis of the individual sensor, not the possible maximum. In other words, with a calibration certificate you know the real uncertainty of the sensor, which helps to improve the measurement uncertainty calculation.

If you have a calibration certificate, look for the uncertainty of the load cell at the load step that is interesting to you. You can add this error as an additional number to your calculation. As the linearity and the hysteresis are included in the uncertainty mentioned in the calibration certificate, you can leave them out.

TIP: Most calibration certificates mention the errors for k=2. Divide the uncertainty by 2 before putting it on your list. [Refer to the next question to find out more about k]

The competition might work differently, but at HBK, the accuracy class describes the biggest error for different characteristics such as linearity, hysteresis, TC0, creep… This makes sense as the biggest possible error is what determines the measurement uncertainty as well as the best possible results of the measurement. 

You cannot use the accuracy class to calculate the measurement uncertainty, but the HBK accuracy class may help you with the sensible selection of the components of your measurement chain in terms of your budget and the given technical requirements.

Lateral forces usually have a negligible impact on the measurement, while bending moments are an important thing to consider in your calculation. Look at the data sheet for details. Estimate the value of the bending moment and calculate its individual error based on the formula shown in this webinar. Finally, the impact of the bending moment is just another number under the square root.

TIP: The influence of bending moments is related to full scale.

No. The GUM (Guide to the Expression of Uncertainty in Measurement) is the standard for measurement uncertainty calculation. The guideline can be used for all kinds of measurements (distance, weight, temperature…); it must, however, be adapted to the individual measurement problem.

TIP: We offer seminars on measurement uncertainty that will familiarize you with the uncertainty calculation of force or torque measurements and show you how to apply the guideline in a practical way.

Related Pages