Statically Testing a Torque Sensor: Using Force and Lever Arm as a Reference

→ Product category: Torque sensors

 

A torque sensor is to be tested at 100 Nm. A second torque transducer is not necessarily required for this purpose. A known torque can also be generated using a defined force and an accurately known lever arm.

The fundamental relationship is:

M = F × l

If, for example, a force of:

200 N

acts perpendicular to a lever arm of:

0.5 m

the resulting torque is:

M = 200 N × 0.5 m = 100 Nm

In practice, however, the task is more demanding than this simple calculation suggests. The actual effective lever arm, the direction of the force, horizontal alignment, sensor mounting, the dead weight of the lever, friction and parasitic forces are all decisive. Even small mechanical errors can be greater than the actual measurement deviation of a high-quality torque sensor.

A reliable static test is therefore only achieved when the force and effective lever arm are known and the torque is introduced into the measuring axis with as little transverse force, bending moment and friction as possible.

For this purpose, ICS Schneider offers, among other products, Torque Sensors as well as Force Sensors and Force Measuring Instruments. One example is the HySense TQ100, a rotating strain-gauge torque sensor for measuring ranges from 1 to 500 Nm.

How torque is generated from force and lever arm

Torque is generated when a force acts at a distance from the axis of rotation.

For the ideal case of a force acting perpendicular to the lever, the following applies:

M = F × l

Where:

• M = torque in Nm,
• F = force in N,
• l = effective lever arm in m.

Torque can therefore be changed in two ways

by increasing the force:

F ↑ → M ↑

or by increasing the lever arm:

l ↑ → M ↑

Example

F = 100 N

l = 0.5 m

results in:

M = 50 Nm

The same torque is generated, for example, with:

F = 50 N

and:

l = 1.0 m

Why the force angle is decisive

The simplified formula:

M = F × l

applies only when the force and lever arm are perpendicular to each other.

In general:

M = F × l × sin(α)

Where α is the angle between the lever arm and the direction of force.

At 90°

the following applies:

sin(90°) = 1

and therefore:

M = F × l

If the angle deviates from 90°

only the component of force perpendicular to the lever contributes to the torque.

This means:

It is not the length of the lever alone that is decisive, but the perpendicular distance between the axis of rotation and the line of action of the force.

Generating torque with reference weights

A particularly straightforward method for static torque testing is to suspend known masses from a defined lever arm.

The gravitational force is calculated from:

F = m × g

The resulting torque is therefore:

M = m × g × l

Where:

• m = mass in kg,
• g = local gravitational acceleration in m/s²,
• l = effective lever arm in m.

For approximate checks

the value:

g ≈ 9.81 m/s²

is often used.

For higher accuracy requirements

however, the gravitational acceleration applicable at the actual location should be used.

The mass of the weights used must also be appropriate for the required uncertainty.

Calculation example using weight and lever arm

A mass of:

20.000 kg

is suspended from a horizontal lever arm of:

0.500 m

.

Using:

g = 9.81 m/s²

the gravitational force is first calculated as:

F = 20 kg × 9.81 m/s²

F = 196.2 N

The reference torque is therefore:

M = 196.2 N × 0.500 m

M = 98.1 Nm

An important practical mistake

is to simply assume:

20 kg × 0.5 m = 10 kgm = 100 Nm

This approximation is not sufficient for a metrological test.

The mass must first be converted into force using gravitational acceleration.

Alternative: measuring force with a reference load cell

Instead of using defined masses, the force acting on the lever can also be measured with a suitable reference load cell.

Then:

M = FRef × l

Example

A reference force sensor measures:

250.0 N

with an effective lever arm of:

0.4000 m

The resulting torque is:

M = 250.0 N × 0.4000 m

M = 100.0 Nm

This method can be particularly practical

when:

• different torque values need to be adjusted continuously,
• large masses are to be avoided,
• a suitable force reference is already available.

The load cell must be installed so that it actually measures the tangential reference force.

Determining the effective lever arm correctly

The total length of the lever is not what matters for the calculation.

The decisive distance is between:

axis of rotation of the sensor

and:

line of action of the reference force

Example

A lever has an overall length of:

600 mm

.

However, the force is applied at a distance of:

500 mm

from the axis of rotation.

The calculation must therefore use:

l = 0.500 m

and not:

0.600 m

When using reference weights

the relevant distance should be determined from the axis of rotation to the actual line of action of the gravitational force.

The geometry of a hook, bracket or knife edge can therefore also be relevant.

Why the lever should be aligned horizontally

With freely suspended weights, the force acts vertically downward.

To ensure that the force acts perpendicular to the lever, the lever should be horizontal.

If the lever is inclined by an angle β relative to the horizontal

the following applies:

M = m × g × l × cos(β)

With a small inclination

the error may initially appear insignificant.

However, it becomes relevant as accuracy requirements increase.

The inclination should therefore not be assessed visually alone.

A suitable spirit level or electronic inclination measurement improves reproducibility.

Taking the dead weight of the lever arm into account

The lever arm itself also has mass.

If its center of gravity is not located exactly on the axis of rotation, its dead weight generates torque even before an additional reference weight is applied.

This initial torque can be

• mechanically balanced,
• compensated with a counterweight, or
• determined and taken into account metrologically.

Simply zeroing the measurement is not always equivalent to mechanical balancing

If the sensor is merely electrically tared with a mounted, unbalanced lever, the mechanical torque caused by the lever continues to act on the sensor.

For a simple functional check, defined taring may be sufficient. For a demanding reference measurement, however, the lever’s own torque should be known or compensated as far as possible.

Mounting the torque sensor correctly

The sensor must be mounted so that the generated torque is transmitted completely through its measuring element.

A typical static setup consists of

rigid reaction support → torque sensor → lever arm → reference force

One side of the sensor is restrained against rotation.

The reference torque is applied to the other side.

It is important

that no additional structure bypasses the sensor and transfers part of the torque directly into the test bench.

A bearing or support that mechanically stabilizes the lever but at the same time absorbs part of the torque will distort the reference.

Avoiding transverse forces and bending moments

A torque sensor is primarily intended to measure torsion.

In a real test setup, additional loads can occur, including:

• radial forces,
• axial forces,
• bending moments,
• mechanical stresses.

A long lever arm can generate considerable transverse forces

The gravitational force does not only generate the desired torque.

It also mechanically loads the shaft, couplings and mounting components.

The permissible transverse and axial loads of the sensor must therefore be taken into account.

The mechanical construction should be

• aligned,
• rigid,
• low-stress,
• reproducible.

A mathematically correct reference torque does not guarantee a correct test result if the sensor is simultaneously influenced by unwanted parasitic loads.

Why friction can distort the reference torque

Ideally, the reference force is transferred to the lever without additional friction.

Potentially problematic components include:

• stiff bearings,
• pulleys,
• guides,
• weights touching surrounding components,
• mechanical stops.

Particularly critical

is a design in which the gravitational force is transferred via a pulley.

Bearing friction and other mechanical effects can cause the theoretical rope force to differ from the force actually acting on the lever.

For a simple and precise static reference, direct vertical force application without unnecessary redirection is generally preferable.

Checking the zero point before loading

Before applying the first load, the unloaded output of the torque sensor should be checked.

The following should be verified

• the system is mechanically unloaded,
• the lever is balanced or its own torque has been taken into account,
• the electrical supply is stable,
• the required warm-up time has been observed,
• the zero point is reproducible.

After a loading sequence

the zero point should be checked again.

A permanent zero shift can indicate:

• mechanical stress,
• overload,
• hysteresis,
• thermal effects.

Applying torque in a controlled manner

Reference weights should not be placed on the lever suddenly.

Impact loads can subject the sensor to loads significantly higher than the final static value would suggest.

The load should therefore be applied

• slowly,
• without shock,
• reproducibly.

After each load change, sufficient stabilization time should be allowed before documenting the sensor output.

Using multiple test points

A test performed only at full scale does not show how the sensor behaves across the entire range.

For a practical multipoint check, for example, the following points can be used

0 %

25 %

50 %

75 %

100 %

of the intended test range.

At each point, the following are compared:

generated reference torque ↔ indicated torque

The measurement deviation can be calculated as

ΔM = Mindication − MRef

or as a relative value:

f = ΔM / MRef × 100 %

Distinguishing between clockwise and counterclockwise torque

Many torque sensors can measure both positive and negative directions of rotation.

It should therefore be determined whether the application requires:

• only one direction of rotation or
• both directions of rotation.

For bidirectional use

measurement sequences for:

CW / clockwise torque

and:

CCW / counterclockwise torque

may be useful.

Good agreement in the positive direction does not automatically mean that the sensor behaves identically under negative torque.

Checking hysteresis and return to zero

For a more meaningful test, torque can not only be increased step by step but also reduced again afterwards.

Example

0 → 25 → 50 → 75 → 100 %

followed by:

100 → 75 → 50 → 25 → 0 %

If the indications differ at the same reference torque depending on whether the load was approached from below or above, hysteresis is present.

After complete unloading, it should also be checked

whether the sensor returns to its original zero value.

Evaluating the sensor output correctly

A torque sensor does not always output torque directly in Nm.

Depending on the device, the output may be:

• mV/V,
• voltage,
• current,
• frequency,
• digital measured values.

With the HySense TQ100

torque is measured using the strain-gauge principle; ICS specifies an output signal of:

12 ± 8 mA ISDS

with integrated direction detection.

For a correct comparison, the complete signal chain must therefore be taken into account:

torque sensor → supply / measuring amplifier → display / data acquisition → scaling

An incorrect scaling factor can otherwise appear to be a sensor error.

Measurement uncertainty of the static reference

The torque calculated from force and lever arm is not completely free of uncertainty either.

Its uncertainty is made up of several contributions.

Typical influencing factors include

• uncertainty of the reference force or mass,
• uncertainty of gravitational acceleration when using weights,
• uncertainty of the effective lever arm,
• angular error of the lever,
• dead-weight torque of the lever arm,
• friction,
• parasitic forces and moments,
• repeatability,
• display resolution,
• temperature.

In simplified terms

for:

M = F × l

the uncertainty of both:

F

and:

l

directly affects the reference torque.

For a simple functional check, a simplified assessment is often sufficient. For a metrologically reliable calibration, however, a complete measurement uncertainty budget is required.

Static check or calibration?

A self-built force-lever-arm setup is very suitable for:

• functional checks,
• plausibility checks,
• troubleshooting,
• intermediate checks of a test bench.

However, it does not automatically become a traceable calibration system

simply because:

M = F × l

is applied mathematically correctly.

For traceable calibration, reference quantities, measurement uncertainty, procedures, environmental conditions and mechanical influences must be appropriately evaluated and documented.

For static torque measuring devices

DIN 51309 is particularly relevant in Germany for the calibration of torque measuring devices for static torque.

For high-accuracy or accredited applications, an appropriately suitable calibration should therefore be used.

ICS Schneider also offers Calibration Services for torque transducers and other measured quantities.

Why a static test does not replace a dynamic test

A rotating torque sensor is often operated under completely different conditions in actual use than during a static check.

During operation, additional influences include:

• rotational speed,
• vibration,
• misalignment,
• dynamic torque fluctuations,
• moments of inertia,
• temperature changes,
• signal transmission during rotation.

A static test therefore shows

whether the sensor provides plausible measurements under a known quasi-static load.

However, it does not automatically confirm its complete dynamic behavior at rated speed.

Good static agreement is an important check – but it is not a substitute for dynamic evaluation if the application requires it.

Practical example: 100 Nm torque sensor

A torque sensor is to be statically tested up to:

100 Nm

.

The effective lever arm is:

0.5000 m

.

For this simplified example calculation:

g = 9.81 m/s²

is used.

Mass	Force	Lever arm	Reference torque
5 kg	49.05 N	0.500 m	24.525 Nm
10 kg	98.10 N	0.500 m	49.050 Nm
15 kg	147.15 N	0.500 m	73.575 Nm
20 kg	196.20 N	0.500 m	98.100 Nm

It is important to note

that these values correspond to the torque actually applied only if:

• the lever arm has been determined correctly,
• the lever is horizontal,
• the weights hang freely,
• the dead weight of the lever is taken into account,
• no relevant friction or parasitic loads occur.

For exactly 100 Nm

with:

l = 0.5000 m

a force of:

F = 200.0 N

would be required.

At:

g = 9.81 m/s²

the required mass would be approximately:

20.39 kg

This calculation shows why kilograms and newtons should not simply be treated as equivalent when testing torque.

Typical error patterns

Observation	Possible cause	Recommended check
All measuring points show almost the same percentage error	lever arm or force reference determined incorrectly	check effective length and reference force
Sensor already indicates torque when unloaded	dead weight of the lever or mechanical stress	balance lever and check zero point
Measured value differs between increasing and decreasing load	hysteresis or friction	perform increasing and decreasing measurement sequence
Measured value changes when the lever is moved slightly	bearing friction or mechanical stress	inspect force application and mounting
Result changes with lever position	lever not horizontal or force direction incorrect	check angle and effective lever arm
Measured value is correct at low torque but not at high torque	non-linearity, deformation or overload of the setup	check lever, mountings and sensor range
Zero point does not return after loading	mechanical residual effect, overload or stress	unload sensor and observe zero-point behavior
Measured value depends on direction of torque	directional dependence or mechanical setup	test CW and CCW separately
Display does not match calculated torque	incorrect electrical scaling	check signal range and scaling factor
Weights cause a fluctuating indication	swinging or dynamic loading	allow weights to settle and wait for stabilization
Lower value is measured when an additional support bearing is used	part of the torque bypasses the sensor	check the load path of the test setup
Static test is correct but the test bench shows deviations at speed	dynamic influence, alignment or couplings	inspect the complete rotating setup

Systematically performing a static test

1. Identify the torque sensor: Check measuring range, permissible loads, direction of rotation and output signal.
2. Define the test range: Determine the maximum required static torque.
3. Dimension the lever arm: Select the length so that the required reference force remains practical.
4. Mount the sensor securely: Restrain one side against rotation and align the measuring axis correctly.
5. Attach the lever: Create a rigid, backlash-free connection to the sensor shaft.
6. Determine the effective lever arm: Measure from the axis of rotation to the actual line of action of the force.
7. Check dead weight: Balance the lever as far as possible or determine its own torque.
8. Align the lever horizontally: With vertically acting gravitational force, establish a 90° angle between force and lever.
9. Connect the electronics: Configure power supply, signal conditioning and scaling according to the sensor specification.
10. Observe warm-up time: Allow sensor and measuring electronics to stabilize.
11. Record zero point: Document the unloaded output.
12. Apply reference force: Apply weights or force reference slowly and without shock.
13. Wait for stabilization: Read the value only when the measurement is stable.
14. Calculate the reference torque: M = F × l or M = m × g × l.
15. Document the sensor value: Compare the reference value with the indicated value.
16. Apply additional test points: Step through the measuring range.
17. Check decreasing sequence: Evaluate hysteresis if required.
18. Check the opposite direction: If relevant to the application.
19. Check the zero point again: Document behavior after complete unloading.
20. Evaluate uncertainty: Consider force, lever arm, angle, friction and repeatability.

Suitable torque and force measurement technology from ICS Schneider

HySense TQ100

The HySense TQ100 is a rotating torque sensor using the strain-gauge measuring principle and slip-ring transmission.

ICS specifies, among other things:

• measuring ranges from 1 … 500 Nm,
• measurement accuracy 0.1 % FS,
• integrated direction detection,
• output signal 12 ± 8 mA ISDS,
• M16 × 0.75, 6-pin electrical connection.

Typical applications include measurements on rotating shafts, friction torque measurements and monitoring of production processes.

HySense TQ110

The HySense TQ110 is also designed as a rotating torque sensor with slip rings and is available for various torque ranges.

Force sensors and force measuring instruments

If the reference torque is to be generated not by known masses but by a measured reference force, ICS Schneider also offers Force Sensors and Force Measuring Instruments for tensile and compressive forces.

Which setup is suitable?

In simplified form:

simple static check → defined lever arm + known mass

variable reference force → lever arm + suitable load cell

traceable precision calibration → suitable torque calibration system

rotating application → supplement static check with testing of the dynamic overall system

Further sensors can be found under Force, Weighing, Speed, Torque and Vibration Sensors at ICS Schneider.

Conclusion

A torque sensor can be checked very effectively under static conditions using a known force and a defined lever arm.

The basic principle is simple

M = F × l

When using reference weights:

M = m × g × l

The effective lever arm is decisive

The distance is measured from the axis of rotation to the line of action of the force, not simply as the total length of the lever.

Force and lever must be perpendicular to each other

With freely suspended weights, this means that the lever arm should be aligned as horizontally as possible.

The dead weight of the lever must not be forgotten

An unbalanced lever generates torque even without an additional reference load.

Parasitic loads can dominate the measurement

Transverse forces, bending moments, friction and mechanical stress should be avoided as far as possible or evaluated where higher accuracy is required.

Multiple test points provide significantly more information

An increasing and decreasing measurement sequence also reveals non-linearity, hysteresis and return to zero.

A static check is not automatically a calibration

For traceable results, reference quantities, procedures and measurement uncertainty must be appropriately qualified.

And a static test does not replace a dynamic investigation

With rotating sensors, additional influences caused by alignment, couplings, vibration and signal transmission can occur at speed.

For practical applications

Determine sensor range → define reference torque → dimension lever arm → mount sensor securely and in alignment → attach lever without backlash → determine effective distance from the axis of rotation → compensate lever dead weight → apply force perpendicular to the lever → check zero point → apply reference force slowly → wait for stabilization → calculate M = F × l → compare sensor value → apply multiple increasing and decreasing load steps → check both torque directions if required → verify zero point after unloading → evaluate force, length, angle and friction influences → perform suitable torque calibration if traceability is required.

FAQ: Statically Testing a Torque Sensor Using Force and Lever Arm

How is torque calculated from force and lever arm?

With perpendicular force application, M = F × l. Force is entered in newtons and the lever arm in meters. The result is given in newton meters.

What is the general torque formula for angled force application?

It is M = F × l × sin(α), where α is the angle between the lever arm and the force.

Why must the force act perpendicular to the lever?

Only the force component perpendicular to the lever generates the maximum calculated torque.

Can I test a torque sensor using weights?

Yes. With a defined lever arm, a reference torque can be generated from a known mass using gravitational force.

How do I calculate the torque generated by a weight?

Using M = m × g × l.

Do 10 kg on a 1 m lever generate exactly 100 Nm?

No. Using the approximation g = 9.81 m/s², 10 kg on a 1 m lever generates approximately 98.1 Nm.

Why must gravitational acceleration be taken into account?

A mass in kilograms is not yet a force. Multiplying it by gravitational acceleration gives the gravitational force in newtons.

Can I simply use 9.81 m/s²?

For many practical checks, this is a useful approximation. For higher accuracy requirements, the local value of gravitational acceleration should be taken into account.

What is the effective lever arm?

The effective lever arm is the perpendicular distance between the axis of rotation and the line of action of the force.

Why must the lever be horizontal when using suspended weights?

Gravitational force acts vertically. With a horizontal lever, the force and lever are at the ideal 90° angle to each other.

What happens if the lever is inclined?

The effective lever arm becomes smaller and the torque actually generated is lower than the simple F × l calculation would suggest.

Does the weight of the lever need to be taken into account?

Yes, if its center of gravity is outside the axis of rotation. In that case, the lever itself already generates torque.

Can I simply zero out the dead weight of the lever?

For a simple comparison test, defined taring can be useful. For higher accuracy requirements, however, the mechanically acting dead-weight torque should be determined or balanced.

Can I use a force sensor instead of weights?

Yes. If the actual reference force is measured with a suitable load cell, the torque can also be calculated using M = F × l.

Where should the force sensor act?

The measured force must act tangentially on the lever at a known position. The effective distance from the axis of rotation must be clearly defined.

Why are transverse forces problematic?

They apply additional loads to the torque sensor and, depending on the setup and sensor, can cause measurement deviations or mechanical overload.

Why are bending moments problematic?

The sensor is intended primarily to measure torsion. Bending represents an unwanted parasitic load and can influence the measurement result.

Can I additionally support the lever?

Only if the support does not bypass the sensor by carrying part of the torque and does not introduce relevant friction. Otherwise, the calculated reference torque no longer corresponds to the torque acting on the sensor.

Why can pulleys be problematic?

Bearing friction and pulley geometry can cause the force actually acting on the lever to differ from the theoretical gravitational force.

Should I apply the weight suddenly?

No. The reference load should be applied slowly and without shock in order to avoid dynamic overload.

How many test points should I use?

For a practical check, several points distributed across the relevant measuring range are useful. The exact number depends on the test task and the required verification.

Why should I test with increasing and decreasing loads?

This makes it possible to identify hysteresis and differences between loading and unloading behavior.

Should I test both torque directions?

If the sensor is used in both directions in the application, clockwise and counterclockwise torque should both be considered.

What does a zero-point shift after loading mean?

It can indicate hysteresis, mechanical stress, temperature changes or overload, among other things.

How do I calculate the measurement deviation?

A simple absolute deviation is ΔM = Mindication − Mref.

What determines the accuracy of the reference torque?

Primarily the reference force or mass, lever arm length, force angle, friction, dead-weight torque of the lever, mechanical force application and repeatability.

Is the force-lever-arm method an official calibration?

Not automatically. For traceable calibration, the references, procedure, environmental conditions and measurement uncertainty must be appropriately qualified and documented.

Which standard is relevant for calibrating static torque measuring devices?

In Germany, DIN 51309 is particularly relevant for the calibration of torque measuring devices for static torque.

Can I statically test a rotating torque sensor?

In principle, its quasi-static response can be checked using a known torque, provided that the sensor and mechanical mounting are suitable for this.

Does a static test also prove accuracy at high rotational speed?

No. Rotational speed, couplings, alignment, vibration, temperature and dynamic loads can introduce additional influences during rotating operation.

What is the HySense TQ100?

The HySense TQ100 is a rotating strain-gauge torque sensor with slip-ring transmission and integrated direction detection.

What measuring ranges are available for the HySense TQ100?

ICS Schneider specifies measuring ranges from 1 to 500 Nm.

Where can I find the HySense TQ100?

Further information is available under HySense TQ100 at ICS Schneider.

Where can I find further torque sensors?

An overview is available under Torque Sensors at ICS Schneider.

Where can I find suitable force sensors?

An overview is available under Force Sensors and Force Measuring Instruments at ICS Schneider.