# Centrifugal acceleration in torque measurement - often underestimated, however, very effective

**What do a roller coaster, a spin dryer and a centrifuge have in common with rotating torque measurement technology? The answer is amazing: centrifugal acceleration. The combination of rotation and dimension results in acceleration. Multiplying acceleration by the existing mass causes high forces that require correspondingly safe structures.**

**Accelerations** in a **roller coaster**, on the one hand, must not be too high to avoid potential** health risks** and, on the other hand, should be high enough to cancel out gravity and induce a feeling of **weightlessness**. Everyone knows how a** spin dryer**, which in fact is a centrifuge, works. Different materials are being separated.

However, the **centrifugal acceleration** occurring in **everyday life** is** relatively low** compared to that occurring during **torque measurement**.

- Centrifugal acceleration in a
**spin dryer**is approximately**400 g**≈ 4,000 m/s² - depending on drum diameter and spin speed -, - in a
**roller coaster**it is approximately**5 g**≈ 50 m/s², - in
**rotating torque transducers**, however, it amounts to**several thousand g**or m/s².

## Gravitational acceleration affects calibration accuracy

**Gravitational acceleration g is the acceleration on a body caused by the Earth's gravitational field.** At different points **on Earth**, it averages ≈ **9.81 m/s²**, however, it varies depending on the centrifugal force of the Earth's center, the oblateness of the Earth and regional circumstances. It is not easy to specify the **acceleration a human being can withstand** without suffering permanent injuries. Literature gives a value of 9 g for trained test pilots wearing protective clothing, German DIN 4112 stipulates a maximum permissible vertical acceleration of **6 g** [1].

Knowing gravitational acceleration is also crucial to exactly representing and transferring the **measurand torque**, since the most accurate calibration machines consist of dead weights (masses) and lever arms. This acceleration was **precisely determined** in **HBM's calibration laboratory** which has been accredited by German Calibration Service; it is **9.810285 m/s²** with an uncertainty of measurement of 0.000005 m/s².

## Centrifugal acceleration and rotational speed

A **torque flange** in a powertrain test bench is a **system rotating** at angular velocity. This creates a **centrifugal acceleration** that depends on the **diameter **and **rotational speed**.

Multiplying this acceleration by a mass or a mass point gives a **centrifugal force**. Depending on the design, these centrifugal forces may **limit the maximum permissible rotational speed**. It is essential to take into account other influencing factors, for example, critical rotational speeds.

**Centrifugal acceleration** is the result of the **square of angular velocity multiplied by the radius r**.

This results in

(equation with numerical values an in m/s^{2} , r in m and n in rpm)

The table below shows which **centrifugal accelerations occur with different torque flanges and selected diameters**. *Table 1: Centrifugal acceleration resulting from rotational speed and design*

It is clearly visible that **rotational speed is predominant over the diameter**. This is obvious since rotational speed appears in the equation as a square value and the diameter only as a linear value.

The **relevance of the flanges' individual nominal (rated) rotational speeds **results from the **different target applications**. Please find below a list of **examples of typical applications with rotational speeds specified in the unit rpm **[3]:

**Globe**approx. 0.000694**Ship propeller**(huge, commercial seagoing vessel) 70 to 150**Main rotor of a helicopter**up to 400**Propeller of a small airplane**2,500**Two-pole induction motor**for 50 Hz mains voltage approx. 3,000**Two-pole generator for 50 Hz**mains voltage (e.g. Europe) 3,000**Two-pole generator for 60 Hz**(e.g. USA) 3,000**Maximum rotational speed of a diesel engine**approx. 5,500**Maximum rotational speed of a gasoline engine**approx. 9,000 up to 18,000**Gas turbines**3,000 up to 100,000**Turbo charger for combustion engines**100,000 up to 300,000

## Centrifugal acceleration depending on rotational speed and design

Often torque flanges are not used at their nominal (rated) rotational speed. The example of the T10FS torque flange is to illustrate the **effects of different rotational speeds and designs**.

*Fig. 1: Centrifugal acceleration depending on rotational speed and design*

Using double logarithmic graphs, the resulting** array of curves** [4] facilitates identification of the **centrifugal acceleration** for **selected radii**.

For example, a **rotational speed of 10,000 rpm** and a radius of 250 mm results in a centrifugal acceleration of 273,878 m/s^{2} ≈ 27,918 g, approx. 30,000 g.*Fig. 2: Array parameter radius r of the circular path*

**Acceleration** is uncritical as long as it does not affect a** mass**. Since in reality this is not the case, **centrifugal force** is of paramount importance. Therefore, with structures rotating at **angular velocity/rotational speed** it is essential to take into account the** resulting forces** instead of the accelerations.

The well-known relationship '**Force equals Mass times Acceleration**'

applies analogously for rotating bodies

The centrifugal force Fz is given by

(equation with numerical values Fz in N, m in kg, r in m and n in rpm)

Considering the **1 euro coin** with a weight of 7.5•10^{-3} kg and the maximum rotational speed of the **T10FS/100 N•m torque flange**, n = 24,000 rpm , r = 59.5 mm, provides an impressive example for this effect.

In the Earth's gravity field, this would correspond to ≈ 287 kg - about 6 cement bags each with 50 kg. Such a coin would be **too heavy** to be carried in a purse.

## Conclusions

There are different kinds of acceleration. The **centrifugal accelerations** created **by rotation** are many times **greater** than the accelerations occurring in our everyday lives. The accelerations produced by rotation, the **resulting forces** and energies are difficult to imagine and need to be **safely endured by the individual structures **to protect persons and material from injury/**damage**. This is a matter for both manufacturers and users.

## References

[1] Gunter Gebauer: Kalkuliertes Risiko: Technik, Spiel und Sport an der Grenze, Bibliografische Information der Deutschen Bibliothek

[2] Rainer Schicker, Georg Wegener: Measuring Torque Correctly, ISBN 3-00-008945-4, Published by Hottinger Baldwin Messtechnik GmbH, Darmstadt, www.hbm.com

[3] de.wikipedia.org/wiki/Drehzahl

[4] www.siart.de/lehre/zentrifuge.pdf