**1. Providing a power signal**

Modern drive concepts with large combustion engines require precise and fast response of the engine's control systems (e.g. for fuel supply) to respond to abruuptly varying loads. Here, it is essential to ensure that sufficient power is supplied at any time and that, at the same time, the engine features low fuel consumption and safe operating parameters. This requires that a power signal is provided which - with vehicles, compressor and pump systems - needs to be generated using special measuring devices. In general, there are three different approaches:

- The power signal is provided
**indirectly**by measuring specific auxiliary quantities such as flow rate, temperature, and pressure and then computing the power. With this approach, the power signal's uncertainty of measurement is very high. An additional drawback is that the values of the auxiliary quantities are not synchronous to the processes determining the engine power. - The power signal is provided
**indirectly**by measuring specific auxiliary quantities**on**the input shaft. This includes all methods involving measurement either of the strain resulting from shaft torsion on its surface or of the shaft's torsion angle. In both cases, the power is computed following the measurement of the auxiliary quantities. - The power signal is provided
**directly**by measuring torque in the input shaft.

The following article compares direct power measurement with indirect power measurement on and in the drive train respectively (approaches b. and c.) with regard to the uncertainties of measurement that can be achieved.

The power transmitted by a rotating shaft is given by
(1)
where *M *is torque and *n *rotational speed. Torque is given by*
*

(2)
where *τ* is the shear stress and *W shaft* the shaft's moment of resistance. The distinctive feature of a shaft that is subjected to torsion only is that both principal normal stresses have the same absolute value, i.e.:
(3)
Since in this case, the center of Mohr's circle is positioned in the origin of its coordinate system, the shear stresses correspond to the absolute value of the principal normal stresses. It follows that
(4)
where ׀σ׀ is the absolute value of the normal stress. The following applies in addition:
(5)
assuming that the input shaft is a cylindrical solid shaft. Resulting from (1) … (5) power is given by
(6)
The normal stress of a torsion shaft is:
(7)
where E is the modulus of elasticity, μ Poisson's ratio and the absolute strain value on the torsion shaft's surface in the principal strain direction. Resulting from (6) … (7) power is given by
(8)
**Example A:** Determining strain using strain gauges
The single error to be allowed for results from the tolerance of the gauge factor, see table 1.
**Example B:** Determining strain by measuring the torsion angle *φ*
The following applies:
(9)
The single errors to be allowed for result from the tolerances of the input drive's diameter *d *and length *l *as well as the measurement error* φ*, see table 1.
Considering (8) and (9) the power determined by measuring the torsion angle is:
(10)

All the parameters to be taken into account for (8) and examples A and B are subject to tolerances. They can be assessed as follows:

Example A requires the strain guage positioning tolerances s as well as the temperature error resulting from lacking or limited thermal compensation to be considered in addition. The values of these tolerances are determined by the quality of the strain gauge installation and will therefore not be take into consideration here.

Without further error analysis, table 1 shows that the total error of the measuring devices described above (approach b) is primarily determines by the tolerance of *E *and* μ*. It can thus not be less that 3 %, however, in practice, it is often substantially higher.

- High resolution (16 ... 19 bit) of the torque signal for recording of minimal amplitude variations
- large bandwidth (up to 6kHz) of the dynamic torque signal for recording of highly dynamic processes in the drive train (e.g. torsional vibration)
- Short signal propagation time for very fast control in the event of varying load conditions
- Robust design and high signal stability for use in extreme ambient conditions
- Excellent repeatability and long-term stability values for use over long periods of time without corrective action
- Visualization of characteristic torque curves for specific cycles enabling data for Condition Based Maintenance (CBM) to be provided

An Introduction to Measurements using Strain Gages

Publisher: Hottinger Baldwin Messtechnik GmbH (1987)

Taschenbuch der Physik

17th edition (2007)

Fachbuchverlag Leipzig im Carl Hanser Verlag

Product and Application Manager, Hottinger Baldwin Messtechnik GmbH

Product and Application Manager, Hottinger Baldwin Messtechnik GmbH

Product and Application Manager, Hottinger Baldwin Messtechnik GmbH