A calibration procedure for a force vector sensor by means of a spherical calibration body

Force standard machines generate a force vector whose direction is determined by the acceleration due to gravity. For the calibration of force vector sensors, different alignments of force vectors - in relation to the coordinate system of the force vector sensor - are required. For that purpose, a special calibration body has been developed. From the signals of the measuring channels of the sensor and from the force vector, a transmission matrix was calculated which provides information about the signals of the single components and which indicates cross-talk of the channels.

Precision force transducers measure the force along an axis which is predetermined by the design of the transducers. To cope with the increasing demand for multi-component force transducers, a special transducer has been developed in a cooperation project: the force vector sensor, which is to be calibrated in the force standard machines of PTB. For that purpose, different procedures are being investigated and compared at PTB (see also: No matching tab handler could be found for link handler key record:tt_news:1555.).

Force standard machines mostly generate defined forces by mass stacks in the gravitational field of the Earth. The weight of these stacks acts - via a movable frame - on the force transducer to be calibrated. The direction of the force vector is thereby determined by the direction of the acceleration due to gravity. Uniaxial force transducers are aligned in such a way that the axis of the force standard machine and the axis of the transducer lie on one straight line. In order to calibrate the force vector sensor, vectors of different directions - in relation to the reference system of the sensor - must be generated. For that purpose, a calibration body has been developed to which the force vector sensor is fastened. Due to the rotation of the calibration body, the reference system of the sensor is turned. The calibration body has been dimensioned in such a way that - due to the rotation - the origin of the reference system always remains in the axis of the force standard machine (Figure 1). This means that the set-up needs to be aligned at the beginning of the measurements only. The inclination of the sensor to the axis of the force standard machine is determined by means of inclination sensors, so that the effective force vector can be determined from it, as well as from the total load exerted by the mass stack.

Figure 1: Force vector sensor with the spherical calibration body in the 100-kN-K-NME

The transmission matrix is determined from the signals of the measuring channels and from the effective force vector. This matrix indicates the measuring signals which are generated on the different channels of the force vector sensor by the single components of the acting force vectors and moment vectors. Among other things, cross-talk of the channels can be determined from the matrix. The decoupling matrix, which is also to be calculated from this matrix, can be lodged in the evaluation program to calculate the components of the force vector and of the moment vector from the measurement values and to correct, thus, the cross-talk.

In the measuring and evaluation program, detailed mathematical models can be lodged. These models do not only correct cross-talk with an equation up to the third degree. The measured force and moment vectors can also be converted into different realization forms such as, for example, components in the x-, y- and z-direction (or amount and direction of the vectors), or they can be transformed into another reference coordinate system.
For this calibration procedure, a comprehensive uncertainty budget is to be established. On the basis of investigations carried out on the measuring set-up and on the basis of comparative measurements with other procedures, the single components of the measurement uncertainty model (Figure 2) are determined. In particular, cross-talk of the channels and the uncertainty of the calibration body with respect to the realization of single load components have to be taken into account.
The aim of these activities is to make a sensor available to the user which can be calibrated as a transfer standard at PTB.

Figure 2: Measurement uncertainty model of the force vector sensor

Contact person:

Falk Tegtmeier, FB 1.2, AG 1.21, e-mail: Falk.Tegtmeier@ptb.de