Measuring system and method for determining a force and/or a torque on a torque-transmitting shaft

A measuring system for determining a force and a torque on a torque-transmitting shaft, wherein the measuring system comprises:

• at least three piezoelements, each of the at least three piezoelements having a piezoelectric crystal oriented in a preferred direction, wherein each of the at least three piezoelements are arranged at different positions about a rotational axis of the torque-transmitting shaft in a force flow transmitted via the torque-transmitting shaft such that a force of the force flow acts on the at least three piezoelements, wherein each of the preferred directions of the piezoelectric crystals lie parallel to a single plane intersected by the rotational axis or in the single plane intersected by the rotational axis, and wherein the preferred directions of the piezoelectric crystals are oriented neither parallel nor antiparallel to one another;
• and
• a signal processing device which is configured to determine the force and the torque using a system of equations for force components and torque components based on measurement signals of individual piezoelements of the at least three piezoelements, wherein measurement signals from all of the piezoelements that have a piezoelectric crystal oriented in a respective preferred direction lying parallel to the single plane intersected by the rotational axis or in the single plane intersected by the rotational axis are used to determine each of the force components and each of the torque components, wherein the systems of equations is:
• S1=a11·Mz+a12·Fx+a13·Fy
• S2=a21·Mz+a22·Fx+a23·Fy
• S3=a31·Mz+a32·Fx+a33·Fy
• SN=aNI·Mz
• and wherein S1-SN are the measurement signals, Mz represents a torque component, Fx represents a first force component, and Fy represents a second force component.