Reducer Torque Measurement

　　When an angular misalignment error Δθ is present, the torque measured by the torque sensor in the instrument represents the resultant torque of the bending moment and the applied torque, and the torque transmitted to the robot reducer under test is less than the value indicated by the torque sensor.

　　Torque exhibits a quadratic relationship with the torque measured by the torque sensor in the instrument; therefore, by establishing the correlation between the sensor’s readings and the additional torque, it is possible to measure the reducer’s input and output torques with high accuracy.

　　 Torque Calibration and Error Compensation

　　The measurement results from the torque sensor in the instrument include an additional torque component, and the sensor’s system accuracy cannot be taken as the instrument’s overall measurement accuracy. Therefore, torque calibration and error compensation are necessary to enhance precision. This paper is an extension of a previous work. Unlike that earlier article, which proposed a method for calibrating the torque sensor, this study focuses primarily on improving the accuracy of TMMISR and TMMOSR, since we have observed that the torque sensor’s accuracy alone does not suffice to define the measurement accuracy of the entire torque‑measurement system.

　　 Torque Calibration Method

　　It is required to compare the system output, whose measurement accuracy is known, with the measurements from a torque sensor to ensure accuracy across the measurement range. In general, high‑accuracy instruments or sensor systems are used as reference standards during calibration.

　　A torque calibration instrument has been designed; certified by an authoritative metrology institute, it can generate standard torque and, when positioned at the TA location, accurately reflects the reducer’s true input and output torques. The instrument incorporates two high‑precision torque output systems, each dedicated to calibrating the torque sensors in the TMMISR and TMMOSR, respectively.

　　 Error Compensation Model  

　　A necessary step in high-precision measurement is error compensation for the torque sensor, which requires performing full-scale data fitting based on 50 discrete standard torque values.

　　A three-layer feedforward neural network based on the BP algorithm can realize a nonlinear mapping from input to output, effectively simulating the relationship between the torque sensor’s measured values and the additional torque in the instrument, thereby ensuring good fitting performance. As shown in Figure 7, the BP neural network algorithm used for torque error compensation consists of a multilayer, unidirectional propagation mapping network, comprising an input layer, an output layer, and hidden layers.

　　The input layer comprises a single node, T_i, representing the measurement output of the torque sensor in the instrument; the number of nodes in the hidden layer is set to 50, as determined experimentally; the output layer contains one node, T_i, which corresponds to the mathematical equation—namely, the additional torque, calculated as the standard torque value minus the measurement from the instrument’s torque sensor. The connection weights from T_i to G_j are denoted by w_ij, and from G_j to the mathematical equation by v_ji. The activation function for the hidden layer is the Tansig function, while the output layer employs the Purlin function. The training algorithm used is Traingdx, enabling the feedforward network to be trained via the fast BP algorithm.