High-Precision Torque Measurement for Industrial Robot Reducers

　　 Vertical Precision Robot Reducer Tester

　　The torque sensor should be positioned as close as possible to the test object to minimize the measurement chain length and reduce sources of error. Both torque‑measurement systems employ strain‑gauge torque sensors to acquire the input and output torques of the robot’s gearbox, with an algorithm converting the frequency signal into torque. Each rotor in the torque sensor is mounted on a shaft and supported by bearings. The misalignment between the gearbox under test and the torque‑sensor rotor must be less than 0.03 mm.

　　When transmitting torque, the hollow shaft shares the torque load circumferentially, theoretically eliminating stress concentrations and misalignment errors. Furthermore, a circle of constant cross-sectional area exhibits superior torsional stiffness per unit length compared to other materials; thus, cylindrical and disc‑shaped supports can significantly enhance structural rigidity while ensuring measurement accuracy. Meanwhile, the plane‑section assumption in material mechanics ensures that, under high torque, the cylindrical support undergoes only circumferential deformation, and this predictable deformation minimizes the impact of misalignment errors on torque‑measurement accuracy. For signal acquisition, PXI‑E measurement and control hardware is employed: torque data are fed into an FPGA‑based processing module and then routed to a signal‑processing module for subsequent calculations.

　　 Torque Analysis

　　The torque sensor readings from the robot reducer tester cannot be used as the input or output torque of the robot reducer. In a precision robot reducer tester, there is a certain distance between the torque sensor and the reducer under test. When positioned at the test location, the red component consists of a bearing, a splined sleeve, and a splined shaft. The individual parts within this red component have varying weights, and misalignment errors lead to uneven friction around it. These factors result in an imbalanced stress distribution at the support points, which in turn causes bending and torsional deformation of the shaft. Consequently, the torque measurement includes an additional torque component. In precision robot reducer testers, the primary contributors to this additional torque are bearing friction and shaft‑system misalignment errors. Below, taking the torque sensor in the TMMISR and the input side of the reducer under test as examples, we analyze the two main sources of this additional torque.

　　 Additional torque caused by bearing friction

　　Regardless of the type of bearing, the drive shaft itself generates frictional torque. The magnitude of this frictional torque depends on factors such as the rotor’s moment of inertia, rotational speed, and material properties. Conventional friction‑torque compensation requires identifying six parameters, and the resulting calculations can be problematic. Since the shaft’s stiffness is related to its frictional torque, the maximum frictional torque can be determined by calculating the shaft’s maximum angular deformation under the action of the peak torque.

  　 (1) Here, D denotes the outer diameter of the shaft, and d denotes the inner diameter. For a solid shaft, the value of d is zero. Calculation of the maximum angular deflection of the shaft.

(2) Here, L denotes the length of the drive shaft, T is the torque measured by the torque sensor in the instrument, and G is the shear modulus of elasticity. The maximum frictional torque of the shaft is calculated as follows.

(3) Here, k₀ is the conversion coefficient and has a linear relationship with the radial offset ΔX of the shaft.

(4) Here, μ denotes the elastic coefficient. The radial displacement ΔX of the shaft is not only related to the coaxiality error Δr of the shaft system but also exhibits a linear relationship with the applied radial force Fr.

　　Additional torque caused by misalignment errors: The splined sleeve and the splined shaft play an important role in the system. Under ideal operating conditions, the torque sensor and the robot reducer under test should be aligned on the same central axis. However, in actual production, the torque sensor and the robot reducer being tested…   An ideal condition in which the speed sensor and the reducer are aligned on the same centerline does not exist. Manufacturing and assembly errors in the components can cause deviations in the shaft’s centerline, as well as radial misalignment between the torque sensor and the robot reducer under test.