## 3 Root Cause Analysis of the Faulty Joint
### Analysis of the Motor Brake  
After analysing the condition of the speed reducer and the motor, we inspected the brake of the motor. The brake of the 5 th joint is a permanent magnet brake that stops the motor when the robot is shut down or when an emergency stop is required. As illustrated in the schematic of Figure 5 this kind of brakes have three main parts: a metallic armature, a field coil and a neodymium (NdFeB) permanent magnet. The brake works in the following way: when the robot shuts down or makes an emergency stop, there is no voltage applied to the coil and the permanent magnet attracts the armature, stopping the rotation of the motor. In contrast, if the robot controller applies 24V to the field coil of the brake, it produces a magnetic field compensating the magnetic field created by the permanent magnet and the motor is released. Figure 4: Mechanical inspection of the gears, bearings and motors of the wrist. We measured the resistance of the brake's coil and compared it with the resistance of a completely new coil. In both cases the values reached \(15.4\,\Omega\). Therefore, the coil of the brake could not be the cause of the detected torque increment. Finally, we inspected the permanent magnets of the brake. The permanent magnets used in this brake are squared NdFeB magnets. We noticed a slight deformation in the corners of the magnets, as some magnetic particles were detached from them. We found the particles filling the space where the magnets are located. Figure 6 shows the permanent magnets inside the brake of the faulty joint compared to a completely new brake. In addition, Figure 6 shows that the colouring of the brake's armature was changed. These kind of stainless steel armatures, have a metallic light silver colour when manufactured. However, the inspected brake had a reddish coloring as a consequence of oxidation. Figure 5: Schematic of the motor brake. Figure 6: The motor brake of the faulty joint and its permanent magnets (**left**) compared to a completely new motor brake (**right**). We performed two tests to diagnose the health status of the permanent magnets. The first test consisted on measuring the M(H) hysteresis curve of the magnets. Then, we magnetized the permanent magnets and measured again the M(H) hysteresis curve after the magnetization. The results of the tests are shown in Figure 7.  
There is a 24% loss from 0.814 T before magnetization to 1.071 T after the magnetization. This significant magnetic field loss has a direct impact in the malfunction of the motor's brake. As a consequence, the brake constantly resists the movement of the motor. This produces the torque increment in the 5 th joint throughout the whole trajectory identified in Section 2. The second test consisted on measuring the magnetic hysteresis curve at different temperatures. Figure 8 shows the different M (H) curves at 26, 80, 100 and 120 \({}^{\circ}\)C and Table 4 shows the magnetic properties of the permanent magnet at these temperature regimes. Br (T) is the residual induction or flux density, that is the magnetic induction corresponding to zero magnetizing force in a magnetic material after saturation. Hci (kA/m) is the intrinsic coercive force of a material and indicates its resistance to demagnetization. Figure 8: Magnetic hysteresis curve of the permanent magnet at 26 (green), 80 (brown), 100 (orange) and 120 \({}^{\circ}\)C (red). Figure 7: Magnetic hysteresis curve of the motor brake’s permanent magnet before (blue) and after (green) magnetization. There are two additional considerations that have to be taken into account. The technical specifications of the 5 th joint's motor indicates that the surface temperature of the motor can reach up to 140 \({}^{\circ}\)C. Therefore, the temperatures inside the motor brake could be even higher than the temperatures reached in the test. Moreover, in the recently published work by [PERSON] [20] the time dependent demagnetization of NdFeB permanent magnets is extensively investigated.