The flexibility of the joint drive system of an industrial robot can cause vibration at the end part, which can lead to motion errors. A method to predict the vibration during the motion of the robot arm is proposed considering the robot joint flexibility. The method combines the internal transfer function of the drive system and the identification of parameters under external excitation. Firstly, the dynamics of the robot joint system are modeled by a double inertia elastic system. The joint system transfer function from the electromagnetic torque to the arm vibration is obtained according to the dynamics model. To solve the unknown parameters in the transfer function, a vibration dynamics model of the joint arm under the external forces on the arm is developed. According to this model, the equivalent stiffness, damping and load inertia of the joint can be obtained by the direct parametric method. Then, the vibration spectrum of the robot arm is derived from the motor electromagnetic torque and joint dynamics models were used to predict the vibration spectrum of the robot arm. The experiments were conducted on a single-joint robot testbed, and on an articulated industrial robot. In both experiments, the key parameters in the system were determined by impact experiments. Then, the vibration signal of the arm during the robot motion was obtained by electromagnetic torque prediction. The predicted vibration signals are analyzed in comparison with the actual vibration signals. The experimental results both show the validity of the vibration prediction.

Rotation vector (RV) reducers have been widely used as an important part of robot joints, and the health monitoring of RV reducers needs to be studied urgently. Traditional vibration analysis faces challenges due to the vibration spectral complexity introduced by time-varying transmission path and interferences of other components in reducers. The rotary encoder contains rich diagnostic information, which provides a new way for fault diagnosis of rotating machinery. This paper presents a feasible strategy for health assessment of RV reducers using encoder signal. In this algorithm, the angle sequence is firstly converted into instantaneous angular speed (IAS) by central difference method (CDM). Then, considering the amplitude modulation characteristics of the fault impact, a scheme for extracting shock transients based on envelope demodulation is determined, and a fault crest proportion index defined on the envelope power spectrum (Epfc) is designed. The optimal filtering band of IAS is determined through the proposed index and band-pass filtering is performed by utilizing Morlet wavelet. Furthermore, band-pass filtering is further implemented on the envelope of the filtered IAS to reduce noise. Finally, transient impulses are extracted by synchronous averaging (SA) to remove the interferences of random shocks. In this step, cross-correlation is employed to correct the phase deviation of the IAS signal and improve the effect of SA. The effectiveness of the proposed method is verified by the fault experiment of RV reducer.

The difficulty of adding external excitation and the asynchronous data collection from the industrial robot operation limited the online parameter identification of industrial robots. In this regard, this study proposes an identification method that only uses the amplitude of the frequency response function (FRF) of the system to identify robot joint torsional stiffness and dynamic parameters. The error criterion function shows that this method is feasible and comparable to applying the complete frequency response for identification. The Levenberg–Marquardt (L-M) algorithm is used to find the global optimal value of the error criterion function. In addition, an operational excitation method is proposed to excite the system. The speed profile is set as a triangle wave to excite the system using rectangular wave electromagnetic torques. The simulation results show that using the amplitude of the FRF to identify parameters applies to asynchronous data. The experiments on a single-degree-of-freedom articulated arm test bench show that the motion excitation method is effective, and both stiffness and inertia are identifiable.

In the identification of industrial robot joint system, in order to obtain the ideal frequency response of the system, additional excitation needs to be applied. The addition of excitation signals such as chirp signals and pseudo-random binary signals will make the instantaneous angular speed (IAS) obtained by the motor encoder present non-stationary characteristics. In order to solve this problem, this paper proposes a method for system identification by IAS extraction under non-stationary conditions. Interferences such as electrical perturbation, quantization error, background noise generally reduce the accuracy of extracted IAS. Firstly, the influence of electrical perturbation on the accuracy of angle calculation is eliminated by utilizing the characteristics of the two-phase encoder signals. Secondly, considering the time-varying characteristics of the rotational speed in the identification process, a non-uniform local polynomial differentiator (NULPD) is proposed to optimize the estimation of IAS and reduce the influence of background noise and sampling error based on local polynomial differentiator (LPD). The IAS estimation under the condition of variable speed is simulated to verify the performance of NULPD. According to the transmission characteristics of the robot joint system, a two-mass dynamic model is established, and the transfer function between the torque and motor speed is obtained. The torque is calculated from the three-phase current signals, and the rotational speed is obtained by the encoder signal. The frequency sweep experiment is carried out on the single-degree-of-freedom articulated arm test bench, where the stiffness and inertias of the system are identified within a certain error range by the proposed method.

Motor gearbox systems are widely used in industrial production, and the variations of gear meshing stiffness generate transient frequency modulation (FM) effects on motor current. The 2nd-order synchrosqueezing transform (SST) is effective for revealing the time-varying frequency characteristics of motor current, thus enabling the monitoring of the condition of the electromechanical system; however, the selection of the window parameter in 2nd-order SST analysis is subjective and lacks specific theoretical guidance. To quantify the analytical limits, this study derives the instantaneous frequency (IF) estimation error function of the 2nd-order SST. The function demonstrates that the factors affecting the IF estimation are the window parameter and the 2nd-order and 3rd-order derivatives of the signal phase. To validate the practical application of the IF estimation error function, a rotating vector (RV) gearbox test bench is constructed. First, the motor current model of the test bench that contains the meshing stiffness is established, which allows the definition of the phase and FM amplitude of the signal. In the analysis of the model simulation, the optimal window parameters for identifying the FM characteristics are determined by comparing the FM amplitudes with the calculated IF estimation errors. With the window parameter determined by model analysis as previous knowledge, the healthy and faulty meshing stiffness characteristics are successfully extracted from the experimental motor currents. As a result, local gear faults in the RV gearbox can be diagnosed intuitively and accurately.

When a robot flexible joint faults, the fault component of the vibration signal is masked by the system dynamic response vibration and interferences. Firstly, the dynamic response vibration is estimated by the method combines a dynamic model and a convolutional neural network (CNN) error compensation model. The estimated dynamic response vibration is taken as the reference signal generated in the operation of healthy condition. In order to separate the fault components from the measured vibration in abnormal condition, an optimal weighted spectral difference method is proposed. The basic idea of the method is to find the optimal difference between the dynamic response vibration and the fault component through a convex optimization model. Finally, the experimental results on a flexible joint robot verify the effectiveness of the proposed method, and the fault components are extracted successfully from the measured vibration.