Authors:Ratni; Azeddine, Benazouz, Djamel Pages: 1 - 12 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 1-12. Azeddine Ratni, Djamel Benazouz Inner race fault in bearing suspension is relatively the common fault in induction motors coupled with a gearbox, their detection is feasible by vibration monitoring of characteristic bearing frequencies. However, vibration signals have numerous drawbacks like signal background noise due to external excitation motion, sensitivity due to the installation position and their invasive measurement nature. For this reason, it is necessary to apply an extremely efficient method known as stator current signal analysis which offers significant savings and implementation advantages over traditional vibration monitoring. This paper represents a mathematical model for electromechanical systems and for rolling-element bearing faults to study the influence of mechanical defects on electrical variables (stator current). The novelty in this work involves three contributions: modelling of rolling bearing faults by external forces applied on the electromechanical system; Physical representation of rolling bearing fault allowing the modeling of the studied system functionality and, the influence of mechanical fault (inner race) in the electrical variables (stator current). Simulation results at the end of this paper demonstrate the effectiveness of the proposed mathematical model to detect gearbox’ bearing fault based on the electrical stator current signal with high sensitivity using fast Kurtogram approach. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2020.21206 Issue No:Vol. 6, No. 1 (2020)

Authors:Nguyen; Vanliem, Le, Vanquynh, Jiao, Renqiang, Yuan, Huan Pages: 13 - 22 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 13-22. Vanliem Nguyen, Vanquynh Le, Renqiang Jiao, Huan Yuan To evaluate the acceleration-frequency characteristics of the suspension system of the heavy vehicles, a nonlinear dynamic model of two-axle heavy vehicles is established. A calculation method based on the complex domain is applied to solve the vibration equations of the heavy vehicle in the frequency domain instead of the traditional time domain. Matlab software is then used to calculate the vibration equations under various operating conditions. The research results show that the resonant frequency of the suspension system is not affected by the vehicle speed and the road surface, while it is clearly influenced by the weight of the vehicle and the stiffness of the suspension system. However, the acceleration-frequency characteristics of the vertical vehicle body, pitching vehicle body, and vertical front/read axles are greatly influenced under various operating conditions, especially at the high speed 30 m.s-1, a wavelength of the road surface 6 m, and 80 % of the vehicle load. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2019.21229 Issue No:Vol. 6, No. 1 (2020)

Authors:Lasisi; N. O., Akinwande, N. I., Oguntolu, F. A. Pages: 23 - 33 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 23-33. N. O. Lasisi, N. I. Akinwande, F. A. Oguntolu In this paper, mathematical model of Monkey-Pox transmission is developed and investigated, using ordinary differential equation. We verified the feasible region of the model and showed the positivity of the solutions. We obtained the disease free equilibrium (DFE). We computed and analysed the effective basic reproduction number (R0) of the model. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2019.21234 Issue No:Vol. 6, No. 1 (2020)

Authors:Tchomeni; Bernard Xavier, Alugongo, Alfayo Pages: 34 - 49 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 34-49. Bernard Xavier Tchomeni, Alfayo Alugongo This paper presents a theoretical and experimental analysis of a coupled lateral and torsional vibrations of two identical rotors interconnected by a flexible Hooke’s joint and modelled as a multibody system with a small misalignment angle. Using energy principle and a Lagrangian transformation, the governing equation of the propeller shaft system is established by considering a nonlinear elastic shaft time-dependent perturbation. To study the sensitivity of the crack for a rotating shaft, the model is enriched by considering the periodical feature of the time-varying stiffness deriving from the crack breathing model. The nonstationary response of a cracked rotor system in the presence of unbalance has been evaluated using orbit patterns and Fast Fourier Transform. The highly oscillated feature of the rotors system is theoretically obtained and experimentally analysed. The analysis demonstrated that the crack parameters in the input shaft tend to inhibit the occurrence of unstable oscillations in lateral deflection, orbit and frequency spectrum of the secondary response. It is also found that the passage of the cracked primary shaft near to an integral multiple of the critical speed leads to the phenomenon of sup-harmonic resonance. Subsequently, the experimental analysis conducted equally indicated that the quantitative relation between the faults and the performance of the transmission is impacted by the time-varying stiffness and is the main cause of the frequency-modulated feature in the Cardan shaft system. Finally, the experimental results were informative for the transient response exploration and comparable to the theoretical findings for validating the proposed twin-rotor model. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2019.21240 Issue No:Vol. 6, No. 1 (2020)

Authors:Lei; Xiaofei, Hou, Heping, Zha, Zhaoshuan, Liu, Shanhui, Xu, Boyang, Liu, Peng Pages: 50 - 56 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 50-56. Xiaofei Lei, Heping Hou, Zhaoshuan Zha, Shanhui Liu, Boyang Xu, Peng Liu The structural vibration of the center impression cylinder in the flexographic printing machine will bring about production quality problems such as printing ghosts. To this problem, it become an important method to analysis the dynamic characteristics of the center impression cylinder. In this paper, a three-dimensional structural model of the central impression cylinder is established, and builds the dynamic model in finite element software. The vibration modes of the central impression cylinder were studied in the simple-supported system at both ends of the static impression cylinder. In view of the real existence of the rotating dynamic load, the evolution law of the natural frequency and mode shape of the cylinder with the rotating dynamic load is discussed. It is found that as the rotation speed increases, the natural frequency undergoes two steps, and the natural frequency after each step will keep continuity with the high first-order natural frequency, and the modal shape is the same as the high-order original mode. Then, the mode shape is continuously changed, not have a step. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2020.21253 Issue No:Vol. 6, No. 1 (2020)

Authors:Nguyen; Vanliem, Jiao, Renqiang, Le, Vanquynh, Wang, Peiling Pages: 57 - 65 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 57-65. Vanliem Nguyen, Renqiang Jiao, Vanquynh Le, Peiling Wang To control the cab shaking of the vibratory roller, an auxiliary damping mount (ADM) used for the cab isolation system in horizontal direction is proposed. Based on the off-road vibratory roller dynamic model under the conditions of the vehicle moving and compacting, the damping characteristic and installation position of the ADM for reducing vibration of the cab are respectively analyzed. The weighted root-mean-square (RMS) of acceleration responses of the vertical driver’s seat and pitching cab angle are chosen as the objective functions. The research results show the cab shaking is greatly reduced by using the ADM in comparison without ADM. Additionally, the drive’s seat vibration is also significantly decreased under both the compacting and moving conditions of the vibratory roller. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2020.21256 Issue No:Vol. 6, No. 1 (2020)

Authors:Ragulskis; K., Ragulskis, L. Pages: 66 - 78 Abstract: Mathematical Models in Engineering, Vol. 6, Issue 1, 2020, p. 66-78. K. Ragulskis, L. Ragulskis The investigated system comprises a mass attached by a deformable link to a fixed foundation, and an elastic-dissipative limiter of motion of that mass. Such types of systems are widely used in different technological devices and machines. This paper is devoted for the improvement of dynamical qualities of such systems. Free and forced stationary harmonic vibrations as well as the qualitative parameters of motions of the system are analyzed in this paper. Characteristics of vibrations are determined using analytical and numerical techniques. It is determined that for the case of zero fastening the values of eigenfrequencies of the system do not depend on the amplitude of excitation. Then the system has an infinite number of multiple eigenfrequencies. In the case of forced harmonic excitation single valued stable motions exist in the vicinity of the resonance. This gives rise to some qualities of the system which are useful in practical applications. Citation: Mathematical Models in Engineering PubDate: 2020-03-31T00:00:00Z DOI: 10.21595/mme.2020.21398 Issue No:Vol. 6, No. 1 (2020)