Unwanted Vibrations Research Articles

Phase-cancellation of velocity oscillations in a flow duct using a slow-sound metamaterial

Self-sustained acoustic oscillations in industrial systems with mean flow can cause unwanted vibrations or noise pollution. Acoustic metamaterials can be engineered and integrated in such systems to prevent these limit cycles. In this study, an acoustic metamaterial is proposed for decreasing the acoustic admittance at the outlet of a contraction in a pipe. It can reduce velocity oscillations by more than 50%, without requiring an enlargement of the pipe or increasing the static resistance to the mean flow significantly. The acoustic metamaterial consists of an array of slow-sound and regular channels, which form a contraction in a pipe. The slow-sound effect shifts the resonances of the respective slow-sound channels. For the frequency of interest, the velocity oscillations of these two types of channels are out of phase, which reduces the spatially averaged velocity oscillations at the outlet of the contraction and therefore decreases its acoustic admittance. The effect is demonstrated experimentally, using impedance measurements and particle image velocimetry. A key achievement of this work is the demonstration of a device that is nearly lossless for the mean (steady) flow, i.e. having a low pressure drop, while being very stiff for the acoustic (oscillating) flow at its nominal working frequency, i.e. low admittance, which was so far a difficult challenge to address.

Semi-analytical formulation to predict the vibroacoustic response of a fluid-loaded plate with ABH stiffeners

Stiffened structures are widely used in aeronautics, marine and rail industries. When stiffeners are integrated into host structures, so-called Bloch-Floquet waves are generated due to interactions between the host’s flexural waves and the stiffeners’ flexural and torsional waves. It is reported in the literature that these waves are often the source of undesirable noise and vibrations when the stiffened structure is excited by a force. To mitigate unwanted noise and vibrations from the stiffened structures, this study proposes to replace common rectangular stiffeners with acoustic black hole (ABH) stiffeners. To do this, a semi-analytical model is initially developed in the wavenumber domain to predict the forced vibroacoustic response of a 2D fluid-loaded infinite plate with stiffeners on one side. In the proposed model, the stiffeners are characterised by their translational and rotational dynamic stiffnesses which can be estimated by a finite element method (FEM). These dynamic stiffnesses are then coupled with the analytical formulation of the fluid-loaded plate to obtain the expressions of the spectral displacement and radiated pressure. Comparisons of the results in terms of the plate’s mean quadratic velocity and radiated sound power for the rectangular and ABH stiffeners show that by using the ABH stiffeners instead of the conventional stiffeners, one can significantly reduce the vibroacoustic response of light/heavy fluid-loaded plates.

Jerk limited continuous tool path generation for flexible systems in non-cartesian coordinate systems

Inspired by computer numerical control (CNC) technology and drastic changes in the world of electronics and microcontrollers, the idea of using non-cartesian coordinate system for CNC machines became a topic of interest. Non-cartesian coordinate systems provide freedom of movement in systems with large working spaces where high dimensional accuracy is not a prime concern. Applications of such systems can be found in murals, where a painting is applied to a large wall of any arbitrary build material. In the present paper, a new design was introduced to automate the process of drawing murals on large surfaces. The proposed mechanism utilized chain and sprocket to overcome the size limitations of traditionally available x-y tables. In addition to that, the developed mechanism does not utilize the common robust structures used in the conventional CNC systems and the tool motion is created using flexible arms that are not heavily constrained. The effect of systems unwanted vibration has been eliminated using continuous trajectory and kinematic profiles. Parametric curve interpolation algorithms for trajectory planning were implemented to increase the flexibility of drawing complex curves. Parametric curves such as B-spline and non-uniform rational B-spline (NURBS) were employed to generate a jerk limited trajectory for motion control and extraction of kinematic profiles. Such trajectory constrains the jerk of the system and guarantees a smooth motion free of feed-rate fluctuations. Compared to other methods available for extracting the kinematic profiles, jerk limited method decreases the travel time and trajectory error. Ultimately, motion commands were produced by using kinematic profiles and the second order Taylor interpolator. STM32746ZG card was used as the main processor and two stepper motors controlled by a Bit Pattern interpolation algorithm were utilized to drive the proposed mechanism. The input pulses of stepper motors were stored as binary bits and transmitted to drivers in real-time. The feedback was also evaluated by two rotary encoders, placed at the end of the motors’ shafts. Encoder data were acquired and transmitted using a TCP/IP protocol to guarantee zero data loss during the transmission.

New Roughness Index of Passenger Car Rotational Vibration

Current road roughness indexes are limited to reflecting the unwanted rotational vibration of vehicles. This study focused on the relationship between the international roughness index (IRI) and rotational vibration around the longitudinal axis (pitch) and horizontal axis (roll) of the vehicle body. Sinusoidal wave input of different wavelengths and phase shifts between the left and right wheel tracks were used as excitation of a full-car model. Marked pitch and roll vehicle vibration were observed at shorter wavelengths (<1 m) and lower speeds (<50 km/h) of harmonic excitation. The IRI was limited to predicting the pitch and roll vibration of the full-car model at lower wavelengths, below 1 m. A simple alternative solution based on the IRI model was proposed as a robust, sensitive tool to detect unwanted rotational vibration of a vehicle. The proposal was based on the IRI approach using an alternative IRI model speed of 30 km/h, instead of the standard 80 km/h. The IRI for 30 km/h was several times more sensitive to pitch and roll vibration in the wavelength band up to 1.5 m than the IRI for 80 km/h. The new approach is recommended as an additional roughness index for monitoring roads with an allowable speed of up to 60 km/h.

Vibration mitigation of a model aircraft with high-aspect-ratio wings using two-dimensional nonlinear vibration absorbers

High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.

Airborne acoustic assessment of impact-resistant fitness flooring systems

Fitness facilities in residential and mixed-used commercial buildings introduce important acoustic design challenges that must be considered in a building. Cardio activities such as running on treadmills, group classes for high intensity training, and weight training areas introduce high levels of unwanted noise and vibration into a building structure. Isolated floor constructions are generally coordinated and implemented during design but are not practical when buildings are completed and occupied. Impact-resistant fitness flooring systems are typically explored and installed as an alternate approach to reduce the transmission of impact noise and vibration. Non-standardized field airborne noise measurements of weight drops were conducted on an existing gym and on four possible impact-resistant fitness flooring upgrades to assess the reduction of impact noise levels in the offices located below the gym. The measurements were also compared to the HVAC background noise levels to observe the increase above background conditions and provide a subjective evaluation. The results of the measurements show that impact-resistant fitness flooring systems provide a noticeable reduction of impact noise, compared to standard fitness flooring systems. The results also show that impact-resistant fitness flooring systems that include specialty engineered shock pads as a base layer provide a significant reduction of impact noise levels.

Vibration Analysis using Finite Element Analysis (FEA): An Evaluation of Pico-Tubular Bulb Type Turbine Blades Fabricated in Composite Materials

Tubular turbines have been widely employed and evolved fast when its introduction in the 1930s due to their strong technical and economic qualities and application. Because its performance and structure differ from those of ordinary vertical shaft units, local and international academics worked extensively on research techniques and technological means using numerical simulation and model testing. The transmissions of a high quantity of power, which may cause unwanted vibrations that reduce efficiency, increase wear, and, in the worst-case scenario, cause serious damage. In this paper, the material propose in order to substantiate that the random excitations and excess vibration of the pico-turbine can be prevented is the use of CFRP (carbon fiber reinforced polymer) and PLA (polylactic acid). In this paper, ANSYS® Mechanical modal simulation is used to evaluate the structures’ robustness behavior of the composite materials that were used as the main material in the fabrication of turbine blades for bulb-type turbine application. The use CFD simulation in SOLIDWORKS® is needed to examine the pressure fluctuation caused by unsteady flow that can contribute in the unwanted pulsation and to conform the modal simulation results. To validate the results, pressure pulsation experimentation is conducted to evaluate the fluctuation of the pressure affecting the blades or in the rotating region and it is analyzed through frequency response domain. Hence, in this paper, it is proven that the vibration behavior of the material is acceptable since the resulting natural frequency provides resulting stress, strain, and deformation that is allowable and below its ultimate tensile strength.

Identifying Factors Influencing the Properties of Vibroacoustic Metamaterials Using Three Different Acoustic Methods

Vibroacoustic metamaterials offer an approach for the targeted damping of unwanted structural vibrations and noise by integrating periodically arranged resonators into a matrix of bulk material. Fabrication using the laser bed powder fusion process allows the targeted integration of bulk resonators and powder depots, leading to an extension of the designable damping properties. Herein, the adaptation of acoustic methods is focused on the characterization of the properties of metamaterial plates. The investigated vibroacoustic metamaterial plates are made of polyamide PA1.2, combining material and structural damping. The vibration behavior of the plates over a range of frequencies using acoustic impedance measurements in a custom‐built measurement tube is investigated and it is compared with structural dynamics experiments using an electrodynamic shaker. The measurements allow for the identification of stop bands (frequency range with high damping) and influencing factors such as metamaterial design, mass, powder amountand surface on the frequency‐dependent damping properties. The adapted technique investigated in this work provides an experimental platform to characterize the complex interplay of acoustic metamaterial design and holds promise for scaling up metamaterial technology for industrial applications due to its simplicity, small space requirement, and low cost.

Comparative analysis for optimal placement of piezoelectric actuators on smart thin plate

In contemporary smart structures, piezoelectric ceramic (PZT) actuators serve a crucial structural function. To construct a smart thin plate that integrates structural health monitoring (SHM) and active vibration control objectives, many placement methodologies were discussed. In current research, two positioning strategies of the attached PZT actuators are compared. The first strategy is a well-known controllability concept where PZT actuators’ optimum positions are obtained by maximizing the eigenvalues of the controllability Grammian matrix. The second strategy employs the energy concept to strategically position PZT actuators so that the utmost amount of exerted work is accomplished by the actuators. Thus, the optimal performance of actuators to provide energy for mitigating unwanted vibrations is maintained, as is the optimal excitation required for SHM in the designated modes. Kirchoff’s classical laminate plate theory (CLPT) is used to define displacements as well as the normal strains of this coupled electro-mechanical system, and then, using the Ritz solution, the modal eigenvalue problem is solved, and mode shapes are obtained. Consequently, normal strains are transformed into spatially dependent functions used to define both the virtual work and the controllability of the Grammian matrix for the PZT actuators as a function of their locations. Finally, iterative optimization based on a genetic algorithm (GA) is used to find the optimum actuator locations in the desired modes. The best location for the PZT actuator or actuators is explored for two specimen plates with different boundary conditions. The results for the two studied positioning strategies are then compared, showing the superiority of the proposed energy-based strategy. Further, a quantitative variance-based uncertainty analysis reveals a low variance of the output results for the proposed strategy.

All-fiber fast acousto-optic temporal control of tunable optical pulses

We demonstrate a new all-fiber electrically tunable modulation method which significantly reduces the response time of a Bragg grating acousto-optic modulator. A 4 cm long device is fabricated with a 1 cm grating inscribed in a suspended core fiber. An acoustic pulse train is switched out of phase along the fiber, damping unwanted natural resonant vibrations inside the grating. The device rise time is decreased from 56 to 9 µs by tuning the duty cycle of the driven electrical signal, contributing to achieve the shortest switching time of 15.6 µs. This tunable temporal response reveals unique features to change the profile of optical pulses. High pulse modulation depths are achieved employing a compact acousto-optic modulator, pointing to fast switching of all-fiber photonic devices.

Harnessing flow-induced vibrations for energy harvesting: Experimental and numerical insights using piezoelectric transducer.

Flow-induced vibrations (FIV) were considered as unwanted vibrations analogous to noise. However, in a recent trend, the energy of these vibrations can be harvested and converted to electrical power. In this study, the potential of FIV as a source of renewable energy is highlighted through experimental and numerical analyses. The experimental study was conducted on an elastically mounted circular cylinder using helical and leaf springs in the wind tunnel. The Reynolds number (Re) varied between 2300-16000. The motion of the cylinder was restricted in all directions except the transverse direction. The micro-electromechanical system (MEMS) was mounted on the leaf spring to harvest the mechanical energy. Numerical simulations were also performed with SST k-ω turbulence model to supplement the experiments and were found to be in good agreement with the experimental results. The flow separation and vortex shedding induce aerodynamic forces in the cylinder causing it to vibrate. 2S vortex shedding pattern was observed in all of the cases in this study. The maximum dimensionless amplitude of vibration (A/D) obtained was 0.084 and 0.068 experimentally and numerically, respectively. The results showed that the region of interest is the lock-in region where maximum amplitude of vibration is observed and, therefore, the maximum power output. The piezoelectric voltage and power output were recorded for different reduced velocities (Ur = 1-10) at different resistance values in the circuit. It was observed that as the amplitude of oscillation of the cylinder increases, the voltage and power output of the MEMS increases due to high strain in piezoelectric transducer. The maximum output voltage of 0.6V was observed at Ur = 4.95 for an open circuit, i.e., for a circuit with the resistance value of infinity. As the resistance value reduced, a drop in voltage output was observed. Maximum power of 10.5μW was recorded at Ur = 4.95 for a circuit resistance of 100Ω.

Mayfly Algorithm for Modelling a Horizontal Flexible Plate Structure

Flexible plates are widely used in engineering and the industry, primarily due to the lightweight nature compared to rigid counterparts. These structures offer benefits such as cost savings, lower energy consumptions and improved operational safety. However, a notable drawback is that flexible structures are vulnerable to unwanted vibrations, which can cause structural damages. Hence, the development of specialized models are essential to effectively addressing this challenge. Researchers have devised various approaches to suppress unwanted vibrations, with contemporary studies often employing system identification techniques utilizing swarm intelligence algorithms to construct dynamic models of flexible structures. Therefore, this research employs the potent mayfly algorithm (MA), known for its effectiveness in optimization tasks. The developed models using MA were then compared with traditional approach known as recursive least square (RLS) through a comparative analysis. The outcome reveals that RLS exhibited the lowest mean square error (MSE) at , while MA had an MSE of Yet, MA adeptly depicted the characteristics of the system, outperforming the RLS in these validation by indicating a 95% confidence level in the correlation test and exhibiting robust stability in the pole-zero diagram. Consequently, MA serves as a fitting algorithm to accurately depict the real behaviour of the flexible plate structure.

Experimental study of taper shape bistable beam for improved vibration energy harvesting

Unwanted vibrations cause discomfort and affect the accuracy of the machinery. Vibrations of low frequency (<30 Hz) are usually inutile. Various researchers focus on harvesting and enhancing energy output through low-frequency vibrations. This paper focuses on improving energy harvesting from low-frequency vibration sources through taper shape (TAP) bistable beam fabricated using thin Piezoelectric Polyvinylidene fluoride (PVDF) film sandwiched between thin copper and aluminium films on both sides. Voltage power output through a PVDF film depends on the film’s strain distribution; hence, in this study, five different beam designs are studied for strain distribution through the ANSYS workbench. Further, an experimental harmonic analysis study for voltage output is performed on rectangular beam (RECT) and TAP beam for both straight and bistable configuration using three different harmonic input conditions, which concluded that the voltage output for the TAP beam is much more than that of the RECT beam, with a much more significant voltage output increase in bistable conditions for all three harmonic input conditions.

Enhancing the Machining Performance of Nomex Honeycomb Composites Using Rotary Ultrasonic Machining: A Finite Element Analysis Approach.

Nomex honeycomb composites (NHCs) are commonly used in various industrial sectors such as aerospace and automotive sectors due to their excellent material properties. However, when machining this type of structure, problems can arise due to significant cutting forces and unwanted cell vibrations. In order to remedy these shortcomings, this study proposes to integrate RUM (rotary ultrasonic machining) technology, which consists of applying ultrasonic vibrations along the axis of rotation of the cutter. To fully understand the milling process by ultrasonic vibrations of the NHC structure, a 3D numerical finite element model is developed using Abaqus/Explicit software. The results of the comparative analysis between the components of the simulated cutting forces and those from the experiment indicate a close agreement between the developed model and the experimental results. Based on the developed numerical model, this study comprehensively analyzes the influence of the ultrasonic vibration amplitude on various aspects, such as stress distribution in the cutting zone, chip size, the quality of the machined surface and the components of the cutting force. Ultimately, the results demonstrate that the application of ultrasonic vibrations leads to a reduction of up to 50% in the components of the cutting force, as well as an improvement in the quality of the machined surface and a reduction in the size of chips.

Optimized design of multiple tuned mass dampers for vibration control of offshore wind turbines

Offshore wind turbines (OWTs) are dynamically sensitive structures to low-frequency wind-wave loadings due to their low damping and high flexibility. This makes them vulnerable to unwanted vibrations in ocean environments. Therefore, there is a need to implement innovative vibration control devices to suppress undesired vibration and ensure their structural safety. A tuned mass damper (TMD) has been a promising solution to control excessive vibrations recently in OWTs due to higher efficiency and low installation cost. However, TMD performance in vibration mitigation of OWTs when placed at a nacelle is still challenging to investigate because the generator torque and pitch control may affect the dynamics of the overall system. In this paper, an optimal multiple TMD system is designed by placing TMDs at optimal locations along the tower, which are defined using the maximum amplitude of the displacements for the first three natural frequencies of the tower. In addition, extensive simulations are carried out with integrated OWT-TMD systems to find the optimal mass ratio values and quantity of the TMDs. The TMD system is also tuned for several scenarios, including operating, parked, and idling conditions under the combined wind-wave loadings. A numerical model of the 5 MW NREL OWT developed in OpenFAST is considered as the baseline in this study. The results show a root mean square (RMS) response reduction of 10.2% and 42% in fore-aft (FA) and side-side (SS) tower displacement with optimally designed multiple TMDs. Moreover, improved mitigation effects on tower base moment of RMS 43.6% and 20.8% are observed in orthogonal directions, respectively. The findings of this paper may have the potential for designing passive TMD systems for vibration reductions in OWT.

Delayed non‐fragile robust control of civil structure considering structural uncertainties, actuator faults, and control force time delays

Active control is an effective strategy for suppressing unwanted structural vibrations. The uncertainties in computational models, actuator faults, and time delays in control forces are the potential threats for control performance improvements. These factors are interconnected and may lead to control system instability and poor control effectiveness. The paper presents a delayed non-fragile robust control (DNR) algorithm for uncertain systems with consideration of actuator faults and time delays. To this end, the existence conditions for the DNR multi-objective controller are derived by utilizing the Lyapunov stability proof and introducing a pole constraint inequality. Then, a dynamic output feedback DNR algorithm is further developed. Finally, two numerical simulation examples are discussed for several ground motions. The results show that the control system based on the proposed algorithm exhibits better stability, robustness, and fault tolerance than the linear quadratic Gaussian (LQG) algorithm. Furthermore, there is no need for additional control energy. Significantly, the control performance of the proposed algorithm can be further enhanced with the decentralized control strategy.

A study of analyzing longitudinal dynamic behavior of a double-rod system with longitudinal nonlinear supports

In engineering, shafting systems are typically subjected to longitudinal vibration excitations, which may result in unwanted vibration. To study the control of longitudinal vibration in shafting systems, they can be simplified to rod structures. Currently, engineers have attempted to apply the nonlinear principle to design nonlinear supports to control the vibration of flexible structures. However, the flexible structures referenced in the literature are usually composed of a single component, which limits the application of nonlinear supports to more complex structures. To explore the potential application of nonlinear supports in marine engineering, this work introduces a longitudinal vibration prediction model for a double-rod system equipped with longitudinal nonlinear supports. The generalized Hamilton principle is used to derive the governing equations for the double-rod system with longitudinal nonlinear supports. The longitudinal vibration responses of the double-rod system are numerically solved using the Galerkin truncation method. The numerical results confirm that a 1-term truncation number guarantees the stability of the longitudinal vibration prediction model. Under certain conditions, the longitudinal vibration responses are significantly affected by longitudinal nonlinear supports. It is recommended to install longitudinal nonlinear supports on both Rod 1 and Rod 2 simultaneously to suppress vibration in the first two main resonance orders. With reasonable excitations, the vibration state and magnitudes of the double-rod system can be effectively controlled by adjusting the longitudinal nonlinear supports. Complex longitudinal vibration responses are more readily induced by altering the parameters of the longitudinal nonlinear support installed on Rod 1. Choosing appropriate parameters for the nonlinear supports on Rod 1 and Rod 2 positively contributes to the reduction of vibration in the double-rod system.

Vibration mitigation using dual-open and infilled trenches in layered soil media: Field tests and numerical simulations

Ground-borne vibrations are increasing at a rapid rate due to the rise in urban expansion and industrial activities. The current solution to mitigate the unwanted vibrations is limited to the use of single trenches that require unrealistic depths. This paper presents the possibilities of using dual open and infilled trenches to mitigate the vibrations generated due to continuous harmonic motions. Full-scale field tests and comprehensive numerical studies were performed to systematically design dual trenches. The field vibration tests were performed under a wide range of frequencies using the Lazan-type mechanical oscillator. Similarly, numerical studies have been performed using finite element analysis software, PLAXIS 2D. Expanded polystyrene (EPS) geofoams of different densities, bentonite, ceramsite, concrete, and sand-rubber mixture were used as the infill materials. The normalized depths of 0.40 and 0.50 were observed as the optimal values to reach an average amplitude reduction ratio (average ARR) of 0.25 for the dual open and EPS15-infilled trenches, respectively. The isolation efficiency of EPS15-infilled trenches was observed to be 178 % higher compared to the EPS48-infilled trenches. The performance difference between EPS15 and ceramsite-filled dual trenches was observed to be only 4 % in terms of average ARR, the former being superior.

Design of the high-speed cam profile for the multi-DOF follower

The multi-degree-of-freedom (multi-DOF) follower may suffer from unwanted vibrations when the cam works at the high speed. The vibrations will cause significant problems of positioning accuracy, noise, wear, forces, and operating costs for the cam-follower mechanism. It is challenging to design high-speed cam profiles for multi-DOF followers because of the complicated dynamics. A novel method is presented to design the cam profile in this article. A polynomial profile filters through a continuous-piecewise smoother to produce the cam profile. While the profile and their derivatives are continuous, the profile provides good performance on the vibration reduction for multi-DOF followers. Simulated and experimental results from a flexible-link manipulator validate the effectiveness of the cam profiles created by the new method.

Magnetorheological Polishing Based on Honing Vertical Mechanism for Inner Surface of Titanium Alloy Pipes

Recently, high internal surfaces for titanium alloy pipes have been required due to the increment of various applications such as aerospace components. In this work, vertical magnetorheological polishing (VMRP) is carried out to achieve high polishing performance on the internal surface of the titanium alloy pipe. A series of comparative experiments were conducted to investigate the polishing mechanism of magnetorheological polishing (MRP) fluid and enhance the polishing performance. It is shown from the experimental results that the VMRP method under the opposite polarity arrangement improves the surface roughness from 47.85% to 83.34% by reducing unwanted vibration and noise during operation. This provides nanoscale surface polishing quality, while such a precision cannot be achieved from the previous horizontal MR polishing apparatus method. It is found that under a 2700 cycle polishing time, a polishing process combining a rough and fine polishing approach with a combination of different particle diameters results in an axial surface roughness of 0.05 μm and circumferential surface roughness of 0.038 μm, respectively. It is also identified that the axial surface roughness of 0.04 μm–0.041 μm is achieved through the combination of high- and low-speed polishing process after 1602 cycles.