Transient Operating Conditions Research Articles

Suitability Study of Biofuel Blend for Light Commercial Vehicle Application under Real-World Transient Operating Conditions

<div>Driving schedule of every vehicle involves transient operation in the form of changing engine speed and load conditions, which are relatively unchanged during steady-state conditions. As well, the results from transient conditions are more likely to reflect the reality. So, the current research article is focused on analyzing the biofuel-like lemon peel oil (LPO) behavior under real-world transient conditions with fuel injection parameter MAP developed from steady-state experiments. At first, engine parameters and response MAPs are developed by using a response surface methodology (RSM)-based multi-objective optimization technique. Then, the vehicle model has been developed by incorporating real-world transient operating conditions. Finally, the developed injection parameters and response MAPs are embedded in the vehicle model to analyze the biofuel behavior under transient operating conditions. The results obtained for diesel-fueled light commercial vehicle (LCV) have shown better fuel economy than LPO biofuel with their developed fuel injection parameter MAP. The maximum BTE obtained was 29.7% for diesel and 29.5% for LPO at 2100 rpm and 20 Nm torque. The mean HC emissions were identified as 0.02046 g/km for diesel and 0.03488 g/km for LPO fuel over the modified Indian driving cycle (MIDC). Except for NOx emission, LPO biofuel exhibited diesel-like performance and emission characteristics under the MIDC.</div>

A method to partition boiling heat transfer mechanisms using synchronous through-substrate high-speed visual and infrared measurements

Heat transfer during boiling involves a variety of transport mechanisms. Available experimental techniques cannot yet fully delineate these mechanisms which has contributed to a long-standing, persistent challenge of constructing accurate mechanistic models for boiling. In this work, we develop a method to identify and distinguish between the individual heat transfer mechanisms that occur during boiling using synchronous, through-substrate, high-speed visual and infrared measurements. Local heat fluxes are deduced from temperature measurements and a synchronized set of binarized phase maps are obtained from processing high-speed visual measurements. Experimental pool boiling investigation of HFE-7100 fluid on an indium tin oxide surface revealed four distinct heat transfer signatures in the heat flux maps corresponding to liquid convection, contact line evaporation, vapor convection, and local microconvection due to rewetting during boiling. To classify these regions, pixel-wise binary and morphological operations are performed on the phase maps of the entire surface. In contrast with prior partitioning techniques which use standalone heat flux measurements, our synchronous high-resolution visualization enables the region classification around fine bubble footprints that otherwise would not be detected with heat flux maps alone. The heat fluxes and superheats are then partitioned into their underlying mechanisms using classified regions from the phase maps. Analysis of the nucleate boiling regime data shows that different mechanisms contribute in varying degrees to the overall heat transfer at different points along the boiling curve: for the surface-fluid combination studied, single-phase liquid heat transfer is the primary contributor at low heat fluxes while at high heat fluxes, contact line evaporation contributed the most. We further employ the experimental approach to partitioning dynamic processes resulting from step increases in heat input demonstrating its potential for investigating transient phenomena such as dryout. The experimental and post-processing method introduced in this study is the first to delineate partitioning between different heat transfer mechanism regions in the presence of multiple interacting bubbles over the entire surface throughout the boiling curve in both steady and transient operating conditions.

Thermal and hydraulic characteristics analysis of horizontal lead-bismuth reactor assembly based on sub-channel analysis code

In this paper, the self-developed subchannel analysis program SACOS-PB was used to analyze the thermal hydraulic characteristics of 127 rods in horizontal lead-bismuth reactor under steady state and typical ocean transient conditions. The results of the steady-state analysis showed that the coolant flow and temperature of the vertical assembly were symmetrically distributed, the coolant flow of the horizontal assembly gradually increased along the gravity direction, the temperature rose first and then fell, and the peak coolant temperature of the cross-sectional channel was about 365 °C. Three typical ocean transient operating conditions, inclined, undulating and swing, were also carried out. The results showed that the maximum temperature of the coolant at the exit of the assembly increased with the increase of the transverse heeling angle and the decrease of the trim angle after the incline motion changes the gravity component. Under the undulating and swing conditions, the coolant hydrothermal parameters fluctuated periodically, and the parameter fluctuation period is 10s in line with the oceanic conditions. In the above transient conditions, the peak coolant temperature at the assembly outlet increases and exceeds 365 °C. Compared with the pitching motion on the Y-axis, the rolling and tumbling motion on the X-axis had a significant effect on the coolant flow rate and temperature distribution. The calculation results can provide support for the analysis study of the safety characteristics of lead-bismuth power units under marine conditions.

Research on the Optimal Design Approach of the Surface Texture for Journal Bearings

Aiming to improve the comprehensive performance of the journal bearing system, this paper presents a multi-objective adaptive scale texture optimization design approach. A mixed lubrication model for the textured journal bearing system is established by considering the effects of cavitation and roughness. The geometrical parameters of the textures were co-optimized using a multi-objective grey wolf optimizer to obtain the optimal texture schemes that are suitable for different operating conditions. Through this approach, the influences of different texture schemes under transient operating conditions can be investigated. According to the results, it was found that different texture schemes result in different friction reduction effects. Proper surface texture is beneficial in increasing the minimum oil film thickness and reducing the possibility of asperity contact. The adaptive scale texture exhibits strong adaptability and achieves significant hydrodynamic effects. Therefore, the developed approach provides valuable insights for the optimization design of journal bearing systems.

Comparative analysis of different FeCrAl alloys in pressurized water reactors

Discussing and researching issues related to their safety is essential to guarantee the continuity of fission systems in generating energy for existing and new electrical matrices. Commercial fission reactors currently in operation have undergone a series of redesigns. One aspect much discussed in recent years is related to research about new fuels and cladding materials. Therefore, in this work, the feasibility of replacing Zircaloy-4 with FeCrAl-based alloys (C06M, C35M, C36M, Kanthal APMT) was evaluated considering these materials' physical–chemical, thermal, and neutronic properties. Moreover, thermal–hydraulic and neutronic simulations have been presented to compare the cladding behavior in a PWR core in steady state and transient operation conditions. The results showed, in a general way, that the analyzed alloys have equivalent properties from a physical–chemical and thermal point of view. Despite the similarity, the Kanthal APMT alloy presented the worst performance, and the C35M alloy showed more advantageous characteristics. Considering the similarities in the composition of the C06M, C35M, and C36M alloys, which have the same elements in their constitution, the alloy with the best thermal performance has the lowest aluminum content. Considering the neutronic behavior, the Kanthal APMT alloy, with more Cr percentile, presents the lowest neutron effective multiplication factor, keff. Axial and radial power distribution did not change significantly after the cladding replacement. Nevertheless, modifications must be made to keep the criticality during the fuel cycle burnup for all FeCrAl alloys.

Prediction of mechanical efficiency of spur gear pairs based on tribo-dynamics model of multi-tooth meshing

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

Overview of Fourth Generation Reactors Studied at the Universidade Federal de Minas Gerais (Brazil)

This paper presents the results of the studies about the Fourth Generation Reactors developed at DENU-UFMG, such as the Very High Temperature Reactor (VHTR), Molten Salt Breeder Reactor (MSBR), Sodium Fast Reactor (SFR) and Gas-cooled Fast Reactor (GFR). These studies evaluate neutronic parameters of the nuclear system at steady state and during the burnup using computer models developed at DENU-UFMG using SCALE 6.0 (KENO-VI/ORIGENS), MCNPX 2.6.0 and MCNP5. The results show that the adopted methodologies confirm the capabilities of the codes to simulate specific situations in steady state or transient operating conditions.

Fatigue life and transmission efficiency prediction of marine timing gears under 3D mixed lubrication state

The timing gears are the core transmission components of marine diesel engine, whose working conditions are complex and harsh, transient and coupled with the microscopic lubrication state, meshing in the mixed lubrication environment with lubrication-contact coexistence, local asperity contact brings stress concentration, further affects the fatigue life and friction loss. In this study, based on a three-dimensional (3D) line-contact mixed lubrication model, dynamic subsurface stress calculation, fatigue life prediction, and friction loss power study were carried out on timing gears, taking into account transient operating conditions and actual surface roughness. For the established simulation model, an equivalent simulation test of line-contact friction of timing gears was carried out, which can realize the measurement of friction coefficient under the condition of different slip-roll ratios, and make up for the deficiency that the traditional test equipment can only carry out the test under the fixed slip-roll ratio. Although the gear meshing process can only be simulated by the disc specimen due to the limitation of the specimen form, this limitation is similar to the simplified form of the simulation model, which can meet the needs of the verification test. The influence of structure and material on the lubrication state, fatigue life and friction power consumption are studied, which provide theoretical guidance for the tribological optimization design and reliability analysis for the marine timing gears.

Low Temperature Combustion Modeling and Predictive Control of Marine Engines

The increase of popularity of reactivity-controlled compression ignition (RCCI) is attributed to its capability of achieving ultra-low nitrogen oxides (NOx) and soot emissions with high brake thermal efficiency (BTE). The complex and nonlinear nature of the RCCI combustion makes it challenging for model-based control design. In this work, a model-based control system is developed to control the combustion phasing and the indicated mean effective pressure (IMEP) of RCCI combustion through the adjustments of total fuel energy and blend ratio (BR) in fuel injection. A physics-based nonlinear control-oriented model (COM) is developed to predict the main combustion performance indicators of an RCCI marine engine. The model is validated against a detailed thermo-kinetic multizone model. A novel linear parameter-varying (LPV) model coupled with a model predictive controller (MPC) is utilized to control the aforementioned parameters of the developed COM. The developed system is able to control combustion phasing and IMEP with a tracking error that is within a 5% error margin for nominal and transient engine operating conditions. The developed control system promotes the adoption of RCCI combustion in commercial marine engines.

Design of Multi-Input Multi-Output Non-linear Model Predictive Control for Main Steam Temperature of Super Critical Boiler

Flexible operation of coal-fired power plants is becoming increasingly necessary for successful integration of large-scale renewable power generation into the power grid. The maximum ramp rate and the number of load cycles are generally limited by the thermal stress experienced by the boiler pressure parts, turbine metallurgy and creep and fatigue of critical thick-walled components Main steam temperature is a critical operating parameter that must be controlled within acceptable limits for safe operation. Main steam temperature deviation beyond acceptable limit has impact on boiler pressure parts and turbine material of construction due to creep and fatigue effect. Base load operating units do not require steep ramp rate and hence recommended ramping rates are kept low within the safe operating zone in comparison to the flexible operation of the units with wide range load change width. Thermal stresses are caused by the temperature changes inside the thick-walled components and turbine steam admission parameters. Hence, the quality of main steam temperature control plays a vital role in flexible operation of the coal fired units. Conventional cascaded PID temperature control loop architecture performs well at steady state condition within a limited variation of load change at low ramp rate but it acts slowly and performs poorly at transient operating conditions of flexible operation of the boiler turbine with wide range load variation and load cycle with high ramp rate and remains far from rated conditions. In this paper, a Multi-Input Multi-Output (MIMO) Non-linear Model Predictive Control (MPC) design for regulation of the main steam temperature of a Once-Through supercritical Boiler is proposed. The controller is based on a non-linear dynamic model which incorporates dynamics of the variables of interest. It has the capability to operate effectively across a wide load range while maintaining main steam temperature within acceptable limits. A notable advancement in this design of MPC is the incorporation of coal flow demand and feedwater flow demand as additional control inputs alongside primary and secondary spray flows. In simulation test cases, the MPC controller demonstrates satisfactory performance and computational efficiency.

Analysis of calculation of fuel rods for strength under transient and steady-state operating conditions

The operating conditions are analyzed, mechanical characteristics are calculated pertaining to the 4-year cycle fuel rods of VVER-1000. The fuel rod strength characteristics are considered as applied to steady-state and transient conditions of reactor operation.The analysis of the per – fuel rod calculations covering a part of fuel assemblies in the VVER-1000 core under steady-state and several transient operating conditions allows one to assess the mechanical state of fuel claddings, the fulfillment of the design criteria of acceptance and to gain the understanding of the effect produced by the reactor control methods on the strength characteristics.Given are the results of computer modelling the stress-strained condition of present-day fuel rod claddings upon the four-year operation within the VVER-1000 core both under steady-state and transient conditions.The calculations involved transients with the application of different control systems, namely, only the boric system and its combination with mechanical organs of control. The calculations evidence that in terms of the strength criteria these algorithms ensure the tolerable local distortions of power rating fields.

Large eddy simulation of combustion instabilities in a co-axial stratified model combustor under transient operating conditions

This work conducted large eddy simulation investigation on the effect of transient time and transient direction on the combustion instabilities in a co-axial stratified model combustor under transient operating conditions. Two transient times, which is greater than and less than the time delay, respectively, 0.1 s and 0.1 ms, were studied in different transient direction. The transient combustion process is analyzed by the global HRR, temperature, CH and CO. The time–frequency analysis of the pilot-stage and main-stage are carried out by FFT and SWT. The mode transition characteristics of the pilot-stage and main-stage are discussed based on the recurrence plots and Poincare plots. Finally, the bifurcations of the HRR and temperature caused by the transient time are analyzed. It was found that the shorter transient time is associated with larger oscillation amplitude of temperature, as well as the greater temperature and HRR gradient, and the maximum oscillation amplitude is larger. Furthermore, due to the shorter transient time in case ⅠⅡ-, the changing rate of heat release rate is approximately 725 J·m−3·s−2, which is significantly greater than the 72 J·m−3·s−2 in case ⅠⅡ+. In case ⅠⅡ-, the maximum CH is 2.0e-12, which is approximately 11 % higher than the maximum value in other cases. Different modes were observed in different transient time and transient direction. Longer transient time is associated with both a greater number of modes and frequency of mode transitions, and higher possibility of excitation oscillation occurring. Under a specific global average mixture fraction of 0.0345, two different flame shapes were observed in separate cases: a stratified flame and an M-shaped flame.

On-road high-emitting vehicle identification by an automatic hyperparameter optimization model based on a remote sensing system

Optical remote sensing systems (RSSs) are ideal for monitoring and identifying high-emitting vehicles on roads, as they can be installed on any road for non-contact measurements. In general, an on-road vehicle is considered a high-emitting vehicle when its instantaneous emissions exceed the specified cut-points, as monitored by RSSs. However, RSS measurements of vehicle emissions are easily influenced by transient operating conditions of passing vehicles and multiple environmental factors, resulting in variable results for the same vehicle, further interfering with the screening of high-emitting vehicles. In this paper, an automatic hyperparametric optimization model is established in an RSS to identify high-emitting vehicles by fusing multi-feature data on environmental factors and vehicle operating conditions obtained from the RSS with the chassis and engine dynamometer test results provided by vehicle inspection stations (VISs). Qualitative and quantitative experimental results show that our model exhibits better recognition performance for high-emitting vehicles in RSSs of different times and sites, which reflects the good self-adaptability of the model. Moreover, the hyperparameters of the model do not need to be manually adjusted, so the model can be automatically trained to meet the requirements of real-time recognition scenarios for high-emitting vehicles on the road.

A new generalized predictive current control algorithm with integration of fractional part function based modulation technique: Single phase self‐balanced type multilevel inverter topologies

SummaryIt is generally impossible to control the inverter output current (IOC) based on operator needs if only pulse width modulation (PWM) techniques are used. Conventionally, authors have reported the finite control set‐based predictive current control algorithm (FCS‐PCCA) to control the IOC with a fast dynamic response. However, this type of algorithm without a PWM stage generates a variable switching frequency (VSF) of operation, and it leads to filter design problems, inequitable thermal stress, and more current distortions that have been presented. To alleviate all these issues, a new generalized PCCA with the integration of a fractional part function‐based single carrier modulation technique (G‐PCCA‐FPF‐SCMT) has been proposed, and it provides constant switching frequency (CSF) of operation. In this technique, the normalized optimum inverter output voltage (N‐O‐IOV) has been fed with FPF‐SCMT. The particular modulation stage implementation is straightforward since even inverter level number increases, the number of references and triangular carrier signals is always only one. The complete control implementation process of the proposed technique is extremely low compared with all traditional CSF‐based PCCAs. To verify the proposed technique experimentally in both steady and transient state operations, one of the conventional five‐level switched capacitor‐based inverter topologies has been considered and elucidated vividly in both open‐loop and closed‐loop operations.

Morphology and nanostructure of soot particles from diesel engine under transient and steady-state operating conditions with a microalgae fuel component, dioctyl phthalate biofuel

In order to adhere to strict emissions standards, it is necessary to reduce diesel particulate emissions under real driving conditions. This can be achieved by reducing the production of soot particles and optimising the combustion process within the combustion chamber. This investigation examines the impact of engine operating conditions (transient and steady-state) on the characterisation of the soot particles. Soot samples from a common rail direct injection (CRDI), turbocharged six-cylinder diesel engine without any aftertreatment devices were collected on TEM grids. This investigation utilised both pure diesel and diesel-dioctyl phthalate (DOP) blends (D90DOP10 and D80DOP20). To correlate the soot characterisation results, diesel particulate emissions were also measured using a fast particle analyser (DMS500). The results indicate that emissions from transient cycles are higher in comparison to steady-state engine operation. Smaller primary particle diameter with a compact structure were observed for transient cycles when compared to steady-state operating conditions. Parameters such as number of primary particles within a single aggregate, radius of gyration, and soot aggregate area were also studied. Nanostructure analysis reveals that the soot particles from transient cycles could have lower oxidation reactivity and longer fringes with less curvature and interplanar spacing.

Flow-induced vibration analysis in a pump-turbine runner under transient operating conditions

The dynamic characteristics of the pumped storage unit (pump-turbine runner) make it highly susceptible to vibrations. Previous studies seldom addressed the clearance variation due to runner vibration, largely because of two challenges: the integration of the moving grid with the clearance and governing equations, and the intricacy of factoring in the entire shaft system's influence on vibration. By employing user-defined functions (UDF), kinematic equations for the pump-turbine runner's rotation and translation were formulated and integrated with computational fluid dynamics results. This paper introduces a computational method to simulate clearance-induced vibration displacement. The study examines the impact of clearance vibration displacement on the pump-turbine's transient flow field and runner vibrations under various operating conditions. Notably, deviations from the rated load condition led to an expansion-contraction trajectory of the runner axis, culminating in chaotic behaviour in the "S" characteristic zone. The correlation between runner vibrations and pressure fluctuations strengthened with the clearance displacement model, especially in narrow labyrinth seal clearances. Simulations also provided a refined estimation of the secondary rotational speed increase during load rejection. The method's reliability is confirmed through field test data comparison, offering a fresh perspective to identify the vibration characteristics of the pump-turbine runner.

Neutronic-thermalhydraulic coupling analysis of heat pipe failure accidents of a new type of megawatt heat pipe reactor

Heat pipe cooled reactors featured with high energy density, long lifecycle, modularity, and compact structure could be ideal power sources for large unmanned undersea vehicles (UUVs). In the early stage of reactor concept design, heat pipe failure accident is usually one of the design basis accidents that need to be considered. In this study, a set of transient analysis models for heat pipe failure accidents of a new type of megawatt heat pipe reactor is established. The models include the point kinetics model, Core Matrix module and Fuel-Heat Pipe module heat conduction models, and radiation heat transfer model for the inner core cavity. 2D-3D combined method is used to solve the heat conduction model in the Fuel-Heat Pipe module. Based on the models, a transient analysis code for heat pipe failure accidents is developed using FORTRAN. The models are separately validated based on the analytical solutions, the experimental data or the CFD results by FLUENT. Neutronic-thermalhydraulic coupling calculation is conducted in normal operation condition and heat pipe failure accidents. The peak temperatures of each region are below their melting points in all presumed heat pipe failure accidents which reflects the good inherent safety of the core. Meanwhile, the calculation results by the code are in good agreement with those of FLUENT, and the maximum relative error of the peak temperature does not exceed 1.5%. The code calculation time is 1/8 of FLUENT ensuring the accuracy of important parameters, effectively reducing the computation costs and improving the computation efficiency. The code also provides a basis for subsequent transient operation condition and typical accidents analysis of this reactor.

Design of improved direct torque control based on a five level torque controller and a new Sugeno-Takagi fuzzy super-twisting controller applied to an induction machine

This paper deals with the design and Hardware In Loop (HIL) verification of a novel intelligent Super-twisting Sliding Mode Speed Controller (STSMSC) based on a Sugeno-Takagi Fuzzy Logic System (STFLS) for an induction motor controlled by an improved Modified Direct Torque Control (MDTC) approach. Indeed, Conventional Super-twisting Sliding Mode Speed Controller (CSTSMSC) is chosen as an alternative solution for attenuating the chattering phenomenon brought on by the discontinuous control law of the First Order Sliding Mode Speed Control (FOSMSC) and maintaining its advantages like simplicity, robustness and accuracy. Moreover, the STSMSC is a type of a second order sliding mode control technique that needs only the information about the sliding surface, not its time derivative. However, the choice parameters of the CSTSMSC existing in the control law effects the tracking accuracy, the overshoot and the amplitude of the chattering. Therefore, an STSMSC based on an STFLS (STFLS-STSMSC) is proposed for online tuning of these parameters in transient and steady state operations. In fact, the STFLS is considered as an intelligent supervisor to adjust these parameter values according to the system state, which consequently provides excellent performance consisting in a higher robustness rate under disturbances and uncertainties, tracking with excellent accuracy and reduced chattering in steady state and transient operations. Numerous simulation and HIL co-simulation results are presented to demonstrate the effectiveness of the suggested STFLS-STSMSC based MDTC implemented on a Xilinx FPGA Zynq 7000 SoC ZC702.

Performance diagnostics of gas turbines operating under transient conditions based on dynamic engine model and artificial neural networks

Gas turbine engines are machines of high complexity and non-linearity. Interpreting the vast amount of data from a gas turbine and converting them into customer value requires the combination of domain knowledge and modern computational intelligence tools. Reaching to an accurate and reliable diagnosis of gas turbines is a process that is becoming increasingly complex. The engines are now expected to operate in more dynamic conditions to compensate for the intermittent nature of renewables. Transient operating conditions will accelerate the deterioration of gas turbine components which motivates the development of new methods and tools to cope with such type of information. In this paper, we propose a novel performance diagnostic method for gas turbines that combines a dynamic engine model with artificial neural networks (ANN). An engine model of a two shaft gas turbine has been developed in MATLAB/Simulink and used by a family of ANNs to detect the degradation of the engine operating under transient conditions, when all of its components are experiencing degradation. The conducted case studies consider various degradation scenarios. The advantage of the proposed method is that it deals effectively with both fixed and time-evolving degradation. Furthermore, in cases where there is limited amount of data for training ANNs the model can fill this gap by simulating plethora of scenarios that can potentially extend the applicability of ANNs to gas turbine diagnostics. The proposed method could be used as a tool for supporting the operation and maintenance activities of gas turbines.

Effects of rolling motion on helical coil once-through steam generator thermal-hydraulic characteristics

Steam generators are essential for the safe, economical, and reliable operation of nuclear reactors. Helical Coil Once-through Steam Generators (HCOTSG) offer unique advantages over other types of steam generators for ship reactors or offshore platforms. To investigate the effect of rolling motion due to ocean conditions on the safe and economic operation of HCOTSG, a new model and a new code are developed in this paper. The program is developed and allows numerical simulation of HCOTSG under ocean conditions. The validity of the code was verified by comparing the simulation results with the design parameters of the Marine Reactor X (MRX) steam generator and the simulation results of other dedicated programs. The code was further used to perform the International Reactor Innovative and Secure (IRIS) transient operating conditions under typical rolling motions. Then, the influences of different swing directions, angles, periods, and positions of swing axes from the origin of the system operating parameters are analyzed.In the cases discussed in this paper, the following conclusions are obtained: (a) The direction of the swing significantly affects the system. The most dangerous situation is around the x-axis, and the case around the z-axis is the safest, in which the rolling situation has little effect on the system because the centripetal force is perpendicular to the tube wall, and the gravitational pressure drop is constant. (b) when the swing angle increases, except the fluctuation speed is faster, the fluctuation range of the parameters also increases. (c) when the swing period changes, the parameters’ fluctuation range also change (d) the orientation of the swing axis from the origin affects the magnitudes of the parameters’ changes (e) the distance of the swing axis from the origin affects the magnitude of the parameter variation and the farther the swing axis is from the origin, the greater the parameter fluctuation.