Search results for: dynamics. modeling

Authors: Lambros V. Skarlas, Grigorios N. Beligiannis, Efstratios F. Georgopoulos, Adam V. Adamopoulos

Abstract:

The aim of this contribution is to present a new approach in modeling the electrical activity of the human heart. A recurrent artificial neural network is being used in order to exhibit a subset of the dynamics of the electrical behavior of the human heart. The proposed model can also be used, when integrated, as a diagnostic tool of the human heart system. What makes this approach unique is the fact that every model is being developed from physiological measurements of an individual. This kind of approach is very difficult to apply successfully in many modeling problems, because of the complexity and entropy of the free variables describing the complex system. Differences between the modeled variables and the variables of an individual, measured at specific moments, can be used for diagnostic purposes. The sensor fusion used in order to optimize the utilization of biomedical sensors is another point that this paper focuses on. Sensor fusion has been known for its advantages in applications such as control and diagnostics of mechanical and chemical processes.

Keywords: Artificial Neural Networks, Diagnostic System, Health Condition Modeling Tool, Heart Diagnostics Model, Heart Electricity Model.

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Authors: A. K. Abdel-Fattah, A. B. El-Tawil, N. A. Harraz

Abstract:

This paper focuses on the operational and strategic planning decisions related to the quayside of container terminals. We introduce an integrated operational research (OR) and system dynamics (SD) approach to solve the Berth Allocation Problem (BAP) and the Quay Crane Assignment Problem (QCAP). A BAP-QCAP optimization modeling approach which considers practical aspects not studied before in the integration of BAP and QCAP is discussed. A conceptual SD model is developed to determine the long-term effect of optimization on the system behavior factors like resource utilization, attractiveness to port, number of incoming vessels to port and port profits. The framework can be used for improving the operational efficiency of container terminals and providing a strategic view after applying optimization.

Keywords: Operational research, system dynamics, container terminal, quayside operational problems, strategic planning decisions.

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Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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Authors: Mohamed Elhakeem, A. N. Thanos Papanicolaou, Christopher Wilson, Yi-Jia Chang

Abstract:

In this study, a physically-based, modeling framework was developed to predict saturated hydraulic conductivity (K_sat) dynamics in the Clear Creek Watershed (CCW), Iowa. The modeling framework integrated selected pedotransfer functions and watershed models with geospatial tools. A number of pedotransfer functions and agricultural watershed models were examined to select the appropriate models that represent the study site conditions. Models selection was based on statistical measures of the models’ errors compared to the K_sat field measurements conducted in the CCW under different soil, climate and land use conditions. The study has shown that the predictions of the combined pedotransfer function of Rosetta and the Water Erosion Prediction Project (WEPP) provided the best agreement to the measured K_sat values in the CCW compared to the other tested models. Therefore, Rosetta and WEPP were integrated with the Geographic Information System (GIS) tools for visualization of the data in forms of geospatial maps and prediction of K_sat variability in CCW due to the seasonal changes in climate and land use activities. 

Keywords: Saturated hydraulic conductivity, pedotransfer functions, watershed models, geospatial tools.

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Authors: Katalina Grigorova, Kaloyan Mironov

Abstract:

The paper focuses on the benefits of business process modeling. Although this discipline is developing for many years, there is still necessity of creating new opportunities to meet the ever increasing users’ needs. Because one of these needs is related to the conversion of business process models from one standard to another, the authors have developed a converter between BPMN and EPC standards using workflow patterns as intermediate tool. Nowadays there are too many systems for business process modeling. The variety of output formats is almost the same as the systems themselves. This diversity additionally hampers the conversion of the models. The presented study is aimed at discussing problems due to differences in the output formats of various modeling environments.

Keywords: Business process modeling, business process modeling standards, workflow patterns, converting models.

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Authors: Cândida M. Pereira, Amílcar L. Ramalho, Jorge A. Ambrósio

Abstract:

In the numerical solution of the forward dynamics of a multibody system, the positions and velocities of the bodies in the system are obtained first. With the information of the system state variables at each time step, the internal and external forces acting on the system are obtained by appropriate contact force models if the continuous contact method is used instead of a discrete contact method. The local deformation of the bodies in contact, represented by penetration, is used to compute the contact force. The ability and suitability with current cylindrical contact force models to describe the contact between bodies with cylindrical geometries with particular focus on internal contacting geometries involving low clearances and high loads simultaneously is discussed in this paper. A comparative assessment of the performance of each model under analysis for different contact conditions, in particular for very different penetration and clearance values, is presented. It is demonstrated that some models represent a rough approximation to describe the conformal contact between cylindrical geometries because contact forces are underestimated.

Keywords: Clearance joints, Contact mechanics, Contact dynamics, Internal cylindrical contact, Multibody dynamics.

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Authors: Ziaddin Daie Koozekanani, Mina Zolfy Lighvan

Abstract:

One of the most challengeable issues in ESL (Electronic System Level) design is the lack of a general modeling scheme for on chip communication architecture. In this paper some of the mostly used methodologies for modeling and representation of on chip communication are investigated. Our goal is studying the existing methods to extract the requirements of a general representation scheme for communication architecture synthesis. The next step, will be introducing a modeling and representation method for being used in automatically synthesis process of on chip communication architecture.

Keywords: Communication architecture, System on Chip, Communication Modeling and Representation

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Authors: M. Pala Prasad Reddy, Jeevamma Jacob

Abstract:

Accurate dynamic modeling and analysis of flexible link manipulator (FLM) with non linear dynamics is very difficult due to distributed link flexibility and few studies have been conducted based on assumed modes method (AMM) and finite element models. In this paper a nonlinear dynamic model with first two elastic modes is derived using combined Euler/Lagrange and AMM approaches. Significant dynamics associated with the system such as hub inertia, payload, structural damping, friction at joints, combined link and joint flexibility are incorporated to obtain the complete and accurate dynamic model. The response of the FLM to the applied bang-bang torque input is compared against the models derived from LS-DYNA finite element discretization approach and linear finite element models. Dynamic analysis is conducted using LS-DYNA finite element model which uses the explicit time integration scheme to simulate the system. Parametric study is conducted to show the impact payload mass. A numerical result shows that the LS-DYNA model gives the smooth hub-angle profile.

 

Keywords: Flexible link manipulator, AMM, FEM, LS-DYNA, Bang-bang torque input.

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Authors: Charles D. Otine, Samuel B. Kucel, Lena Trojer

Abstract:

Selecting the data modeling technique for an information system is determined by the objective of the resultant data model. Dimensional modeling is the preferred modeling technique for data destined for data warehouses and data mining, presenting data models that ease analysis and queries which are in contrast with entity relationship modeling. The establishment of data warehouses as components of information system landscapes in many organizations has subsequently led to the development of dimensional modeling. This has been significantly more developed and reported for the commercial database management systems as compared to the open sources thereby making it less affordable for those in resource constrained settings. This paper presents dimensional modeling of HIV patient information using open source modeling tools. It aims to take advantage of the fact that the most affected regions by the HIV virus are also heavily resource constrained (sub-Saharan Africa) whereas having large quantities of HIV data. Two HIV data source systems were studied to identify appropriate dimensions and facts these were then modeled using two open source dimensional modeling tools. Use of open source would reduce the software costs for dimensional modeling and in turn make data warehousing and data mining more feasible even for those in resource constrained settings but with data available.

Keywords: About Database, Data Mining, Data warehouse, Dimensional Modeling, Open Source.

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: D. Šedivý, S. Fialová

Abstract:

The main purpose of this study is to show differences between the numerical solution of the flow through the artificial heart valve using Newtonian or non-Newtonian fluid. The simulation was carried out by a commercial computational fluid dynamics (CFD) package based on finite-volume method. An aortic bileaflet heart valve (Sorin Bicarbon) was used as a pattern for model of real heart valve replacement. Computed tomography (CT) was used to gain the accurate parameters of the valve. Data from CT were transferred in the commercial 3D designer, where the model for CFD was made. Carreau rheology model was applied as non-Newtonian fluid. Physiological data of cardiac cycle were used as boundary conditions. Outputs were taken the leaflets excursion from opening to closure and the fluid dynamics through the valve. This study also includes experimental measurement of pressure fields in ambience of valve for verification numerical outputs. Results put in evidence a favorable comparison between the computational solutions of flow through the mechanical heart valve using Newtonian and non-Newtonian fluid.

Keywords: Computational modeling, dynamic mesh, mechanical heart valve, non-Newtonian fluid, SDOF.

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Authors: Haowei Chen, Kaiqi Xiong

Abstract:

We have developed a better model for understanding the dynamics of malware spread in WMNs in this paper. The suggested model provides an insight into how viral propagation with energy exhaustion and various dispersed node densities might function. Based on a theoretical examination of the suggested model, we conclude that the threshold parameter could be used to identify the dynamics of viral spread globally. When the threshold is less than 1, the virus may be contained, but if it is greater than 1, a pandemic may result. Lastly, we discuss the various viral propagation strategies in relation to the distributed node densities and communication radii in WMNs. The aforementioned numerical simulation findings could serve as a guarantee of the theoretical analyses’ correctness.

Keywords: Bluetooth Security, Malware Propagation, Wireless Mesh Networks, Stability Analysis.

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Authors: Spiros Mazarakis, George Matzavinos, Peter P. Groumpos

Abstract:

Economic models are complex dynamic systems with a lot of uncertainties and fuzzy data. Conventional modeling approaches using well known methods and techniques cannot provide realistic and satisfactory answers to today-s challenging economic problems. Qualitative modeling using fuzzy logic and intelligent system theories can be used to model macroeconomic models. Fuzzy Cognitive maps (FCM) is a new method been used to model the dynamic behavior of complex systems. For the first time FCMs and the Mamdani Model of Intelligent control is used to model macroeconomic models. This new model is referred as the Mamdani Rule-Based Fuzzy Cognitive Map (MBFCM) and provides the academic and research community with a new promising integrated advanced computational model. A new economic model is developed for a qualitative approach to Macroeconomic modeling. Fuzzy Controllers for such models are designed. Simulation results for an economic scenario are provided and extensively discussed

Keywords: Macroeconomic Models, Mamdani Rule Based- FCMs(MBFCMs), Qualitative and Dynamics System, Simulation.

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Authors: Adla Bentellis, Zizette Boufaïda

Abstract:

Nowadays, the pace of business change is such that, increasingly, new functionality has to be realized and reliably installed in a matter of days, or even hours. Consequently, more and more business processes are prone to a continuous change. The objective of the research in progress is to use the MAP model, in a conceptual modeling method for flexible and adaptive business process. This method can be used to capture the flexibility dimensions of a business process; it takes inspiration from modularity concept in the object oriented paradigm to establish a hierarchical construction of the BP modeling. Its intent is to provide a flexible modeling that allows companies to quickly adapt their business processes.

Keywords: Business Process, Business process modeling, flexibility, MAP Model.

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Authors: Harish Kumar, Hussein Yahia, Oriol Pont, Michel Haissaguerre, Nicolas Derval, Meleze Hocini

Abstract:

The analysis to detect arrhythmias and life-threatening conditions are highly essential in today world and this analysis can be accomplished by advanced non-linear processing methods for accurate analysis of the complex signals of heartbeat dynamics. In this perspective, recent developments in the field of multiscale information content have lead to the Microcanonical Multiscale Formalism (MMF). We show that such framework provides several signal analysis techniques that are especially adapted to the study of heartbeat dynamics. In this paper, we just show first hand results of whether the considered heartbeat dynamics signals have the multiscale properties by computing local preticability exponents (LPEs) and the Unpredictable Points Manifold (UPM), and thereby computing the singularity spectrum.

Keywords: Microcanonical Multiscale Formalism (MMF), UnpredictablePoints Manifold (UPM), Heartbeat Dynamics.

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Authors: Hidetoshi Nonaka, Masahito Kurihara

Abstract:

In this paper, an authentication system using keystroke dynamics is presented. We introduced pressure sensing for the improvement of the accuracy of measurement and durability against intrusion using key-logger, and so on, however additional instrument is needed. As the result, it has been found that the pressure sensing is also effective for estimation of real moment of keystroke.

Keywords: Biometric authentication, Keystroke dynamics, Pressure sensing, Time-frequency analysis.

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Authors: Azam Marjani, Saeed Shirazian

Abstract:

This work deals with modeling and simulation of SO2 removal in a ceramic membrane by means of FEM. A mass transfer model was developed to predict the performance of SO2 absorption in a chemical solvent. The model was based on solving conservation equations for gas component in the membrane. Computational fluid dynamics (CFD) of mass and momentum were used to solve the model equations. The simulations aimed to obtain the distribution of gas concentration in the absorption process. The effect of the operating parameters on the efficiency of the ceramic membrane was evaluated. The modeling findings showed that the gas phase velocity has significant effect on the removal of gas whereas the liquid phase does not affect the SO2 removal significantly. It is also indicated that the main mass transfer resistance is placed in the membrane and gas phase because of high tortuosity of the ceramic membrane.

Keywords: Gas separation, finite element, ceramic, sulphur dioxide, simulation.

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Authors: Song Meng, Dianfu Ma, Yongwang Zhao, Jianxin Li

Abstract:

Cooperative visual modeling is more and more necessary in our complicated world. A collaborative environment which supports interactive operation and communication is required to increase work efficiency. We present a collaborative visual modeling framework which collaborative platform could be built on. On this platform, cooperation and communication is available for designers from different regions. This framework, which is different from other collaborative frameworks, contains a uniform message format, a message handling mechanism and other functions such as message pretreatment and Role-Communication-Token Access Control (RCTAC). We also show our implementation of this framework called Orchestra Designer, which support BPLE workflow modeling cooperatively online.

Keywords: colllaborative framework; visual modeling; message handling mechanism

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Authors: Zoltan Theisz, Gergely Mezei

Abstract:

Modern industrial automation relies on service oriented concepts of Internet of Things (IoT) device modeling in order to provide a flexible and extendable environment for service meta-repository. However, state-of-the-art meta-modeling techniques prefer design-time modeling, which results in a heavy usage of class sometimes unnecessary static subtyping. Although this approach benefits from clear-cut object-oriented design principles, it also seals the model repository for further dynamic extensions. In this paper, a dynamic multi-level modeling approach is introduced that enables dynamic subtyping through a more relaxed partial instantiation mechanism. The approach is demonstrated on a simple sensor network example.

Keywords: Meta-modeling, dynamic subtyping, DMLA, industrial automation, arrowhead.

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Authors: Gláucya C. Boechat, Jeneffer C. Ferreira, Edson C. B. Carvalho

Abstract:

This paper presents a boarding on biometric authentication through the Keystrokes Dynamics that it intends to identify a person from its habitual rhythm to type in conventional keyboard. Seven done experiments: verifying amount of prototypes, threshold, features and the variation of the choice of the times of the features vector. The results show that the use of the Keystroke Dynamics is simple and efficient for personal authentication, getting optimum resulted using 90% of the features with 4.44% FRR and 0% FAR.

Keywords: Biometrics techniques, Keystroke Dynamics, patternrecognition.

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Authors: Hidetoshi Nonaka

Abstract:

This paper presents an interactive modeling system of uniform polyhedra using the isomorphic graphs. Especially, Kepler-Poinsot solids are formed by modifications of dodecahedron and icosahedron.

Keywords: Kepler-Poinsot solid, Shape modeling, Polyhedralgraph, Graph drawing.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Based on the component approach, three kinds of dynamic load models, including a single –motor model, a two-motor model and composite load model have been developed for the stability studies of Khuzestan power system. The study results are presented in this paper. Voltage instability is a dynamic phenomenon and therefore requires dynamic representation of the power system components. Industrial loads contain a large fraction of induction machines. Several models of different complexity are available for the description investigations. This study evaluates the dynamic performances of several dynamic load models in combination with the dynamics of a load changing transformer. Case study is steel industrial substation in Khuzestan power systems.

Keywords: Dynamic load, modeling, Voltage Stability.

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Authors: D. He, Y. Pang, G. Lodewijks

Abstract:

Belt conveyors play an important role in continuous dry bulk material transport, especially at the mining industry. Speed control is expected to reduce the energy consumption of belt conveyors. Transient operation is the operation of increasing or decreasing conveyor speed for speed control. According to literature review, current research rarely takes the conveyor dynamics in transient operation into account. However, in belt conveyor speed control, the conveyor dynamic behaviors are significantly important since the poor dynamics might result in risks. In this paper, the potential risks in transient operation will be analyzed. An existing finite element model will be applied to build a conveyor model, and simulations will be carried out to analyze the conveyor dynamics. In order to realize the soft speed regulation, Harrison’s sinusoid acceleration profile will be applied, and Lodewijks estimator will be built to approximate the required acceleration time. A long inclined belt conveyor will be studied with two major simulations. The conveyor dynamics will be given.

Keywords: Belt conveyor, speed control, transient operation, dynamics

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Authors: A. Retbi, M. Khalidi Idrissi, S. Bennani

Abstract:

The success of an e-learning system is highly dependent on the quality of its educational content and how effective, complete, and simple the design tool can be for teachers. Educational modeling languages (EMLs) are proposed as design languages intended to teachers for modeling diverse teaching-learning experiences, independently of the pedagogical approach and in different contexts. However, most existing EMLs are criticized for being too abstract and too complex to be understood and manipulated by teachers. In this paper, we present a visual EML that simplifies the process of designing learning scenarios for teachers with no programming background. Based on the conceptual framework of the activity theory, our resulting visual EML focuses on using Domainspecific modeling techniques to provide a pedagogical level of abstraction in the design process.

Keywords: Educational modeling language, Domain Specific Modeling, authoring systems, learning scenario.

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Authors: Heiko Weiß, Andreas Meister, Christoph Ament, Nils Dreifke

Abstract:

Linear actuators are deployed in a wide range of applications. This paper presents the modeling and system identification of a variable excited linear direct drive (LDD). The LDD is designed based on linear hybrid stepper technology exhibiting the characteristic tooth structure of mover and stator. A three-phase topology provides the thrust force caused by alternating strengthening and weakening of the flux of the legs. To achieve best possible synchronous operation, the phases are commutated sinusoidal. Despite the fact that these LDDs provide high dynamics and drive forces, noise emission limits their operation in calm workspaces. To overcome this drawback an additional excitation of the magnetic circuit is introduced to LDD using additional enabling coils instead of permanent magnets. The new degree of freedom can be used to reduce force variations and related noise by varying the excitation flux that is usually generated by permanent magnets. Hence, an identified simulation model is necessary to analyze the effects of this modification. Especially the force variations must be modeled well in order to reduce them sufficiently. The model can be divided into three parts: the current dynamics, the mechanics and the force functions. These subsystems are described with differential equations or nonlinear analytic functions, respectively. Ordinary nonlinear differential equations are derived and transformed into state space representation. Experiments have been carried out on a test rig to identify the system parameters of the complete model. Static and dynamic simulation based optimizations are utilized for identification. The results are verified in time and frequency domain. Finally, the identified model provides a basis for later design of control strategies to reduce existing force variations.

Keywords: Force variations, linear direct drive, modeling and system identification, variable excitation flux.

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Authors: Bassam Atieh Rajabi, Sai Peck Lee

Abstract:

Business Process Modeling (BPM) is the first and most important step in business process management lifecycle. Graph based formalism and rule based formalism are the two most predominant formalisms on which process modeling languages are developed. BPM technology continues to face challenges in coping with dynamic business environments where requirements and goals are constantly changing at the execution time. Graph based formalisms incur problems to react to dynamic changes in Business Process (BP) at the runtime instances. In this research, an adaptive and flexible framework based on the integration between Object Oriented diagramming technique and Petri Net modeling language is proposed in order to support change management techniques for BPM and increase the representation capability for Object Oriented modeling for the dynamic changes in the runtime instances. The proposed framework is applied in a higher education environment to achieve flexible, updatable and dynamic BP.

Keywords: Business Process Modeling, Change Management, Graph Based Modeling, Rule Based Modeling, Object Oriented PetriNet.

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

Abstract:

This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, control systems, observer systems, unscented Kalman filter, nonlinear vehicle dynamics.

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Authors: Ke Zhao, Ballarat Colin Richardson, Jerry Courvisanos, John Crawford

Abstract:

Climate change has profound consequences for the agriculture of south-eastern Australia and its climate-induced water shortage in the Murray-Darling Basin. Post Keynesian Economics (PKE) macro-dynamics, along with Kaleckian investment and growth theory, are used to develop an ecological-economic system dynamics model of this complex nonlinear river basin system. The Murray- Darling Basin Simulation Model (MDB-SM) uses the principles of PKE to incorporate the fundamental uncertainty of economic behaviors of farmers regarding the investments they make and the climate change they face, particularly as regards water ecosystem services. MDB-SM provides a framework for macroeconomic policies, especially for long-term fiscal policy and for policy directed at the sustainability of agricultural water, as measured by socio-economic well-being considerations, which include sustainable consumption and investment in the river basin. The model can also reproduce other ecological and economic aspects and, for certain parameters and initial values, exhibit endogenous business cycles and ecological sustainability with realistic characteristics. Most importantly, MDBSM provides a platform for the analysis of alternative economic policy scenarios. These results reveal the importance of understanding water ecosystem adaptation under climate change by integrating a PKE macroeconomic analytical framework with the system dynamics modelling approach. Once parameterised and supplied with historical initial values, MDB-SM should prove to be a practical tool to provide alternative long-term policy simulations of agricultural water and socio-economic well-being.

Keywords: Agricultural water, Macroeconomic dynamics, Modeling, Investment dynamics, Sustainability, Unemployment, Economics, Keynesian, Kaleckian.

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Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

Abstract:

In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

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Authors: Yuan L. Lai, Yong R. Chen, Jui P. Hung, Tzuo L. Luo, Hsi H. Hsiao

Abstract:

Chatter vibration has been a troublesome problem for a machine tool toward the high precision and high speed machining. Essentially, the machining performance is determined by the dynamic characteristics of the machine tool structure and dynamics of cutting process. Therefore the dynamic vibration behavior of spindle tool system greatly determines the performance of machine tool. The purpose of this study is to investigate the influences of the machine frame structure on the dynamic frequency of spindle tool unit through finite element modeling approach. To this end, a realistic finite element model of the vertical milling system was created by incorporated the spindle-bearing model into the spindle head stock of the machine frame. Using this model, the dynamic characteristics of the milling machines with different structural designs of spindle head stock and identical spindle tool unit were demonstrated. The results of the finite element modeling reveal that the spindle tool unit behaves more compliant when the excited frequency approaches the natural mode of the spindle tool; while the spindle tool show a higher dynamic stiffness at lower frequency that may be initiated by the structural mode of milling head. Under this condition, it is concluded that the structural configuration of spindle head stock associated with the vertical column of milling machine plays an important role in determining the machining dynamics of the spindle unit.

Keywords: Machine tools, Compliance, Frequency response function, Machine frame structure, Spindle unit

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