Ender Cigeroglu

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the normal force acting on the contact interfaces, quasistatic contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the normal load. A friction model is employed to determine the three-dimensional nonlinear contact forces, and the relationship between the contact forces and the relative motion is utilized by the harmonic balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations in the harmonic balance method, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that the effect of rotational motion is significant, particularly for the in-phase vibration modes. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method. DOI: 10.1115/1.2940356

Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

a r t i c l e i n f o

A New Structural Modification Method with Additional Degrees of Freedom for Dynamic Analysis of Large Systems

Structural modification techniques are widely used to predict the dynamic characteristics of modified systems by using the information of the original and modifying systems. Nowadays, due to the increased computational power, large finite element models are regularly used. During design optimization, modifications are done on the original structure in order to meet the design requirements which require reevaluation of the dynamic response of the structure. This is a time consuming process since for each modification, the whole structure needs to be analyzed. In this study, a new structural modification method is proposed in order to decrease the computational effort during the design optimization. Proposed method uses the modal data of the original system and system matrices of the modifying structure in order to predict the modal data of the modified system which can be used for the dynamic analysis. Initially, the application of the method is presented on a lumped parameter model. Later, the proposed method is applied on a finite element model of a cantilever beam which is modified by additional systems having different number of total degrees of freedom (DOFs) and different number of connection DOFs. Modal data of the original structure and the system matrices of the modifying part are extracted from a commercial finite element software. The modal information obtained from the proposed method and the one obtained from finite element software are compared and it is observed that they are in perfect agreement if all information of the original structure is used. The effect of reduction of the original structure is as well investigated and the performance of the developed method is studied for varying the size of the modifying system. The computation time required for the determination of frequency response function is compared with other structural modification methods where significant improvement in computation time is observed.

Vibration Fatigue Analysis of a Cantilever Beam Using Different Fatigue Theories

In this study, vibration fatigue analysis of a cantilever beam is performed using an in-house numerical code. Finite element model (FEM) of the cantilever beam verified by tests is used for the analysis. Several vibration fatigue theories are used to obtain fatigue life of the cantilever beam for white noise random input and the results obtained are compared with each other. Fatigue life calculations are repeated for different damping ratios and the effect of damping ratio is studied. Moreover, using strain data obtained from cantilever beam experiments, fatigue life of the beam is determined by utilizing time domain (Rainflow counting method) and frequency domain methods, which are compared with each other. In addition to this, fatigue tests are performed on cantilever beam specimens and fatigue life results obtained experimentally are compared with that of in-house numerical code. It is observed that the accuracy of the damping ratio is very important for accurate determination of fatigue life. Furthermore, for the case considered, it is observed that the fatigue life result obtained from Dirlik method is considerably similar to that of Rainflow counting method.

Chatter Reduction in Turning by Using Piezoelectric Shunt Circuits

In this paper, the effect of piezoelectric shunt damping (PSD) on chatter vibrations in turning process is studied. Chatter is a self-excited type of vibration that develops during machining due to process-structure dynamic interactions resulting in modulated chip thickness. Chatter is an important problem, since it results in poor surface quality, reduced productivity and reduced tool life. The regenerative chatter results from phase differences between two subsequent passes of the cutting tool and occurs earlier than mode coupling chatter in most cases. In regenerative chatter theory, stability limit in the cutting process is inversely proportional to the negative real part of frequency response function (FRF) of the cutting tool-workpiece assembly. If the negative real part of the FRF at the cutting point can be decreased, depth of cut, in other words productivity rates, will increase. In piezoelectric shunt damping method, an electrical impedance is connected to a piezoelectric transducer which is bonded to the main structure. In this study, resistive – inductive – capacitive shunt circuit is used, whose elements are optimized with genetic algorithm to minimize the real part of the FRF for certain target frequencies. Afterwards, the effect of the optimized piezoelectric shunt damping on the absolute stability limit of the cutting process is investigated.

Nonlinear Time-Varying Dynamic Analysis of a Multi-Mesh Spur Gear Train

The nonlinear dynamics of a multi-mesh spur gear train is considered in this study. The gear train consists of three spur gears, with one of the gears in mesh with the other two. Dynamic model includes gear backlash in the form of clearance-type displacement functions and time variation of gear mesh stiffness. The system is reduced to a two-degree-of-freedom definite model by using the relative gear mesh displacements as the coordinates. The equations of motion are solved for periodic steady-state response by using Harmonic Balance Method (HBM). The accuracy of the HBM solutions is demonstrated by comparing them to direct numerical integration solutions. Floquet theory is applied to determine the stability of the steady-state solutions. Two different loading conditions, where the system is driven by the middle gear and driven by one of the end gears, are considered. Phase difference between the two gear meshes is determined under each loading condition and natural modes are predicted for each loading condition. The forced response due to the combination of parametric excitation and static transmission error excitation is obtained and effects of loading conditions and asymmetric positioning on the response are explored.

Output Only Functional Series Time Dependent AutoRegressive Moving Average (FS-TARMA) Modelling of Tool Acceleration Signals for Wear Estimation

In this paper, tool vibration signals obtained from a turning process are used for tool wear estimation purposes. During the cutting process, tool acceleration signals are recorded for different levels of wear. Due to non-stationarity of tool/holder systems response, Time dependent time series model of Functional Series Time dependent AutoRegressive Moving Average (FS-TARMA) type is used for modelling the signals and extraction of wear sensitive features that will be exploited in a wear estimation algorithm. Results of the analysis through FS-TARMA, reveals its higher accuracy with respect to stationary type models, since it captures time dependent properties as well, which can be used in an online tool wear estimation algorithm.

Structural Coupling of Two-Nonlinear Structures

In mechanical design, modeling and analysis of a complex structure can be simplified with dividing the structure into substructures; therefore, any change in the structure can be addressed easily which is referred as “structural coupling”. Utilization of proper coupling techniques, it is possible to understand the behavior of the whole structure by considering the behavior of its substructures. For linear structures, coupling is a common technique; however, in most of the engineering structures, nonlinearities are also encountered; therefore, it is required to extend linear coupling methods to nonlinear systems. Although, there exists studies on nonlinear coupling, existing methods are limited to coupling of structures where one substructure is linear and the other is nonlinear or two linear substructures coupled with a nonlinear element. In this paper, a structural coupling method is proposed to couple two-nonlinear substructures. Similar to linear coupling methods, the proposed method considers the compatibility of internal forces at the connection degrees of freedom in addition to displacements. Since, the substructures are nonlinear, the resulting system of nonlinear differential equations are converted into a set of nonlinear algebraic equations by using Describing Function Method, which are solved by using Newton’s method with arc-length continuation.

A new sliding-mode controller design methodology with derivative switching function for anti-lock brake system

In this study, anti-lock brake system control using sliding-mode controller is investigated. Different alternatives for the switching function and the sliding surface, involved in the structure of the sliding-mode controller, are explored. It was aimed to reach a better controller performance with less chattering and robustness to actuator imperfections. Regarding applicability, tire force response was modeled as a uniformly distributed uncertain parameter during controller designs. Controllers are simulated for both constant and varying coefficient of friction roads, with optimized design parameters. The effects of actuator first-order dynamics and transportation delay, which come up in practical implementations, were considered. The sliding-mode control structure which employs derivative switching function with integral sliding surface is originally proposed in this study. It is found to produce less chattering and provide more robustness, which could not be achieved side by side using former designs.