Structural Frequency Response Function Research Articles

Structural damage detection based on structural macro-strain mode shapes extracted from non-stationary output responses

Abstract Long-gauge fiber Bragg grating strain sensors have been widely employed because of their broader measuring range and higher sensitivity. However, current structural damage detection methods using macro-strain modal parameters are based on structural frequency response function or stationary power spectrum density, which are not applicable to non-stationary responses. To overcome this limitation, an improved method is proposed in this paper for structural damage detection based on structural macro-strain responses under unknown multi-point non-stationary excitations. First, a new concept of macro-strain energy spectrum transmissibility (MEST) is proposed using structural non-stationary macro-strain responses, and it is derived that MEST at a certain system pole equals the ratio of macro-strain mode shape. Then, the singular value decomposition technique is adopted for the MEST matrix to identify structural natural frequencies and macro-strain mode shapes. Finally, two damage detection indicators are constructed based on the identified normalized macro-strain mode shape (NMMS). The first indicator is the difference in structural NMMS before and after structural damage. The second one is based on the curvatures of structural NMMS, which can be used for structures without intact baseline. Numerical verifications are conducted to identify beam-type structural damage under multi-point non-stationary excitations or vehicle loads. Five damage scenarios with different measurement noise levels are investigated, and damage detection results validate the effectiveness of the proposed method.

Identification of modal parameters and relaxation parameter for exponential non-viscous damping system using stochastic subspace method

Non-viscous damping parameters can be identified approximately based on the frequency response function of structures. However, it is difficult or expensive to perform vibration test and layout enough amount measured points for structures. The stochastic subspace method can identify modal damping parameters only using responses data from partial measured points. This paper extends the stochastic subspace method from the viscous damping system to non-viscous damping system. In addition, the eigenvalues of the second-order form equation of motion are proved equally to the state space formulation. The identified procedure of the proposed method is given in detail. Finally, the method is validated using three numerical examples for assessing its accuracy.

Vibration and bandgap characteristics analysis of multiple beams with arbitrary connection angles

Multi-coupled beam structures can be encountered in a wide range of engineering disciplines. Due to the possible periodicity of structures, it is important to investigate their vibration and bandgap characteristics. In this study, an accurate wave-based analytical model for the in-plane vibration of a multi-coupled beam structure with arbitrary coupling angles is developed. The reflection and transmission matrices corresponding to the incident waves arriving at the angular junctions from different directions are derived. By combining these reflection and transmission matrices, the free and forced vibrations of the multi-coupled angle beam structures can be analyzed systematically and concisely. The theoretical analysis results are in good agreement with those calculated from the FEM analysis results, which verifies the accuracy of the current method. Moreover, the analytical expression of the bandgap characteristics of infinite multi-coupled beam structures is formulated. The bandgap characteristics results of the infinite multi-coupled beam structures coincide well with the frequency response function (FRF) of the finite multi-coupled beam structures, which verifies the correctness of the analytical expression of bandgap analysis. Further results show that a low-frequency and wide bandgap can be obtained by choosing the appropriate lattice constants and junction angles, which has positive significance for the efficient design and vibration attenuation of multi-coupled beam structures in practical engineering.

Mistuning Sensitivity of a Fan Bladed-Disk With Geometrical Nonlinearities

Abstract In order to decrease their environmental impact, turbo-engine manufacturers tend to increase the span of fan blades while maintaining a slender profile. This design leads to more pronounced geometrical nonlinear effects. Computing the frequency response function of such structures is complicated due to the size of their associated finite element model. Classical substructuring approaches are no longer efficient to reduce the size of the problem as all the nodes of the system must be kept since they experience nonlinear behaviors. Different reduction methodologies have been defined in the past decades to tackle such nonlinear systems. Among these strategies, the direct normal form (DNF) extends the theory of normal form to finite element models. This methodology is here applied to a single blade model. Based on the assumption of a fairly rigid disk and the cyclic symmetric properties, a full cyclic symmetric reduced-order model is computed. In this work, this methodology is extended to account for random mistuning. Such a strategy allows to perform, for instance, fast parametric studies. This paper studies the sensitivity of the random mistuning on a nonlinear open rotor system in order to help turbo-engineers in their design phase. Three ranges of the excitation level are studied. At a low level of excitation, the system is close to the linear case. For higher forcing amplitude, a high amplification factor (AF) due to the merge of an isolated branch is observed, which is detrimental for the structure. For the last range (containing the highest forcing amplitudes), the nonlinearities are highly activated, and low values of the amplification factor are obtained due to the spread of the vibrational energy over the frequency range.

Advanced numerical techniques for predicting frequency response functions

Numerical methods have been widely used to predict Frequency Response Functions (FRF) of structures. The FRF can be used to characterize structural dynamics and support sound and vibration control. Generally, frequency sweep is conducted in the FRF calculations to identify damping and resonant frequencies of structures under excitations. However, as numerical models are getting complex and larger, the demands for computational resources (e.g., CPU time, memory, disk space) are greatly increased. Lately, high performance computing (HPC) at the DoD HPC center has been used with advanced numerical techniques to reduce the overall computational time. Those advanced numerical techniques include Krylov subspace and Galerkin Projection (KGP) and Pade Approximation. Significantly CPU time reduction has been demonstrated for relatively smaller FE models. This paper will further discuss adaptive KGP by automating the frequency sweep process via calculated relative residues, then combine with Finite Element Tearing and Interconnecting (FETI) to solve for FRF of a large FEM model in the order of 60M DOF. A flat plate with viscoelastic layer will serve as an example to demonstrate accuracy and efficiency of AKGP with FETI. The benefits of using HPC with advanced numerical techniques to solve for large FEM models are clearly displayed.

Receptance coupling substructure analysis based FRF modeling for multi-segment shell with nonlinear joint interface

Multi-segment shell typical of underwater vehicles is currently important underwater equipment. Stealth performance is a key indicator to improve the working capacity of underwater vehicles. Low-noise design is an important means to improve stealthy performance. Accurate and effective identification of its structure Frequency Response Function (FRF) is the premise of low-noise design. However, the multi-section shell joint interface has many connection points, complex transmission path and typical nonlinear characteristics, which challenges the acquisition of its structural FRF. The Receptance Coupling Substructure Analysis (RCSA) is used to segment the multi-stage shell, which can realize the integration of finite element method and experimental method, and provide an effective way to obtain the FRF of multi-segment shell. At the same time, the multi-segment shell is a typical thin-wall structure, and its actual buckling process under impact is a nonlinear (large deformation) process. Therefore, the nonlinear joint interface is constructed based on linear connection, and the RCSA for nonlinear joint interface is studied. On the basis of accurately obtaining the FRF, it is of theoretical and application significance to study the low noise design of shell.

Targeted modal response control of structures with inerter-based vibration absorbers considering modal interaction effects

Inerter-based vibration absorbers (IVAs) have been widely studied for the vibration control of multi-degree-of-freedom (MDOF) structures. Common analytical optimization strategies of IVAs for controlling the modal response of a specific mode neglect the contributions from non-resonant modes (denoted as modal interaction effects hereafter), which could weaken the validity of the optimum solution, while directly employing numerical search methods usually implies expensive computational costs in repeatedly evaluating control objectives under different sets of IVA parameters. To aim at both accuracy and efficiency of optimum design solution of IVAs for targeted modal response control, the Sherman-Morrison inversion (SMI) is exploited in this paper to derive explicit expressions of frequency response functions (FRFs) of IVA-controlled structures based on an MDOF model established in modal coordinates. In this way, the non-zero off-diagonal elements and precise expressions of diagonal elements in the FRF matrix are explicitly incorporated in the design process, with full account for modal interaction effects. The SMI is further implemented to calculate the FRF matrix of structures controlled by multi-IVA (MIVA) in an iterative manner, and subsequently, design strategies for targeted modal control using (M)IVA are proposed with particular focuses on wind-resistance and seismic design. Based on a high-rise building taken as the case study, the accuracy and efficiency in calculating the FRF matrix are quantitively assessed by Monte Carlo simulations. Two design examples, i.e., using a single tuned inerter damper (TID) for wind-resistance design and using a multi-TID for seismic design, are presented to validate the precision and efficiency of proposed design strategies. The results indicate that modal interaction effects are increasingly important for the design of (M)IVAs having larger inertance or being tuned to higher modes.

Using a rhythmic human shaker to identify modal properties of a stationary human body on a footbridge

Dynamic properties of the human body are basic parameters in biomechanics and many related areas. Experimental test is the most reliable manner to obtain dynamic parameters of the human body. Traditional method usually employs shaking table test or well-designed test rig driven by a mechanical shaker, which is always expensive and sometimes not available. This paper presents a simple but efficient transmissibility-based procedure for testing the dynamic properties of a human body. The excitation is generated by a human shaker with rhythmic movement acting on a flexible structure (either a footbridge or a long-span floor). Wide band excitation frequency can be generated even excite in a narrow-band owing to the multi-harmonics of the footfall force. The procedure consists of two main steps, namely, to identify the modal properties of the supporting structure and to establish the transmissibility of the human body. The human excitation force is found to be highly correlated with the body motion based on simultaneous footfall measurement and 3D motion tracking. To this end, the human excitation force is reconstructed and calibrated using the human body motion. The structural frequency response function is established using the footfall force and the bridge acceleration. Then the modal properties of the supporting structure, i.e. the vibration frequencies, mode shapes, and damping ratios and modal mass, are identified. The performance of human excitation method is checked by conventional ambient vibration testing and impact testing methods. Transmissibility of the human body is obtained by motion measurement at the supporting point and the stationary human body. The identified resonance frequency of the human body is further modified to obtain its natural frequency since the body is heavily damped. The feasibility of the procedure is demonstrated in identification of the dynamic properties of a footbridge with a stationary occupant having different postures.

The balanced proper orthogonal decomposition applied to a class of frequency-dependent damped structures

A model reduction technique aimed at computing efficiently Frequency Response Functions of damped structures is presented. The frequency-dependent complex moduli are approximated by a mini-oscillators model, known as the Golla–Hughes–MacTavish (GHM) model, which permits to recast the original problem as a more familiar second-order, constant-coefficient system of equations. The matrix system, although much larger, is then treated by application of the Balanced Proper Orthogonal Decomposition (BPOD) which aims at approximating the transfer function matrix, or equivalently the admittance matrix, connecting forces and displacements at a specified set of points of the vibrating structure. All the necessary ingredients of the reduction strategy as well as its efficiency measured in terms of data reduction, accuracy and computational cost are shown. Two illustrative examples of increasing complexity involving a clamped cantilever beam and a realistic windshield are presented. It is shown that the admittance matrix can be approximated by matrices of very small size which computation can be speeded up via diagonalization. It is concluded that the application of BPOD combined with the GHM decomposition of the frequency-dependent algebraic system proves extremely efficient for the modeling of vibrating structures made of different materials, either viscoelastic or purely elastic.

Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test

Establishing an accurate, fast, and low-risk flutter boundary prediction method is of great significance for flight vehicle design. In this paper, a ground flutter boundary prediction method (GFBP) based on experimental structural frequency response functions (FRFs) is proposed. A low-order multi-input multi-output (MIMO) aeroelastic system is established by combining the structural FRFs acquired from a ground test and the calculated unsteady aerodynamic FRFs in physical coordinates. The multivariable Nyquist criterion is used to predict the flutter boundary. A fixed-root aluminum plate wing is selected as the research model. A GFBP experiment is carried out for the wing’s normal state, leading-edge clump weight state, and trailing-edge clump weight state. The feasibility and accuracy of the proposed method are verified by comparison with theoretical flutter results, in which the errors of flutter speed and frequency in the test statistics are no more than 1.7%. In a simulation model established by the proposed method, Monte Carlo simulation is used to study the influence of deviations in the mode frequency and damping of the structural FRFs and deviations in the positions of excitation and measurement points in the ground test. The experiment and simulation results show that the proposed method can predict the flutter boundary accurately with accurate positions of excitation and measurement points, and it has good robustness to deviations in the mode frequency and amplitude of the structural FRFs.

Extension of the Harmonic Balance Method for dynamic systems with Iwan joints

In many applications it would be advantageous to be able to compute the nonlinear Frequency Response Functions (FRF) of structures containing bolted interfaces, but to do this with time integration is expensive so more efficient methods are desired. Harmonic Balance methods are typically more efficient, yet they are difficult to apply to systems with joints because one must track the state of many points on a surface and their highly nonlinear evolution from stick to slip in each cycle of vibration. This paper proposes an adaptation of the alternating frequency time harmonic balance method that is able to compute the steady-state response and consequently the nonlinear FRFs of systems with Iwan elements in an accurate and efficient manner. Rather than including the state of all of the sliders in the state vector, the points at which the displacement across the joint reverses are identified and used as a surrogate, greatly reducing the number of state variables and making the state variables more continuous. Furthermore, the nonlinear force and the Jacobian only need to be computed for the degrees of the freedom related to the joints, improving the efficiency of the approach. While the damping in the hysteretic system is not velocity dependent, an effective damping is introduced and added to the Jacobian to improve convergence of the Newton–Raphson algorithm for frequencies near the resonance. The proposed method, dubbed as “Hysteresis Identification via Reversal Points or (HIRP)”, is tested on various models with multiple DOF and Iwan elements, including a relatively high order model of two beams with two bolted joints. The results obtained show the capability of the proposed method and its efficiency and accuracy for realistic, industrially relevant models.

Structural Reanalysis Based on FRFs Using Sherman–Morrison–Woodbury Formula

Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

Investigation of the Acoustic and Mechanical Properties of Homogenous and Hybrid Jute and Luffa Bio Composites

ABSTRACT Design and development of new biomaterials has become a necessity due to adverse effects of chemical materials on people and nature. As the mechanical properties of biomaterials are not as good as those of chemical materials, their different configurations should be developed and tested before considering them for practical applications. Acoustic and mechanical properties of homogenous and hybrid jute and luffa biocomposites are investigated here. Homogenous and hybrid composites using jute and luffa fibers and epoxy are designed and manufactured and methods for identification of the acoustic and mechanical properties are summarized. Acoustic and structural frequency response functions are measured using homogenous and hybrid composite plates to determine their natural frequencies and loss factors. Using the experimental modal parameters of the plates and their theoretical models, elasticity moduli of biomaterials are determined. The acoustic absorption properties and transmission losses of homogeneous and hybrid composites are determined using impedance tube method. Results show that homogenous and hybrid jute and luffa composites can have moderate absorption coefficients (0.1 for a thickness of 4 mm) and superior damping performance of luffa and stiffness property of jute can be used together to produce hybrid composites with high damping (2.2–2.6%) and elasticity modulus (3–5 GPa).

Rainbow metamaterials for broadband multi-frequency vibration attenuation: Numerical analysis and experimental validation

In this study, we propose a ‘rainbow’ metamaterial to achieve broadband multi-frequency vibration attenuation. The rainbow metamaterial is constituted of a Π-shaped beam partitioned into substructures by parallel plates insertions with two attached cantilever-mass acting as local resonators. Both resonators inside each substructure can be non-symmetric such that the metamaterial can have multi-frequency bandgaps. Furthermore, these cantilever-mass resonators have a progressively variant design along the beam, namely rainbow-shaped, for the purpose of achieving broader energy stop bands. Π-shaped beams partitioned by parallel plate insertions can be extended to honeycomb sandwich composites, hence the proposed rainbow metamaterial can serve as a precursor for future honeycomb composites with superior vibration attenuation for more industrial applications. A mathematical model is first developed to estimate the frequency response functions of the metamaterial. Interaction forces between resonators and the backbone structure are calculated by solving the displacement of the cantilever-mass resonators. The plate insertions are modeled as attached masses with both their translational and rotational motion considered. Subsequently, the mathematical model is verified by comparison with experimental results. Metamaterials fabricated through an additive manufacturing technique are tested with a laser doppler receptance measuring system. After the validation of the mathematical model, a numerical study is conducted to explore the influences of the resonator spatial distributions on the frequency response functions of structures. Results show that for metamaterials with both symmetric and non-symmetric resonators, rainbow-shaped resonators can introduce inertial forces inside wider frequency range when compared to the periodic resonators of the same total mass, hence broader bandgaps. Meanwhile, the attenuation inside the bandgaps decreases when the bandgap become broader. Metamaterials with broadband multi-frequency range vibration attenuation can be achieved with non-symmetric sinusoidally varying resonators.

Recent developments of faster numerical methods for fluid-structure interaction analysis

Frequency Response Functions (FRF) haves been used to aid noise and vibration designs in various industries. Those design considerations include resonance avoidance, vibration reduction, etc. Numerical methods have been widely applied to predict Frequency Response Functions (FRF) of structures. However, the computational resources (i.e., CPU time, memory, disk space) needed to solve large and detailed numerical models are getting large. Furthermore, the need to resolve resonant response peaks can drive up the number of FRF calculations required. Lately, advanced numerical techniques based on a Krylov subspace and Galerkin Projection (KGP) and Pade Approximation have been demonstrated that they can significantly accelerate the overall process by approximating the frequency dependent response (calculating the forced response at only a few frequencies, then using KGP or Pade approximates to reconstruct the FRF for the rest of desired frequency points.) This paper will present the latest enhancements to the KGP: modeling of viscoelastic material via its complex modulus representation and adaptive capability (AKGP) in automating the frequency sweep process via calculated tolerance error. To illustrate the accuracy and efficiency of the new enhancements, a numerical example will be exercised and used as a benchmark to compare different numerical tools with and without the AKGP.

Removing mass loading effects of multi-transducers using Sherman-Morrison-Woodbury formula in modal test

In the modal test of lightweight structures, the measured data is easily polluted by mass loading effects of transducers. A method is proposed to eliminate the influence of sensors for accurately estimating the frequency response functions (FRFs) of structures. Considering the situation that the multiple accelerometers lead to changes in the dynamic stiffness matrix, the corrected FRFs are derived from the original measured signals based on the Sherman-Morrison-Woodbury formula. The salient feature of the proposed strategy is that the adverse effects of sensors can be eliminated in only one step. Numerical simulations are conducted by employing a six-degrees of freedom spring-mass system, modal frequencies and mode shapes with high accuracy are obtained by measured signals. Experimental investigation is undertaken by using a laboratory solar panel. Results show that the effects of multi-transducers mass can be removed efficiently and the corrected FRFs are in good agreement with the targeted values. The excitation and measurement points are regarded as active coordinates, and the computational efficiency can be significantly improved when the presented method is applied on active coordinates.

Remote acoustic detection of cuts in a vibrating plate with stochastic input forcing in a reverberant environment.

A mechanical structure subject to vibratory forcing will often radiate sound. When remotely recorded, this sound depends on the vibratory forcing, the structure's frequency response function, and the structure-to-receiver acoustic propagation. Thus, successful remote acoustic detection of changes in a structure's vibration response between baseline and subsequent test recordings may require compensation for possible baseline-to-test changes in vibratory forcing and acoustic propagation. Compensation schemes for unknown structural forcing in an unknown reverberant environment that allow such remote detection are described here and found to be successful when the random forcing has a consistent power spectrum and the structure-radiated sound is recorded with an array of receivers. In particular, experimental results are presented for remote acoustic detection of 13-76 mm cuts in a vibrating 0.30-m-square by 3-mm-thick edge-clamped aluminum plate subject to 0.1-2 kHz base excitation in a reverberant laboratory. Radiated sound from the plate is recorded remotely with a 15-element microphone array and processed with the synthetic time reversal blind deconvolution algorithm to compensate for unknown reverberation. Cut detection success is compared for frequency-sweep and random-input forcing when this forcing is known and unknown, and when there are plate-to-array geometric changes between the baseline and test measurements.

Vibration analysis for detecting failure mode and crack location in first stage gas turbine blade

Structure frequency response testing “modal analysis” is an integral part of the development and testing of structures such as pistons, turbine blades, compressor blades, crankshafts, and connecting rods. The usefulness of this technique lies in the fact that the energy in an impulse input is distributed continuously in the frequency domain. Thus, an impulse force will excite all resonances within given frequency range. To detect a fault in the structure, one may require frequency response functions (FRFs) of structures in both conditions, before (healthy structure) and after (failed structure) fault occurs. Now by extracting modal properties from collected FRFs and by comparing modal properties, one can detect and locate the structural faults. A case study is presented in order to detect failure mode and locate cracks on a 30 MW first stage gas turbine blade made of nickel based super alloy IN738LC, which has failed after rendering a useful life of 72000 h. The root causes of failure are detected by comparing the failed blade experimental model with the failed blade computational model. It is observed that the frequencies of the real failed blade experimental model are lesser than the computational model of the failed turbine blade. This is due to the metallurgical defects, which result in loosening of stiffness at the leading and trailing edges of the blade. Further, the stress concentration areas noticed on leading and trailing edges in computational model of the failed blade at the sixth mode are well corroborated with the cracked zone seen on leading and trailing edges of a real case failed turbine blade, collected from the site. It is concluded that the blade has failed due to that the resonance at sixth modal frequency. Scanning electron microscope (SEM) images reveal the presence of corrosion pits on the surfaces of the turbine blade that lead to surface degradation, which results in crack initiation and its propagation with high-cycle fatigue. It is concluded that the failure of turbine blade occurs due to high cycle fatigue.

High speed tooltip FRF predictions of arbitrary tool-holder combinations based on operational spindle identification

Abstract The chatter vibrations in milling are avoided by selecting spindle speeds and depth of cuts from the stability lobes. However, it has been well observed that the structural dynamics of the spindle system change as a function of speed and even feed. As a result, the measurement of spindle structure's Frequency Response Function (FRF) at zero speed does not lead to an accurate prediction of stability lobes, hence the productive cutting conditions cannot be estimated accurately. In this study, an in-process identification of speed dependent FRF of the spindle structure is proposed. The spindle FRF is either measured during the rotation via impact testing, or FRF is identified from the inverse solution of critical stability limits. The tool-holder is decoupled from the spindle FRF using receptance coupling method, which leads to speed and/or feed dependent spindle shaft FRF. The tool tip FRF is then predicted by coupling the Timoshenko beam based tool-holder to spindle. The proposed method is validated in milling tests. It is shown that the chatter free material removal rates can be more accurately predicted when the spindle speed and feed dependent machine tool dynamics are considered.

Frequency Analysis of the Tool with and without Wear during Turning by Modal Analysis

The stability of a cutting process directly influences the quality of a final surface. The control of the cutting process is an important problem for machining technology. Instabilities usually manifest as harmful chatter vibrations generated during cutting. Modal testing is a form of vibration testing which is able to determine the Frequency Response Function (FRF) of the mechanical test structures. In this context, we realized a study of vibration and of deformation between a tool without defect and a tool with two cases of defects. These defects have a random shape (any form), and the contact length tool-work piece, is considered the length of defects Lc=1 mm and the height of wear has been studied for two cases: VB=0.1 and 0.2 mm. In this paper, the main focus is creating a predictive model based on vibrations of body mass. The body mass mean the amount of material that constituting the cutting tool. The loss of a part of this mass makes the tool lighter; it increases the vibration of the tool. In addition to that, the Finite Element Method (FEM) modal analysis was used to obtain the natural frequencies. In this analysis we use ANSYS software based on (FEM), it is known for its high performance, quality and ability to solve all kinds of challenging simulations. The main idea is to create defects (wear) on the flank surface in order to create a model prediction. After the creation of defects, we start the modal analysis to study the deformation and the frequency of the tool. The results indicate that the frequency response and harmonic response analysis simulated by ANSYS with various defects created. First analysis is frequency response; we find the natural frequencies vary depending on the defect. When the tool is not defective we find the natural frequencies equal 337.77 Hz but in a tool with defects (VB=0.1-0.2 and 0.3 mm) we find the natural frequencies equal 340.36 Hz, 340.69 Hz and 341.11 Hz, this shows that the quality of the surface of the defect and its shape have an impact on the vibration of the tool. Then we based on a mathematical model to compare the results of the FEM where it shows a satisfactory correlation. In addition, the results of second analysis indicate that the deformation simulation by ANSYS with varying defects created. It increases with these defects: when VB=0.1 mm, we find that the maximum normal elastic deformation equal 0.16344 mm/mm and for VB=0.2 mm, we find that the maximum normal elastic deformation equal 0.16863 mm/mm, but for a new tool we find that the maximum normal elastic deformation equal 0.014976 mm/mm. This paper is designed to be beneficial for researcher’s engineers in manufacturing area In order to provide an advance vision about the vibration and the deformation evolution of the cutting tools when there are defects (wear) at tool tip.