Determination of Machine Tool Frequency Response Function During Cutting

The dynamic compliance (frequency response function - FRF) of a machine tool structure in the cutting zone under a cutting load is one of the major dynamic characteristics that define a machine’s cutting performance. The roundness and surface finish define the quality of the manufactured parts. These characteristics are developed during finishing and semi-finishing cuts. The kinowledge of machine tool dynamic compliance, defined in these steady-state cutting conditions, ensures parts quality and increase in machine tool productivity. The dynamic compliance is usually evaluated in tests, which are performed by means of hammers or vibrators (exciters). During these tests the machine does not cut and the machine components do not move relative to each other. The loads in the machine during cutting are defined by different internal and external sources that are acting in different points of the machine and in different directions. The real spectrum and frequency range of these forces is unknown. Experimental data acquired by different types of tests clearly show the difference in dynamic compliance for the same machine tool during cutting and idling. The machine tool dynamic tests performed by different types of external exciting devices do not take in consideration the real load conditions and interactions of moving components, including the cutting process itself and external sources of vibration. The existing methods of experimental evaluation of machine tool dynamic compliance during steady-state cutting condition require dynamometers to measure the cutting force and a special sensor to measure relative displacement between the cutting tool and workpiece. The FRF that is computed from these measurements represents a dynamic characteristic of the close loop system (machine structure and cutting process) and only under certain conditions may be considered as FRF of machine tool structure itself. The theory of stationary random processes allows defining the cutting conditions, under which the obtained data represent the FRF of machine tool structure, and provide estimations of random and bias errors of this evaluation. The simplified methodology of FRF estimation, based only on measurement of the spindle and tool vibration, is also presented in this paper. This methodology is used on an assembly line to obtain FRF for machine tools performance comparison and quality assurance.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Control Valve Design Impact on Piping Vibration

Vibration of the recycle piping system on the Main Oil Line (MOL) Export Pumps from a platform in the North Sea raised concern about pipe breakage due to fatigue. Failures had already occurred in associated small bore piping and the instrument air supply lines and control accessories on the recycle flow control valves. Concern also existed due to the vibration of non-flowing pipe work and systems such as the deck structure, cable trays and other instrumentation, which included fire and gas detection systems. Many changes involving bracing of small bore attachments, stiffening of supports, adding supports and stiffing the deck structure were implemented without resolving the problem. The vibration was finally solved by adding enough pressure stages to assure the valve trim exit velcoities and energy levels were reduced to levels demonstrated historically as needed in severe service applications. This vibration energy reduction was more than 16 times. This was achieved by reducing the valve trim exit velocity from peaks of 74 m/s to 12 m/s (240 ft/s to 40 ft/s).

Multi-Axial Fatigue Damage Models of Fiber Reinforced Composites

Fiberglass reinforced composites are extensively used in various structural components. In order to insure their structural integrity, their monotonic and fatigue properties under multiaxial stress fields must be understood. Combined in-phase tension/torsion loading is applied to [±45°]4 E-glass/epoxy composite tubes under monotonic and fatigue conditions to determine the effects of multiaxial loading on its failure. Various monotonic and fatigue damage criteria are proposed. These models considered failure mode (failure plane), the energy method and the effective stress-strain method. It is observed for the majority of experiments, the failure initiated at the outer lamina layer at 45° to the tube axis. A damage criterion for multiaxial monotonic loading is proposed considering both normal and shear stress contributions on the plane of failure. The experimental data show an excellent agreement with this proposed model for various loading conditions. Other failure models are currently under investigation utilizing the stresses and strains at the composite laminate as well as stress and strain at the outer lamina layer. Multiaxial fatigue failure models are proposed considering again the plane of failure. Since the plane of the failure is subjected to mean and cyclic stresses (shear and normal) and mean and cyclic strains (shear and normal), the fatigue damage models consider the contributions of these stresses and strains to the fatigue life of the composite tube. In addition to the fatigue damage model based on the plane of failure, a multi-axial fatigue failure model is proposed considering the mean and cyclic energy during fatigue experiments. The experimental data show a good correlation between the proposed damage parameters and fatigue life of specimens with some scatter of the data. Other fatigue failure models are currently under investigation considering the loading frequency and visco-elastic properties of the composite.

Performance Evaluation of Notched Biaxial Braided Composites

Braided composites have good properties in mutually orthogonal directions, more balanced properties than traditional tape laminates, and have potentially better fatigue and impact resistance due to the interlacing. Another benefit is reduced manufacturing cost by reducing part count. Because of these potential benefits braided composites are being considered for various applications ranging from primary/secondary structures for aerospace structures [1]. These material systems are gaining popularity, in particular for the small business jets, where FAA requires take off weights of 12,500 lb. or less. The new process, Vacuum Assisted Resin Transfer Molding (VARTM), is low cost, affordable and suitable for high volume manufacturing environment. Recently the aircraft industry has been successful in manufacturing wing flaps, using carbon fiber braids and epoxy resin and the VARTM process. To utilize these VARTM manufactured braided materials to the fullest advantage (and hence to avoid underutilization), it is necessary to understand their behavior under different loading and environmental conditions. This will reduce uncertainty and hence reduce the factor of safety in the design. It is well known fact that the strength of the composite structure reduces because of discontinuities and abrupt change in the cross-section. Accurate knowledge of strength and failure mechanism of notched and unnotched composites is very important for design of composite structures. This research addresses the behavior of notched braided composites under static tensile loading.

Molecular Dynamics Study of Metal Fatigue Process

Molecular dynamics study was conducted to understand fatigue process in metals and to predict fatigue failure. As the first step, a pure metal like copper was considered for the study with defects at the atomic level such as vacancies or dislocations. The study was focused on identifying parameters which can provide indications of progressive damage accumulation in the material under cyclic loading. The results obtained by simulations were compared to macroscopic observations in the experimental studies

Passive Vibration Damping of Aluminum by 1-3 Piezocomposites

The effective properties of 1-3 piezocomposites are used to examine their passive vibration damping characteristics. An aluminum cantilever beam bonded with 1-3 piezocomposite dampers is modeled by means of “ANSYS” and “SIMULINK” softwares to investigate the dynamic behavior of the system. A method of determining the damping ratio introduced by the piezocomposite damper in conjunction with a simple resistive electrical circuit is established. The effect of volume fraction of the 1-3 piezocomposite on the damping of the system is analyzed. Damping ratio is observed to increase with rising volume fraction. At low volume fractions, the participation of piezoelectric fibers in the load-bearing pattern is to a lesser extent and hence the damping ratio is low. On the contrary as the volume fraction rises, the involvement of piezoelectric fibers increases resulting in higher damping ratios. Given that the inherent material damping in the aluminum beam is 0.0002, the additional damping provided by the bonded piezoelectric strips goes up to a maximum of 0.0042. Finally, the methodology developed in this paper can be used to model any type of vibratory structural system to determine the damping introduced by the piezocomposites.

Application of Operational Modal Analysis to a Machine Tool Testing

Modal analysis testing of a mechanical structure is performed usually by artificial excitation of a structure and measuring input forces and output responses of a mechanical system. The excitation is either transient (impact hammer testing), random, burst-random or sinusoidal (shaker testing). The modern signal processing tools enable to determine properties of a mechanical structure such as resonance frequencies, damping ratios, and mode patterns by measuring the response of the structure without using an artificial excitation. The advantage of this technique is that modal parameters of a structure may be evaluated while the structure is under actual operating conditions. That will allow developing a model within true boundary conditions and actual force and vibration levels. The machine tool structure characteristics that effect productivity and quality have to be evaluated by testing. These characteristics include natural frequencies, modes of vibration, and external sources of high level vibration. Not all modes of machine tool structure effect machine quality. As a result only the modes that are excited during cutting have to be taken in the account. This approach narrowed the frequency range, which has to be considered in test. The machine tool during cutting and/or idling is loaded by a set of external and internal exciting forces. Spectrum, frequency range and application points of these forces are unknown in many cases. Under these exciting forces the vibration between the tool and workpiece, and vibration of machine tool components are sums of many independent vibrations and may be considered as stationary random processes. This assumption allows applying the theory of stationary random processes to machine tool dynamic testing during cutting. Several characteristics of random processes are used to separate harmonic vibration from narrow-band random vibration at natural frequencies. The spectral analysis of machined surface profiles and its correlation with observed vibration allows choosing modes that have to be developed. The analysis of these modes provides a basis for machine tool structure improvement. The proposed experimental approach was verified by experiments at different machine tools. Results of these tests are presented in the paper.

FE Calculations of J-Integrals on Crack Length in a Constrained Elastomeric Disc With Crack Surface Pressures and Isothermal Loads

In this study, we performed linear and nonlinear FE (Finite Element) analyses to compute J-integrals for a centrally perforated star-shaped disc, which is made of an elastomeric material, under crack surface pressures and isothermal loads. Deformations of the disc were constrained by a circular steel ring enclosing the disc. Different crack sizes were assumed to exist in the front of the star-shaped notches. For linear the analysis, material compressibility was modeled with Poisson’s varying form 0.48 to 0.4999. In addition, with the presence of the crack surface pressure, the J-integral needs to be modified by including an additional line integral. Numerical studies showed that the value of the J-integral increases with the increase of the crack length, reaches a maximum value at 1in of crack length, and then decreases gradually. Both linear and nonlinear analyses agree qualitatively but differ quantitatively. It was also found that values of the J-integral strongly depend upon the material compressibility.

CFD Studies on Burner Secondary Air Flow

In many fossil power plants operating today, there is insufficient means to assure the proper balancing of the secondary airflows between the individual burners of wall-fired units in addition there is a problem of dust deposition on the floor. This mismatch leads to decreased boiler efficiency and increased emissions. In this study, a Computational Fluid Dynamics (CFD) modeling of a fossil power plant wind box scale model is performed using the commercial software CFX5.6. The model solves the three dimensional Reynolds averaged Navier-Stokes equations with the K-epsilon turbulence model. The CFD results are validated by the experimental data taken from a 1/8th scale model of a wall fired fossil unit. Simulations under various flow conditions are obtained to identify the optimum design in terms of the equalization of the secondary airflow through the burners.