Torsional Natural Frequencies Research Articles

An improved analysis of free torsional vibration of axially loaded thin-walled beams with point-symmetric open cross-section

The objective of the paper is to analyze the influence of bimoment induced by constant axial loads on the free motion of thin-walled beams with point-symmetric open cross-section. For various boundary conditions, a closed-form solution for natural frequencies of free harmonic vibrations was derived by using a general solution of governing differential equations of motion based on Vlasov's theory. In order to investigate the effect of the bimoment on natural frequencies, the numerical examples with symmetric Z cross-section are given. The obtained results, verified using an ANSYS finite element model, demonstrate that the influence of the bimoment is important in the assessment of torsional natural frequencies.

The Effect of Bit Type on Reactive Torque and Consequent Tool-Face-Control Anomalies

Summary The oil-and-gas drilling industry has developed a large body of knowledge about methods for drilling directional wells with steerable motors. Experience indicates that more-aggressive drill bits are harder to steer. This is commonly attributed to the fact that bits with higher aggressivity produce larger torque changes for a given change in bit weight. The actual mechanics, however, of tool-face disorientation during slide events is poorly understood. This paper reports on tests conducted on a full-size drill rig aimed at understanding the mechanics of tool-face control. Tool-face orientation and other data were measured downhole at 100 Hz. Nine different bits ranging from polycrystalline diamond compact (PDC) to hybrid to roller-cone bits were tested on an adjustable-kick-off (AKO) motor bottomhole assembly (BHA) in slide mode. These tests confirm the common industry notions about the effect of aggressivity on tool-face control. They also show that angular motion of the BHA while sliding is overdamped. Tool-face orientation consequently follows the average of the torque signal generated by the bit. Furthermore, the tool-face orientation is more easily disoriented by a torque signal at a frequency near to or less than the torsional natural frequency of the drillstring. PDC bits excite this more readily than bits with rolling cones. We also identify a tool-face disorientation anomaly that we call a fast torque anomaly (FTA). FTAs occur because the bent motor/AKO has a preferred angular orientation in the borehole. FTAs have not been previously recognized, probably because they are not identifiable in mud-pulse signals. A BHA suffering FTAs would simply appear as a chaotic and profound loss of tool-face control in mud-pulse data. Hybrid and roller-cone bits caused fewer FTAs than PDC bits.

Aerodynamic stability of long span suspension bridges with low torsional natural frequencies

Classical flutter of suspended bridge decks can be avoided if the torsional frequencies are lower than the vertical. Wind tunnel tests of single boxes and twin box section models with torsional natural frequencies above and below the vertical frequency has been conducted. Flutter was avoided in all tests where the torsional frequency was lower than the vertical. But too low torsional stiffness caused large static displacements of the girder at medium–high wind speeds and steady state oscillations driven by a combination of torsional divergence and stalling behavior at the critical wind seed. In order to design aerodynamically stable suspension bridges with low torsional natural frequencies it is suggested to increase the mass moment of inertia and provide adequate torsional stiffness by the main cables spacing.

Optimization of flatbed trailer frame using the ground beam structure approach

An alternative lightweight flatbed trailer design is achieved through a multi-stage optimization procedure. Topology optimization is used to obtain the optimal layout of flatbed trailer frame beams that provide minimum compliance when subjected to bending loads and exhibits maximum torsional natural frequency. The ground structure approach is used to define the trailer frame layout by generating numerous beams connected to predefined points in the trailer. Topology optimization is formulated as a multi-objective problem subject to a mass constraint. Responses and sensitivities are evaluated using ANSYS, and the optimization problem is solved using the moving asymptotes method. The thicknesses, widths, and heights of the C-channel beams are optimized for further weight reduction while at least maintaining the structural performances of the original design. Size and shape optimizations are performed using OptiStruct. The new optimal design is approximately 13% (275 kg) lighter than and as stiff as the original design for bending loads. However, the former has 3.5 times higher torsional natural frequency than the latter. Moreover, the new optimal design has positive manufacturability because the channel beams will be made out of commercially available sheet metals. The same fabrication technology as for a conventional flatbed trailer is possibly to be used.

Nonlinear vibration response analysis of a rotor-blade system with blade-tip rubbing

An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015; J Sound Vib 357:168–194, 2015). In the proposed model, the shaft is discretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single- and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single- and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency \((f_\mathrm{r})\) coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, \(4f_\mathrm{r})\) and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

TORSIONAL NATURAL FREQUENCY TUNING BY MEANS OF PNEUMATIC FLEXIBLE SHAFT COUPLINGS

This article deals with the use of pneumatic flexible shaft couplings as device for tuning torsional natural frequencies of mechanical systems. These couplings are using air bellows as flexible elements. Their torsional stiffness can be changed by air pressure change, the natural frequencies of whole mechanical system may be adjusted on desired value.

Dynamic Analysis of a One-cylinder Engine Crankshaft

The article deals with the vibration analysis of a one-cylinder engine crankshaft. For the analysis, a sequential torsional multi-mass vibration model was created of the crank-mechanism. The natural frequencies and natural modes of the crankshaft were determined from this model. The results of the torsional model were verified with a 3D finite element model, which consists of not only the torsional, but every other natural frequency and mode of the crankshaft. From the torsional natural frequencies and the harmonic expansion of the excitation forces, the critical speeds were determined, where resonance phenomena can occur. The relative angular deflection of the two ends of the crankshaft was also determined which characterizes the torsional stiffness of the crankshaft. From the angular velocity function of the clutch, the measure of speed irregularity of the clutch was defined.

A new dynamic model of rotor–blade systems

A new dynamic model of rotor–blade systems is developed in this paper considering the lateral and torsional deformations of the shaft, gyroscopic effects of the rotor which consists of shaft and disk, and the centrifugal stiffening, spin softening and Coriolis force of the blades. In this model, the rotating flexible blades are represented by Timoshenko beams. The shaft and rigid disk are described by multiple lumped mass points (LMPs), and these points are connected by massless springs which have both lateral and torsional stiffness. LMPs are represented by the corresponding masses and mass moments of inertia in lateral and rotational directions, where each point has five degrees of freedom (dofs) excluding axial dof. Equations of motion of the rotor–blade system are derived using Hamilton׳s principle in conjunction with the assumed modes method to describe blade deformation. The proposed model is compared with both finite element (FE) model and real experiments. The proposed model is first validated by comparing the model natural frequencies and vibration responses with those obtained from an FE model. A further verification of the model is then performed by comparing the model natural frequencies at zero rotational speed with those obtained from experimental studies. The results shown a good agreement between the model predicted system characteristics and those obtained from the FE model and experimental tests. Moreover, the following interesting phenomena have been revealed from the new model based analysis: The torsional natural frequency of the system decreases with the increase of rotational speed, and the frequency veering phenomenon has been observed at high rotational speed; The complicated coupling modes, such as the blade–blade coupling mode (BB), the coupling mode between the rotor lateral vibration and blade bending (RBL), and the coupling mode between the rotor torsional vibration and blade bending (RBT), have also been observed when the number of blades increases.

A new analytical approach for determination of flexural, axial and torsional natural frequencies of beams

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

Torsional Vibration Analysis of Reciprocating Compressor Trains driven by Induction Motors

The dynamic study of electric motor driven compressors, for Oil&Gas (O&G) applications, are traditionally performed in two steps separating the mechanical and the electrical systems. The packager conducts a Torsional Vibration Analysis (TVA) modeling the mechanical system with a lumped parameter scheme, without taking into account the electrical part. The electric motor supplier later performs a source current pulsation analysis on the electric motor system, based on the TVA results. The mechanical and the electrical systems are actually linked by the electromagnetic effect. The effect of the motor air-gap on TVA has only recently been taken into account by adding a spring and a damper between motor and ground in the model. This model is more accurate than the traditional one, but is applicable only to the steady-state condition and still fails to consider the reciprocal effects between the two parts of the system. In this paper the torsional natural frequencies calculated using both the traditional and the new model have been compared. Furthermore, simulation of the complete system has been achieved through the use of LMS AMESim, multi-physics, one-dimensional simulation software that simultaneously solves the shafts rotation and electric motor voltage equation. Finally, the transient phenomena that occur during start-up have been studied.

A parametric study of coupled‐mode flutter for MW‐size wind turbine blades

AbstractWith the increasing size of offshore wind turbine rotors, the design criteria used for the blades may also evolve. Current offshore technology utilizes three relatively stiff blades in an upwind configuration. With the goal of minimizing the mass, there is an interest in the lightweight rotors that instead utilize two flexible blades oriented downwind. These longer blades are more flexible and thus susceptible to experience flow‐induced instability. Coupled‐mode flutter is one of the destructive aeroelastic instabilities that can occur in flexible structures subjected to aerodynamic loading. Because of variation in one of the system parameters, e.g., flow velocity, structural modes coalesce at a critical flow velocity, and coupled‐flutter occurs. In the present work, a parametric study is conducted in order to study the influence of the natural frequencies in the torsional and flapwise directions on the critical flutter speed for wind turbine blades. Three MW‐size wind turbine blades are studied using a three‐dimensional blade model, which includes coupled flapwise and torsional displacements. The results show that the three blades have very similar behavior as the system parameters vary. It is shown that the first torsional natural frequency and the ratio of the first torsional natural frequency to the first flapwise natural frequency are the most critical parameters affecting the onset of instability. Critical flutter speeds even lower than the blade rated speed can be observed for blades with low torsional natural frequencies. Copyright © 2015 John Wiley & Sons, Ltd.

Gear Tooth Surface Damage Fault Detection Using Induction Machine Stator Current Space Vector Analysis

A noninvasive technique for the diagnosis of gear tooth surface damage faults based upon the stator current space vector analysis is presented. The torque oscillation profile produced by the gear tooth surface damage fault in the mechanical torque experimented by the driven electrical machine is primarily investigated. This profile consists of a mechanical impact generated by the fault followed by a damped oscillation that can be identified through the mechanical system torsional natural frequency and damping factor. Through theoretical developments, it is shown that the periodic behavior of this particular shape produces fault-related frequencies in the stator current and harmonics integer multiple of the rotation frequency in the stator current space vector instantaneous frequency. The fault signature related to the gear tooth surface damage fault is predicted through the numerical simulation. The simulation results are validated through experimental tests, illustrating a possible noninvasive gear tooth surface damage fault detection with a fault sensitivity comparable to invasive methods. A dedicated experimental setup, which is based on a 250-W squirrel-cage three-phase induction machine that is shaft connected to a single-stage gear, has been used for this purpose.

Application of Concrete Segment Panels for Reduction of Torsional Vibration Responses of Girder Bridges

The dynamic flexural behaviour of railway bridges is influenced by the torsional behaviour, and the flexural response tends to be amplified as the flexural natural frequency (the 1st vibrational mode) and torsional frequency (the 2nd vibrational mode) are adjoining. To avoid this phenomenon, the installation of concrete segment panels was considered for the reinforcement of torsional stiffness by connecting bottom flanges between girders. This alternative can increase the torsional stiffness by providing the restraint in torsional vibration and reduce the influence of torsional behaviour on the amplification of flexural responses. This study investigates the effect of the concrete segment panels on the control of torsional dynamic responses and on the increment of torsional frequency. The excitation tests on a full-size bridge specimen with 30 m span length were conducted with respect to the installation length of concrete panels up to 7 m from each ends. The results show that the installation of concrete segment panel augments the torsional frequency up to 22 % while the flexural frequency keeps its original value. It is concluded that the dynamic behaviour of girder bridges can be controlled by the adjustment of installation length of concrete panels, thereby reducing the torsional responses.

Numerical Analysis on Variation of Dynamic Response of Girder Bridges with Torsional Reinforcement Panels

The dynamic flexural behaviour of the railway bridge is influenced by its torsional behaviour. Especially, in the case of girder railway bridges, the dynamic response tends to amplify when the natural frequency in flexure (1st vibration mode) is close to that in torsion (2nd vibration mode). In order to prevent such situation, it is necessary to adopt a flexural-to-torsional natural frequency ratio larger than 120%. This study proposes a solution shifting the natural frequency in torsion to high frequency range and restraining torsion by installing concrete panels on the bottom flange of the girder so as to prevent the superposition of the responses in the girder bridge. The applicability of this solution is examined by finite element analysis of the shift of the torsional natural frequency and change in the dynamic response according to the installation of the concrete panels. The analytical results for a 30 m-span girder railway bridge indicate that installing the concrete panels increases the natural frequency in torsion by restraining the torsional behaviour and reduces also the overall dynamic response. It is seen that the installation of 100 mm-thick concrete panels along a section of 4 m at both extremities of the girder can reduce the dynamic response by more than 30%.

A COMPUTATIONAL APPROACH FOR EVALUATING HELICAL COMPRESSION SPRINGS

Helical compression springs are generally synthesized and evaluated by determining the maximum torsional stress, fatigue life, natural frequency, and/or load loss due to stress relaxation. To this end, researchers have developed finite element analysis (FEA) modeling methods to simulate the design performance of helical compression springs. The intent of this paper was to make a useful contribution to the published works for evaluating round wire helical compression springs. Specifically, commercially available FEA software was used to construct a structural model of a helical compression spring to simulate its full range of compression. The proposed FEA modeling methodology considers coil-to-coil contact and the end coils were modeled as rigid surfaces. With 9 mm of compression, the predicted spring rate correlated with the analytically calculated value to within 5%.

Stochastic analysis of flow-induced dynamic instabilities of wind turbine blades

Wind turbine blades continue to grow in length to extract more energy from the wind. This trend results in more flexible blades that are more susceptible to flow-induced instabilities. Recent studies have shown that coupled-mode flutter can be a major concern for future wind turbine blades. In this work, we study the influence of uncertainty in system parameters on the onset of coupled-mode flutter for wind turbine blades. We consider two major sources of randomness: (i) flow forces through a random lift coefficient and (ii) structural properties through a random variation of the blade׳s torsional natural frequency. We use a linear stability analysis in order to predict the onset of instability and we apply the method to the NREL 5MW wind turbine blade. Both normal and uniform probability distributions are considered to describe the random parameters. For each case, the coefficient of variation (cov) is set to be equal to 0.1 and 0.2, which has been shown in the literature to be a plausible variability. We show that randomness in both the flow forces and the structural properties affect the onset of instability. In all the cases, the higher cov values result in non-negligible occurrence of instability at a blade critical rotor speed considerably lower than the value found in the absence of randomness. It is also found that the structural randomness can decrease the critical speed for the onset of coupled-mode flutter to speeds lower than the wind turbine׳s designed operational speed.

ON DRILL-STRING NATURAL TORSIONAL VIBRATIONS

When drilling oil wells, drill-pipe strings are the main components that constrain reliability and efficiency of drilling rigs. The highest number of drill-string failures is caused by pipe parting. It is suggested that pipe-parting failures are preceded by the formation of a portion having a through-thickness radial lengthwise cut or a notched portion with a smaller cross-sectional area. Neither lengthwise cut nor crack in the rod can be determined using natural frequencies of longitudinal or flexural vibrations, because in the zone of the cut there is no reduction of the area and axial moments of inertia in the rod’s cross section. Therefore, this article deals with natural torsional vibrations of a drill string having damages as a through-thickness radial lengthwise cut and as a lateral notch. It has been found that in the case of the cut or the notch located within the vibration node, natural frequencies do not depend on the lengths of these damages. As the length of the cut or the notch increases, the lower frequencies of natural torsional vibrations will decrease. For the drill-string lengthwise through-thickness cut, changes in the natural torsional vibration frequencies are considerable as compared to similar frequencies for the drill string having a lateral notch. Using two natural torsional vibration frequencies, we can determine the initial coordinate and length of the through-thickness radial lengthwise cut on the drill string. Using three natural torsional vibration frequencies, we can determine the coordinate, length and parameter of the notch.

Aeroelastic stability of a cantilevered plate in yawed subsonic flow

The aeroelastic stability of cantilevered plates with their clamped edge oriented both parallel and normal to subsonic flow is a classical fluid–structure interaction problem. When the clamped edge is parallel to the flow the system loses stability in a coupled bending and torsion motion known as wing flutter. When the clamped edge is normal to the flow the instability is exclusively bending and is referred to as flapping flag flutter. This paper explores the stability of plates during the transition between these classic aeroelastic configurations. The aeroelastic model couples a classical beam structural model to a three-dimensional vortex lattice aerodynamic model. The aeroelastic stability is evaluated in the frequency domain and the flutter boundary is presented as the plate is rotated from the flapping flag to the wing configuration. The transition between the flag-like and wing-like instability is often abrupt and the yaw angle of the flow for the transition is dependent on the relative spacing of the first torsion and second bending natural frequencies. This paper also includes ground vibration and aeroelastic experiments carried out in the Duke University Wind Tunnel that confirm the theoretical predictions.

Electromechanical Coupling Vibration of Rolling Mill Excited by Variable Frequency Harmonic

Using torque telemetry system to test the mechanical drive system of rolling mill,it is found that the torsional vibration and current signal in the electric drive system have the same obviously vibration frequency. The model of cycloconverter, synchronous motor and mechanical drive system of rolling mill are built and analysed by Matlab/Simulink and ANSYS.The simulation results show when the harmonic torque frequency and the torsional vibration natural frequency of for mechanical drive system are equal or close, the strong torsional vibration arouse It is proved that the convertor output current harmonics can induce the electromechanical coupling vibration of main mechanical drive system under the certain conditions.

Methodology for bus structure torsion stiffness and natural vibration frequency prediction based on a dimensional analysis approach

Engineering bus design requires testing of bus structures prototypes in order to guarantee a certain level of strength and an appropriate static and dynamic behavior of the bus superstructure when exposed to road loads. However, experimental testing of real bus structures is very expensive as it requires expensive resources and space. If testing is done on a scale bus model the previous required expenses are considerably reduced. Therefore, a novel methodology based on dimensional analysis applied to bus structure prediction to evaluate the bus structure static and dynamic performance is proposed. The static performance is evaluated attending to torsion stiffness and the dynamic in terms of the natural vibration frequencies and rollover threshold. A scale bus has been manufactured and dimensionless parameters have been defined in order to project the results obtained in the scale bus model to a larger model. Validation of the proposed methodology has been carried out under experimental and finite element analysis.