Blades and Towers Modal Analysis Code (BModes): Verification of Blade Modal Analysis Capability

Moment of Inertia Measurement of a CubeSat Through Object Motion Tracking of Trifilar Pendulum Oscillations

Torsional vibrations experienced by drill strings can be detrimental to drilling operations. With a goal of understanding torsional vibrations experienced by drill strings and determining means to attenuate undesired vibrations, the authors have studied the effect of adding a sinusoidal modulation to a constant rotation speed of a drill string. A combination of modeling, analysis, and experiments is used to explore the influence of this rotation input modulation on the system response. The drill string is modeled as a modified Jeffcott rotor, which is described by a system with three degrees of freedom. Considering the case of forward whirling of a rotor in continuous contact with a stator, the equations of motion are reduced to a single degree-of-freedom nonlinear oscillator describing the torsional motions. In order to understand the fast time scale and slow time scale components of the motion, the method of direct partitions of motions is used to determine an approximate response to the nonlinear oscillator. The obtained results of the analysis illustrate that with the sinusoidal modulation of the rotor drive speed, the equivalent torsion stiffness can be enhanced and the character of the friction force at the contact can be made smooth. The analyses helps bring forth the stabilizing influence of the added sinusoidal input to the rotor drive speed. Over the considered parameter ranges, the numerical results obtained with the full three degree-of-freedom model and the reduced single degree-of-freedom model are found to be in agreement with each other. Furthermore, the results from these models are found to compare well with those obtained by using the method of direct partition of motions. Experiments with a laboratory scale drill-string arrangement are to be carried out to validate the analytical and numerical findings and further explore the effectiveness of the drive speed modulation on the rotor dynamics. Introduction Slender rotating structures are used in many engineering applications. Drill strings are long rotating slender structures, which are used in drilling operations. A schematic of a rotary drill rig is shown in Fig. 1 (e.g., Liao, Balachandran, Karkoub, and Abdel-Magid, 2011). Drill strings experience different types of vibrations (axial, torsional, and lateral vibrations) that may lead to detrimental failures of a drilling system. Drill-string vibrations have attracted the attention of many researchers, and many models have been developed to understand them. Since drill strings have a large length-to-diameter ratio, typically, the first torsional natural frequency and first lateral natural frequency are close to each other. This frequency proximity and the nature of the system allows for coupling and energy transfer between the associated vibration modes. Here, as a step towards developing further understanding, a drill string is modeled as an extended planar Jeffcott rotor with gravity acting normal to the rotor. Due to the planar motions, no gyroscopic effects are considered. The extended model, which was earlier considered in the work of Vlajic, Liu, Karki, and Balachandran (2014), is shown in Fig. 2. The model is described with three degrees of freedom (DOF), namely, x and y to account for lateral motions, and theta to account for torsional motion. A large number of research efforts have focused on controlling drill-string vibrations by using different feedback control algorithms, which need measurements along the drill string. In this work, the authors propose a different control approach to mitigate whirling motions during continuous rotor-stator contact. This can be compared to a situation of a drill string being in continuous contact with the borehole. The approach is open loop in implementation and this approach is based on adding a high frequency input to the drive speed of the drill string. Given the open-loop nature, the method does not depend on any measurements along the drill string or rotary table, which could be attractive for a practical stand point. Although the current focus is on motions of a rotor with continuous stator contact, it is planned to study stick-slip and non-contact cases in the future. System Modeling, Studies, and Results As previously mentioned, the drill string is modelled as a Jeffcott rotor with three DOF. Proceeding along the lines of the group's prior work (Vlajic, Liu, Karki, and Balachandran, 2014), after some approximations for the continuous rotor-stator contact case, the 3 DOF system is reduced to a single second-order nonlinear differential equation governing the torsional motion. In Fig. 3, for a representative case with a constant drive speed, the torsional state histories obtained for the full model and the reduced model are plotted. It is noted that the final state of the motion is captured quite well. To further analyze the response during forward whirling, the reduced-order model was nondimensionalized and an approximate solution was obtained by using the method of direct partitions. This method allows one to separate slow scale motions from fast scale motions. As discussed, in the group's prior work, this method can be useful to examine whirling motions. The results obtained by directly integrating the full model as well as the reduced-order model have been compared with that obtained by using the method of direct partitions of motions. It is seen that the perturbation analyses is able to provide an approximate solution that compares well with the numerical results obtained through direct integrations. Next, this analysis is used to examine the influence of the addition of secondary frequency component. It is seen that the addition of the secondary frequency, a high-frequency one, helps smooth out the friction coefficient variation with respect to the relative speed at contact. This is found to have a beneficial effect on the motion and helps suppress large-amplitude torsional motions. Stability analysis was also conducted to examine this effect. Concluding Remarks A study has been conducted to examine the influence of sinusoidal modulation of rotor drive speed in a system, wherein the rotor experiences continuous stator contact. A single degree of-freedom reduced model is developed to study the torsion response and it is found that the addition of a high frequency input can be beneficial in attenuating rotor motions. This is believed to be useful for developing open-loop control schemes for attenuating forward whirling motions of drill strings. Results obtained from a lab scale experimental arrangement will be used to examine the effect of this drive speed modulation further and they will be reported in the conference presentation. Future studies could build on the current effort to examine cases of backward whirling. Acknowledgment: The authors would like to gratefully acknowledge the support received from the Qatar National Research Fund for NPRP Project 7-083-2-041, to pursue this collaborative work between the University of Maryland, College Park, MD, USA and Qatar University, Doha, Qatar.

A novel compliant mechanism with three degree of freedom (DOF) is proposed, based on the method of Freedom and Constraint Topology (FACT). One movement and two rotations are obtained in Case 3, Type 2 freedom space. A redundant constraint is added to improve the symmetry. The finite element modal (FEM) is established and static force analysis is conducted. Results demonstrate that the compliant mechanism is decoupled. Modal analysis is carried out with the finite element method. And four orders natural frequency and main vibration mode are obtained.

Analytical and numerical study of the effects of an elastically-linked body on sloshing

Stabilization of the non-trivial relative equilibria of a gyrostat with an elastic element in a circular orbit

Determination Of Rigid Body Characteristics From Time Domain Modal Test Data

Structural acoustics analysis of automobile parts by using finite element method

The validity of a rigid body model of a cricket ball-bat impact

Integrable cases of the problem of the free motion of a gyrostat

Based on the principle of axial active magnetic bearing system with single degree of freedom, the difference between magnetic system vibration mode and the traditional bearing system vibration mode were described. Initial four order natural frequencies and vibration mode were calculated by the module of modal analysis of ANSYS11. Axial displacement and control current influence on natural frequencies and vibration mode were also analyzed. At last they were compared with the results of experimental modal analysis. Analysis shows that there was a certain difference between the results of finite element method and experimental model analysis, but the difference was small. It provided theoretical basis for flexible system design and dynamic design.

Though more obscure than traditional flight analysis, the tendency for a rigid body to flutter or tumble in flight during unstable conditions has been analyzed through physical experiments since the 1960s. In more recent years, similar conditions have been subjected to numerical simulation to further understand the effects of dimensionless properties on unstable body motion. It is important to understand dimensionless scaling relationships to compare properties of a body to that of a scaled model or for adjusting data when manufacturing limitations exist. For example, if the geometry of a scaled object could easily be manufactured, within tolerance, but material properties force the mass moment of inertia (MMOI) to deviate from an accepted value, dimensionless scaling relationships could aid in corrections for the desired MMOI. For tumbling bodies, two important properties are the angular velocity and the mass moment of inertia. However, the relationship between dimensionless MMOI and dimensionless angular velocity remains unclear. The purpose of this study was to understand how changing MMOI affects the behavior of angular rates for a rigid body, influenced by repeatable initial conditions and try to characterize that relationship. Using four blocks of varying size and MMOI, a series of tests were conducted to subject the blocks to a range of angular velocities between 0.3 radians/sec and 36.5 radians/sec. Body rates were difficult to measure using standard recording devices; therefore, two different high-speed camera systems were used to calculate body rates. Methods: Four different block sizes were manufactured to receive two additional masses. The additional masses were inserted symmetrically about the x, y, and z axes of the block. In order to change the MMOI of the block while also preserving its mass, geometry, and density, the additional masses were placed in one of three locations. The first of four different tests involved exposing the blocks to the same initial force at a location that produced rotation about the z axis. Supported uniformly by free jets of air, the blocks traveled horizontally across a flat table. A Photron SA5 was used to record a trajectory at 500 fps, and the software Tracker was used to evaluate rates. The second test evaluated body rates as the blocks fell from a height of 243 cm. For each randomized test, the MMOI of the block was changed by adjusting the location of additional masses. Again, using a Photron SA5, high speed video was taken at 500 frames

The double slanted cantilevers are used in some micro-structure designs, which have some unique characters. In this paper, the mathematical model of the double slanted cantilevers with irregular cross-section was investigated based on the theory of material mechanics. The moment of inertia and principal axes of the cross-section was derived on some hypothesis. The displacement sensitivity was also analyzed. And FEM simulations validate the calculations. Introduction The cantilever structure is widely used in micro-structure sensors [1], such as the accelerometer and the gyroscope used in inertia navigation system [2], and micro probe used in biochemistry detection [3]. The mechanical character of the cantilever has a close relationship with its dimensions, as well as its moment of inertia and Young’s modulus, etc. The double slanted cantilever has a good performance in a mechanical sensor [4]. But there is no detailed mathematical analysis for the double cantilevers structure. This paper discussed the mechanical characteristics of a kind of double slanted cantilevers based on a mathematical model. The model grounds on the theory of mechanics of materials. For the cantilevers researched in, there is a mass block suspended on the end. And the cantilevers are slanted to the same direction with a specific angle. Modeling of the double slanted cantilevers The model of the double slanted cantilevers with a block is established as following. As is shown in Figure 1 (a), the big mass block, CEP2P3P4P1DF, which can be seen as a rigid body, is suspended on the two slanted cantilevers at point C and point D. While the two slanted cantilevers, AC and BD, which are flexible, are fixed to a base at point A and point B. The point O is the centroid of the mass block. And the cross-section is shown in Figure 1 (b), which is an irregular hexagon, equivalent to a parallelogram cut off two identical isosceles triangles at the sharp angles.

We consider the torque-free rotation of a rigid body with three distinct moment of inertia values and angular velocity components. As can be seen in the Dzhanibekov and tennis racket phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the principal intermediate moment of inertia, an unstable rotation is produced that leads to the basis of this phenomena. In this publication, the above phenomena are examined and explained analytically and applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. To begin the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Second, we further look at the limiting axisymmetric cases and examine the effect as the intermediate moment of inertia is varied. Lastly, the analytical expressions are compared with the numerical simulation to validate the results. The complete solution is then summarized and shown to clearly prove that the conservation of angular momentum is indeed preserved in the phenomena.

The structure of the long-span transmission tower is a typical nonlinear structure with the characteristics of great height, large line span, heavy overall weight and flexible tower body. The current design code only analyzes the traditional tower types, but the analysis of the truss structure of transmission tower is limited. Aiming at improving the design defects of the structure of long-span transmission towers, this paper uses the finite element software APDL to build the three-dimensional finite element model of a long-span transmission tower, to carry out the modal finite element analysis as well as to extract the specific parameters of each modal finite element mode: Modality, Natural frequency of vibration, Periodicity. The results show that the natural vibration period of the main machinery of this type of steel transmission tower is about 0.37–1.37 s; The structure of the long-span transmission tower has certain displacements in six degrees of freedom, in which the value of the X-dimensional displacement is the largest. There are some large displacements and local torsion in the high-order mode, combined with the results of modal analysis, so it is suggested to consider the structural improvement or external reinforcement of the weak parts of the long-span transmission tower.

The article discusses Takens embedding for 2D and 3D visualization of 1D time series data. The paper considers the use of topological data analysis in conjunction with Takens embedding to analyze the output information of a dynamic system - a rigid body. 3D images of curves constructed from three components of the angular velocity vector of a rigid body for various values of the main moments of inertia are constructed. Three-dimensional images of the curves constructed on the basis of the Takens embedding for the component of the angular velocity of a rigid body for various values of the principal moments of inertia are constructed. Distances between 3D images of curves are determined by constructing persistent landscape functions. Using the method of topological data analysis in conjunction with Takens embedding for image comparison allows you to classify and identify images and output information of the instrumental composition.