Regenerative braking converts from thermal energy to electric energy and stores the electric energy different from conventional frictional braking. The regenerative braking system is a key technology for electric and hybrid electric vehicles to increase fuel efficiency. This brake system generates frictional braking force by an electro-mechanical brake and regenerative braking force operated by an electric motor. However, there are several problems due to each different characteristic of frictional brake and regenerative brake. First, the friction coefficient is changed depending on temperature, so the sum of brake torques of two brake systems is not steady. Second, characteristic differences between two brake systems generate the unexpected deceleration at transient region when shifting both systems. These problems cause unstable vehicle motion and uncomfortable feeling to drivers. To solve these problems, the thermal model of frictional brake system is developed to predict the temperature variation of the system, and then frictional brake force is calculated more accurately. From the predictive frictional brake force, a compensation control algorithm is developed to maintain the requirement of total brake force. In addition, the concurrence control algorithm is proposed that the controller gain is modified considering the dynamic characteristic of frictional brake system. Finally, the cooperative control algorithm combined two algorithms are developed to improve the vehicle driving stability and ride comfort. The performance simulator for hybrid electric vehicle is developed to tune the parameters of brake systems in the lab by using MATLAB/Simulink. The various simulations and simple experiments are implemented in order to verify the proposed algorithms, and the improvement of vehicle driving stability is proved by using the developed algorithms.
Force measurement systems using zero-compliance mechanism has been proposed and developed. In this system, the force to be measured acts on a target body (point of force) suspended by a zero-compliance mechanism consisting of two suspensions connected in series through a detection point. One of the suspensions is operated to cancel the displacement of the other. The force can be estimated from the displacement of the detection point or the relative displacement of the point of force to the detection point. The proposed force measurement system has a variety of configurations. They are classified according to location of active element, actuator for the active element, location of positive-stiffness element and control method of achieving zero-compliance. Several apparatuses developed based on the basic concept are introduced.
Comparing with other industrial structures, the nuclear reactors needs strengthen safety standard. In this research we focus on the reactor internal which are main components in the nuclear reactor. The reactor internal are classified as seismic category I which requires complete level of the seismic analysis. The seismic analysis of the reactor internal is generally performed with the numerical method such as the FE method. The main purpose of the seismic analysis of the reactor internal is to identify the accurate dynamic behaviors, and it requires thorough inspection of the fluid-structure interaction between internals and inner coolant. Thus, it needs detailed analysis model which can reflect accurate dynamic characteristics of the reactor internal for obtaining the reliable results. However, a numerous number of degrees of freedom in the detailed FE model causes large computation costs, thus, it needs to reduce the size of the FE model for performing the seismic analysis. In this thesis, we suggest to apply the model reduction methods, which reduce the overall degrees of freedom of the total system, in order to perform the seismic analysis efficiently. The final purpose of this thesis is constructing the vibration analysis model of the reactor internal using the model reduction method which satisfies accuracy and efficiency. To develop this, researches are progressed as follows. First we constructed detailed FE model of the reactor internal. In order to verify the FE model, the modal test with the scaled-down model which reflects the geometries and boundary conditions of the original reactor internal is performed. Second, the model reduction methods using this thesis are reviewed and application method for the reactor internal is introduced. The validity of the model reduction method is verified with the simple numerical examples and the detail application method is suggested. Then, it is applied to the reactor internal in the APR (Advanced Power Reactor) 1400 and the system-integrated small modular nuclear reactor (SMART; System-integrated Modular Advanced ReacTor), and the reduced models of the reactor internal are verified in the static and dynamic problems. Finally, the seismic analysis was performed with the suggested reduced model which most satisfies efficiency and accuracy. With the seismic analysis model, the time history analysis is performed to extract important seismic responses at the specified locations. Moreover, the stress analysis is also performed to identify that the reactor internal satisfy the seismic design, and design modification is suggested to reduce the stress intensity at the support locations. As a result, the reduced model shows reliable results compared with the full model, moreover, it shows great efficiency by reducing total computation time. The reduced model is expected for applying other types of vibration analyses such as the flow-induced vibration analysis and loss of the coolant accident analysis, and it can contribute to the improvement of structural integrity assessment of the reactor.
Squeal often generates in car disc brakes. Brake squeal gives discomfort for driver. Also, it is misled abnormality of the system, therefore car maker has many troubles with claims from customers. Disc brake squeal is classified in terms of its generation mechanism. It has been found in previous studies that two types of squeal exist in disc brakes. One is called out-of-plane squeal, and the other is called in-plane squeal. There are many reports that treat the out-of-plane squeal caused by Coulomb friction. Recently, the occurrence of in-plane squeal has been increasing, and the mechanism of in-plane squeal is not yet fully understood. This paper clarifies the characteristic of the in-plane squeal by using an actual machine experimentally. The vibration mode of in-plane squeal is investigated. Additionally, the effect of brake pad thickness on squeal and the frictional characteristics of disc brakes are investigated. From these experiments, the generation mechanism of in-plane squeal is confirmed. A simple analytical model is also set up. The analysis model was consisted of disc and brake pads which are expressed as beams with a concentrated mass model. It is confirm that the characteristics of the unstable vibration agree well with those of the in-plane squeal generated in the floating type of car disc brake. And influence on in-plane squeal by additional mass to rotor using this linear analysis model is investigated.
In recent years, increment of speed and power of automobiles, railways and aircrafts contribute to be required high load power, durability and safety for the machine parts. In the automotive industry, it has been advocated to secure competitiveness by quiet and comfort of the car. However, complex friction vibration resulting from the pursuit of high-functionality has become a problem frequently. In particular, in the disc brake, although braking and safety driving at high speed driving has been demanded, still vibration problems that occur have needed to be solved. In late years, in these development trends, the problem of new vibration that called hot judder that produce heat occurs frequently in disc brakes. However, the automotive industry has not been clarified also generation mechanism not only prevent method because hot judder has phenomena due to heat and vibration. In previous study, hot Judder cause a buckling due to thermoelastic instabilities (TEI) over time by causing disk rotor and brake pad induce thermal expansion to unevenness the contact force. However, studies from the viewpoint of the self-excited vibration with thermoelastic due to friction has not been researched, the generation mechanism of hot judder is not clarified. We deal with hot judder as a self-excited vibration, and clarify the generation mechanism of the vibration.
This study concerns in-plane squeal of disk brake. In disk brake which is used in motor vehicle, as a result of progress in reducing out-of-plane squeal which caused by the coupling of the natural vibration of the out-plane direction of the disk and caliper of natural vibration, In-plane squeal which is caused by disk vibrates in the circumferential direction has become a problem. However, in-plane squeal has remained in the confirmation of the phenomenon caused by the test using actual equipment to this, the essence of the phenomenon is not clear. And since the deformation, such as expansion and contraction in the in-plane direction of the disk is not transmitted vibration in the air, there is a question of whether not the squeal does not occur. In this study, we focused on the natural vibration which disk brake vibrate in in-plane and out-plane at the same time, as a cause of in-plane squeal. At first, we verify the natural vibration mode by impact for disk brake which in-plane squeal has occurred. Secondly, reproduce the squeal and make the grasp of the in-plane squealing phenomenon by experimental apparatus which simplified a structure of the disk brake. Then from the results, we create an analysis model that be composed of only the essential elements that affect the squeal and to verify the validity of the squeal mechanism that is proposed by complex eigenvalue analysis of the model.
A long flexible shaft such as a lance tube in a soot blower and a drillstring in a rotary drilling system exhibits friction-induced vibration resulting in a whirling motion. This paper investigates the behavior of a vertical flexible shaft whirling due to the frictional force and examines the effect of an intermediate support on the whirling motion. The experimental system investigated has a vertical shaft which rotates at a constant speed by means of a motor mounted at the top end of the shaft. The bottom end of the shaft is located at the center of a rubber ring so that the frictional force acts when the shaft is deflected. The results of the experiment clarifies the frequency and amplitude of the whirl at various speed of the shaft rotation as well as an effective position of the intermediate support for suppressing the vibration.
Gears of automatic transmissions are shifted with friction force of a multiplate wet clutch. In the wet friction clutch, undesirable vibration and noise can occur when gears are shifted. In this study, we conducted experiments on vibration and noise to understand the generation mechanism in a wet clutch system. An experimental setup was designed to realize a system composed of a transmitting shaft and a clutch drum to fix a separator plate (S/P) in a wet friction clutch. A friction plate (F/P) was rotated by a motor and the S/P was pressed down on F/P. The shaft was supported by a leaf spring which gave the torsional stiffness. The vibration of the transmitting shaft and the S/P were measured with a laser displacement sensor and a 3-axis accelerometer, respectively. Another 3-axis accelerometer was attached to the top of the clutch drum to measure the bending vibration of the shaft-clutch drum system. The sound pressure was measured with a microphone. The results to be obtained are as follows: (1) The S/P's out-of-plane and radial acceleration waveform of around 120 Hz and the sudden increase of sound pressure of around 940 Hz were observed just after the contact state between the S/P and the F/P transited from stick to slip. (2) The S/P's circumferential acceleration waveform of around 470 Hz was observed at the same timing. (3) The clutch drum's circumferential and radial acceleration waveform of around 500 Hz and its out-of-plane acceleration waveform of around 260 Hz were observed just after the contact state between the S/P and the F/P transited from stick to slip. (4) The clutch drum's circumferential and radial acceleration waveform of around 1460 Hz was observed just after the relative velocity between the S/P and the F/P marked its local maximum value.
Generating mechanism of self-excited vibration of a friction clutch due to asymmetricity in the stiffness matrix is studied theoretically. It was shown that asymmetricity in the stiffness matrix is generated by nonlinearity of the disk springs, which connect the friction disks in a rotating disk, and imperfection of the spring constants in circumferential direction. Eigenvalue analyses has shown the possibility of generation of the self-excited vibration. Furthermore, drastic increase in the real part of the eigenvalue occurs when two natural frequencies coincide. Generation condition of the self-excited vibration is sensitively changed depending on nonlinearity of the springs, thrust force and number of revolutions of the disk. The natural modes and time histories in the self-excited vibration are also investigated.
Pattern formation phenomena due to time delay often occur in contact rotating systems. In the previous study, we have established a stability analysis method based on the existence condition in stable and unstable boundary in not only the system with a single time delay but also the system with multiple time delays. In case of the system with a single time delay, it is possible to obtain large amount of information in small amount of calculation time since the fundamental equations are expressed as the generalized eigenvalue problem. However, in case of the system with multiple time delays, calculation time is increased, because another method, for example Newton's method, is required to solve the fundamental equations. To reduce the calculation time, we have proposed iterative calculation method which divides the fundamental equations into equations with small dimensions. However, the proposal method was not applicable when the number of polygons is increased. Therefore, in this report, we improved the iterative calculation method by switching a formula to be solved. In addition, we verify the accuracy of the improved method and compare it with the conventional method in calculation time.
Recently, aircraft parts have been lightened for low fuel consumption. However, the parts such as jet engine turbine case reduce heat resistance for thinning. So it has been required thinning with heat resistance material. However, cutting heat resistance workpiece of low stiffness that thinning causes contributes chatter vibration. In this study, the phenomenon of chatter vibration is elucidated and predicted. By chatter vibration measurement in several workpiece, chatter vibration frequency and chatter vibration mode in cutting workpiece were found out. Chatter vibration measurement was practiced with 72 displacement sensors to circumferential direction. It turned out chatter vibration is similar to the natural vibration of workpiece and self-excited vibration, which is caused by coupling two vibrations near the cutting tool position. To confirm the relationship between chatter vibration and natural vibration, natural vibration of several workpiece got. By impact test, workpiece's natural frequency and natural vibration mode were found out. Modal analysis by impact test impacted 72 points of the test piece to circumferential direction. It turned out vibration mode at the lowest natural frequency accord with occurred chatter vibration mode. Vibration mode at the lowest natural frequency depends on workpiece's size. These phenomena are compared with the experiment of the different work of the diameter that reached in the past. It shows a similar tendency. So chatter vibration mode is predicted by vibration mode at the lowest natural frequency found thickness and length that became no dimension at a diameter.
This paper theoretically investigated the unstable vibrations of the blades of floating offshore wind turbines. The blade is modeled as a rigid flat plate and pinned to the rotating shaft by a rotational spring. The blade is subjected to the vertical, harmonic excitation due to waves and the wind with vertically uniform speed. The equation of motion for the inclination of the blade includes the parametric excitation terms which have the excitation frequency of the wave and the rotational speed of the blade. In the theoretical analysis for the linearized model, the periodic solution of the blade at the boundaries of the unstable regions is assumed to determine the expression for the unstable regions, and the influence of the wave excitation and the stiffness of the rotational spring on the unstable regions are examined. These theoretical results are compared with the simulation results. As a result, it is found that the amplitude of the wave excitation affects the number and the width of the unstable regions. In the theoretical analysis for the nonlinear model, the swept sine test is conducted to calculate the frequency response curves. It is found that the frequency response curves bent to the left due to the soft-type nonlinearity of the system, but the rotational speeds at the unstable regions calculated in the linearized model are almost in agreement with the results of the swept sine tests.
For the forced excitation of a large structure such an airplane using one actuator, all of the natural vibration modes cannot be excited because the vibration does not propagate in the entire structure. Therefore, vibration test of a large structure uses a lot of actuators. When we drive a lot of actuators by multi-point excitation using centralized control, we have to adjust command signals, such as excitation frequencies, magnitude and phase of the excitation force, to every natural vibration mode. However, it takes a long time to measure natural vibrations in this way. Thus, we use a method for driving at resonance point by using the self-excited vibration generated by the local feedback control that an excitation point corresponds to a vibration detection point. However, the self-excited vibration cannot excite all of the natural vibration modes because some natural vibration modes have changed to the other one which is easily excited. Then, we use forced entrainment to excite all of the natural vibration modes by giving continuous exciting force to the actuator situated on the tip of the object in order to synchronize the self-excited vibration actuators. We carried out an experiment about excited point and excited force performing more appropriate, and as a result, we found an appropriate those. Therefore, we carried out an experiment about excited point and excited force performing more appropriate, and as a result, we found an appropriate those. By doing forced entrainment properly, all of the natural vibrations could be measured.
This study applies a self-organizing map (SOM) to a structural health monitoring (SHM). The SOM is a kind of neural network and visualizes complex relationship of multi-dimensional data. The learning by the SOM enables us to convert the nonlinear statistical relationships among high-dimensional data into simple geometric relationships, usually a two dimensional grid of nodes. The SHM is a technique which diagnoses the structural safeness and finds damages from structural response. The present method uses the SOM to discriminate between vibration response of intact and damaged structures. In this method, we estimate the damage by visual change of the SOM. The present method requires only information about output signal of vibration without any prior information or numerical models of structures, allowing to accept the complicated and unknown structure. The effectiveness of present method is evaluated with the Carbon Fiber Reinforced Plastic (CFRP). The obtained results from numerical analysis and experiment revealed that our method is effective in SHM problems.
We have developed a Duffing oscillator forced by a relaxation oscillator, the dynamical behavior of which is determined by the duty ratio of discharge to charge duration for the relaxation oscillation as a bifurcation parameter. The forced Duffing oscillator undergoes a period-doubling bifurcation into chaos as the duty ratio increases. We have implemented the Duffing oscillator using an iron cantilever settled between two magnets and the relaxation oscillator using a timer circuit and a programmable accelerator. The actual motion of the forced Duffing oscillator was observed using a high-speed camera to verify its chaotic motion. We discuss the applicability of the coupled nonlinear oscillators to an actuator for mixing fluids.
The symptoms of a hand-arm vibration syndrome characterized by Raynaud's disease are caused by long-term use of hand-held vibrating tools, and by excessive exposure to hand-arm vibrations. The purpose of this research is to develop a hand-held vibrating tool using self-synchronization phenomena in order to solve the problem of the hand-arm vibration syndrome. We focus on the development of a vibration mechanism for an electric hammer used to crush concrete, rock ground and asphalt. In the previous report, an elementary models, the impact model with one oscillator and that with two oscillators, suitable for an electric hammer were proposed and it was analytically and experimentally confirmed that the synchronized solutions in two oscillator model are able to achieve a good balance between vibration control and excitation. In this report, we suggest a hand-held new two oscillator model aiming at practical use with the knowledge that we got from previous two oscillator model and perform a study on optimal design of new one by numerical computation.
To use elliptical vibration, it can separate and transport the work which material and shape is similar at the same time. When the vertical vibration of elliptical vibration is larger than 1.0G, works jump and the characteristics of transportation change considerably. But some works don't jump because negative pressure is caused on contact face. As a result, it is possible to separation and transportation by the presence of jump. However, it is difficult to separate works with little difference and tiny works. In this study, authors try these works by using elliptical vibration which has high frequency of driving frequency. But authors are concerned that transportation velocity of tiny works decrease by using elliptical vibration which has high frequency of driving frequency. So, authors think that to separate and to transport of the works need to take steps to cope with the situation by raising the horizontal acceleration of the elliptical vibration. First, author examined that the influence of driving frequency on jump limit and stability of the separation. Next, authors examined that the influence of driving frequency and horizontal acceleration of elliptical vibration on transportation velocity. Finally, from a result of these examinations, authors choose optimal driving condition of the tiny works with little difference in the face side and reverse side. In this condition, authors try separation and transportation a lot of tiny works at fast and stable using elliptical vibration.
An overhead traveling crane is widely used at ports and factories, and it plays an important role in the mass transportation system. The main trouble in operation of the overhead traveling crane is that the residual vibration of a cargo often occurs at the end of motion. At present, the prevention of the residual vibration has to depend on the proficient skills of operators. Therefore, the automatic operation system of the overhead traveling crane is strongly desired for an efficient and safe transportation. In our former research, a new type of open-loop control method has been proposed for suppressing the residual vibration. This method is based on the dynamical property that the residual vibration does not occur in a linear undamped system when it is excited by an external force which does not involve the components of natural frequencies of the system. The authors have applied this property to a nonlinear damped system and developed an efficient method to derive an adequate orbit of the trolley of the overhead traveling crane which enables complete prevention of the residual vibration of the cargo. However, there is a problem that fast motion of the trolley results in large swing motion of the cargo. This paper proposes an optimization method to design the motion of the trolley which minimizes the angular displacement of the cargo during transportation.
In this paper, we treat the point-to-point (PTP) motion of a rotary crane system, whose load attached to a boom moves in the two-dimensional plane, and then propose a feedforward control technique for suppressing the residual sway motion after positioning. In particular, we attempt to add robustness to parameter variations on the proposed feedforward control technique. In the proposed control technique, the trajectory for the PTP motion is expressed by the combination of cycloidal and trigonometric functions. The profile of the generated trajectory depends on the coefficients of the trigonometric function. Thus, we tune the coefficients by a particle swarm optimization algorithm so as to minimize the residual sway motion, in which the objective function for the tuning is defined to consider the robustness to parameter variations. By driving the boom of the rotary crane along the obtained optimal trajectory, the antisway motion can be realized even if the parameter of the system varies, i.e., the proposed method can establish a robust feedforward control. Results obtained from simulations and experiments demonstrate the effectiveness and feasibility of the proposed vibration control technique.
This study develops a Active Wheel Damper Device (AWD) that can be attached easily to the boom sprayer. The AWD achieves lightweight and higher inertia by the flywheel and can be mounted on the flexible structure easily. In addition, this AWD can construct realize sky-hook control easily because of it can measure the absolute angular velocity of the flexible structure by the gyro sensor. Therefore, the AWD uses Sky-hook with Disturbance Cancellation (SWDC) control that combined control system of sky-hook control and disturbance cancellation control. Damping performance of AWD has been confirmed by presented studies, but for practical use of AWD, reduction of production cost of AWD is more necessary. Then, we suppose deterioration of resolution due to using the low cost and low resolution controller. In addition, we examine whether the performance of AWD can be kept when adding the dynamic quantizer. In the previous study, we have shown the influence of torque of motor on control performance, but not yet carried out a study on the effect of the sampling period. In this paper, we clarify the relationship between the sampling period of the controller and the maximum torque of the motor by introducing angular-momentum resolution.
This study evaluates the vibration-isolation performances of the vibration-isolation table when the continuous increase / decrease method of the actuator number based on the proposed force re-distribution method is applied. This study deals with a vibration-isolation table supported by redundant number actuators to distribute the load on each actuators, which means that the table is supported by actuators more than the degrees of freedom (DOF) of the table's motion. And, authors have proposed the technique to change a control system stably when increasing / decreasing the number of the actuators according to change of weight and / or a center of gravity of the load object or actuator breaks down. Therefore, this study evaluates the control performances of the technique for increasing / decreasing the number of actuators by the frequency response for disturbance input when increasing / decreasing the number of actuators. The proposed method is a basic technology necessary for the realization of long-term continuous operation while replacing the actuator to avoid from performance deterioration, and realizing scalability which is the ability to flexiblly add/remove the actuators to support the vibration-isolation table.
The author have studied damping devices which utilizes nonlinearity. Among them, switched shunt damping using PZT element is a techniquewhich utilizes the switch of the inductancein the shunt circuit. This dampingtechniqueis applicable to thin plates and beams, but not to massive bodies. In this report, based on the knowledge obtained from the switched shunt damping, a new damping device which is applicable to massive bodies is discussed. An inductance in an LCR circuit corresponds to a mass in a mechanical vibratory system. Thus, this report proposes a damper in which additional mass is switched on or off using friction force like a clutch mechanism. Its damping performance is discussed through numerical simulation.
This paper deals with practical vibration control of electromagnetic vibration of the inverter motor stator. The iron stator of the inverter motor is modeled by a perfect circular ring. To quench the forced vibration of the stator caused by the rotating distributed electromagnetic force, single mass is set on the circular stator, and it is supported by the two springs. Moreover, two Houde dampers are installed on the outside of the circular stator. The solutions of forced vibration are obtained by using the ring theory and the finite element method. The following were made clear; (1) By setting an mass at the position of hoop of cos mode and setting spring supports at the position of hoop of sin mode, those resonance frequencies are separated enough each other. As a result, the vibration amplitude of motor stator becomes lower. (2) Moreover by setting two Houde dampers with the interval of hoop and node of the considered mode, the vibration of stator is quenched over wide frequency region around the resonance. (3) It is shown by the finite element method that the legs of motor stator have the similar effect as spring supports. (4) The results obtained by the ring theory coincide with those by the finite element method qualitatively.
The vibration suppression characteristics of two DOF dynamic absorber with proportional damping coefficients for two DOF system are investigated. We found that there are no fixed points in the frequency response function, but there are four concentration points for small proportional coefficients for the damping. Two concentration points are near the first natural frequency of original system, and another two concentration points are near the second natural frequency. Then we treat the concentration points as the fixed points, and the fixed points theory by Den Hartog is applied. The dynamic absorber with mass proportional damping is more efficient than stiffness proportional damping, but the difference is a little. Then the dynamic absorber with stiffness proportional damping is practical because the mass proportional damping means the sky hook damper and is difficult to install.
The present study investigates the vibration suppression for a structure with low natural frequency using a dynamic absorber which is connected to a main system with two magnetic springs. It is important for the assurance of safety and the improvement of reliability to suppress vibration of flexible structures such as skyscrapers and space structures whose natural frequencies are very low. Though some countermeasures against a low frequency vibration such as a pendulum dynamic absorber have been proposed, the passive control technique for a very low frequency vibration can stand further improvement. In the present experimental apparatus, the main system and the dynamic absorber are composed of two rigid body pendulums in order to have a very low natural frequency. Two magnetic springs connecting between the main system and the dynamic absorber are composed of three permanent magnets whose same magnetic poles are faced each other and can adjust the natural frequency of the dynamic absorber by changing the distance between the magnets. It was confirmed by conducting the time history response analysis by the direct numerical integration that it is effective for the transient response by tuning to the optimal parameters of the dynamic absorber derived according to the fixed point theory. Furthermore, free vibration test results using the experimental apparatus revealed the effect of the dynamic absorber with magnetic spring on a very low frequency vibration and the experimental results agreed qualitatively with the numerical analysis results.
Achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified that the active wave controller includes √s and √s terms. Those terms are realized as a 1/2-order derivative and 3/2-order derivative using fractional calculus. The active wave controller is realized as connected using fractional calculus, which is shown to be an important step for analysis. Results show that the control effect is extremely high when both a shear-force actuator and a bending-moment actuator are applied. However, the control effect is degraded considerably when only the bending-moment actuator is used because it is not called perfect active-wave-control anymore. As a subject for future work, the realization of the perfect active wave control supplemented with a shear-force actuator can be pointed out. A noncontact-type shear-force actuator using an electromagnet and so on will be required.
A torque converter is an element to transfer torque from the engine to the gear train in an automatic transmission vehicle. There is a damper spring on the lock-up clutch in the torque converter that reduces the amplitude of vibration caused by engine combustion. The damper is designed using a piecewise-linear spring with three stages in order to address a problem of space limitations. However, the damper causes a nonlinear vibration called subharmonic vibration of order 1/2. The frequency of the subharmonic vibration is half of the engine forced vibration frequency. In this study, in order to clarify the occurrence mechanism of the subharmonic vibration caused by the non-linearity of a piecewise-linear spring, fundamental experiments and numerical analysis were performed. The experimental setup is single-degree-of-freedom system that has two stiffness stages and the numerical analysis was performed under same condition as the experiment by using shooting method. According to the results of the experiments and numerical analysis, it was found that the subharmonic vibration occurs when the excitation frequency is near the twice of the resonance frequency and the equilibrium point is around a switching point of spring stiffness, and the smaller stiffness ratio and larger damping can suppress the subharmonic vibration. Also, the experimental and analytical results were well agreed with each other and the correctness of the experimental results were confirmed.
This paper proposes a new method for design of damping in the roller pendulum system to be used for dynamic vibration absorber. Generally the shape of the roller using cylindrical, but in a proposed method using a regular polygonal prism. At first, damping characteristics of typical rigid polygonal prism is discussed theoretically. Next, natural frequency of roller pendulum is discussed theoretically. Finally, vibration characteristic of polygonal roller is confirmed by numerical calculation based on rigid multi-body dynamics.
This paper investigates the vibration control of inclination systems by using pendulum vibration absorbers (PVAs). Two kinds of structures are examined; the first one, named as system A, is an SDOF inclination structure to which a pendulum is attached and is subjected to an external, harmonic moment, and the second one, named as system B, is a 2DOF structure, consisting of the vertical and inclination vibrations, to which two pendula are attached and subjected to an external, harmonic force. In the theoretical analysis, van der Pol's methods are employed to determine the frequency response curves. The response curves are compared with simulation results to verify the validity of the theoretical analysis. The autoparametric resonances in the pendula occur when the natural frequencies of the structures and pendula satisfy the 2:1 tuning conditions, and then the vibrations of the structures can be suppressed. The influence of the position of pendula on the performance of the PVAs is investigated. The influence of the deviation of the tuning conditions on the performance of the PVAs are also investigated. The deviation causes Hopf bifurcation to appear, followed by amplitude modulated motions including chaotic vibrations. In system B, a PVA for the vertical vibration of the structure works more effectively when it is attached near the position of the external force.
Elevator rope for high-rise building vibrates largely due to the resonance of the building and the elevator rope by the displacement of the building induced by strong winds and earthquakes. As building heights increase, elevator rope becomes longer. These factors cause problems of collisions and entanglement to the hoistway equipment of the elevator. Therefore, suppression of elevator rope vibration is desired. In previous paper, when elevator cage is stationary, a practical method for reducing the rope vibration by using vibration suppressors is proposed for relaxing the restricted elevator operation. The advantage of using the vibration suppressors for reducing the rope lateral vibration is demonstrated through numerical calculation. Further, an exact solution to the free vibration of the rope with vibration suppressors located at 1/N from both ends of the rope has been presented in the case where N is an odd number. However, in the case where N is an even number, no exact solution of the free vibration has yet been obtained. In this paper, an exact solution to the free vibration of this case (N is an even number) is presented, when center position of the rope is pulled. The rope is modeled with string. Finite difference analyses of the rope vibration with vibration suppressor are also performed. The calculated results of the finite difference analyses are in good agreement with those of the exact solution.
A rational method of dimensional reduction is developed in order to analyze accurately a nonlinear vibration generated in a large-scale structure with locally strong nonlinearity, asymmetry and non-proportional damping. In the proposed method, the state variables of linear nodes are transformed into the modal coordinates by using the complex constrained modes that is obtained by fixing the nonlinear nodes, and a small number of modal coordinates that have a significant effect on the computational accuracy of the solution are selected and utilized in the analysis by combining them with the state variables of nonlinear nodes that are expressed in the physical coordinates. The remaining modes that have little effect on the computational accuracy are appropriately approximated and are eliminated from the system. From the reduced model constructed by these procedures, the steady state periodic solution and the stability, the transient solution and the quasi-periodic solution can be computed with a very high degree of computational accuracy and at a high computational speed.
In this study, a new analytical procedure on nonlinear vibrations of a post-buckled stepped beam. The beam is divided into a few segments to express the geometry of the stepped beam. The deflection of the beam is expanded with the mode shape function that is expressed with the product of truncated power series and trigonometric functions. Taking the axial displacements, the deflections, slopes, bending moments and shearing forces at the nodes of the segments as unknown variables, nonlinear coupled ordinary differential equations are derived with the Galerkin procedure. Different from the previous analysis, the axial displacements at the both ends of the segments are expressed in terms of deflection, which makes it possible to consider nonlinear coupling between lateral and axial deformation of a stepped beam. These numerical results on nonlinear vibrations are compared with the experimental results.
This paper propose the method that obtain a reduced-order model without exchange of the base vectors. The results are as follows: 1) The proposed method will increase sequentially correction terms from the linear eigen mode using samples of the solution space. 2) Proportional to the number of correction terms, the reduced-order model will have a good accuracy for the motion with a larger amplitude.
This study was intended to reduce the gear noise, and for this purpose, the visualization of strain distribution in gear teeth was accomplished by means of the combination of photo-elasticity technique and a high-speed camera. Prior to finding the mechanical factor of the gear noise, the dynamic strain distribution in gear teeth under lubricated condition was studied by the photo-elasticity technique in this paper. Gear teeth under operation are exposed to severe and complex condition of high contact pressure in meshing area and slipping surface with different curvature. For that reason, serious problems might have been taken place on the noise, vibration and lubrication during operation. Regarding to the gear noise, there have been appeared lots of researches, and a variety of effects on the gear noise have been put together systematically. However, the relationship between the gear noise and the condition of meshing has not been clarified yet. In order to understand the mechanism at the meshing point, it is important to know the dynamic strain distribution in gear teeth during operation. In this experiment, the gears were made of transparent epoxy resin. The photo-elasticity technique was applied for visualization of strain distribution around meshing area of gears, and the fringe patterns caused by strain distribution were recorded by a high-speed camera. As a result, the change of the strain distribution by number of meshing was observed, and the effect of slipping contact and grease became apparent from the strain distribution.
Collision vibration systems are usually modeled as a nonlinear spring whose characteristics are described by the broken line model. These systems are called piecewise-linear systems. A piecewise-linear system is highly nonlinear, and it is usually difficult to predict the system response using any general analytical solution. If the effects of design parameters such as clearance size and dynamic nonlinearity of the systems are known, the structures can be designed to be safer and more comfortable. This paper deals with forced collision vibration in a mass-spring system for two-degree-of-freedom. The analytical model is mass-damper-spring system having two masses in which one mass is subjected to an exciting vibration with arbitrary functions. Then the restoring force, which has characteristics of an asymmetric piecewise-linear system, collides elastically to another mass when amplitude of the mass increases farther than clearance. In order to analyze resulting vibration and colliding force, the Fourier series method is applied and analytical solutions for this system are derived. Next, following the analytical solutions, numerical calculations are performed. Effects of amplitude ratio of excitation, nonlinearity of the system and mass ratio on the resonance curve and colliding force are shown numerically. For verification of the analytical solutions, numerical simulations are performed by the Runge-Kutta method, and numerical results based on analytical solutions are compared with numerical simulation results. As a result, the analytical solutions are in a fairy good agreement with the numerical simulation results.
This research deals with rebound vibration behavior of mirror inside a SLR camera. The differences of the mirror vibration phenomena is tested by using the two-rectangular-metal-plates model, which is bonded by double-sided tape. This bonded mirror model is fixed by a bolt and a nut on the horizontal rotatable shaft. In collision experiment, the bonded mirror model swings down freely and rotates about a shaft. Vibration behavior of mirror models is measured by laser displacement meter. As a result, the variation of maximum rebound angles have relationship with stopper position and the bonded position of the double-sided tape. The rebound angle is suppressed by changing the bonded position of mirror model in particular. In the experiment condition which is measured lower rebound angle, the mirror part and the body part show at a different vibration behavior and generate the opposite force each other.
The uneven-exposure is rarely occurring at the msanufacturing stage in the focal-plain-shutter for SLR camera. The possible cause of unevenness-exposure is shutter-blades vibration. The cause of vibration is the gap between the shutter blades and pins. This study focuses on the backlash of arm with drive-unit. Simplify shutter-blades model is used on transient motion experiment. The motion of the blade is measured by laser displacement meter and high speed camera. As the result, it became clear that the blade collides with pins and vibrates. The amount of vibration was decided by maximum displacement of the blade tip. The maximum displacement is calculated theoretically. The theoretical value corresponded reasonably well with measurement value. The maximum displacement became small when the distance between hole center and pin center on horizontal axis becomes large.
Response characteristics of a single-degree-of-freedom linear system subjected to non-Gaussian random excitation are investigated. The excitation is assumed to be a stationary stochastic process characterized by the non-Gaussian probability density and the power spectrum with the bandwidth and dominant frequency parameters. As the probability density of the excitation, bimodal distribution and Laplace distribution are used. The excitation is generated by solving an Itô stochastic differential equation numerically. Monte Carlo simulation is performed to obtain the stationary response distribution of the system. The response characteristics are discussed by using the maximum value of the absolute value of the cross-correlation function between the excitation and the response. It is observed that the response distributions become similar to each other when the maximum values are almost the same value. The shape of the stationary response distribution becomes the shape of the distribution of the excitation when the maximum value is close to one. When the maximum value is around 0.85, the stationary response distribution becomes the middle shape between the distribution of the excitation and the Gaussian distribution. When the maximum value is less than 0.6, the stationary response distribution becomes almost Gaussian distribution. The shapes of the stationary response distributions can be predicted roughly from the maximum value of the absolute value of the cross-correlation function without numerical simulation, because the maximum value of the cross-correlation can be calculated from the frequency response function of the system and the power spectrum of the excitation regardless of the distribution of the excitation.
The analytical method using the equivalent non-Gaussian excitation method and the Hermite moment model is proposed to obtain the stationary response distribution and the mean upcrossing rate of linear systems subjected to non-Gaussian random excitation. The excitation is prescribed by the non-Gaussian probability density function and the power spectrum. In this paper, the stationary response distribution of the system is obtained by using the Hermite moment model. The parameters in the model are determined based on the higher-order statistical moments of the response, which are calculated from the moment equations for the response and the excitation by utilizing the equivalent non-Gaussian excitation method. From the resulting response distribution, we obtain the mean upcrossing rate of the stationary response of the system. In numerical examples, the proposed method is applied to a linear system subjected to non-Gaussian excitation with Rayleigh and generalized Gaussian distributions. The analytical results are compared with Monte Carlo simulation results. It is shown that this method is valid for the non-Gaussian excitation with the asymmetric or heavy-tailed distribution and a wide range of the bandwidth.
This paper investigates the vibrations of two-layer ceiling beams (consisting of upper and lower beams) connected by a spring and dashpot when the upper beam is subjected to external harmonic excitation. In the theoretical analysis, the modal analysis approach is used to determine the natural frequencies and vibrational modes of the system, and frequency response curves of the two beams. In the numerical calculation, two cases are examined. One is the case A where the two beams have an identical material and dimension, and the other is the case B where the two beams have an identical material and different dimensions. As a result, in Case A, when the spring is connected at the middle of the beams, as its spring constant K increases, the natural frequencies corresponding to the vibrational modes with the two beams in phase are constant, and the natural frequencies corresponding to the vibrational modes with the two beams out of phase increase. When K reaches a threshold value Kc, two of the natural frequencies are identical, and a magnitude relationship of these two natural frequencies is switched. When the spring is attached at a position of a certain loop of the vibrational modes with the two beams out of phase, the natural frequencies become largest. The appearance of the vibrational mode depends on the position of the external excitation, and the lower beam does not always vibrate. In Case B, the resonance frequencies shift to the excitation frequency lower than in Case A. When the two beams vibrate out of phase, the amplitudes at the peaks of the response curves significantly decrease as the viscous damping coefficient of the dashpot increases.
In this study, a new analytical method on natural frequencies and vibration modes of a thin shell-panel with clamped edge is presented. At the boundaries of two opposite edges, the shell panel is simply supported, and at the other two edges the panel is simply supported or clamped. Coordinate function of deflection is assumed with the product of power series and trigonometric function. Neglecting the effect of in-plane inertia force, the Donnell type equations are applied as the governing equation of the shell-panel. Stress function is obtained which satisfies exactly the compatibility equation with the inhomogeneous term due to the coupling with deflection and the in-plane boundary conditions. Applying Galerkin method to equation of motion, natural frequencies and vibration modes are calculated and compared with the exact result.
The objective of this study is to clarify the vibration generation mechanism of agricultural machinery caused by the interaction between the tire lugs and the road surface. It is important to investigate the lug excitation force occurring on a rolling agricultural tire in order to clarify the vibration generation mechanism. In our previous study, it is confirmed that the dynamic behavior of rolling tire is influenced by the vibration characteristics of the tire and only the rigid modes can affect the rolling tire behavior. Therefore, we modeled the tire as a circular rigid ring supported on an elastic foundation with a contact patch slip model in order to estimate the lug excitation force. An important aspect of tire modelling is the identification of the tire model parameters. In this research, the tire wheel system is modeled as a circular rigid ring connected to the wheel through the tire sidewalls with a contact patch slip model. As for an agricultural tire, the out-of-plane dynamics is also important because of cross-stich lugs. This model can describe not only the in-plane tire dynamics but also out-of-plane tire dynamics. The equations of motion of the dynamic tire model are derived and the equations of motion are rearranged to describe the in-plane and the out-of-plane dynamics. From the rearranged equations of motion, frequency equations are derived separately and calculation procedure for obtaining the natural frequencies of the rigid ring model is formulated. Furthermore, the model parameters are identified by minimizing the difference between measured and calculated natural frequencies using Downhill Simplex method. The natural frequencies and natural modes predicted by the calculation using the identified model parameters show good agreement with those obtained experimentally.
This paper discusses a new method for identifying asymmetric nonlinear vibrating systems. To understand the current status of infrastructures through their asymmetric and nonlinear vibrating behavior, system identification for those vibrating systems is very important. Identification problem of nonlinear stiffness parameter (not including asymmetricity) in vibrating systems can be solved by a method of averaging. The authors proposed such a method in a previous paper. However, there is a problem that conventional methods including the one in the previous paper cannot address the sign of nonlinear parameters and identification of asymmetric vibrating systems. Therefore, this paper proposes a new system identification method to solve these problems by identifying appropriate sign of nonlinear parameters based on movement of center-of-vibration. In this paper, identification experiment is conducted using numerical investigation, Runge-Kutta method. A nonlinear coefficient is considered in two cases: positive number and negative number. In both cases, the proposed method gives good estimated results which show good agreement with the true values when there is sufficient number of data samples available for system identification, e.g. more than 600 samples. On the other hand, estimation error in identification increases when there is small number of data samples less than 200 or data samples have small amplitude.
Vibration reduction is important to improve ride quality of railway vehicles. Damping is one of the essential characteristics of vibration phenomenon and therefore estimating and increasing damping performance of car body is considered as a significant problem. This study is aiming to identify mass, stiffness and damping matrices (called characteristic matrices in this study) from frequency response function which is obtained by some realistic excitation testing. In a previous research, Chen showed a method which estimated characteristic matrices using a response result of vibrating all particles of a kinetic model. However, it’s not realistic to apply this method in railway vehicles because it needs driving point response measurement for all reference points. In this report, we developed a procedure to estimate those matrices from frequency response functions obtained by single driving point. And we validated the proposed procedure numerically by using simple four degrees of freedom kinetic models. Since the identification procedure uses complex natural modal properties of the objective system, we firstly checked the influence by the accuracy in modal property estimation. Then we also investigated the influence of the noise contamination in measured data. It has been found that accurate modal estimation is essentially important to obtain characteristic matrices successfully. And this procedure is relatively robust against noise contamination.
In reciprocating compressors, unexpected accidents have been reported under long-term operation. Although these machines are managed by monitoring and regular maintenance, it is difficult to predict a sudden accident or a damaged part far from preventing a fatal trouble in advance. The purpose of this study is to establish a new monitoring technique to detect the state of sliding and connecting parts, where it is known that some failure often occurs. In this paper, we examined the feasibility of estimation for the state of the sliding parts in a reciprocating compressor using both the vibration characteristics in the experiment for the small apparatus and in the eigenvalue analysis based on the mathematical model. To estimate the state of the sliding portion, each spring constant is identified solving an optimum problem with constraint. Moreover, we introduce an individual parameter identification method, where assuming that the initial value for each spring constant is larger, parameter identification is carried out. As a result, it is found that we can estimate the position that has undergone changes in the rigidity of the sliding parts comparing each error function for the individual parameter identification.
In the present study, it is intended to carry out reports on the non-linear vibration system identification intended for the magnetic spring model. Higher frequency response can be effectively estimated by higher order spectral analysis. This shows an example in numerical analysis result is obtained by presenting the effectiveness of experimental identification result including the present method using the magnetic spring model.
This paper studies the dynamic characteristics of a viscoelastic material experimentally and the construction of equivalent stiffness models for the material numerically. For this purpose, the vibration tests for the viscoelastic material are carried out under the different strain amplitudes in vibration, and the master curve, which indicates the dynamic characteristics of the material for wider range of frequency, is obtained numerically by applying the W.L.F. rule. Fractional derivative models for the stress-strain relationship are then assumed for the material, and the parameters of the model are identified for each master curve, respectively. In minimizing the sum of differences between master curve’s values and the estimated values given by the assumed model is minimized numerically by using the Solver Procedure of the Microsoft EXCEL in the present study. Finally, the applicability of the fractional derivative models is discussed by comparing the numerical results.
Smartphones have been extensively used worldwide in recent years, and have functions to transfer information effectively by vibrating a panel. The panel is made of glass and fixed to the mobile phone's body by an adhesive tape. However, the vibration intensity is not strong enough and needs to be improved. Although a vast literatures dealing with vibration of plates exists, there has not been reported vibration of the glass panel fixed by the adhesive tape. This report presents simulation and experimental study on the forced vibration of glass panel used in the mobile phone. First, the authors derive an expression of the displacement of the plate by using Rayleigh-Ritz method. Here, the edges of the plate fixed by the adhesive tape are modeled by translational springs and rotational springs. Second, an experiment is conducted by using the modal analysis technique for glass test models. Third, spring constants are identified by using the Genetic Algorithm (GA) compared to natural frequencies obtained in the experiment. Fourth, steady-state response and mode shapes are calculated by using the derived equations for the plate with simply or elastic supported edges, respectively. Finally, both results are compared to confirm the validity of the present calculation method.