Dynamic Unbalance Research Articles

Optimal Design for Biped Robot Parallel Ankle Joint

After analyzing the motion mechanism of human ankle, a new type of parallel ankle joint mechanism for a biped robot is designed. The parameterized model of the mechanism is established and its kinematic and dynamic analyses are carried out, with the conclusions of the first-order influence matrix of the parallel mechanism and the relationship between the driving force in the concertina motion and the zero moment point trajectory. Considering the great difference between the actual angular velocity and the driving moment in the biped robot’s walking ankle joint, the structure parameters of the parallel mechanism are optimized through iterative calculation according to the dynamic characteristics of the ankle joint during walking, which make the driving peak power and speed of the two driving elements of the ankle joint tend to coincide and reduce the dynamic unbalance in the biped robot’s walking ankle joint. According to the analysis of the experimental results of the biped robot’s ankle joint motion, the peak-power used to drive the optimized parallel ankle joints is only about half of that used to drive serial joints, which lowers the demand of the design power for the driving components. On the premise that the dynamic characteristic of biped robot ankle joints during walking are satisfied, choosing driving components with lower power is beneficial to the reduction of bulk, mass and the energy consumption of the joints.

Monte Carlo simulation of stage separation dynamics of a multistage launch vehicle

This paper provides the formulation used for studing the cold and hot separating stages of a multistage launch vehicle. Monte Carlo simulation is employed to account for the off nominal design parameters of the bodies undergoing separation to evaluate the risk of failure for the separation event. All disturbances, effect of dynamic unbalance, residual thrust, separation disturbance caused by the separation mechanism and misalignment in cold and hot separation are analyzed to find out nonoccurrence of collision between the separation bodies. The results indicate that the current design satisfies the separation requirements.

Coupled torsional-lateral vibration of the unbalanced rotor system with external excitations

The coupled torsional-lateral model of the rotor system is set up and governing equations are derived using the Lagrange approach with six degrees of freedom. The gyroscopic effect and gravity are included. Two kinds of unbalance, namely static unbalance and dynamic unbalance, are considered in the rotor system. Torsional and lateral motions are subjected to external excitations. Through numerical simulation, the developed model is used and the coupled torsional-lateral vibrations of the unbalanced rotor system under external excitations are investigated. Some new phenomena are found and discussed.

링크모션 펀치프레스의 다이나믹 발란싱

In a link motion punch press, numerous links are interconnected and each link executes a constrained motion at high speed. As a consequence, dynamic unbalance force and moment are transmitted to the main frame of the press, which results in unwanted vibration. This degrades productivity and precise stamping work of the press. This paper presents an effective method for reducing dynamic unbalance in a link motion punch press based upon kinematic and dynamic analyses. Firstly, the kinematic analysis is carried out in order to understand the fundamental characteristics of the link motion mechanism. Then design variable approach is presented in order to automate the model setup for the mechanism whenever design changes are necessary. To obtain the inertia properties of the links such as mass, mass moment of inertia, and the center of mass, 3-dimensional CAD software was utilized. Dynamic simulations were carried out for various combinations of design changes on some links having significant influences on kinematic and dynamic behavior of the mechanism.

Oscillation adjuster and oscillation adjusting method

A vibration controller controls vibrations generated in a driven object included in a system subject to vibrations due to the dynamic unbalance or eccentricity of a rotating member driven for rotation by an electric motor. An angular position transforming unit ( 45 ) and an angular velocity transforming unit ( 47 ) transform the output signal of a rotating motion measuring means (C 1 ) into an angular position and an angular velocity, respectively. A sine calculating unit ( 55 ) calculates the sine of an angle obtained by adding up the angular position and a predetermined phase angle provided by a phase adjusting unit ( 49 ) by an adder ( 53 ). A multiplier ( 61 ) calculates the product of the output of a gain adjusting unit ( 57 ) that multiplies the output of the sine calculating unit ( 55 ) by a predetermined gain and the output of a multiplier ( 59 ) that calculates the square of the angular velocity. Again adjusting unit ( 57 ′) multiplies the output of a sine calculating unit ( 55 ′) by a predetermined gain. An adder ( 68 ) adds up the respective outputs of the multiplier ( 61 ) the gain adjusting unit ( 57 ′) and a specified torque calculating unit.

External and internal coupling effects of rotor's bending and torsional vibrations under unbalances

External and internal bending–torsion coupling effects of a rotor system with comprehensive unbalances are studied by analytical analysis and numerical simulations. Based on Lagrangian approach, a full-degree-of-freedom dynamic model of a Jeffcott rotor is developed. The harmonic balance method and the Floquet theory are combined to analyze the stability of the system equations. Numerical simulations are conducted to observe the bending–torsion coupling effects. In the formulation of rotordynamic model, two bending–torsion coupling patterns, external coupling and internal coupling, are suggested. By analytical analysis, it is concluded that the periodic solution of the system is asymptotically stable. From numerical simulations, three bending–torsion coupling effects are observed in three cases. Under static unbalance, synchronous torsional response is observed, which is the result of external coupling under unbalanced force. Under dynamic unbalance, two-time synchronous frequency torsional response is observed, which is the result of internal coupling under unbalanced moment. Under comprehensive unbalance, synchronous and two-time synchronous frequency torsional components are observed, which are the results of both external and internal couplings under unbalanced force and moment. These observations agree with the analytical analysis. It is believed that these observed phenomena should make sense in the dynamical design and fault diagnostics of a rotor system.

DISTURBANCE ATTENUATION IN TURNTABLE DYNAMIC UNBALANCE ON THE BASIS OF MULTI-PERIOD FINITE- DIMENSIONAL REPETITIVE CONTROL

The turntable having multi-period disturbance torque is obtained by setting up the dynamic unbalance model of three-axis turntable. The multi-period disturbance torque is related to three-axis rotate speed of turntable and influences localization precision, position precision and speed precision of turntable. In order to attenuate system disturbance torque of three-axis turntable, the method of multi-period finite-dimensional repetitive control is proposed and proves to be a success in attenuating the systematic error of turntable caused by multi-period disturbance. The result of simulation shows that multi-period finite-dimensional repetitive control can attenuate dynamic unbalance disturbance of turntable system effectively.

Weak and strong nonlinearities in magnetic bearings

This paper presents analysis of dynamic properties of a rigid rotor supported on passive magnetic bearings. Forced vibrations excited by dynamic unbalance are investigated both without and with the contact between the shaft and the emergency retainer bearing. The influence of weak nonlinearity of the magnetic force field on response curves is investigated on a 4 DOF system without impacts. The effects of impacts in the retainer bearing are studied on a 2 DOF system showing strong nonlinearities. Hertz's impact law and material, viscous and Coulomb-friction damping are applied for modelling the dynamic contact between the rotor and the bearing. The vibration behaviour of the system is characterized by periodic, quasi-periodic and chaotic responses.

Analysis of Faulty Vibration by Three-Dimensional Information

Some kind of machine faults such as unbalance, misalignment, looseness, and eccentricity occupy the most part of the category of fault of structure. It is important to diagnose these faults accurately to prevent the recurrence of the same fault. The unbalance includes static unbalance, couple unbalance, quasi-static unbalance and dynamic unbalance. The misalignment includes parallel misalignment and angular misalignment. In any fault of structure, vibrations both perpendicular and parallel to the rotation shaft occur, and the diredional characteristics of vibration change with the type of machine fault. If we measure vibrations in three directions by a conventional unidirectional type of vibrometer, the measured data does not include enough information for diagnosis. It is extremely difficult to diagnose the fault of structure accurately only by this information. lt is necessary to observe and analyze the movement of measured point in order to diagnose the fault and search its causes by using three directional information processing technology that measures orthogonal three directional vibrations simultaneously and uses the phase information among them. To realize it, the analysis technique of vibration information in 3-dimensional space is necessary. In this paper, we describe a new hand-held type triaxial vibrometer and its pickup. The operation principle is quite different from conventional triaxial pickups. A detailed operation principle of the new pickup is reported. Finally we propose new display method and data processing technique of vibration in 3-dimensional space.

Dynamic analysis of a spatial coupled timoshenko rotating shaft with large displacements

The dynamic simulation is presented for an axial moving flexible rotating shafts, which have large rigid motions and small elastic deformation. The effects of the axial inertia, shear deformation, rotating inertia, gyroscopic moment, and dynamic unbalance are considered based on the Timoshenko rotating shaft theory. The equations of motion and boundary conditions are derived by Hamilton principle, and the solution is obtained by using the perturbation approach and assuming mode method. This study confirms that the influence of the axial rigid motion, shear deformation, slenderness ratio and rotating speed on the dynamic behavior of Timoshenko rotating shaft is evident, especially to a high-angular velocity rotor.

F-6-3-4 Modeling of a flywheel suspension mechanism for internal disturbance estimation

As the requirement for pointing accuracy of applications spacecraft such as land observation satellite becomes higher, the attitude control is subject to more and more demanding accuracy requirement. This results in the necessity of managing internal disturbance attributed to mechanical moving parts such as rotating mirror, solar array driving mechanism, and so on. Flywheels used for attitude control actuator can be a major cause of the internal disturbance. In this paper, the disturbance torques and forces induced by a flywheel is investigated precisely based on the rotor dynamics and the contact dynamics of the supporting bearings. The wheel rotor model includes static and dynamic mass unbalance as in the common practice. The bearing model with six (6) balls reflects the actual hardware currently manufactured, which uses an angular contact bearing with relatively small preload pressure to reduce the friction torque. The most challenging part of the modeling is the contact dynamics of the bearing unit consisting of inner lace-balls-retainer-outer lace configuration. At the contact point, the normal force is a nonworking constraint force while tangential and axial forces are normally working forces given as a function of velocity components at the contact. Taking this situation into account, a flywheel model is established as a multibody system with seven (7) degrees of freedom. Based upon this modeling, spinning rigid body dynamics is evaluated as well as the precise estimation of the disturbance torques and forces, and compared with the experimental results obtained from the low friction test-bed.

3204 輪軸の静および動不つりあいが輪軸振動に与える影響(OS.6 運動・振動とその制御)

This paper describes the influence of the wheelset static and dynamic unbalance on the wheelset vibration. In the case of the model used in numerical analyses, smaller static unbalance means lager dynamic unbalance and larger lateral vibration of the wheelset. So, it can not be said that the policy of reducing static unbalance to the minimum is best.

Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model

In the paper, dynamic interaction between elastic high-speed-train car wheelset and track is studied using a discrete-continuous mechanical model. The model enables to investigate the influence of the parametric excitation from the track as well as static and dynamic unbalances of wheels and brake disks on the dynamic response of the wheelset running at various speeds on the track of various average vertical stiffness. From the results of numerical simulation it follows that particularly severe periodic resonances occur for the track of large stiffness, yielding high vertical dynamic contact forces between the wheels and rails. The maximum dynamic response has been obtained for parameters corresponding to the conditions at which the phenomenon of grumbling noise generation is usually observed in reality.

Design of attitude control system for injection of spinned payloads

One of the missions that the upper propulsive stage (UPS) of a launcher has to perform is the spinned injection of a payload into a geostationary transfer orbit, to achieve the passive stabilization of satellites until the circularization impulse. Precise specification at the injection, in particular on the orientation of the payload's geometric axis, require an active attitude control of the spinned composite (UPS + payload). This paper presents the design of the attitude control system (ACS), to achieve accurate control of the composite angular momentum orientation and composite nutation, in the presence of dynamic unbalance. This design is restricted to the main features of the ACS propulsive subsystem (thrust level, minimum impulse bit or MIB, dispersions) and is obtained with sufficient convergence conditions of a Lyapunov function. The benefits of on-board estimation of the dynamic unbalance are also evaluated. The results, confirmed by simulation, show that the proper use of the gyroscopic torques can achieve the required specifications with low constraints on the ACS propulsive subsystem. Such a subsystem, well fitted to a non-reusable stage such as the UPS, can also be implanted on spinned satellites to control their orientation.

Analysis of deceleration phenomenon of high speed rotor systems

The problem of decelerating a rotor from a high speed through its critical speeds has received very little attention in technical literature although transient processes occurring during coastdown of machinery usually provide a lot of information about their tribodynamics. The problem of deceleration is critically examined and the governing equations for a mechanical system are derived using Lagrangian dynamics. The governing non-linear equations have been solved under quasi-static conditions. The results confirm the relationship between dynamic unbalance, damping and the deceleration during coastdown.

円筒プランジ研削における振動抑制の一方法

For the purpose of obtaining practical guidelines for controlling the vibration that produces on the plunge-cut ground surface the local variations of the light reflectivity, the mechanism by which the dynamic unbalance of the rotating grinding wheel generates the dynamic variation of the instantaneous stock removal and hence the onset of the grinding vibration has been studied by theoretical analysis as well as grinding experiments. Experiments have also been carried out to optimize the method of varying the rotational speed of the wheel, of which effect was demonstrated by a former study. By monitoring the oscillation of the machine body at the frequency of the wheel rotation, it is first recommended to adjust the wheel balance to minimize the monitored oscillation prior to the dressing operation. The subsequent grinding operation has to be carried out without introducing any balance adjustment and wheel speed variation after the dressing. Effect of the balance adjust procedure in suppressing the grinding vibration is further enhanced by introducing the wheel speed variation. According to grinding test results comparing the rectangular and triangular patterns of the wheel speed variation, the former has been found more effective, which at a ±10% range variation for 4 minutes period seems to result in an optimum effect for practice.

新型の液体注入式研削と石オートバランサ

This paper describes the principle, prototype design and experimental evaluation of the performance of a new balancer system developed for automatic compensation of the dynamic unbalance of a grinding wheel. The system consists of a high response micro-delivery injector and a twenty-four-chambered pocketed ring. The balance accuracy equals the product of the mass of unit quantity of the liquid injected for every revolution of the wheel and the radius of pocketed ring. Characteristics of a prototype balancer has been found experimentally to well follow the theoretical prediction and the system is capable of suppressing the wheel head vibration to less than 0.01, μm amplitude.

Whirl Speeds and Unbalance Response of Multibearing Rotors Using Finite Elements

This paper presents dynamic modeling of rotor bearing systems with rigid disks, distributed parameter finite rotor elements and flexible, discrete multibearings. The previous works have included the effects of rotary inertia, gyroscopic moment, axial load, internal viscous and hysteretic damping and transverse shear deformations, but have not considered them all in the same model. A computer program is developed in this work to calculate the forward and backward whirl speeds, the corresponding mode shapes, the dynamic unbalance response of multibearing rotor systems and to evaluate rotor stability. It utilizes the banded property of the system matrices to reduce the computational effort for the complex eigensolution. A combined bisection and inverse iteration technique is used for the complex eigen-value problem. The combined effect of shear deformations and internal damping on the stability, forward and backward whirl speeds, as well as on the response to unbalance excitation, are investigated with the numerical examples given. This study confirms that any inherent material damping in the shaft itself does not affect the unbalance response if the bearings are isotropic, which is, however, not the case when the bearings are orthotropic causing elliptical synchronous whirl orbits.

On the Shaft End Torque and the Forced Vibrations of an Asymmetrical Shaft Carrying an Asymmetrical Rotor

In a rotating asymmetrical shaft with an asymmetrical rotor, the increase rate of total energy and the torque applied to the shaft end change with the angular positions of the static and dynamic unbalances. The response curve also changes with the angular positions of the rotor unbalances. With a rotor mounted on the middle of an asymmetrical shaft, the parallel motion of the rotor is not connected with its conical motion, and the shaft end torque can be directly obtained from the equilibrium of forces and moments. The shaft end torque in an asymmetrical shaft and an asymmetrical rotor changes with the angular positions of rotor unbalances in a similar way to the response curve.

Dynamic Behavior of an Automatic Balancer : Application to Dynamic Unbalance

Dynamic Behavior of an Automatic Balancer : Application to Dynamic Unbalance