Dynamic Response of Horizontal Axis Spinning Washing Machine

One of the primary challenges in diagnostic health monitoring and control of wind turbines is compensating for the variable nature of wind loads. Given the sometimes large variations in wind speed, direction, and other operational variables (like wind shear), this paper proposes a data-driven, online rotor model identification approach. A 2 m diameter horizontal axis wind turbine rotor is first tested using experimental modal analysis techniques. Through the use of the Complex Mode Indication Function, the dominant natural frequencies and mode shapes of dynamic response of the rotor are estimated (including repeated and pseudo-repeated roots). The free dynamic response properties of the stationary rotor are compared to the forced response of the operational rotor while it is being subjected to wind and rotordynamic loads. It is demonstrated that both narrowband (rotordynamic) and broadband (wind driven) responses are amplified near resonant frequencies of the rotor. Blade loads in the flap direction of the rotor are also estimated through matrix inversion for a simulated set of rotor blade input forces and for the operational loading state of the wind turbine in a steady state condition. The analytical estimates are shown to be accurate at frequencies for which the ordinary coherence functions are near unity. The loads in operation are shown to be largest at points mid-way along the span of the blade and on one of the three blades suggesting this method could be used for usage monitoring. Based on these results, it is proposed that a measurement of upstream wind velocity will provide enhanced models for diagnostics and control by providing a leading indicator of disturbances in the loads.

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Radiotracer detergency testing in a horizontal-axis washing machine

Journal of Surfactants and Detergents ◽

10.1007/s11743-999-0070-y ◽

1999 ◽

Vol 2 (2) ◽

pp. 167-173 ◽

Cited By ~ 1

Author(s):

Deborah K. Passwater ◽

Kirk H. Raney

Keyword(s):

Horizontal Axis ◽

Washing Machine

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Suspension Design Optimization of a Washing Machine: Part I — Modeling and Validation Results

19th Design Automation Conference: Volume 1 — Mechanical System Dynamics; Concurrent and Robust Design; Design for Assembly and Manufacture; Genetic Algorithms in Design and Structural Optimization ◽

10.1115/detc1993-0300 ◽

1993 ◽

Author(s):

O. S. Türkay ◽

A. K. Tuğcu ◽

I. T. Sümer ◽

B. Kiray

Keyword(s):

Design Optimization ◽

Experimental Validation ◽

Linear Time ◽

Optimization Method ◽

Companion Paper ◽

Simulation Software ◽

Horizontal Axis ◽

Washing Machine ◽

Rigid Body Dynamic ◽

Linear Time Invariant

Abstract The development of a non-linear time invariant rigid body dynamic model and the experimental validation of the suspension system of a horizontal-axis washing machine has been discussed in previous works by the authors. In this paper (Part I), modeling and experimental validation of a different suspension configuration of a test washing machine is assessed. The simulation model predicts the transient and steady-state vertical and horizontal amplitudes within maximum errors of 10% and 14%, respectively. The results are consistent with the results of the previous work. Thus, the simulation software code is verified for a generalized suspension design optimization of horizontal-axis washing machines. In a companion paper (Part II), various formulations are discussed to select an objective function for parametric suspension design optimization and a parametric grid optimization method is implemented to the test washing machine introduced in this paper.

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Stability and dynamic analyses of a horizontal axis washing machine with a ball balancer

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2015.01.001 ◽

2015 ◽

Vol 87 ◽

pp. 131-149 ◽

Cited By ~ 10

Author(s):

Hai-Wei Chen ◽

Qiu-Ju Zhang ◽

Xiao-Qing Wu

Keyword(s):

Horizontal Axis ◽

Washing Machine ◽

Dynamic Analyses

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Semiactive Vibration Control for Horizontal Axis Washing Machine

Shock and Vibration ◽

10.1155/2015/692570 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Barış Can Yalçın ◽

Haluk Erol

Keyword(s):

Vibration Control ◽

Dynamic Stability ◽

Control Method ◽

Angular Position ◽

Angular Acceleration ◽

Suspension System ◽

Horizontal Axis ◽

Washing Machine ◽

Vibration Data ◽

Semiactive Suspension

A semiactive vibration control method is developed to cope with the dynamic stability problem of a horizontal axis washing machine. This method is based on adjusting the maximum force values produced by the semiactive suspension elements considering a washing machine’s vibration data (three axis angular position and three axis angular acceleration values in time). Before actuation signals are received by the step motors of the friction dampers, vibration data are evaluated, and then, the step motors start to narrow or expand the radius of bracelets located on the dampers. This changes the damping properties of the damper in the suspension system, and thus, the semiactive suspension system absorbs unwanted vibrations and contributes to the dynamic stability of the washing machine. To evaluate the vibration data, the angular position and angular acceleration values in three axes are defined in a function, and the maximum forces produced by semiactive suspension elements are calculated according to the gradient of this function. The relation between the dynamic stability and the walking stability is also investigated. A motion (gyroscope and accelerometer) sensor is installed on the top-front panel of the washing machine because a mathematical model of a horizontal axis washing machine suggests that the walking behavior starts around this location under some assumptions, and therefore, calculating the vibrations occurring there is crucial. Semiactive damping elements are located under the left and right sides of the tub. The proposed method is tested during the spinning cycle of washing machine operation, increasing gradually from 200 rpm to 900 rpm, which produces the most challenging vibration patterns for dynamic stability. Moreover, the sound power levels produced by the washing machine are measured to evaluate the noise performance of the washing machine while the semiactive suspension system is controlled. The effectiveness of the proposed control method is shown through experimental results.

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Flutter Limit Investigation for a Horizontal Axis Wind Turbine Blade

Journal of Vibration and Acoustics ◽

10.1115/1.4039402 ◽

2018 ◽

Vol 140 (4) ◽

Cited By ~ 9

Author(s):

Mennatullah M. Abdel Hafeez ◽

Ayman A. El-Badawy

Keyword(s):

Dynamic Response ◽

Wind Turbine ◽

Turbine Blade ◽

Nonlinear Partial Differential Equations ◽

Stability Limit ◽

Wind Turbine Blade ◽

Horizontal Axis ◽

Horizontal Axis Wind Turbine ◽

Centrifugal Stiffening ◽

Aeroelastic Model

This work presents a new aeroelastic model that governs the extensional, chordwise, flapwise, and torsional vibrations of an isolated horizontal axis wind turbine blade. The model accounts for the sectional offsets between the shear, aerodynamic, and mass centers. The centrifugal stiffening effects are also accounted for by including nonlinear strains based on an ordering scheme that retains terms up to second-order. Aerodynamic loading is derived based on a modified Theodorsen's theory adapted to account for the blade rotational motion. A set of four coupled nonlinear partial differential equations are derived using the Hamiltonian approach that are then linearized about the steady-state extensional position. The finite element method (FEM) is then employed to spatially discretize the resulting equations with the aim of obtaining an approximate solution to the blade's dynamic response, utilizing state space techniques and complex modal analysis. Investigation of the blade's flutter stability limit is carried out. Effects of parameters such as wind speed and blade sectional offsets on the flutter limit and dynamic response are also investigated.

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