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Engineering Vibration Analysis with Application to Control Systems - Knovel

Further, a vibration sensor is mounted to the drum for measuring the amount of vibration produced at the drum Alternatively, vibration sensor may be located on the body of the laundry machine, in order to measure the amount of vibration actually transmitted to laundry machine In the present embodiment, directly measuring the excitation frequency is unnecessary, e. Rather, a vibration sensor , such as an accelerometer, is used as a feedback sensor to directly measure the amount of vibration occuring at the drum In the alternative, the excitation frequency may be measured and used in the present invention in addition to or instead of a signal from a vibration sensor.

For the purposes of illustration, a vibration sensor is used in all embodiments of the present invention. The vibration sensor is electrically connected to an electronic controller , as well as to inlet valve and outlet valve The weight comprises an empty enclosed chamber of constant volume. The mass of weight when empty is m o A. The mass may be adjusted by adding or releasing fluid to the weight Although the present embodiment uses fluid to change the mass of weight , other means may be used to change the mass, for example, sand may be added and removed from the weight.

However, fluid is the preferred substance for use with the present embodiment. A fluid source is connected via inlet hose to the weight The electronic controller operates inlet valve to control the amount of fluid permitted to flow into the weight from the fluid source Likewise, the electronic controller operates outlet valve , which is connected to an outlet hose , to control the evacuation of fluid from the weight Outlet hose may be connected to a drain which is external to the laundry machine, or may alternatively drain into the same drainage channel as the laundry machine, or may further be pumped back into the fluid source container using a pump not shown.

The total mass of the weight , when filled with fluid, is initially chosen, off-line, based upon the lowest excitation frequency present in the system for which reduction is contemplated. The stiffness, k, of the spring is optimized for a medium value of the excitation frequency.

Module Description

If the excitation frequency increases, the total mass, m, should be reduced. If the excitation frequency decreases, then the outlet valve is closed and the inlet valve is opened, causing an increase in the total mass, m of the vibration absorber. Thus the system can be adapted on-line to changes in the excitation frequency. More particularly, FIG. In that embodiment, the stiffness, k, of the spring can be written as: EQU2 Wherein D is the diameter of the coil wire, G is the shear modulus of the spring, R is the mean coil radius of the spring, and N is the number of active coils in the spring.

Based upon equation 5 , in order to change the stiffness, k, of the spring, and thus adapt the vibration absorber, on-line, the number of active coils in the system must be changed. A vibrating body e. A small stepper motor or a DC motor is mounted to the vibrating body A helical spring is attached to the motor shaft of the stepper motor and is passed through a support bracket A mass is attached to the free end of an active spring When the motor rotates in one direction i.

According to equation 5 , increasing the number of active coils will decrease the stiffness, k, of the spring If the motor is driven in the opposite direction, it will retract coils of the spring up through the bracket , thus reducing the number of active coils and increasing the stiffness, k. The motor is controlled by an electronic controller which may be identical to that used in connection with the embodiment of FIG.

Similarly, a vibration sensor may be connected to either the vibrating body or the structure mechanically connected to the vibrating body via the mounts , as described in connection with FIG. System is similar to that of system of FIG. Likewise, a vibration sensor may be connected to either the vibrating body , or to the base structure Further, a controller is used to adjust the stiffness, k, of the spring in response to a signal from the vibration sensor.

However, the present embodiment of the system differs from that shown in FIG.

Engineering vibration analysis with application to control systems

An air pump is used to increase the air pressure inside the air bag , which is the pneumatic spring. A discharge valve , controlled by the electronic controller , may be opened to reduce the air pressure. The stiffness of the pneumatic spring is given in terms of the air pressure as: EQU3 where P is the air pressure inside the air bag, V is the volume of the air bag, A is the contact area between the air bag and the vibrating body , and n is the polytropic constant. The electronic controller is used to regulate the air pressure inside the air bag, and thus, the stiffness, k of the pneumatic spring.

In yet another embodiment of the present invention, shown in FIG. The shape memory material may be activated by an electric current generated by current source in response to sensed vibrations.


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Strips of shape metal alloy springs may be connected between the vibration absorber weight and the vibrating body A current source would provide sufficient current to the shape metal alloy springs via conductors to change the stiffness, k, of the springs Further, the number of shape memory alloy strips embedded in the spring material and connected to the current source may be varied such that current may be selectively supplied by the current source to particular strips, as determined by a signal from the controller, so that the stiffness of the springs may be adjustable in a continuous, rather than a discrete manner.

For example, the stiffness of the springs may be varied along a continuum of stiffnesses depending on the number and location of embedded shape memory alloy strips to which the current is supplied e. Further, it may be possible to continuously, rather than discretely, change the stiffness of the springs by varying the level of applied current so as to prevent a complete martinsite transition of the shape memory material, and thus vary the stiffness.


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  5. As with the previously described embodiments, the signal generated by the electronic controller is in response to a vibration signal obtained from a vibration sensor Additionally, it is possible that a vibrating body may be excited by two independant, time varying frequencies. As such the excitation force may be written as:. In cases where two such independent time varying frequencies exist, the adaptive-passive vibration absorber of the present invention may be adapted to include two adaptive vibration absorbers cascaded in series or placed along the same vibration axis.

    As such, cascaded adaptive passive vibration absorbers may be implemented using various combinations of classical systems and the embodiments described in FIGS. Furthermore, it should be noted that an adaptive vibration absorber may be composed of both adaptive stiffness and adaptive mass components. If using an adaptive spring is desired, then the resulting stiffnesses may be found by: EQU5 To guarantee physically realizable values for these stiffnesses, the following should be satisfied: EQU6 For cases wherein the mass is adapted for changes in frequency, then the following equations should be used.

    EQU7 For either of the above cases, cascaded adaptive vibration absorbers may be implemented using a combination of designs described in FIGS. Furthermore, it should be noted again that an adaptive vibration absorber can be comprised of both adaptive stiffness and adaptive mass components. This may be seen in FIG. As such, a hybrid of individual designs described in FIGS. In one example of the use of the present invention, there is shown in FIG. The system shown in FIG. In this type of system the vibrating body is separated from the main structure by means of an intermediate body or mounting system.

    The objective of the intermediate body is to minimize the transmission of vibration from the vibrating body to the main structure. As discussed herein, if the frequency of the vibrating body is variable, then passive mounts will not be effective to minimize vibration transmission over the entire frequency spectrum. As such, some form of adaptive mounts are desirable. In general, the system of FIG. The main structure 80'is composed of several vibrational modes which are coupled together, and the vibrating body 95' is assumed to be rigid with a mass M.

    In the system of FIG. Thus to find the optimal values of k o and b o , it is necessary to maximize the term 1-T 2. Maximizing 1-T 2 results in the following equations for optimal mounting system: EQU9 Z 1 and Z 2 may be obtained from a modal analysis of the main structure. However, prior art systems have adjusted the damping force using electro-rhealogical E-R fluid, shape memory alloys, or a hydraulic damper with a variable orifice. These systems have been studied by the inventor and others, and seem too complex.

    19. Introduction to Mechanical Vibration

    This invention uses a design for an adaptive mount as shown in FIG. Based on a nominal vibrating frequency and off-line modal analysis of the main structure, the passive mount characteristics k o , b o may be derived from equations 16 and 17 , and passive mounts having those characteristics may be embedded in the passive mount or connected in parallel with an adaptive vibration absorber.

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    The present vibration absorber may be adapted on-line using the designs of FIGS. Readers should be guaranteed that authors of publications present the results of their work in a clear, reliable and honest manner regardless of the fact whether they are the direct authors of publication or they took benefit of specialized help natural or legal person.

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    In order to submit your article please fill the form below. The template of the manuscript can be found here You are obliged to accepts the terms and end ethical guideline which could be found here [form submissionForm]. Vibrations in Physical Systems Vol. Find out more Accept. WE ARE 12!

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    Most machines and structures are required to operate with low levels of vibration as smooth running leads to reduced stresses and fatigue and little noise. This book provides a thorough explanation of the principles and methods used to analyse the vibrations of engineering systems, combined with a description of how these techniques and results can be applied to the study of control system dynamics. Numerous worked examples are included, as well as problems with worked solutions, and particular attention is paid to the mathematical modelling of dynamic systems and the derivation of the equations of motion.

    All engineers, practising and student, should have a good understanding of the methods of analysis available for predicting the vibration response of a system and how it can be modified to produce acceptable results. This text provides an invaluable insight into both. Some slight wear and bending to cover. Sticker on inside back cover. Delivery FAQs. Returns policy. This item will be dispatched to UK addresses via second class post within 2 working days of receipt of your order. Any additional courier charges will be applied at checkout as they vary depending on delivery address.

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