Dynamic Vibration Absorber Application

Dynamic Vibration Absorber Application. Application of dynamic vibration absorbers in structural vibration control under multifrequency harmonic excitations ScienceDirect Author HL Sun PQ Zhang HB Chen K Zhang XL GongCited by Publish Year 2008.

History and Principle of OperationDynamic ModelDamped Dynamic Vibration AbsorberApplication ExampleSolutionsFurther OptimizationApplication NotesConclusionsBibliographyThe dynamic vibration absorber was invented in 1909 by Hermann Frahm (US Patent #989958 issued in 1911) and since then it has been successfully used to suppress windinduced vibration and seismic response in buildings Characteristics of DVA were studied in depth by Den Hartog (1985) In the industry it has been primarily used to suppress vibration caused by a resonance condition in machinery A DVA sometimes referred to as a tuned mass damper consists of a springmass system installed on a vibrating machine In its classic form its natural frequency is tuned to match the natural frequency of the machine it is installed on Because of this tuning a DVA exerts a force on the main system that is equal and opposite to the excitation force canceling vibration at the resonant frequency In modern applications the goal is to assure the performance within specifications over a wide frequency range while minimizing the size of the device A DVA is viewed by many engineers as a singl For simplicity we will consider a dynamic model for a machine as a single degree of freedom system consisting of a single mass and a single spring We will use a similar model for the dynamic vibration absorber When the DVA is installed on the main system the result is a two degree of freedom system whose dynamic model is shown in Figure 2 In this system the coordinate x1 corresponds to the displacement of the main mass M and the coordinate x2 corresponds to the displacement of the absorber mass m The main system&#39s stiffness is represented by the equivalent spring K while the absorber system has the spring k The absorber system has a viscous damping element c while the main system is considered undamped The main system is excited by a periodic force F that in rotating machines is usually represented by residual imbalance force but could be any periodic excitation originating in the machine such as vane passing excitation in centrifugal pumps The system above is describe By adding viscous damping c to the absorber system a better attenuation in a wide frequency range can be achieved A relatively small amount of damping is needed to reduce vibration at the two natural frequencies For best effect a damped DVA should be optimized so that its tuning and damping ratios are calculated and adjusted for a specific mass ratio (Den Hartog pp 100 103) An optimized damped DVA has the same amplification factor for both natural frequencies This amplification factor X can then be calculated for any mass ratio An optimally tuned and damped system response is shown in Figure 7 The value of X is shown as well This result demonstrates that an optimized damped dynamic absorber suppresses resonance vibration within a wide frequency range This is a universal solution as it works for any frequency range The amplification factor is controlled by the mass ratio so an absorber can be designed to meet a specific vibration limit For variable speed pump applications a DVA can be designed with various optimization criteria The following example demonstrates three types of possible optimization The first solution uses an undamped DVA This solution is easy to design and implement but it requires a quite large absorber mass The second solution is an optimally tuned and damped DVA It is a universal solution for any operating speed range The third solution is optimized for the smallest absorber size Let&#39s assume that a pump motor in Figure 1 is operating at 1760rpm with a 30 percent speed turn down This defines the speed range of 1230rpm to 1760rpm For the purpose of this example let&#39s assume that the system has a natural frequency at 1800rpm The mass of the motor is 500lbs and the mass of the rotor is 200lbs The rotor is balanced to the grade G63 according to ISO1940 The maximum allowable vibration limit is 025in/s RMS Let&#39s design a dynamic vibration absorber to bring the vibration of t Common to all three solutions is the calculation of the maximum amplification factor allowable within the operating speed range For this reason steps 1 through 3 below apply to all three solutions Step 1Find the residual imbalance force For simplicity we assume that the residual imbalance is in single plane The following formula can be used Step 2Find the static deflection of the main mass under the excitation force This value would be the magnitude of vibration if no structural amplification existed To do this we will first find the equivalent system stiffness Step 3Find the allowable amplification factor X To do this we first need to convert the vibration level to peak mils from RMS velocity to find the maximum allowable displacement of mass M Solution 1 Undamped DVA The response plot for an undamped DVA solution is shown in Figure 8 This absorber uses the mass ratio μ = 025 and tuning ratio f = 070 There is no analytical formula that would help to arrive to thi Excitation forces in pumps and other rotating machines are typically functions of rotating speed Further optimization is possible if these relationships are known For example the imbalance force is proportional to the square of rotation speed In the application example above it was considered constant for clarity If we consider a proper relationship for the imbalance force the absorber mass can be further reduced because the excitation force will be lower for the lower end of the operating speed range The curves in the above example show response in the units of displacement Similar analysis can be done for units of velocity or accelerationReal life designs may not fit exactly into the dynamic model used in this article Additional analysis may be requiredAs vibration at the main system mass is suppressed the absorber mass vibration is not This should be considered in the design of the absorber spring elementOne of the advantages of a dynamic vibration absorber is that it can be tested and fine tuned without the main system Absorber mass natural frequency and the damping ratio are independent of the Parametric analysis of the main mass response in a system equipped with a dynamic vibration absorber demonstrates that resonance vibration can be successfully controlled in such a system for a wide operating speed range Various optimization methods provide a range of options for applications with variable speed machines The application example proves the feasibility of a solution involving a dynamic vibration absorber Frahm H Device for Damping Vibrations of Bodies US Patent #989958 1911 Den Hartog J P Mechanical Vibrations New York Dover 1985 (Reprint 4th edition New York McGrawHill 1956) Liu K Liu J “The damped dynamic vibration absorbers revisited and new result” Journal of Sound and Vibration 284 (2005) 11811189 flashlakeheaduca/~kliu/JSV_2005_1pdf.

(PDF) Dynamic Vibration Absorbers and its Applications

The use of dynamic vibration absorbers to control the vibration of a structure in both narrow and broadbands is discussed in this paper As a benchmark problem a plate incorporating multiple.

Application of dynamic vibration absorbers in structural

The dynamic vibration absorber was invented in 1909 by Dynamic Vibration Absorbers – Application with Variable Speed Machines Yuri Khazanov PE InCheck Technologies Inc If a resonance condition occurs in the fi eld one effective and low cost method to alleviate it is to install a dynamic vibration absorber This discussion explains how a dynamic vibration absorber can.