enidine

Technical Section:Vibration and ShockVibrationThis outline of basic vibration theory is intendedto present a simplified approach to the applicationand sizing of isolators. It will enable the designengineer to select the proper isolator to reduce theharmful effects of vibration. Obviously, real-lifesituations are more complex than this simplifiedapproach indicates.Vibration is defined as a magnitude (force,displacement, or acceleration) which oscillatesabout a reference point. Vibration is commonlyexpressed in terms of frequency, cycles persecond or Hertz (Hz).Vibration problems generally fall into two classes:1. Force excitation: The isolator is used to protectthe supporting structure from forces generated bythe supported mass (see Figure 1). An example isthe use of motor mounts in an automobile.2. Motion excitation: The isolator is used toprotect the supported mass from disturbances of thesupporting structure (see Figure 2). An example isthe use of mounts under a coordinate measuringmachine.Natural Frequency is the frequency of vibration thatwill occur if a system is disturbed from its normalposition and allowed to vibrate freely. For ourENIDINE INCORPORATEDpurposes, the natural frequency can be defined as afunction of mass and stiffness or spring rate. If thespring rate is linear, the load vs. deflection curve is astraight line (Figure 3). For instance, a load of100 lbs. will cause a deflection of .20 in.This spring will have a stiffness of:K = __ W=100 ___ = 500 lbs./in.D .20Where: K = Stiffness (lbs./in.)W = Weight of load (lbs.)D = Deflection (in.)If we assume the supported item is a rigid body,the system will have a well-defined NaturalFrequency (f n ).f i1i Kgn = 2π Wor, removing the constants:Kif n = 3.13 WWhere: W =g =Weight of load (lbs.)Acceleration due to gravity(386 in./sec. 2 )π = 3.1416If the frequency of the input that we are isolatingfrom (the forcing frequency) is defined as f f , it can beshown that if the spring has been selected so that:Supported objectis the sourceof vibrationLoad vs. DeflectionFigure 1lbs.Supported structureis the source ofvibrationin.Figure 2 Figure 34