Vibration is defined as small oscillations about some equilibrium point. The main characteristics of vibration are amplitude and frequency.
Figure 23.1 illustrates the movement of a piston driven by a crankshaft moving up and down in a cylinder. The position of the centerline of the piston above the centerline of the cylinder (equilibrium position) is assumed positive. When the piston is at top dead center, the piston centerline will be at the maximum positive distance above the cylinder centerline.
The plot of the piston versus time is given by a sine curve. The period of the sine wave is 1 s (the frequency is 1 Hz). The maximum peak (or amplitude) of the motion is D.
The energy produced by the motion is related to the area under the curve (Fig. 23.1c). The rms value of the amplitude is equal to 0.707 times the peak value of the amplitude. It represents the steady value of the amplitude that gives the same energy as the sine curve.
THE APPLICATION OF SINE WAVES TO VIBRATION
Any vibration can be described by a sine wave. The crankshaft/piston arrangement shown in Fig. 23.1 can be described by the spring mass system shown in Fig. 23.2.
Figure 23.3 illustrates the variation of velocity with time. The velocity curve is actually a cosine wave. It leads the displacement curve by 90°.
The maximum acceleration occurs at top dead center. The largest force exerted on the connecting rod is the force required to change the direction of the piston. Figure 23.4 illustrates the variation of acceleration with time. The acceleration curve is 180° out of phase with the displacement curve and 90° out of phase with the velocity curve.
The amplitude of displacement is proportional to the amplitude of acceleration (with a minus sign). Since the accelerometer sensors (measuring acceleration) are inexpensive and easy to use, the amplitude of displacement is often in units of acceleration, known as “G’s” of acceleration. It is convenient to express vibration acceleration in terms of gravitational acceleration g.
