What is the phase difference between acceleration and velocity in SHM?

Let me try. Use the illustration to follow with me. I’ll focus on the lowest point of this beam and trace its motion from left to right.At left side just in the second the beam moves to the right (at 0 deg or zero part of the cycle), displacement is min (0), velocity increasing from zero and acceleration is at max. At the center in the second the beam moves to the right(at 90 deg or ¼ of the cycle), the displacement is in the mid but increasing, velocity is max and acceleration mid but decreasing. At the right side the second beam stops (at 180 deg or ½ of the cycle), the displacement is max, velocity decreasing to zero, acceleration is min (0) .

Based on the above, displacement and acceleration are swapping i.g. completely opposite in phase or have a difference of 180 deg or ½ of the cycle.

Vibe-RaterThink of it in reverse!!Instead of the "lagging" phase angles in your practical applications, consider the mathematical "derivatives", ie rates of change.For sinusoidal signals, the derivative of a signal leads that signal by 90 degrees.Velocity is the rate of change of displacement so it leads displacement by 90 degrees.

Acceleration is the rate of change of velocity, so it leads velocity by 90 degrees.

Hi Vibe-RaterAs ‘greybeard’ stated acceleration as the rate of change of velocityMay be off your point but from a CSI L1:Displacement measures the distance the shaft moves in relation to a reference point. As you will want the total movement the measurement is taken from peak-peak valveVelocity measure the displacement of the shaft in relation to time. You can think of velocity as the rate at which your machine moves

Acceleration measure the change in velocity in relation to time, as when you accelerate a car

Vibe-RateAnd from some other resource a definition isWhat exactly is "acceleration" ? Acceleration measures the rate of change of velocity (how quickly the velocity is changing). There are two methods of applying an acceleration force (deceleration is simply a negative acceleration):1.A Pushing Action similar to you compressing a spring between your hands. The more you compress a spring, the more force it pushes back with. If you were to push a pillow block bearing away from its "at-rest" position, it would push back. If you went farther, it would push back more. That is a simple way to visualize the acceleration force we are measuring. The amount of movement at a particular frequency is a combination of the force being generated by the rotation of the rotor (unbalance, for intsance, is simply a centrifugal force due to a heavy spot on a rotor), the stiffness and masses of the materials and structure involved and other variables that are structure related.

2. A Striking Action similar to you hitting a nail with a hammer. This action can be extremely destructive since it can cause structural flaws (cracks, for instance) to develop. Consider a jack hammer. It is the striking action that breaks up the cement. One example In the case of a rolling element bearing, a rolling element may pass a defect on one of the races and an impact results similar to hitting a pothole with your car.

You won't hear much complex math stuff here... just a simple way I remember it. I got this from a vendor instructor...When you sit in a car and step on the gas:First: You feel the accelerationSecond: You start moving at some velocityThird: After some time you've moved (been displaced) from one point to anotherAccelerationleads Velocityleads Displacement

For those knuckle-draggers, like me, that need simple stories, mnemonics, and nursery rhymes to remember important stuff... hope this helps.

Machine Survey,Sounds like the analogy I have used to teach many courses. Vibration (motion) starts with a force that causes acceleration (F = M*A). Velocity and displacement are the result.

Walt

Nicolet used a piston in an internal combustion engine. Displacement was the distance from top dead center to bottom dead center. Velocity was zero when the piston was at either end and maximum as it passed through the mid point. Accleration was the force exerted to reverse the direction of the piston as it reached the extremes, except that when the piston was at top dead center, the acceleration force to reverse the direction was 180 degrees out of phase with the displacement and vice versa for bottom dead center.

Maybe it will make sense if you help them figure it out for themselves1. Ask them to draw a sin wave.2. Ask them to draw another sin wave representing the slope (derivative) of the first sin wave. (give them some hints... the derivative passes through zero at max and min of original waveform... is positive in increasing areas and negative in decreasing areas).3. Ask them to estimate the lag between two waveforms in degrees, remembering 360 degrees = 1 cycle, 180 degrees = half cycle, 90 degrees = quarter cycle. 4. Ask them which one is leading and which is lagging.5. If they have worked through all the questions, they have proved that a derivative leads the original signal by 90 degrees.

Now a possible wrench in the works, in vibration when we say "phase" we usually mean lag (this is a setting in the analyser). In that case (when using lag angle as phase), the "phase" angle of the derivative will be 90 less than the phase angle of the original signal. That may or may not seem natural depending on what you're used to. I guess if you think of phase as time, that is natural because the leading signal hits a peak at a lower time value than the lagging signal

If you start with acceleration, then you are moving forward in time, and velocity and displacement are lagging behind. If you start with displacement, then you have to look back in time for velocity and acceleration that already occurred. Do you want to move forward or backward in time?El'Pete, if you draw a sin (Sine) wave does that make you a Sinner?

Walt