Machine Vibration Measurement Flashcards
What mathematical functions can be used to express the properties of waves?
Trigonometric sine and cosine functions.
What is the Fourier Transform used for?
To determine the frequency spectrum of a waveform.
True or False: The same tools used for analyzing water waves can be used for mechanical vibrations.
True.
What is an example of the Fourier Transform applied to music?
The spectrum analyzer display on high-quality audio reproduction equipment.
How can the technology used in audio spectrum analyzers be applied to machine vibration?
It can indicate sources of vibration by analyzing different frequencies generated by machine components.
What is the formula for Newton’s Second Law of motion?
F = ma
Describes how the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass.
What does differentiation in calculus involve?
A variable is proportional to the rate-of-change of two others
Results in a division of units and is relevant for converting position to velocity and velocity to acceleration.
What does integration in calculus involve?
A variable is proportional to the accumulation of the product of two others
Results in a multiplication of units and is relevant for converting acceleration to velocity and velocity to position.
What are Fourier transforms used for?
Decomposing vibrational wave signals into constituent harmonic frequencies
Any repetitive waveform can be expressed as a series of sinusoidal waves of different frequencies, amplitudes, and phase shifts.
What is the relationship between acceleration and force according to Newton’s Second Law?
Acceleration is directly proportional to force and inversely proportional to mass
This principle is relevant for calculating the force developed on a machine part from vibration.
Fill in the blank: Differentiation results in a ______ of units.
division
Fill in the blank: Integration results in a ______ of units.
multiplication
True or False: Fourier transforms can only be applied to linear waveforms.
False
Any repetitive waveform is mathematically equivalent to sinusoidal waves.
What kind of waves does Fourier transform analyze?
Sinusoidal waves
These waves can have different frequencies, amplitudes, and phase shifts.
What is the significance of harmonics in Fourier transforms?
They are integer multiples of the frequencies of sinusoids
Harmonics help identify which parts of a machine are vibrating the most.
What principle enhances problem-solving abilities in engineering?
Mastering the applications of fundamental principles
A wide variety of topics should be considered for better learning.
What mathematical function is used to express vibration physics?
Cosine function
The cosine function alternates between extreme values of +1 and -1.
What does ‘I’ represent in the vibration formula?
Displacement as measured by sensor at time t
Displacement is a key variable in understanding vibration.
What is represented by ‘D’ in the vibration equation?
Peak displacement amplitude
D is a coefficient relating the cosine function to peak displacement.
What does ‘w’ stand for in the formula for vibration?
Angular velocity
Angular velocity is typically expressed in units of radians per second.
What is the meaning of ‘b’ in the vibration equation?
Bias air gap measured with no vibration
It accounts for any offset in the measurement.
What does ‘t’ represent in the context of vibration physics?
Time (seconds)
Time is critical in describing the motion and changes in displacement.
What is the unit of the product ‘wt’ in the vibration formula?
Radians
‘w’ is in radians per second and ‘t’ is in seconds.
At time-0, what is the value of the cosine function?
+1
This occurs when the mass is aligned with the sensor.
What is the angular velocity for a wheel spinning at 1720 RPM?
Approximately 180.1 radians per second
This value is significant for calculating angle and displacement.
What does ‘v’ represent in the context of motion?
Velocity of an object
Velocity is the rate at which displacement changes over time.
In physics, how is velocity mathematically defined?
As the time-derivative of displacement
This relationship can be expressed using calculus notation.
What does ‘z’ denote in the context of motion?
Displacement (position) of an object
Displacement is crucial for understanding motion and velocity.
What is the relationship between displacement and time in the context of velocity?
Velocity is the rate at which displacement changes over time
This relationship is fundamental in physics.
Fill in the blank: The angle between the off-center mass and the sensor is calculated using _______.
T = Dcos(wt) + b
This equation incorporates displacement, angular velocity, and bias.
True or False: The cosine function’s argument is the product of angular velocity and time.
True
This product determines the angle used in the cosine function.
What is the equation for velocity derived from displacement?
V = -wD sin(wt)
Where D is peak displacement, w is angular frequency, and t is time.
What is the relationship between peak displacement and velocity?
The velocity of the wheel’s wobble increases linearly with speed (w)
This is because an increase in rotational speed means the wheel displaces the same vibrating distance in less time.
What is the equation for acceleration derived from velocity?
a = -wD cos(wt)
Acceleration is the time-derivative of velocity.
How does acceleration relate to peak displacement and speed?
The acceleration of the wheel’s wobble increases with the square of the speed (w)
This indicates that higher speeds lead to greater acceleration for the same peak displacement.
What principle from Newton’s Second Law relates acceleration to lateral force?
P = ma
Where P is the lateral force, m is the mass of the wheel, and a is the lateral acceleration.
True or False: The derivative of a constant is always zero.
True
This principle simplifies calculations when differentiating equations.
Fill in the blank: The derivative of a cosine function is _______.
-sin(wt)
This is a fundamental rule from calculus.
What happens to the rate of change of a waveform as its frequency increases?
The rate of change must increase as well
This is because higher frequency means less time for the waveform to travel the same amplitude.
What does the notation ‘d/dt’ represent in calculus?
The derivative with respect to time
This notation is used to indicate the process of differentiation.
What is the significance of a constant multiplier in a function’s argument during differentiation?
The multiplier is applied to the entire derivative
This applies to both sine and cosine functions.
What is the formula for vibrational force experienced by a wheel as rotational speed increases?
F = ma = -mw’D cos wt
How does vibration affect high-speed rotating machinery?
Vibration can be terribly destructive due to enormous forces generated by small lateral displacements.
What happens to the vibrational force when rotational speed is doubled?
The force quadruples.
What happens to the vibrational force when rotational speed is tripled?
The force increases by 9 times.
What assumption is made about displacement (D) in calculating vibrational forces?
It is assumed to be constant.
What effect does centrifugal force have on an imbalanced rotating shaft?
It bends the rotating shaft, placing the mass farther from the centerline.
In the United States, how is vibrational displacement (D) measured?
In mils, with one mil being 0.001 inch.
How is vibrational velocity measured?
In inches per second.
What unit is often used to represent acceleration in vibrational physics?
The unit of G, representing multiples of Earth’s gravitational acceleration.
What is the peak displacement (D) of a rotating machine vibrating in a sinusoidal manner at 1720 RPM?
2 mils (0.002 inch).
What is the frequency of rotation for a machine operating at 1720 RPM?
28.667 Hz.
What is the angular frequency (ω) in radians per second for a machine rotating at 1720 RPM?
180.1 rad/s.
What is the period (T) of a machine vibrating at a frequency of 28.667 Hz?
34.88 ms.
