Mechanical Vibrations International Islamic University Islamabad. Abbas Raza Asst.Prof.

What Is Vibration? Vibration is the physical movement or oscillation of a mechanical part about a reference position.

What Is Vibration? Why do we care about vibration? Vibration is: Wasted energy A major cause of premature component failure Cause of aircraft noise which contributes to crew and passenger discomfort

What is Vibration? Scientific Definition Engineering Definition Any motion that repeats itself after an interval of time Engineering Definition Deals with the relationship between forces and oscillatory motion of mechanical systems

Why is Vibration Important? The Tacoma Narrows Bridge Disaster November 7, 1940

Why is Vibration Important? Amplitude of oscillation reached 14 feet!

What was the cause?

…Caused Wind-Induced Vibration (?) Vortex Shedding …Caused Wind-Induced Vibration (?)

Why is Vibration Important?

Why is Vibration Important?

Why is Vibration Important?

Wing Flutter Failures

Basic Concepts Every object has: Frequencies at which it “likes” to vibrate Characteristic geometries of vibration

Basic Concepts Every object has: Frequencies at which it “likes” to vibrateç Characteristic geometries of vibration

1 Modeling Vibration The Ingredients: Realistic Addition: Inertia (stores kinetic energy) Elasticity (stores potential energy) 1 Realistic Addition: Energy Dissipation

1 2 Modeling Vibration The Ingredients: Realistic Addition: Inertia (stores kinetic energy) Elasticity (stores potential energy) 1 2 Realistic Addition: Energy Dissipation

1 2 3 Modeling Vibration The Ingredients: Realistic Addition: Inertia (stores kinetic energy) Elasticity (stores potential energy) 1 2 Realistic Addition: Energy Dissipation 3

1 2 3 Modeling Vibration The Ingredients: Realistic Addition: Inertia (stores kinetic energy) Elasticity (stores potential energy) 1 2 3 Realistic Addition: Energy Dissipation

m k c Modeling Vibration The Ingredients: Realistic Addition: Mass, m Stiffness, k m k c Realistic Addition: Damping, c

How is this model useful? k c

Basic Concepts Resonance

Basic Concepts Resonance A vibration of large amplitude Occurs when an object is forced near its natural frequency

Resonance A vibration of large amplitude Occurs when an object is forced near its natural frequency Object

Resonance A vibration of large amplitude Occurs when an object is forced near its natural frequency Object Model

Vibration Absorbers Used to eliminate vibration of an object Object (that vibrates too much)

Vibration Absorbers Used to eliminate vibration of an object (‘absorbs’ vibration) Object (that vibrates too much)

Choose these to eliminate motion of object. Vibration Absorbers Used to eliminate vibration of an object Vibration Absorber Choose these to eliminate motion of object. Object (that vibrates too much)

Vibration Absorbers

“Characteristic Geometry” of Vibration Mode Shapes “Characteristic Geometry” of Vibration Mode Shapes Resonance Natural Frequencies

Terminology Now it is important to understand some common terms used for vibration analysis and their applications.

Terminology Amplitude Amplitude is an indicator of the severity of a vibration. Amplitude can be expressed as one of the following engineering units: Velocity Acceleration Displacement

Velocity is the rate of change in position Terminology Velocity Velocity is the rate of change in position Typical velocity units are: IPS (Inches Per Second), mm/sec (millimeters per second) Velocity is the most accurate measure of vibration because it is not frequency related. 0.5 IPS @ 1000 rpm is the same as 0.5 IPS @ 10000 rpm.

Terminology Acceleration Acceleration is the rate of change of velocity and is the measurement of the force being produced. Acceleration is expressed in gravitational forces or “G’s”, (1G = 32.17 ft/sec/sec) Acceleration is frequency related, in that 1 g @ 1000 rpm is not the same as 1 g @ 10000 rpm.

Terminology Displacement Displacement is a measure of the actual distance an object is moving from a reference point. Displacement is expressed in “mils” 1 mil = .001 inch Displacement is also frequency related, in that 10 mils @ 1000 rpm is not the same as 10 mils @ 10000 rpm.

Terminology - Continued Unit Modifiers: Since vibration is transmitted as an AC signal, there are four Unit Modifiers that may be used to condition the signal. These modifiers have a direct impact on the measurement value. If the wrong modifier is used, the measurement could be either too high, or too low, thus causing possible maintenance action to be, or not to be, accomplished erroneously.

Unit Modifiers: Peak to Peak - the distance from the top of the positive peak to bottom of the negative peak. Peak - the measurement from the zero line to the top of the positive peak. Average (AVG) - .637 of peak. Root Mean Square (RMS) - .707 of peak.

Terminology Frequencies The rate of mechanical oscillation in a period of time. Frequency can be expressed in one of the following units: RPM - Revolutions per Minute CPM - Cycles per Minute CPS - Cycles per Second Hz - Hertz, 1 Hz - 1 Cycle per Second (to convert from Hz to RPM or CPM, apply the following formula: Hz * 60 = RPM.

Types of Vibration Vibration can be classified into one or more of the following categories: Periodic Random Resonant Harmonic

Terminology - Types of Vibration Periodic Repeats itself once every time period Result of a mass imbalance in a component or disc. As the component rotates, it produces a “bump” every rotation which is referred to a the once-per-revolution or “1P” vibration. This vibration is usually correctable by balancing.

Terminology - Types of Vibration Random Do not repeat themselves Not related to a fundamental frequency. An example - the shock that is felt as a result of driving down the road and hitting a pothole

Terminology - Types of Vibration Resonant The natural frequency at which an airframe or mechanical system is inclined to vibrate. All things have one or more resonant frequencies. Resonant vibrations are the result of a response in a mechanical system to a periodic driving force.

Terminology - Types of Vibration Harmonic Exact multiples of a fundamental frequency Classified in terms as 1st, 2nd, 3rd…..

Terminology Bandwidth Upper and lower frequency limits of the survey being acquired - either hardware set (with the use of an external band pass filter) or software controlled by the analyzer. Setting the frequency bandwidth is a way of eliminating vibration data or noise that is of no interest for your particular application. In the survey above, the frequency bandwidth is 0 CPM to 3000 CPM

Terminology Resolution The resolution of a spectrum is the number of lines or points used to plot the spectrum. The higher the number of lines, the more data acquired.