Natural Frequencies and Resonance

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1 Natural Frequencies and Resonance A description and applications of natural frequencies and resonance commonly found in industrial applications Beaumont Vibration Institute Annual Seminar Beaumont, TX February, 2010 Ray D. Kelm, P.E. Kelm Engineering, LLC Natural Frequency Description A natural frequency exists when the properties of the system allow excessive response at a specific frequency, known as the natural frequency What types of systems? Mechanical Machinery, piping, drive shafts Acoustical Pulsations in piping Noise in closed chamber/buildings Electronic Resistor and capacitor circuits Natural Frequency Examples Ringing a bell A swing set or pendulum The sound of a musical instrument Cantilever beam Piping sections Natural Frequency Description Natural frequencies occur around us all the time An example of a natural frequency is a single degree of freedom spring mass system The mass (brown box) is suspended by a linear spring (shown as the coil). Natural Frequency Physical systems respond to various inputs with oscillating motion. Higher amplitudes occur when driven at the system s natural frequencies. Common single degree of freedom example is a mass-spring system. 1 Frequency, Hz 2 K M 1

2 Natural Frequency Test Data The response varies with frequency due to the reaction of stiffness and mass: Below ω d Response controlled by stiffness Above ω d Response controlled by mass Near ω d Response limited by damping Changing Natural Frequencies Frequency, Hz 1 2 K M To increase the natural frequency either: Increase stiffness OR decrease mass To decrease the natural frequency either: Decrease stiffness OR increase mass Changing Natural Frequencies, cont. Field Test of Natural Frequency Frequency, Hz 1 2 K M To increase frequency by 10% requires 121% of the starting stiffness To decrease frequency by 10% requires 121% of the starting mass Natural Frequency Explanation Simple example with mass (m), stiffness (k), and damping (c). F spring F F F mass damping applied k x m c F mass x t 2 F x damping 2 m x c x t F spring kx F spring k x Influence of Mass and Stiffness Displacement, Inches/Lb Acceleration, In/sec^2/Lb Single DOF System Response per Pound of Applied Force M 10 Lb 1000 K Lb/in Mass Stiffness 0.01 Controlled Controlled Region Region Natural Frequency at 100 Hz Frequency, Hz 2

3 Impact of Damping on Response Observing Damping The level of damping can be found from the decay from a step change. Low damping results in a long response High damping results in few response cycles Shaft suspended from rigid supports Almost no damping (<1%) Very long time response Typical Test Results Common Level of Damping Welded structures and systems with rigid supports 1-2% of critical damping Piping in plants 1-3% of critical damping Shafts in hydrodynamic bearings 5-10% of critical damping Quantifying Damping Damping is measured and reported using logarithmic decrement, amplification factor, and critical damping ratio All refer to the same thing but are used in different forms Damping Equations 3

4 What is Log Dec? A documentation of damping based on the decay rate of a step change. What is Critical Damping? 1/2 POWER METHOD OF CALCULATING DAMPING Nc=266 NATURAL FREQUENCY Damping Equations N1= HZ AT ½ POWER AMPLITUDE N2=266.4 HZ AT ½ POWER AMPLITUDE.707 MAX ½ POWER METHOD OF 266 CALCULATING DAMPING N 115 C Q * 115 N 2 N1 2*Q Amplification Factor and Damping Welded structures and piping will commonly have damping ratios of about 0.5 to 3% of critical damping. 0.5% = => Q = 1/(2 x 0.005) = 100 1% = 0.01 => Q = 1/(2 x 0.01) = 50 3% = 0.03 => Q = 1/(2 x 0.03) = 16.7 Common Critical Speed Review 4

5 Cantilever Beam Modes Clarification of Terms Natural frequency All structures have natural frequencies They are defined by mass and stiffness The presence of a natural frequency has no bearing on the vibration of the structure unless there is force input at the same frequency If there is little or no force input, there will be little or no response Resonance Resonance is the condition observed when a structure responds at a natural frequency due to dynamic force that exists at the natural frequency Resonance cannot occur unless a natural frequency is present The response amplitude at a resonant condition is governed by the damping in the system Critical speed This is a special subset of resonance A critical speed is the presence of resonance that is excited by harmonic vibration at an integer order of operating speed The most common example of a critical speed is unbalance response exciting the 1st critical speed during coastdown of a rotating machine Critical Speed on Motor Observed during Coastdown Casing Resonance on PD Blower (Impact test) Resonance in Blower Pipe Drain Valve 5

6 Torsional Natural Frequencies on Reciprocating Compressor Documenting Natural Frequencies Bump test Most common method Easy to do with simple equipment Coastdown test Need multichannel test equipment and tach Modal test Impact hammer and multichannel test equipment Measuring Natural Frequency Bump test Impact component with appropriate device Observe vibration response When a natural frequency exists, the component will vibrate when impacted at an amplitude that is proportional to the amount of energy applied at the natural frequency. Common Bump Test Test Pitfalls There are challenges that can result in large errors Avoided with proper techniques and instrumentation Pitfall # 1- Background noise Background vibration produces peaks that are not related to the bump but are there all the time. Always take a sample without the impact to document the levels of background vibration. 6

7 Pitfall # 2 Hammer is Too Hard Using too hard of a hammer/tip Hard hammer (like a ball peen hammer) will produce low level input at a very broad frequency range ALWAYS use the softest tip that will produce the necessary frequency response Wood is a good choice Impact Hammers Hardness of Object for Bump Hard objects provide high force with very broad energy Soft objects provide more energy at low frequencies Pitfall # 3 Setup Error Most analyzers have windowing and trigger options. There are several options for a successful test using different window/trigger options Hanning Window Force and Exponential Window 7

8 Good Bump Response Pitfall # 4 Operator Error It is always a good idea to follow some basic procedures for a good bump test How to do Single Channel Test Mount sensor and record vibration without impacting the structure and observe the amplitude (time waveform) and frequency content (spectrum) with the analyzer capturing data in a free run mode Impact the structure while viewing a live time waveform (set to trigger when impact occurs) Impact can be done in a way that in general a blunt blow is applied to the machine of interest such as: Dead blow hammer Block of wood (4 x4 3feet long) Set window to Hanning (normal default) and adjust trigger event to occur at about 45% into the time waveform record. Look of good Single Channel Test Amplitude in time waveform prior to impact is small Impact (and ringing) occurs near the middle of the window Amplitude at the impact location is large relative to the start of the waveform Spectral plot shows clean peaks with small floor level Single Channel Test What is Modal Analysis? A way to better understand resonances Structures Rotating Equipment Parts (turbine blades, disks, rotors, machinery casings) An analytical method A field test method A comparison of theory and test A way to provide insight (animations) An essential rotordynamics tool 8

9 Basic Modal Test Force Input Response Time waveforms Spectrums Calculated H(ω) Coherence Movers or Shakers? Shakers Produce high energy input Can provide continuous energy input Periodic or non-periodic input Reduce the need for windows Shakers, cont. Relatively long setup time, often requiring special fixtures The shaker is attached to the structure, which can change the modal response of the structure depending on the size and attachment method used Cannot easily excite multiple locations with the same shaker due to relatively long setup time Hammers Hammers Structure can be impacted in many locations with little setup time No fixtures are required 9

10 Hammers, cont. Relatively low amount of energy can be applied to the structure Difficult to do with much background vibration (noise) Requires careful selection of hammer size and hammer tip to get good quality data Hammer Selection Impact hammers come in a wide variety of sizes 16 Lb sledge hammer is capable of producing about 5,000 Lb force with a 1 mv/lb force head Hammer Selection Impact hammers come in a wide variety of sizes 16 Lb sledge hammer is capable of producing about 5,000 Lb force with a 1 mv/lb force head Spectral Plots, Hammer MDOF Response Spectra Coherence 10

11 Near 1.0 Depends on # of samples What is Good Coherence? Multiple DOF Mode Plotting using Imaginary Typical Magnitude Plot Mode Overlap 11

12 Demonstrations 12