vibration_training[1].pptx

126
1 71535 B © Copyright SPM Instrument AB 1997 Training Program On Vibration Analysis

Upload: c-j-siva-shankar

Post on 15-Sep-2015

5 views

Category:

Documents


0 download

TRANSCRIPT

Training Course Vibration

Training Program On Vibration Analysis#71535 B Copyright SPM Instrument AB 1997

What Is Vibration?

It is the response of a system to an internal or external force which causesthe system to oscillate.#71535 B Copyright SPM Instrument AB 1997What Is Vibration Analysis?Vibration analysis is a non-destructivetechnique whichhelps early detection of machineproblems by measuring vibration.

#71535 B Copyright SPM Instrument AB 1997Detection By Vibration Analysis1. Unbalance(Static, Couple, Quasi-Static), 2. Misalignment(Angular, Parallel, Combination)3. Eccentric Rotor, Bent Shaft4. Mechanical Looseness, Structural Weakness, Soft Foot5. Resonance, Beat Vibration6. Mechanical Rubbing7. Problems Of Belt Driven Machines8. Journal Bearing Defects9. Antifriction Bearing Defects (Inner race, Outer race, Cage, Rolling Elements)10.Problems of Hydrodynamic & Aerodynamic Machines (Blade Or Vane, Flow turbulence, Cavitation)11.Gear Problems (Tooth wear, Tooth load, Gear eccentricity, Backlash, Gear misalignment, Cracked Or Broken Tooth)12.Electrical Problems of AC & DC Motor ( Variable Air Gap, Rotor Bar Defect, Problems of SCRs)#71535 B Copyright SPM Instrument AB 1997Basic Theory Of VibrationSimple Spring Mass SystemUpper LimitNeutralPositionLower PositionDisplacementMax AccMim VelMax AccMim VelMax VelMim AccIt follows sine curve.#71535 B Copyright SPM Instrument AB 1997Frequency & AmplitudeFrequency:How many times oscillation is occurringfor a given time period?Units: CPS(Hz), CPM

Amplitude:It is the magnitude of vibration signal.Units: Micron, MM/Sec, M/Sec2#71535 B Copyright SPM Instrument AB 1997Physical Significance Of Vibration CharacteristicsFrequency - What is vibrating?Source of the vibration.

Amplitude - How much is it vibrating?Size (severity) of the problem. Phase Angle - How is it vibrating? Cause of the vibration.#71535 B Copyright SPM Instrument AB 1997

60 RPM= 1 Rev / s= 1 HzFrequency Measurement#71535 B Copyright SPM Instrument AB 1997Amplitude Measurement 1. Displacement : Total distance traveled by the mass. Unit : Microns2. Velocity : Rate of change of displacement. It is themeasure of the speed at which the mass is vibrating during its oscillation.Unit : MM/Sec, Inch/sec3. Acceleration :It is the rate of change of velocity. The greater the rate of change of velocity the greater the forces (P=mf) on the machines.Unit : M/Sec2, Inch/sec2#71535 B Copyright SPM Instrument AB 1997

BCAabcttt#71535 B Copyright SPM Instrument AB 1997

t+adv#71535 B Copyright SPM Instrument AB 1997Physical Significance Of Vibration Amplitude Displacement : Stress Indicator

Velocity : Fatigue Indicator

Acceleration : Force Indicator#71535 B Copyright SPM Instrument AB 1997VIBRATION SENSITIVITYDISPLACEMENTVELOCITYACCELERATIONFREQUENCYCPM60600600060000600 00010

1

.1

.01

.001When To Use Disp., Vel. & Acc.?#71535 B Copyright SPM Instrument AB 1997What Is The Advantage Of Using Velocity?Flat frequency range compared to displacement & acceleration.Almost all machines generate fault frequency between 600CPM to 60KCPM Velocity indicates fatigue.Velocity is the best indicator of vibration severity.#71535 B Copyright SPM Instrument AB 1997Scales Of Amplitude PeakPeak to PeakRMSAv.Peak - aPeak to Peak - 2aRMS - 0.707 aAverage - 0.637 a#71535 B Copyright SPM Instrument AB 1997Vibration TransducersProduces electrical signal of vibratory motion

Proximity Probe - DisplacementVelocity Probe - VelocityAccelerometer - Acceleration#71535 B Copyright SPM Instrument AB 1997Proximity Probe

#71535 B Copyright SPM Instrument AB 1997Permanently installed on large machines Measures relative displacement between the bearing housing and the shaft.Called Eddy Current ProbeFrequency range 0 to 60,000 CPMUsed 900 apart to display shaft orbit

#71535 B Copyright SPM Instrument AB 1997Velocity Probe

#71535 B Copyright SPM Instrument AB 1997Oldest of all.Produces signal proportional to velocity.Self generating and needs no conditioning electronics.It is heavy, complex and expensive.Frequency response from 600CPM to 60,000CPMTemperature sensitive

#71535 B Copyright SPM Instrument AB 1997Accelerometer

#71535 B Copyright SPM Instrument AB 1997Produces signal proportional to acceleration of seismic mass.Extremely linear amplitude sense. Large Frequency rangeSmaller in size

#71535 B Copyright SPM Instrument AB 1997Phase#71535 B Copyright SPM Instrument AB 1997What Is Phase?Phase is a measure of relative time difference between two sine waves.

#71535 B Copyright SPM Instrument AB 1997Importance Of PhasePhase is a relative measurement.Provides information how one part of a machine is vibrating compared to other.Confirmatory tool for problems like- 1. Unbalance(Static, Couple, Quasi-Static). 2. Misalignment(Angular, Parallel, Combination). 3. Eccentric Rotor, Bent Shaft. 4. Mechanical Looseness, Structural Weakness, Soft Foot. 5. Resonance. 6. Cocked bearing.

No correlation with Bearing defects, Gear defects, Electrical motor defect.#71535 B Copyright SPM Instrument AB 1997The Phase Angle is the angle (in degrees) the shaft travels from the start of data collection to when the sensor experiences maximum positive force.

For example, the phase angle is 90 if the sensor experiences its maximum positive force at 90 after data collection was initiated by the tachometer.How Phase Angle Is Measured?#71535 B Copyright SPM Instrument AB 1997Step - 1

The tachometer senses the notch in the shaft and triggers data collection. At this point force equals zero.#71535 B Copyright SPM Instrument AB 1997Step - 2

The high spot (heavy spot) rotates 90 to the sensor position.At this point the unbalance force produces the highest positive reading from the sensor.#71535 B Copyright SPM Instrument AB 1997Step - 3

The high spot rotates 90 additional degrees, the force experience by the sensor is again zero.#71535 B Copyright SPM Instrument AB 1997Step - 4

The high spot rotates 90 additional degrees opposite the sensor position.At this point the unbalance force produces the highest negative reading from the sensor.#71535 B Copyright SPM Instrument AB 1997Step - 5

The high spot rotates 90 additional degrees to complete its 360 revolution, the force experienced by the sensor is again zero.#71535 B Copyright SPM Instrument AB 1997Phase AngleDuring the 3600 shaft rotation, the sensorexperiences its maximum positive force when the shafts heavy spot is 900 from its initial position when data collection wasinitiated by the tachometer.

This measurements phase angel = 90#71535 B Copyright SPM Instrument AB 1997FFT Spectrum Analysis#71535 B Copyright SPM Instrument AB 1997What Is FFT?Known as Fast Fourier Transformation.Developed by J.B. Fourier in 1874.#71535 B Copyright SPM Instrument AB 1997FFT mathematically converts overall complex signal into individual amplitudes at component frequencies

#71535 B Copyright SPM Instrument AB 1997Different machinery problems cause vibration at different frequencies.

Overall vibration coming out from machine is combination of many vibration signals form various machine parts and its structure.

FFT is a method of viewing the signal with respect to frequency. #71535 B Copyright SPM Instrument AB 1997CPM

t

CPMtPure sinus 2 sine waves #71535 B Copyright SPM Instrument AB 1997

CPMPure sinus 3 sine waves Complex motionCPMCPM#71535 B Copyright SPM Instrument AB 1997Spectrum Analysis Techniques#71535 B Copyright SPM Instrument AB 1997Step - 1Collect useful informationHistory of machine.Control room data - speed, feed, temperature, pressure etc.Name plate details - bearing no, no of gear teeth etc.Design operating parameters, critical speed.#71535 B Copyright SPM Instrument AB 1997Step - 2 : Identify the type of measurement procedure:

1. Identify measurement type-Disp, Vel, Acc.#71535 B Copyright SPM Instrument AB 1997Conversion Of SpectrumsDisplacement - Microns

Displacement - MicronsSpeed - 2889 RPMVelocity - mm/sAcceleration - m/s2#71535 B Copyright SPM Instrument AB 19972. Measurement direction - Hori, Vert, Axial.

#71535 B Copyright SPM Instrument AB 1997

#71535 B Copyright SPM Instrument AB 1997Step - 3Analyze:1. Evaluate overall vibration reading of the entire machine. (a) Identify 1x RPM peak. (b) Locate highest amplitude. (c) What is the direction of the highest amplitude? (d) What is the frequency of the highest amplitude? 2. See the values of Shock pulse, HFD etc.3. See the trend - in case of sudden increase the problem severity increases. 4. Analyze the frequency for possible defects.5. Analyze the phase readings for confirmation if necessary.#71535 B Copyright SPM Instrument AB 1997Manual Vibration Analysis#71535 B Copyright SPM Instrument AB 1997Detection By Vibration Analysis1. Unbalance(Static, Couple, Quasi-Static), 2. Misalignment(Angular, Parallel, Combination)3. Eccentric Rotor, Bent Shaft4. Mechanical Looseness, Structural Weakness, Soft Foot5. Resonance, Beat Vibration6. Mechanical Rubbing7. Problems Of Belt Driven Machines8. Journal Bearing Defects9. Antifriction Bearing Defects (Inner race, Outer race, Cage, Rolling Elements)10.Hydrodynamic & Aerodynamic Forces (Blade Or Vane, Flow turbulence, Cavitation)11.Gear Problems (Tooth wear, Tooth load, Gear eccentricity, Backlash, Gear misalignment, Cracked Or Broken Tooth)12.Electrical Problems of AC & DC Motor ( Variable Air Gap, Rotor Bar Defect, Problems of SCRs)#71535 B Copyright SPM Instrument AB 1997Unbalance#71535 B Copyright SPM Instrument AB 1997Causes Of UnbalanceUneven distribution of mass of rotor.Dirt accumulation on fan rotors.Rotor eccentricityRoller deflection, especially in paper machinesMachining errorsUneven erosion and corrosion of pump impellersMissing balance weights#71535 B Copyright SPM Instrument AB 1997Types Of UnbalanceStatic UnbalanceCouple UnbalanceOverhang Rotor Unbalance#71535 B Copyright SPM Instrument AB 1997Static UnbalanceDetection:Highest horizontal vibrationAmplitude increases as square of speed. Dominant frequency at 1x rpmHorizontal to vertical phase difference 900 on the same bearing housing

#71535 B Copyright SPM Instrument AB 1997CorrectionCan be corrected by one balance weight in one plane of rotor center of gravity.#71535 B Copyright SPM Instrument AB 1997Couple UnbalanceDetection:High horizontal & some times axial vibration Dominant frequency at 1x RPM1800 phase difference between both bearings horizontal as well as vertical direction.

#71535 B Copyright SPM Instrument AB 1997CorrectionIt requires two plane balancing#71535 B Copyright SPM Instrument AB 1997Overhung Rotor UnbalanceDetection:High horizontal & axial vibration Dominant frequency at 1x RPMAxial readings will be in phase but radial phase readings might be unsteady.

#71535 B Copyright SPM Instrument AB 1997CorrectionOverhung rotors might be having both static and couple unbalance and each of which requires correction.#71535 B Copyright SPM Instrument AB 1997Misalignment#71535 B Copyright SPM Instrument AB 1997Causes Of MisalignmentThermal expansion - Most machines align cold.

Machine vibrations.

Forces transmitted to the machine by pipe or support structure.

Soft foot.

Direct coupled machined are not properly aligned.

Poor workmanship.#71535 B Copyright SPM Instrument AB 1997Types Of Misalignment1. Off set

2. Angular

3. Skew - Combination of offset & angular

#71535 B Copyright SPM Instrument AB 1997Diagnosis Of Misalignment#71535 B Copyright SPM Instrument AB 1997Angular - Axial vibration at 1X RPMOffset - Radial vibration at 2X or 3X RPM

Harmonics (3X-10X) generates as severity increases. If the 2X amplitude more than 50% of 1X then coupling damage starts. If the 2X amplitude more than 150% of 1X then machine should be stopped for correction.1.Vibration Spectrum Analysis:

#71535 B Copyright SPM Instrument AB 19972. Vibration Phase Analysis:Angular - 1800 phase shift in the axial direction across the coupling.

Offset - 1800 phase shift in the radial direction across the coupling. 00 to 1800 phase shift occur as the sensor moves from horizontal to the vertical direction of the same machine.

Skew - 1800 phase shift in the axial or radial direction across the coupling.#71535 B Copyright SPM Instrument AB 1997Misaligned Or Cocked Bearing1. Predominant 1X & 2X in the axial direction.

2. 1800 Phase shift top to bettom and/or side to side of the axial direction of the same bearing housing.

#71535 B Copyright SPM Instrument AB 1997Bent ShaftDiagnosis:1. High 1X axial and high 1X radial if bent is near the center.2. High 2X axial and high 2X radial if bent is near the coupling.3. The phase of the 1X component 1800 at opposite ends of rotor.4. Phase difference of 1800 between left & right hand side and also upper & lower sides of the same bearing housing in the axial direction.5. Amplitude of 1X & 2X rpm will be steady. 6. High bearing temperature.

#71535 B Copyright SPM Instrument AB 1997Eccentric RotorWhen center of rotation is offset from geometric center.Dominant frequency 1X.Horizontal to Vertical phase difference either 00 or 1800 at the same bearing housing (Both indicate straight-line motion).

#71535 B Copyright SPM Instrument AB 1997ResonanceOccurs when forcing frequency coincides with system natural frequency.Causes amplitude amplification which results catastrophic failure.Requires changing of natural frequency or change of operating speed.Bode plot is used to identify resonance.#71535 B Copyright SPM Instrument AB 1997Beat VibrationIt is the result of two closely spaced frequencies going into and out of synchronization with one another. The spectrum will show one peak pulsating up and down. Low frequency vibration 5 to 100 CPM. Beat frequencies are not normally a problem when the differences exceed 150 to 200 CPM. #71535 B Copyright SPM Instrument AB 1997Mechanical Looseness#71535 B Copyright SPM Instrument AB 1997CausesIt alone can not create vibration but in the influence of Unbalance, Misalignment, Bearing problems it amplify the amplitude.It should be corrected first.#71535 B Copyright SPM Instrument AB 1997Types1. Structural frame/base looseness (1X)2. Cracked structure/bearing pedestal (2X)3. Rotating looseness - Loose bearing/improper fit between component parts. (Multiple)#71535 B Copyright SPM Instrument AB 19971. Structural frame/base looseness (1X)Caused by-1. Structural looseness/weakness of machine feet, baseplate & concrete base.2. Deteriorated grouting.3. Deterioration of frame or base4. Soft foot.5. Loose holding down bolts.

#71535 B Copyright SPM Instrument AB 1997AnalysisDominant freq 1X. Similar to unbalance & misalignment.Horizontal to vertical phase diff 00 or 1800 at the same bearing housing. 1800 phase diff in the vertical direction between two surfaces.#71535 B Copyright SPM Instrument AB 19972. Cracked structure/bearing pedestal (2X)Caused by-1. Crack in the structure or bearing pedestal.2. Occasionally on some loose bearing housing bolts.3. Loose bearing or improper component fit.

Analysis-1. 2X RPM amplitude is > 150% of 1X RPM amplitude in radial direction.2. Amplitudes are somewhat erratic.3. 2X RPM phase somewhat erratic.#71535 B Copyright SPM Instrument AB 19973. Rotating loosenessCaused by-1. Loose rotor.2. Bearing loose in the housing.3. Bearing loose in the shaft.4. Excessive bearing internal clearance. #71535 B Copyright SPM Instrument AB 1997Analysis1. Generates running speed harmonics up to 20X RPM.2. Generates low amplitude frequencies of 1/2x (i.e. .5x, 1.5x, 2.5x) and 1/3 x also.3. Presence of 1/2x will indicate more advanced looseness problems like presence of rub. It indicate other problems like unbalance and misalignment.4. Phase measurement will be erratic.5. Phase for loose rotor will vary from one measurement to next.6. Bearing loose on the shaft will generate 1x RPM peak.7. Bearing loose in the housing will generate 4x RPM peak.

#71535 B Copyright SPM Instrument AB 1997Journal Bearing#71535 B Copyright SPM Instrument AB 1997Cause: Excessive clearance and light radial loading.This results in the oil film building up and forcing the journal to migrate around in the bearing at less than one-half RPM. Oil whirl is a serious condition and needs to be corrected. It can create metal to metal contact.Oil Whirl

#71535 B Copyright SPM Instrument AB 1997A symptom peculiar for journal bearings is oil whirl.It shows up as a vibration of approx. 0.42-0.48 X RPM.Oil whirl can be diagnosed by increasing the load which will decrease the subsyncronous vibration.frequencymm/s rms0.45X2X1Xsevere oil whirl will cause looseness#71535 B Copyright SPM Instrument AB 1997Journal Looseness(Rotating Looseness)

#71535 B Copyright SPM Instrument AB 1997Rotor RubSpectra similar to mechanical looseness.It may be partial or full annular rub.Often excites one or more resonances.It can excites high frequencies. Cascade diagram and shaft orbit are very helpful in diagnosing rubs.#71535 B Copyright SPM Instrument AB 1997Rolling ElementBearing#71535 B Copyright SPM Instrument AB 1997Why Does Bearing Fail?1. Improper lubrication2. Contaminated lubrication3. Heavier loading from unbalance, misalignment, bent shaft etc.4. Improper handling or installation.5. Old age (Surface fatigue) .#71535 B Copyright SPM Instrument AB 1997Bearing Failure Detection

#71535 B Copyright SPM Instrument AB 1997Bearing Failure StagesEarliest indications of bearing problems appear in the ultrasonic frequency ranging from 1,200k to 3,600 kCPM. Spike Energy, HFD, and Shock Pulse evaluate these frequencies.Stage - 1

#71535 B Copyright SPM Instrument AB 1997Stage - 2Slight bearing defects begin to ring bearing component natural frequencies, which predominantly occur in 30k to 120K CPM range. Sideband frequencies appear above and below natural frequency peak at the end of stage 2.

#71535 B Copyright SPM Instrument AB 1997Stage - 3Bearing defect frequencies and harmonics appear. More defect frequencies appear and nos of sidebands grow, both around these and bearing natural frequencies. When well-formed sidebands accompany bearing defect frequency harmonics Bearing has to be replaced.

#71535 B Copyright SPM Instrument AB 1997Stage - 4Towards the end-Amplitude of 1X and other running speed harmonics will increase. Discrete bearing defect and component natural frequencies actually begin to disappear and are replaced by random, broad band high frequency noise floor. Amplitude of both high frequency noise floor and spike energy may decrease, but prior to failure, spike energy will usually grow to excessive amplitudes.

#71535 B Copyright SPM Instrument AB 1997Rolling element bearingsFTF = Fundamental Train FrequencyBSF = Ball Spin FrequencyBPFO = Ball Pass Frequency Outer raceBPFI = Ball Pass Frequency Inner raceFTF..121.dDcosFRPMBSF..D.2d1.dDcosF2RPMBPFO.NFTFBPFI.N(RPM - FTF)RPM = Shaft rotation

d = Rolling element diameter

D = Pitch diameter

N = No. of rolling elements

= Contact angle

#71535 B Copyright SPM Instrument AB 1997Rolling element bearingsWhat do the bearing frequencies mean?If:FTF = 0.381 * RPMBSF = 1.981 * RPMBPFO = 3.047 * RPMBPFI = 4.952 * RPMThe cage rotates 0.381 revolutionsThe ball spins 1.981 revolutions4.952 balls pass an inner race defect3.047 balls pass an outer race defectDuring one shaft revolution:#71535 B Copyright SPM Instrument AB 1997Gear Box#71535 B Copyright SPM Instrument AB 1997RPM1RPM2Z1Z2GMF (Gear Mesh Frequency)Z1 .RPM1 = Z2 .RPM2where Z = no. of teeth and RPM shaft speedGear boxMating gears produce only one Gear Mesh Frequency#71535 B Copyright SPM Instrument AB 1997Gear Box DefectsTooth wearGear eccentricity & backlashGear misalignmentCracked or broken toothHunting tooth#71535 B Copyright SPM Instrument AB 1997frequencyvelocitytimevelocitySpur gear produce vibration in radial direction and helical gear produce in radial & axial directions.Sideband spacing reveals the defective gear or pinion.All analysis should be done at maximum load.Z.RpsZ.Rps+2 RpsZ.Rps+RpsZ.Rps-2 RpsZ.Rps-Rps1/RpsGear box#71535 B Copyright SPM Instrument AB 1997Normal SpectrumAll peaks are of low amplitudesNo natural frequency of gear excited

#71535 B Copyright SPM Instrument AB 1997Tooth Wear

GMF may not changeHigh amplitudes of side bandsPresence of natural frequency of gear (fn)#71535 B Copyright SPM Instrument AB 1997Gear Eccentricity & BacklashExcites GMF, fn & their side bandsHigh amplitudes of side bandsSideband spacing reveals the defective gear or pinion.

#71535 B Copyright SPM Instrument AB 1997Gear Misalignment

Excites harmonics of GMF with side bandsAmplitudes 2GMF or 3GMF higher than 1GMF#71535 B Copyright SPM Instrument AB 1997Cracked / Broken Tooth

High amplitudes of 1x RPM of gear or pinionExcites gear natural frequency.Time waveform indicates spikes at 1/RPM of broken or cracked tooth. Amplitudes of impact spikes in time waveform will be higher than that of 1xRPM in FFT.

#71535 B Copyright SPM Instrument AB 1997Hunting Tooth1. Faults on both gear & pinion occured during manufacturing.2. Causes high vibration at low frequencies (less than 600CPM)3. Gear set emits growling sound.#71535 B Copyright SPM Instrument AB 1997Hunting Tooth FrequencyIt is the rate at which a tooth in one gear mates with a particular tooth in the other gear.

For well designed gearboxes HTF is low.HTF = GMF . (lowest common prime factor) /(Z1.Z2)Ex:Z1 = 63, Z2 = 12Z1 = 63 = 7.3.3Z2 = 12 = 3.2.2lowest common prime factor = 3HTF = GMF. 3 / (63.12) = GMF / 252

#71535 B Copyright SPM Instrument AB 1997Belt Drive

BF (Belt Frequency) = Rps. .D / L

BF is the rotational frequency of the belt. Worn or mismatched belts will produce radial vibration at BF and its harmonics. 2.BF is often dominantwith 2 sheaves in the system. BF is a subsyncronous vibration (below 1X).

#71535 B Copyright SPM Instrument AB 1997forceEccentric sheaves will generate strong 1X radial components.A common condition.Looks like unbalance, but shows at both sheaves.Belt DriveEccentric sheaves#71535 B Copyright SPM Instrument AB 1997

Belt Drive

Off-setAngularAxial vibrations at 1X and BF with harmonics.Sheave misalignment#71535 B Copyright SPM Instrument AB 1997FansFan Blade Pass Frequency = RPM x no. of fan blades(FBPF)Mainly radial vibrations

FBPF with 1X RPM sidebands.

Unbalanced horizontal or axial vibrations.

Inadequate blade clearance (at FBPF or RPM harmonics)

Uneven velocity distribution across fan inlet gives FBPF vibrations#71535 B Copyright SPM Instrument AB 1997Vibration signature depends upon operating condition.pressure, temperature, speed, cavitation.

Centrifugal pumpsat Vane Pass Frequency = RPM . no. of impeller vanesand harmonics.

Gear pumpsat Gear Mesh Frequency and 1X sidebands

Screw pumpsat thread rate = RPM . number of threads and its harmonics.Pumps#71535 B Copyright SPM Instrument AB 1997Electrical Motors#71535 B Copyright SPM Instrument AB 1997

Asyncronous AC motorsRunning speed:where p = number of polesf = line frequency

If no. of poles = 2.The motor will have a sync. RPM of 3000where fs = slip frequencyAC Motorsfs = RPMsync - RPM#71535 B Copyright SPM Instrument AB 1997AC MotorsAll electrical machines vibrates at 2 . line frequency.

The reasons are expanding and collapsing magnetic fields.

This vibration is normal (to a degree).

The amplitude is a measure of the quality of the construction.#71535 B Copyright SPM Instrument AB 1997Coast Down TestVibration suddenly drops down after switching off the powerAC Motors#71535 B Copyright SPM Instrument AB 1997AC MotorsFaults possible to detect with vibration analysis:Rotor thermal bowAir gap eccentricityLoose rotorEccentric rotorLoose windings

Necessary data:No. of stator slots (SPF)No. of rotor bars (RBPF)Line frequency(LF)Slip frequency(SF)#71535 B Copyright SPM Instrument AB 1997In order to find 2 X slip sidebands around FL, a analyzerwith high resolution, and preferably zoom around 50 Hzis needed.

current clampFrequency analysis of input currentAC Motors#71535 B Copyright SPM Instrument AB 1997D.C. MotorBroken field windingBad SCRsLoose connections Loose or blown fusesShorted control cardsFaults possible to detect with vibration analysis:#71535 B Copyright SPM Instrument AB 1997IdentificationBroken field winding, Bad SCRs, Loose connections Peaks at 6.LF

Loose or blown fuses, Shorted control cardsPeaks at 1.LF to 5.LF For 3 phase rectified D.C. motors #71535 B Copyright SPM Instrument AB 1997-suppresses vibrations not synchronous with the measured object.30One measurement1X2X3X301X2X3XAverage of 10 measurementsSampling always starts attacho signal from roll 1.Synchronous time averagingRoll 1Roll 2VIBRPM#71535 B Copyright SPM Instrument AB 1997EnvelopingDetects low amplitude high frequency repetitivebearing or gear mesh defects.

These defects emit repetitive low energy impact signals that are highly pulse shaped and of very short duration. They generate harmonics in thevery high frequency ranges.

These techniques filter out low frequency vibration energies and therefore isolate & emphasize specific high frequency signals.#71535 B Copyright SPM Instrument AB 1997

ISO 2372 Class Class Class Class Class Class Limits1 Step#71535 B Copyright SPM Instrument AB 1997Case - 1 Pump Impeller WearSummaryThis case documents a 100 hp monitored over a period of 2 years (1500 rpm).

An increase of overall vibration levels and spectrum showed high vane pass levels of 3 x RPM.#71535 B Copyright SPM Instrument AB 1997The pump has 3 vanes on the impeller and an internal inspection indicated impeller wears.

Impeller changed and both the overall levels of vibration and the vane pass frequency returned to normal, acceptable levels.

#71535 B Copyright SPM Instrument AB 1997AnalysisOverall Vibration Levels:Overall vibration levels were on the boarder line of being in an alarm state for several months and remained stable, it was decided to monitor closely. Then suddenly overall vibration levels jumped to 0.95 inch/sec ie 390 % change.#71535 B Copyright SPM Instrument AB 1997Vibration Spectrum:The frequency spectrum collected from the pump inboard bearing shows a predominant peak at a frequency of 3000 rpm. The spectral plot showing the historical growth in amplitude of this predominant peak.

It is noted that the machine deterioration appears more severe on the basis of overall readings than on the basis of the frequency spectrums.#71535 B Copyright SPM Instrument AB 1997One possible explanation for the observation is that there was an increase in vibration amplitudes at frequencies beyond the range.

#71535 B Copyright SPM Instrument AB 1997Theoretical Consideration:Problems with blades and vanes are usually characterized by high vibration or near the harmonic frequency corresponding to the rotation speed X No. of blades. Blade pass frequency usually exists in normal operating machines, but harmonics usually indicates problem.#71535 B Copyright SPM Instrument AB 1997Problem Diagnosis:

The data collected pointed towards the pump impeller as the source of high vibrations because of dominant peaks at the blade pass frequency as well as growing side band harmonics.#71535 B Copyright SPM Instrument AB 1997ResultsCorrective Action:The pump impeller was removed and replaced.

Findings:Overall vibration reading taken after repair amplitudes significantly reduced.

#71535 B Copyright SPM Instrument AB 1997ConclusionsThe objective of this case was to demonstrate the concept that the blade pass frequency (No. of blades x shaft speed) and surrounding harmonics gives an indication of impeller condition. This case over all vibration increases trend stopped the machine and changed impeller.#71535 B Copyright SPM Instrument AB 1997Vibration signature of the pump took on a new shape without high amplitudes at blade pass frequency and the overall vibration levels returned to acceptable levels.#71535 B Copyright SPM Instrument AB 19978 647 544 862 8 648

.MCAD 304020000 1 74 43 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 4 3 2 0 0

{1:N}NAME:1024

.EQN 0 46 35 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 3 -46 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 6 0 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 0 25 42 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*\(2)

.EQN 40 -23 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 51 4 39 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@200&&(_n_u_l_l_&1024)&{0:i}NAME

0 0 1 0 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 53 14 12 0 3

8 855 536 1006 8 856

.MCAD 304020000 1 74 46 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 4 3 2 0 0

{1:N}NAME:1024

.EQN 0 46 35 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 3 -46 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 6 0 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 0 25 42 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*\(2)

.EQN 40 -23 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 26 0 46 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@200&&(_n_u_l_l_&1024)&{0:i}NAME

0 1 0 0 0 5 0 0 1

0 1 0 0 0 5 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 57 14 12 0 2

8 647 544 862 8 648

.MCAD 304020000 1 74 48 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 2 26 48 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 2 -23 2 0 0

{1:N}NAME:1024

.EQN 3 0 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 1 25 47 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*\(2)

.EQN 5 -25 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 40 2 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 26 0 46 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@20&&(_n_u_l_l_&1024)&{0:i}NAME

0 1 0 0 0 5 0 0 1

0 1 0 0 0 5 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 57 14 12 0 2

8 855 536 1029 8 856

.MCAD 304020000 1 74 48 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 2 26 48 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 2 -23 2 0 0

{1:N}NAME:4096

.EQN 3 0 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 1 25 47 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*\(2)

.EQN 5 -25 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 40 2 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 26 0 46 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@100&&(_n_u_l_l_&1024)&{0:i}NAME

0 1 0 0 0 5 0 0 1

0 1 0 0 0 5 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 0 1 57 14 12 0 2

8 647 534 862 8 648

.MCAD 304020000 1 74 54 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 2 26 48 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 2 -23 2 0 0

{1:N}NAME:1024

.EQN 3 0 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 6 0 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 0 28 50 0 0

({0:noise}NAME)[({0:i}NAME):({0:rnd}NAME(2)-1)

.EQN 8 -28 49 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)*4+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*1.76*\(2)+({0:noise}NAME)[({0:i}NAME)*5+{0:sin}NAME({0:\p}NAME*({0:i}NAME*10)/(10))*\(2)+

{0:sin}NAME({0:\p}NAME*({0:i}NAME*2.12)/(10))*\(2)*2.6

.EQN 32 2 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 26 0 46 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@200&&(_n_u_l_l_&1024)&{0:i}NAME

0 1 0 0 0 5 0 0 1

0 1 0 0 0 5 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 0 1 57 14 12 0 2

8 855 536 1029 8 856

.MCAD 304020000 1 74 54 0

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 0 3

.CMD PLOTFORMAT

0 0 1 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 21 15 0 1 3

.CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=1

.CMD SET ORIGIN 0

.CMD SET TOL 0.001000000000000

.CMD SET PRNCOLWIDTH 8

.CMD SET PRNPRECISION 4

.CMD PRINT_SETUP 1.200000 0.989583 0.000000 0.000000 0

.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*

.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFAULT_TEXT_PARPROPS 0 0 0

.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables

.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants

.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text

.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1

.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2

.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3

.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4

.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5

.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6

.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7

.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=1 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1

.CMD UNITS U=1

.CMD DIMENSIONS_ANALYSIS 0 0

.CMD COLORTAB_ENTRY 0 0 0

.CMD COLORTAB_ENTRY 128 0 0

.CMD COLORTAB_ENTRY 0 128 0

.CMD COLORTAB_ENTRY 128 128 0

.CMD COLORTAB_ENTRY 0 0 128

.CMD COLORTAB_ENTRY 128 0 128

.CMD COLORTAB_ENTRY 0 128 128

.CMD COLORTAB_ENTRY 128 128 128

.CMD COLORTAB_ENTRY 192 192 192

.CMD COLORTAB_ENTRY 255 0 0

.CMD COLORTAB_ENTRY 0 255 0

.CMD COLORTAB_ENTRY 255 255 0

.CMD COLORTAB_ENTRY 0 0 255

.CMD COLORTAB_ENTRY 255 0 255

.CMD COLORTAB_ENTRY 0 255 255

.CMD COLORTAB_ENTRY 255 255 255

.TXT 6 1 1 0 0

Cg b73.000000,73.000000,16

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\fs32 Hanningfnster}}

.EQN 2 26 48 0 0

({0:x}NAME)[({0:i}NAME):512

.EQN 2 -23 2 0 0

{1:N}NAME:1024

.EQN 3 0 3 0 0

{0:i}NAME:0;{1:N}NAME-1

.EQN 5 0 4 0 0

({0:hanning}NAME)[({0:i}NAME):(1-{0:cos}NAME(2*{0:\p}NAME*({0:i}NAME)/({1:N}NAME)))

.EQN 0 29 5 0 0

({0:rect}NAME)[({0:i}NAME):1

.EQN 5 -28 40 0 0

({0:window}NAME)[({0:i}NAME):({0:hanning}NAME)[({0:i}NAME)

.EQN 6 0 41 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)

.EQN 0 28 50 0 0

({0:noise}NAME)[({0:i}NAME):({0:rnd}NAME(2)-1)

.EQN 8 -28 49 0 0

({0:x}NAME)[({0:i}NAME):{0:sin}NAME({0:\p}NAME*({0:i}NAME)/(10))*\(2)*4+{0:sin}NAME({0:\p}NAME*3*({0:i}NAME)/(10))*\(2)+{0:sin}NAME({0:\p}NAME*5*({0:i}NAME)/(10))*1.76*\(2)+({0:noise}NAME)[({0:i}NAME)*5+{0:sin}NAME({0:\p}NAME*({0:i}NAME*10)/(10))*\(2)+

{0:sin}NAME({0:\p}NAME*({0:i}NAME*2.12)/(10))*\(2)*2.6

.EQN 32 2 13 0 0

({0:w}NAME)[({0:i}NAME):({0:window}NAME)[({0:i}NAME)*({0:x}NAME)[({0:i}NAME)

.EQN 0 21 14 0 0

({0:w}NAME)[(10)={0}?_n_u_l_l_

.EQN 4 -21 15 0 0

{0:spec}NAME:{0:FFT}NAME({0:w}NAME)

.EQN 0 18 16 0 0

{1:K}NAME:({1:N}NAME)/(2)

.EQN 0 9 17 0 0

{0:j}NAME:0;{1:K}NAME

.EQN 4 -27 18 0 0

({0:spec}NAME)[({0:j}NAME):({0:spec}NAME)[({0:j}NAME)*\(2)

.TXT 0 19 19 0 0

Cg a48.000000,48.000000,20

{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0

\fcharset0\fnil Arial;}}\plain\cf1\fs20\b \pard {\b0 (rms - vrde / topp)}}

.EQN 4 -25 43 0 0

&&(0&_n_u_l_l_)&(|(({0:spec}NAME)[({0:j}NAME)))@400&0&(0&400)&{0:j}NAME

0 1 0 0 1 0 0 0 1

0 1 0 1 0 20 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 1 1 55 22 12 0 2

.EQN 26 0 46 0 0

&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:i}NAME)@200&&(_n_u_l_l_&1024)&{0:i}NAME

0 1 0 0 0 5 0 0 1

0 1 0 0 0 5 0 0 1

0 1 0 0 1 1 NO-TRACE-STRING

0 2 1 0 1 1 NO-TRACE-STRING

0 3 2 0 1 1 NO-TRACE-STRING

0 4 3 0 1 1 NO-TRACE-STRING

0 1 4 0 1 1 NO-TRACE-STRING

0 2 5 0 1 1 NO-TRACE-STRING

0 3 6 0 1 1 NO-TRACE-STRING

0 4 0 0 1 1 NO-TRACE-STRING

0 1 1 0 1 1 NO-TRACE-STRING

0 2 2 0 1 1 NO-TRACE-STRING

0 3 3 0 1 1 NO-TRACE-STRING

0 4 4 0 1 1 NO-TRACE-STRING

0 1 5 0 1 1 NO-TRACE-STRING

0 2 6 0 1 1 NO-TRACE-STRING

0 3 0 0 1 1 NO-TRACE-STRING

0 4 1 0 1 1 NO-TRACE-STRING

0 0 1 57 14 12 0 2