Basic Vibration SeminarALPS Maintaineering Services, Inc

Rationale Inefficiencies and wastages abound in both manufacturing and service systems as a result of poor machine maintenance procedures. Moreover, technical and technological inability to monitor equipment conditions, and prescribe the corresponding maintenance procedures aggravates the problem situation. This seminar is presented to provide ideas on the needs of maintenance systems for a comprehensive and integrated methodology in machine troubleshooting.

ObjectivesAt the end of the seminar, the participant is expected: To be introduced to the concepts of predictive maintenance and condition monitoring, particularly vibration analysis. To become familiar with the VA techniques which enhance the efficiency, reliability and safety of equipment.

About the speaker President, ALPS Maintaineering Services, Inc Professional Electrical Engineer 2030 Certified Vibration Specialist I, Vibration Institute of USA Certified Condition Monitoring Engineer, IFS Germany Certified Alignment Specialist, Fixturlaser AB, Sweden Practiced vibration analysis and alignment since 1992 Lecturer, National Engineering Center, UP Diliman, Quezon City. 2000 - present Application Engineering, SKF Philippines, Inc. 1990 - 1997 Electrical Superintendent, Semirara Coal Corporation. 1983 1990 Electrical Supervisor, North Davao Mining Corporation. 1981 1983 Electrical Engineering Instructor, University of Mindanao, Davao City. 1980 1981 Master of Engineering Education, UP Diliman. 1979-1980

Basic Machine VibrationsAn analyst without a knowledge of the basics is like a machine with an inferior foundation.

What is vibration? Vibration is a "back and forth" movement of a structure. It can also be referred to as a "cyclical" movement

What Is Vibration Caused By ?Imperfections in the Machine caused by: Design Assembly Manufacture Operation Installation Maintenance

What Is Vibration Caused By ? What Are Some Common Machine Problems That Generate Mechanical Vibration: Misalignment Unbalance Worn belts & pulleys Bearing Defects Hydraulic Forces Aerodynamic Forces Reaction Forces Reciprocating Forces Bent Shafts Rubbing Gear Problems Housing Distortion Certain Electrical Problems Frictional Forces

What Are Some Common Machine Problems That Amplify Mechanical Vibration (But Don't Cause It): Resonance Looseness

Why Do We Measure Vibration ?1. Assess the condition (primarily the bearings) of a machine. By performing this task effectively, we can eliminate catastrophic failures due to component degradation. 2. Diagnose the root cause(s) of any excessive (destructive) vibration. By performing this task effectively, we can extend the life of bearings and other components that are absorbing the stresses and fatiguing forces that are causing the symptom of excessive vibration.

Why Do We Measure Vibration ?It should be understood that short-term event-based failures (i.e. loss of lubrication, sudden fracture of a component, etc.) are not protected against via any program that only collects data periodically. The time between onset and failure in these cases - which are rare may take only minutes (in extreme cases), hours, days or weeks. For example, many programs are based on monthly data collection. Any event occurring during that month interval may cause failure prior to the next data collection. This is not a failure of the program or the technology any more than driving a fork truck into a machine and destroying it. The good news is that the vast majority of potential and actual failures will NOT fall into this category and DO lend themselves to being detected, monitored and corrected through a well-run vibration program. .

What Does The Transducer Actually Detect ? Its the movement of

Vertical Oblique Horizontal Axial

What Vibration "Characteristics" Do We Measure ?

Amplitude

Frequency

How much movement occurs? Severity of vibration

How often the movement occurs? Whats the defect or root cause?

PhaseIn what direction is the movement?

Common Bearing Numbering Convention

Consistency Is The Key

Common Bearing Numbering Convention

Belt drives can be oriented in any direction and thereby require a directional convention.

Vertical machines present another opportunity to assign a directional convention since parallel to the shaft (axial) is now straight up out of the ground

Amplitude Severity of vibration based on ISO 10816 What are its units? Displacement - measures the total distance the transducer (bearing) travels back and forth during one 'cycle' of movement (a 'cycle' is the process of moving from one extreme to the other and back again to the starting point). Velocity - measures the maximum speed the transducer achieves during a cycle. Acceleration - measures the force(s) that are causing the back and forth movement.

How much Displacement Unit?15 10

Amplitude

F = 1/T

1 2 3 4Tim e

T

5 0 -5 -10 -15

The periodic motion isa sine wave.

Acc(t ) = A. sin( .t + ) = pulsation in rad/s = phase

English or 'Imperial' Units: Mils (1 mil = 0.001") Metric Units: Microns (1 um = 0.001 mm) Conversion::1 Mil = 25.4 um

Convert the unitsAcc(t ) = A. sin( .t + )

Acc(t ) =

Amplitude

dVel (t ) dt

15 10 5 0 -5 -10 -15

Acclration Niveau C/C Niveau 0/C Niveau eff

temps

Vel (t ) = Acc(t )dt

Vel (t ) =

dDisp (t ) dt

Vite sse15 10 5 0

Acc(mG ) Vel (mm / s ) 2. .FDisp (t ) = Acc(t )

-5 -10 -15

15 10 5

Dplacement

Vel ( mm / s ).1000.2. 2 Disp ( mc / c) 2. .F

0 -5 -10 -15

Effect of parameter conversion

sAmplitude

v

a

Frequency

Measuring How Much Velocity? Displacement, we were concerned with the total distance traveled (stress-related failures). Velocity measures the how often (frequency) the stress (displacement) is being applied. Velocity is measure of the likelihood of FATIGUE being the mode of failure. Fatigue failures are by far and away the most common cause of general machinery failures. Velocity is the best monitoring tool for general machines.

Measuring How Much Velocity? Specialty machines, components or specific problems may not be best monitored by velocity. Examples of machines, components and problems not suited to velocity are gears and certain electrical symptoms (i.e. very high frequency vibration: >120,000 cycles per minute) and very slow-speed equipment (< 100 rpm). It should be noted that even though velocity is suited to monitor problems in the 60kcpm - 150kcpm range, it may be advantageous to use our third amplitude unit acceleration - in those cases.

The Velocity Sine Wave15 10 Amplitude 5 0 -5 -10 -15 tempsAcclration Niveau C/C Niveau 0/C Niveau eff

English or "Imperial": Inches per Second (ips -or- in/sec) Metric: Millimeters per Second (mm/sec) Conversion::1 ips = 25.4 mm/sec

Measuring "How Much" In Acceleration Units

Acceleration measures how rapidly the velocity is changing. Acceleration is measure of the likelihood of APPLIED FORCE being the mode of failure. Applied force failures occur at higher frequencies - almost invariably 60,000 cycles per minute and higher. There are a limited number of high frequency generating machinery problems. Those problems include primarily rolling element bearing defects and gears. English or Metric - G's (1 g = force of gravity)

What Does Frequency Tell Us?Frequency is the reciprocal of Time: F = 1/T Example: If F = 50Hz then T = 1/50 = 20 ms

F=1 T=12 4 6 8 10 12 14

F=50 T=2016 18 20 ms

Frequency Identifies The Vibration Source

Amplitude Guidelines For "Other" Equipment Types: Slow Speed: Typically generates lower amplitudes. For shafts < 600 rpm, Time Domain plots should be used Complex Vibration Generators: Typically generates higher amplitude levels

Manufacturers vibration guidelinesEnglish Units: in/sec < 0.45 0.45 - 0.90 w / no peak > 0.45 Metric Units: mm/sec < 11.4 11.4 - 22.8 w / no peak > 11.4 Classification: Excellent Good Fair Rough Very Rough

0.45 - 0.90 w / 1+ peaks > 0.45 11.4 - 22.8 w / 1+ peaks > 11.4 > 0.90 w / no peak > 0.90 Peak(s) > 0.90 > 22.8 w / no peak > 22.8 Peak(s) > 22.8

The successful analyst will also get to "know" the machines and their typical vibration patterns. That knowledge is possibly the analyst's strongest line of defense against unexpected failures.

What Does Phase Tell Us? Phase enables us to compare the relative direction of movement of various locations on a machine Accessories used with vibration analyzer Strobe light Optical Phase Sensor

Phase Convention In order to discuss phase at the most basic level, we need a convention to use. Phase is represented by the 360 of a circle. Since a high degree of accuracy is not required in a simple, general phase analysis (what we will be discussing here), phase is most easily referred to in terms of clock face numbers: 1 o'clock through 12 o'clock. The phase "angle" is based on where the mark appears (the red key in the example shown here) on the clock face. It is shown here at 12 o'clock but could appear at any angular location. Applications requiring more precise detail (i.e. balancing or phase monitoring on a turbine) will require the use of specific angular references (0 - 359).

Usefulness of Phase Analysis Aids in determining the following problems Unbalance Misalignment Bent shaft

Generic Fault CharacteristicsMechanical Bearings/Electrical Lube/Cavitation/Gears

it allows for preliminary identification of the source of the vibration.

Time Waveform for low speed

Identify bearing defects due to shock loads

Trend Plot Severity of Vibration

A trend plot offers limited analysis tools (there is no identification of specific frequencies, for instance) but can be an important indicator of developing problems.

Trend Plots for Bearing Defect

Defect Factor Identify bearing noise Down trend indicates wear

Bearing Defect Factor The specific DEFECT FACTOR (unit DEF) can monitor from the early beginning to the uniform wear of the rolling element bearing. DEF is suitable for motors and pumps.12 9 6 3 0 Defect Factor

DEF

Peak Value

RMS Value

Peak Factor

GOOD

BADOne scale for all the rotational speed

Trend Plots for Bearing Defect

Acceleration OVL Identify Lubrication Problem

Trend Plots for Bearing Defect

Kurtosis Identify Bearing DefectProblem due to shock loads, mounting, handling

Bearing Defect Frequencies

C1 Bearing defect located at cage : l1 defect located at rolling elements B1 defect located at outer race E1 defect located at inner race Conclusion: since there is no harmonics located at 200 2000 Hz, no defect

Peak or RMS Values It doesn't matter which value you use - RMS or Peak - so long as you are CONSISTENT (another very important convention) !! Amplitude is, after all, simply a number from which we make certain generalizations about the machine condition. There is no exact, precise number above which disaster awaits and below which you are safe. Be aware of the conversion if comparing values between programs that use RMS and Peak values. This applies to spectrum plots as well.

Database AcquisitionDecisions are only as good as the facts they are based on

Database Set up A crucial step for any monitoring program is, unfortunately, right at the beginning - database setup. This is unfortunate because it is a crucial task that is performed when the people doing it are most likely inexperienced and of limited education in the field. Once created, it is very difficult to develop new ideas or drastically change things without creating a colossal mess. A monitoring program tracks the condition of your equipment through the measurement of vibration amplitudes on a regular interval. Deviation from the norm then triggers further investigation to determine the source and correct the actual cause of the excessive vibration.

Purpose of Monitoring Program To be sure, a well designed vibration monitoring program will nearly always give you a specific direction in which to search for a problem and it will help you prioritize work by gauging the severity and source of most of the problems you will encounter. However, further analysis, or at the very least confirmation checks, are always a wise course of action to take before proceeding with any corrective actions.

Transducers/Sensors Accelerometer Velocity Transducer Displacement Transducer Proximity Probes

Not recommended

Snapping Method

Magnet Mounting of Accelerometers500 mV/g Accelerometer

High Strength Magnet

Rocking Method (Recommended)

500 mV/g Accelerometer

Magnet Mounting of Accelerometers

High Strength Magnet

Summary The creation of a database, with all the associated decisions that must be made, is a job that requires a very good technical understanding of vibration analysis, machinery operational characteristics and good doses of common sense. Always question what you are doing, especially whether or not the desired goals are being achieved and, if not, what other methods might be used to achieve those goals.

Sample DatabaseLubrication ISO 10816 Vibration Defect Factor Unbalance/misalign Looseness Soft foot Kurtosis Belt Frequencies

Data Processing II Analyser : further expertise 1 or 2 channels Structure analysis transfer function and coherence Journal bearing Orbit display III Balancing: In situ correction of unbalance 1 to 4 plans 1 or 2 channels

Data Processing IV Order analysis Machine analysis during startup or shutdown Determination of resonance, critical speed, instability IV DAT Long time acquisition for expertise using post-processing (vib-Graph) For Collector and Analyser modes

Integrated sensors :

Data Processing

Pyrometer with laser-sighting for contact-less measurement (up to 30 cm) for temperature from 0 to 200C Tachometer with laser-sighting (0 to 60 000 tr/mn up to 2m) e-Tag : contact-less automatic identification of measurement point using electronic tags. Learning mode to avoid manual input of codes. Other inputs : Compatible with standard and tri-axial accelerometers Compatible with proximity probes Voltage input +/- 10V and +/- 24V

Vibration velocity 10-1000 Hz according to ISO 2954, ISO 10816 2Hz-300 Hz for reciprocating machines (VDI2063) Detection RMS, peak, peak/peak true and equivalent Display : bar graph, engineering unit and dB Tools for rolling element bearings : Defect Factor (speed 600 to 6000 rpm and Kurtosis for low speed machines)12 9 6 3

Data Processing

Data Processing Frequency range : 0 to 40 kHz Number of lines : 100 to 12800 Zoom : 2 to 128 Envelop : adjustment of band with and central frequency Overlapping : 0, 50, 75 % Averaging : 1 to 4096 with linear, exponential or peak hold Weighting window : Rectangular, Hanning, Flat-top Single or double integration for measurement of vibration velocity or displacement.

Data Processing Synchronous analysis :triggering on analysed signal or trigger input. Post or pre-trigger delay on + or - slope Display of instantaneous spectrum or averaging Cursors : single, harmonic and side band Display : Lin / Log, automatic scaling, engineering unit / dB, Hz / RPM Analysis on all type of signal : vibration, force, pressure, current,.

Data Processing Number of samples : 256 to 32768(512K with DAT option)

Sampling frequency : 1,28 Hz to 102,4 kHz Single or double integration for measurement of vibration velocity or displacement. Averaging : 1 to 4096 with linear, exponential or peak hold Synchronous analysis :triggering on analysed signal or trigger input. Post or pre-trigger delay on + or - slope Demodulation of band pass filtered signal (envelop) Analysis on all type of signal : vibration, force, pressure, current,.

Time wave : instantaneous, averaged, envelop Orbit Auto-spectrum : power / RMS, instantaneous / averaged, zoom, envelop Cross-spectrum instantaneous / averaged Amplitude, phase, real part and imaginary part Shock acquisition : shock weighting window, averaging acceptance Transfer function Transmissibility Coherence

Data Processing

Fault DiagnosisFrequencies are the key to the analysis

What is FFT? FFT Fast Fourier Transformation Whereas a Trend is amplitude values versus time, a "Spectrum" Plot is amplitude versus frequency. A spectrum, a.k.a. an "FFT", allows you to assess severity (with the amplitude) and helps identify the source (with the frequency). This is the most commonly used analysis tool and is usually sufficient protection for general speed machinery.

FFT Tools Moveable Cursor - A "base" cursor that can be moved to any frequency and identifies the amplitude at that frequency. Harmonic Cursors - Activating this tool creates additional cursors (as many as are required) that appear at integer multiples of the base cursor. If the base cursor is located at 1x rpm, harmonics will appear at 2x, 3x, 4x, etc. This is the most important analysis tool available. All harmonic cursors are at higher frequencies than the base cursor. Sideband Cursors - Activating this tool creates additional cursors at frequencies to either side of the base cursor. If the 1st (closest) sideband cursors are located 50 cpm to either side of the base cursor, additional sideband cursors (as many as required) will each be located an additional 50 cpm away. For instance, the 2nd sideband cursors will be 100 cpm away from the base cursor, the 3rd will be 150 cpm away, etc.

FFT TerminologyCommonly used terms include: Fundamental Frequency - 1x rpm. Remember that a belt drive, for instance, has three fundamental frequencies. Dominant Frequency - Frequency at which the highest amplitude occurs. Synchronous Vibration - Vibration harmonically related to a fundamental frequency. Non-synchronous Vibration - Vibration not harmonically related to a fundamental frequency. Sub-synchronous Vibration - Vibration occurring at a frequency below the fundamental frequency.

Fundamental/Dominant Frequency

Running speed (Fundamental)

Synchronous VibrationHarmonics

Non-synchronous VibrationNon-synchronous

Sub-synchronous VibrationSub-synchronous

How is an FFT Analyzed1. 2. 3. 4. 5. What is the dominant peak & amplitude? At what frequency? What failure pattern it corresponds to? Is there any harmonics or sub-synchronous? Is there any indication of bearing problems? 5.1 Acceleration OVL 5.2 Defect Factor 5.3 Bearing Defect Frequencies 5.4 Kurtosis

FFT Resolutions

It determines the accuracy of the frequency data you are analyzing Frequency is how we identify the source of the vibration.

Time Domain Time domain analysis is a powerful but intimidating tool Slow Speed Equipment (< 300 rpm) Sleeve Bearings (particularly if readings reflect true shaft movement) Gear Applications

This is where Kurtosis is applied

Bearing defect due to mounting problem (Kurtosis)

Enveloping

Processing of Enveloping Filters are used to help process the signal and focus on any impacts that may be occurring. The filters come in two classes: Envelope filter - this type of filter sets a frequency 'envelope' that includes a high frequency (Fmax) and a low frequency (Fmin). Any vibration occurring outside that range is filtered out. Hi-Pass filter - this type of filter eliminates the Fmax but still sets an Fmin filter below which all vibration influences are filtered out. Each manufacturer sets up its own signal processing and filters. Therefore, although they each provide similar information, they are not directly comparable in the amplitude realm.

Words of Warning The enveloping spectrum is extremely sensitive. It will pick up impact energy that is not necessarily a problem or is a very early stage problem. For instance, it can detect bearing defects before they have migrated to the surface of the bearing. Pulling the bearing at that point will not reveal a defect and may cost you something more valuable than money credibility. Enveloping spectra should be used in conjunction with other analysis tools (velocity and acceleration spectra, thermography, time domain, your experience, etc.) before performing any corrective actions. It is a powerful tool but must be used with care. Like other aspects of vibration analysis, experience will help greatly as it is acquired.

Spectral Analysis

FREQUENCY

FFT SPECTRUMAMPLITUDE

FREQUENCY

UnbalanceDominant peak

Causes of Unbalance Deposit & built-up of dirt Corrosion & wear Eccentricity

Misalignment

Symptoms of misalignment Wearing of coupling inserts Broken coupling bolts Damage foundation Excessive vibration

Pulley Misalignment Symptoms Premature wearing of belts Belts went out from sheave Broken motor shaft

Looseness Looseness from bolts and nuts Bearing casing or shafting Foundations

Belt Problems Worn-out, mismatch belts, loose belt or over tension belts

Eccentric or bent shaftRADIAL 1X RPM ECCENTRIC PULLEY

1 x rpm is dominant peak measured axial

.

Sleeve bearing looseness Presence of 1x rpm with harmonics

Oil Whirl High Radial Vibration at 0.42 - 0.48 x RPM.

Cocked Bearing / Shaft Bent Through Bearing

Cocked Bearing / Shaft Bent Through Bearing Creates similar or even identical vibration symptoms (with the exception of phase) to misalignment - primarily angular misalignment (axial vibration). Must be diagnosed with axial phase analysis or inspected for.

Bent Shaft @ Bearing Vibration symptoms very similar to direct drive angular misalignment. High axial vibration @ 1x & 2x rpm. 2x rpm radial component often as high or higher than 1x component. Axial phase shift around the face of the bearing equal to change in transducer location (twisting action).

Lubrication Problems Acceleration Overall value is trended: Causes: Over lubrication Insufficient lubrication Contamination High oil level Wrong application of lubricant

Soft foot or air gap problem 120 Hz (7200 CPM) plus sidebands, beating 2x with 120 Hz. Correct distortion on motor bedplate Eliminate excessive bearing clearance. Imbalance voltage

Resonance It is important to note that resonance does not cause vibration it amplifies it.

CavitationCavitation symptoms: High frequency, random vibration. Sounds like the pump is pumping gravel. Although amplitudes may or may not be high enough to affect bearing life significantly, cavitation causes excessive wear on the impeller and other internal components. May come and go from one collection to the next as load varies. First step should be to assess operational parameters - flow rates and pressure - that can also influence this vibration. Actual flow & pressure should be compared to the pump curve and design point of the pump. Insufficient flows and/or pressures lead to cavitation. Second step should be an inspection of the internal components for excessive wear with particular attention paid to the impeller vanes.

Recommended Actions:

Gears Normal Gear Drive Symptoms: Amplitude peaks at 1, 2 and/or 3x GMF. Low amplitude and few sidebands around 1, 2 and/or 3x GMF at 1x rpm of gear with problem

Gear Eccentric or bent shaftEccentric Gear Or Gear On Bent Shaft Symptoms: Higher amplitudes at 1, 2 and/or 3x GMF. High amplitude sidebands around 1, 2 and/or 3x GMF at 1x rpm of gear with problem. Higher amplitudes at 1x rpm of gear with problem and, if the problem is severe, running speed harmonics of that frequency. Inspect gears for wear patterns and check for proper mesh depth. Inspect gears for proper backlash (similar symptoms)

Recommended Actions:

Gear Excessive BacklashExcessive Backlash Symptoms: Higher amplitudes at 1, 2 and/or 3x GMF. High amplitude sidebands around 1, 2 and/or 3x GMF at 1x rpm of one or both of the gears. Amplitude peak at resonant frequency of the gear(s). Sidebands at 1x rpm surrounding the resonant frequency. Inspect gears for proper backlash. Inspect gears for wear patterns and check for proper mesh depth.

Recommended Actions:

Gear Wear (Tooth Wear)Gear Wear Symptoms: Higher amplitudes at 1, 2 and/or 3x GMF. High amplitude sidebands around 1, 2 and/or 3x GMF at 1x rpm of the worn gear. Amplitude peak at resonant frequency of the gear(s). Sidebands at 1x rpm of the worn gear surrounding the resonant frequency. Inspect gears for wear patterns and check for proper mesh depth (similar symptoms see previous page). Inspect gears for proper backlash.

Recommended Actions:

Gear LoadGear Load Symptoms: Higher amplitudes at 1, 2 and/or 3x GMF. Recommended Actions: None unless there is an increase in sideband activity or the appearance of possible gear resonant frequencies

Gear MisalignmentGear Misalignment Symptoms: Highest amplitudes at 2x GMF. Amplitude peaks at other GMF harmonics - 1x, 3x, etc. High amplitude sidebands particularly around 2x GMF at 1x or even 2x rpm. Shaft running speed harmonics - 2x and even 3x rpm. Inspect gears for wear patterns misalignment causes uneven wear. Check for external problems - shaft alignment, soft foot, etc.

Recommended Actions:

Hunting Tooth FrequencyHunting Tooth Symptoms: Amplitude peaks at 1 x FHT and possibly 2 x FHT. Sidebands of FHT around 1x rpm (of each shaft). Sidebands of FHT around 1x GMF and harmonics. Pulsing, growling noise coming from gearbox or drive. Inspect gears for damage.

Recommended Actions:

Machine Condition EvaluationAmplitudes determines a machine condition

Broad Band Vibration Criteria for Specific Machine ISO 10816-3Velocity mm/s in/s Peak RMS 0.28 0.45 0.71 1.12 1.80 2.80 4.50 7.10 11.20 18.00 28.00 45.00 0.02 0.03 0.04 0.06 0.10 0.16 0.25 0.40 0.62 1.00 1.56 2.51 Velocity Range Limits and Machine Class Small Machines Class I Good Satisfactory Unsatisfactory (Alert) Unacceptable (Danger) Satisfactory Unsatisfactory (Alert) Unacceptable (Danger) Satisfactory Satisfactory Unsatisfactory (Alert) Unsatisfactory (Alert) Unacceptable Unacceptable (Danger) (Danger) Medium Machines Class II Less Rigid Rigid Support Support Class Class III IV

Good

Good

Good

Broad Band Vibration Criteria for Specific Machine ISO 10816-3 The pre set thresholds (alarm and danger) given by the standards are overall of velocity with the bandwidth from 10 to 1000 Hz (ISO 10816-1). The rotational speed have to fit with the range from 600 to 12000rpm.

Periodic MonitoringCost effective monitoring means higher profits, recognition, and a better quality of life.

Periodic Monitoring is important There are vibrations whose level goes beyond the danger limit of ISO 10816 but still operational because bearings are still working. There are vibration whose level is excellent but bearing failed.

Excellent Vibration with bearing defect

Periodic Monitoring is important Hence, its best to monitor periodically To determine the condition of machine if affected by the adjacent machine. To predict when to conduct a corrective maintenance, place an order for spare parts, and Monitor the condition of bearing when it will be replaced.

Alignment ToleranceAlignment Rotational Acceptable Tolerance Alignment Rotational Acceptable Tolerance Condition Speed mils mm Condition Speed mils mm Parallel 0 - 1000 5 0.13 Angular 0 - 1000 4 0.1 Offset 1 - 2000 4 0.1 Error 1 - 2000 3.5 0.08 2 - 3000 3 0.07 2 - 3000 2.5 0.07 3 - 4000 2 0.04 3 - 4000 2 0.06 4 - 5000 1.5 0.03 4 - 5000 1.5 0.05 5 - 6000 < 1.5 < 0.03 5 - 6000 1.5 0.04