1702ME402 MEASUREMENTS AND METROLOGYjeevamalar.weebly.com/uploads/2/8/9/8/28980229/unit_5... ·...
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UNIT V
LASER AND ADVANCES IN
METROLOGY
Lecture by
Dr. J.Jeevamalar, M.E., Ph.D.
Associate Professor/ Mechanical
E.G.S. Pillay Engineering College,
Nagapattinam
1702ME402 – MEASUREMENTS
AND METROLOGY
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SYLLUBUS
Interferometer: NPL Flatness, Laser, Michelson
Computer Aided Inspection - Digital Devices - MachineVision System
Coordinate Measuring Machine: Basic concept, Types,Constructional features, Probes, Accessories
Machine Tool Metrology - Surface RoughnessMeasurement - Straightness Measurement -Squareness Measurement
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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PRECISION INSTRUMENTS BASED ON LASER
• Laser stands for "Light Amplification by Stimulated Emission ofRadiation". Laser instruments are devices to produce powerful,monochromatic collimated beam of light in which the waves arecoherent.
• The development of laser gives production of clear coherent light.The biggest advantage of this coherent light is that whole energyappears to be coming from a very small point.
• The laser beam can be focused easily into either a parallel beam orinto a very small point by the use of lens.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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PRINCIPLE OF LASER
• The principle involved in laser is when the photon emitted duringstimulated emission has the same energy, phase and frequency asthe incident photon.
• The photon comes in contact with another atom or molecule in thehigh energy level E2, then it will cause the atom to return to groundstate energy level E1 by releasing another photon.
• The sequence of triggered identical photon from stimulated atom isknown as stimulated emission.
• This multiplication of photon through stimulated emission leads tocoherent, powerful, monochromatic, collimated beam of lightemission. This Light emission is called laser.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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LASER METROLOGY
• A laser beam projected directly onto a position detector is amethod of alignment used in a number of commercially availablesystems. The laser with its highly controlled frequency modes andcoherent output are used extensively for interferometery
• Laser is suitable for more general applications where a convenient,collimated and high intensity source is required Precision, accuracy,no contact and hot moving parts.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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LASER MEASURING MACHINES
1. Laser Telemetric System
2. Laser and LED Based Distance Measuring Instruments
3. For Profile Checks
4. Scanning Laser Gauge
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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1. LASER TELEMETRIC SYSTEM
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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Advantages:
• It is possible to detect changes in dimensions when components are moving.
• It is possible to detect changes in dimensions when product is in continuous processes.
• There is no need to wait for taking measurements when the product is in hot conditions.
• It can be applied on production machines and controlled them with closed feedback loops.
• It is possible to write programs for the microprocessor to take care of smoke, dust and other airborne interference around the work piece being measured.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. LASER AND LED BASED DISTANCE MEASURING INSTRUMENTS
Advantages:
1. It is very reliable because there is no moving part.
2. Instrument response time is in milliseconds.
3. The output is provided as
0 – 20 mA.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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3. FOR PROFILE CHECKS
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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4. SCANNING LASER GAUGE
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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INTERFEROMETRY
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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USE OF LASER IN INTERFEROMETRY
• The laser in interferometery is to find accurate measurementlength.
• It reduces the most time taken arid skill required like at methodsused for finding the length.
• The accuracy of measurement is the order of 0.1m in 100m.
• In modified laser designs, a single frequency is selected from thecoherent beam and used for interferometric measurement.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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LASER INTERFERMETER
• The laser interferometery involves the following components,
1. Two frequency laser source.
2. Optical elements.
3. Laser heads measurement receiver.
4. Measurement display.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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AC LASER INTERFEROMETER
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. OPTICAL ELEMENTS
The various optical elements are,
a. Beam splitters.
b. Beam benders.
c. Retro reflectors.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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a. Beam splitters
It is used to divide the laser beam into separate beams along different axes.
It is possible to adjust the spitted laser's output intensity by having a choice of beam splitter reflectivities.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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b. Beam benders
• It is used to deflect the lightbeam around comers on it pathfrom the laser to each axis.
• The beam benders are just flatmirrors, but having absolutely flatand very high reflectivity.
• Normally, the beam deflection isavoided for not to disturb thepolarizing vectors.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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c. Retro Reflectors
• They are plane mirrors, roof prisms orcube comers.
• The cube comers are three mutuallyperpendicular plane mirrors, and thereflected beam is always parallel tothe incident beam in these devices.
• In case of AC laser interferometer measurements, two retro reflectors areused.
• When plane mirror is used as retro reflectors in plane mirrorinterferometer, it must be flat with in 0.06 micron per cm.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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3. LASER HEAD'S MEASUREMENT RECEIVER:
• It is used to detect the part of the returning beam as f1 – f2 and a Doppler shifted frequency component ∂f .
4. DISPLAY:
• The measurement display has a microcomputer to compute and display results.
• The signals from reference receiver and measurement receiver located in the laser head are counted in two separate pulse counters and subtracted.
• Other input signals for correction are temperature co-efficient of expansions. Air velocity is also displayed.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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OTHER TYPES OF INTERFEROMETERS
1. Michelson Interferometer
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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the conditions for improving michelson interferometer are ,
1. Use of laser light source for measuring longer distances
2. Instead of using mirror the cube corner reflector is best suitable for reflecting the light.
3. Photocells can be employed to convert light intensity variation in voltage pulses to given direction of pc change.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. Twyman - Green Interferometer
Used as a polarizing interferometer with variable amplitude balancing between sample and reference waves.
For an exact measurement of the test surface, the instrument error can be determined by an absolute measurement.
This error is compensated by storing the same in microprocessor system and subtracting from the measurement of the test surface.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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It has the following advantages,
• It permits testing of surface with wide varying reflectivity.
• It avoids undesirable feed back of light reflected of the tested surface and the instrument optics.
• It enables utilization of the maximum available energy.
• Polarisation permits phase variation to be effected with the necessary precision.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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LASER INTERFEROMETER APPLICATIONS
1. Linear measurement
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. Angular measurement
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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COORDINATE MEASURING MACHINES
• The term measuring machine generally refers to a single-axis
measuring instrument.
• Such an instrument is capable of measuring one linear dimension
at a time. The term coordinate measuring machine refers to the
instrument/machine that is capable of measuring in all three
orthogonal axes.
• Such a machine is popularly abbreviated as CMM. A CMM
enables the location of point coordinates in a three-dimensional
(3D) space.
• It simultaneously captures both dimensions and orthogonal
relationships. Another remarkable feature of a CMM is its
integration with a computer.
• The computer provides additional power to generate 3D objects as
well as to carry out complex mathematical calculations. Complex
objects can be dimensionally evaluated with precision and speed.Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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CO-ORDINATE MEASURING MACHINE
Construction of CMM:
• The co-ordinate measuring machine has movements in X-Y-Z which can be easily controlled and measured.
• Each slide in three in three directions has transducer which gives digital display and senses +ve or –ve direction.
• The measuring head has a probe tip, which can be different kinds like taper tip, ball tip etc.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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• Four elements,
1. Three axis motion structure
2. Probing system
3. m/c controller & computer hardware
4. Application software
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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1. Three axis motion structurei. The Axis Coordination
- each axis fitted with transducer for positional feedback
- Axis movement through precision guide ways ( air bearing)
- frame material – aluminium alloys, ceramic, SiC
ii. Length Measurement M/C- measuring scales & scale readers
- stainless steel & glass scale
- having electro optical reader heads for exact position
iii. Base With Table- attached with base
- Granite material
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. Probing System
-for gathering data
- end of probe : hard ball (steel or ruby)
3. M/C Controller & Computer Hardware
- axis controller, probing, programming, control ofmeasuring m/c, data acquisition and evaluation
-computers can also used to control
4. Application SoftwareDr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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TYPES OF CMM
1. a/c to control system,a. Manual CM
b. Computer Numerical Control
2. a/c to design of main structure,a. Cantilever type. b. Bridge type.
c. Articulated arm d. Gantry Type
3. a/c to mounting stylea. Bench top
b. Free standing
c. Portable & hand held
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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1. Cantilever type• supports probe from
movable vertical support
2. Bridge type• horizontally suspended
• x-axis carries the bridge
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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4. Gantry Type
• frame structure raised
on side supports similar
to bridge style
3. Column Type• portable or tripod mounted
• probe can be placed in many
different directions
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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5. Horizontal arm CMM
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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TYPES OF PROBES
1. Contact Type,
a) Hard Or Fixed Type
b) Touch Trigger
c) Displacement Probe
2. Non- Contact Type,
a) Optical Probe
b) Acoustical Probe
c) Laser Probe
d) Vision Probe
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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FEATURES OF CMM
1. In faster machines with higher accuracies, the stiffness toweight ratio has to be high in order to reduce dynamic forces.
2. All the moving members, the bridge structure Z- axis carriageand Z-column are made of hollow box construction.
3. Errors in machine are built up and fed into the computersystem so that error compensation is built up into thesoftware.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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4. All machines are provided with their own computers and theCMM can able to measure three-dimensional object fromvariable datums.
5. For compensation of temperature gradient, thermocouples areconnected with the machine and interfaced with the .computer. This will provide the CMM in high accuracy andrepeatability.
6. Rapid growth in software for three and four axes movementsenable CMM to measure hole center distances and formmeasurements such as turbine blades, cam profiles
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CAUSES OF ERRORS IN CMM 1. The table of CMM may not have perfect geometric form.
2. The probes may have a degree of run out.
3. Some perpendicularity errors occur when probe is moving up and down.
4. Dimensional errors of a CMM is influenced by,
a. Straightness and perpendicularity of the guide ways.
b. Scale division and adjustment of scales.
c. Probe length and probe structure.
d. Interpolation error due to digitization.
e. Errors of data feeding by operators into computers.
f. Specimen weigh, clamping, surface finish and hardness.
g. Environment. 5. The other errors can be controlled by the manufacturer and
minimized by the measuring software.
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6. The length of the probe should be minimum and rigid in order to reduce deflection.
7. The weight of the work piece may change the geometry of the guide ways and therefore, the work piece must not exceed maximum weight
8. Variation in temperature of CMM, specimen and measuring lab influence the uncertainty of measurements.
9. The smoke particle, a finger print, a dust particle and human hair may introduce uncertainty in measurement.
10. The translational errors result from errors in the scale division and errors in axis direction.
11. Perpendicularity error occurs if the three axes are not orthogonal.
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PERFORMANCE OF CMM
1. Geometrical accuracies such as positioning accuracy, straightness and squareness
2. Measuring accuracy in terms of axial length measuring accuracy.
3. Volumetric length measuring accuracy and length measuring repeatability i.e., CMM has to be tested as complete system.
4. Environmental effects have great influence for the accuracy testing, including parameters, vibrations and relative humidity and required.
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APPLICATIONS OF CMM
1. CMM finds applications In automatic, machine tool, electronics, space and many other large companies.
2. For development of new products and construction of prototype.
3. It is very much useful in checking NC produced work piece in various steps of production.
4. For aircraft and space vehicle, hundred percent inspections are carried out by using CMM.
5. Used for determining the dimensional accuracy of the components.
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6. Its ideal for determination of shape and position, maximum metal condition, linkage of results etc.
7. Best suited for the test and inspection of test equipment - gauges & tools.
8. Sorting tasks to achieve optimum pairing of components with tolerance limits.
9. Used for low degree of utilization like gear tester, gauge tester, length measuring machine-measuring microscope etc.
10. For ensuring economic viability of NC machines by reducing their downtime for inspection results.
11. Helps in reading cost, rework cost at the appropriate time with a suitable CMM.
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ADVANTAGES OF CMM
1. The inspection rate is increased.
2. Improved accuracy of machined parts.
3. Minimisation of operator error.
4. Skill requirements of the operator is reduced.
5. Reduced inspection fixturing and maintenance cost.
6. Uniform inspection quality.
7. Reduction in calculating and recoding time and errors.
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8. Reduction in setup time.
9.Compensation for misalignment.
10. No need of separate go/no go gauges for each feature.
11. Reduction of scrap and good part rejection.
12. Provision of a permanent record for process Control.
13. Reduction in offline analysis time.
14. Simplification of inspection procedures.
15. Possibility of reduction of total inspection time.
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DISADVANTAGES OF CMM
1. The lable and probe may not be in perfect alignment.
2. The probe may have run out.
3. The probe moving in Z-axis may have some perpendicular errors
4. Probe will move in X and Y direction but not be square to each other.
5. There may be errors in digital system.
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FEATURES OF CMM SOFTWARE
1. Measurement of diameter, centre distance, length.
2. Measurement of plane and spatial curves.
3. Minimum CNC programme.
4. Data communications.
5. Digital input and output command.
6. Programme for the measurement of spur, helical, bevel and hypoid gears.
7. Interface to CAD software.
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DIGITAL DEVICES
• Digital indication is better by far when an exact initiative value is desired.
• The important elements of any electronic signal readout system are the scale unit or transducer and the Counter of digital readout unit
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THE ADVANTAGES OF DIGITAL SYSTEMS
1. Measuring element is free from errors.
2. Learning time is short.
3. More accurate measurement.
4. Excessive reading errors can be eliminated.
5. Clear readability of digital readout is advantageous for persons with impaired vision.
6. The display can be zero wherever it is desired.
7. BCD output makes the instrument computer compatible.
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COMPUTER BASED INSPECTION
MACHINE VISION
• Machine vision is the ability of a computer to see
the object.
• Also called as computer vision or artificial
vision.
•It is technique which allow a sensor to view the
object and derive a mathematical or logical decision
without human intervention.
•Functions of machine vision,1. image sensing
2. image analysis
3. image interpretation
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Stages of Machine Vision
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• Stages of Machine Vision
1. Image generation and digitization
• The primary task in a vision system is to capture a 2D or 3D image
of the work part. A 2D image captures either the top view or a side
elevation of the work part, which would be adequate to carry out
simple inspection tasks. While the 2D image is captured using a
single camera, the 3D image requires at least two cameras
positioned at different locations. The work part is placed on a flat
surface and illuminated by suitable lighting, which provides good
contrast between the object and the background. The camera is
focused on the work part and a sharp image is obtained. The image
comprises a matrix of discrete picture elements popularly referred
to as pixels. Each pixel has a value that is proportional to the light
intensity of that portion of the scene. The intensity value for each
pixel is converted to its equivalent digital value by an analog-to-
digital converter (ADC).Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. Image processing and analysis
• The frame buffer stores the status of each and every pixel. A number
of techniques are available to analyse the image data. However, the
information available in the frame buffer needs to be refined and
processed to facilitate further analysis. The most popular technique
for image processing is called segmentation. Segmentation involves
two stages: thresholding and edge detection. Thresholding converts
each pixel value into either of the two values, white or black,
depending on whether the intensity of light exceeds a given threshold
value. This type of vision system is called a binary vision system. If
necessary, it is possible to store different shades of grey in an image,
popularly called the grey-scale system. If the computer has a higher
main memory and a faster processor, an individual pixel can also
store colour information. Edge detection is performed to distinguish
the image of the object from its surroundings. Computer programs are
used, which identify the contrast in light intensity between pixels
bordering the image of the object and resolve the boundary of the
object.Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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3. Image interpretation
• Once the features have been extracted, the task of identifying the
object becomes simpler, since the computer program has to match the
extracted features with the features of templates already stored in the
memory. This matching task is popularly referred to as template
matching. Whenever a match occurs, an object can be identified and
further analysis can be carried out. This interpretation function that is
used to recognize the object is known as pattern recognition. It is
needless to say that in order to facilitate pattern recognition, we need
to create templates or a database containing features of the known
objects. Many computer algorithms have been developed for template
matching and pattern recognition. In order to eliminate the possibility
of wrong identification when two objects have closely resembling
features, feature weighting is resorted to. In this technique, several
features are combined into a single measure by assigning a weight to
each feature according to its relative importance in identifying the
object. This adds an additional dimension in the process of assigning
scores to features and eliminates wrong identification of an object.Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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4. Generation of actuation signals
• Once the object is identified, the vision system should direct the
inspection station to carry out the necessary action. In a flexible
inspection environment, the work-cell controller should
generate the actuation signals to the transfer machine to transfer
the work part from machining stations to the inspection station
and vice versa. Clamping, declamping, gripping, etc., of the
work parts are done through actuation signals generated by the
work-cell controller.
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Surface Roughness Measurement
Factors affecting surface roughness are,
1. Work piece
2. material Vibrations
3. Machining type Tool
4. Fixtures
The geometrical irregularities can be classified as
1. First order2. Second order 3. Third order
4. Fourth orderDr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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1. First order irregularities
They are caused by lack of straightness of guide ways on which tool must move.
2. Second order irregularities
They are caused by vibrations.
3. Third order irregularities
They are caused by machining.
4. Fourth order irregularities
They are caused by materials.
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ELEMENTS OF SURFACE TEXTURE
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ELEMENTS OF SURFACE TEXTURE
1. Profile
It is the contour of any section through a surface.
2. Lay
It is the direction of the 'predominate surface grooves that are produced by machining.
3. Flaws
It is the surface irregularities or imperfection due to cracks, blow holes, scratches etc.
4. Actual surface
It is the surface of a part which is actually obtained.Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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5. Roughness
It is finely spaced irregularities. It is also called primary texture.
6. Sampling lengths
It is the Length of profile necessary for the evaluation of~ irregularities.
7. Waviness
It is the surface irregularities which are of greater spacing than roughness.
8. Roughness height
It is rated as the arithmetical average deviation.
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9. Roughness width
It is the distance parallel to the normal surface between successive peaks.
10. Mean line of profile
A Line divides the effective profile such that within the sampling length is called as mean line or profile.
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Analysis of surface finish
1. The average roughness method.
2. Peak to valley height method
3. From factor
1. Average roughness measurement
The assessment of average roughness is carried out by
a. Centre line average (CLA)
b. Root mean square (RMS)
c. Ten point method
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a. CENTRE LINE AVERAGE (CLA)
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B. ROOT MEAN SQUARE (RMS)
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C. TEN POINT METHOD
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2. PEAK TO VALLEY HEIGHT METHOD
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METHODS OF MEASURING SURFACE FINISH
The methods used for measuring the surface finish are classified into,
1. Inspection by comparison
2. Direct Instrument Measurements
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1. Inspection by comparison
a. Touch Inspection.
b. Visual Inspection.
c. Microscopic Inspection.
d. Scratch Inspection.
e. Micro Interferometer.
f. Surface photographs.
g. Reflected Light Intensity
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2. Direct Instrument Measurements
1. Stylus probe instruments
2. Tomlinson surface meter
3. Profilometer
4. Talyor- Bobson - Talysurf
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1. STYLUS PROBE INSTRUMENTS
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2. TOMLINSON SURFACE METER
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3. PROFILOMETER
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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4. TALYOR- BOBSON -TALYSURF
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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MACHINE TOOL METROLOGY
• The accurate production of the component parts dependsupon the accuracy of the machine tools.
• The quality of piece depends on,
1. Rigidity and stiffness of machine tool and its components.
2. Alignment of various components in relation to oneanother.
3. Quality and accuracy of the control devices and the drivingmechanism.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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• The alignment accuracy of the machine tools is checked by somegeometric tests. They are,
1. Geometrical Test
• Dimensions of components, position of components anddisplacement of component relative to one another are checked.
a. Static tests:
• Checks the alignment accuracy of the varies parts of machine tools
b. Dynamic tests:
• Performed under dynamic loadig conditions
2. Practical Test
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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VARIOUS GEOMETRICAL CHECKS ON MACHINE TOOL
• Straightness.
• Flatness.
• Parallelism, equidistance and coincidence.
• Squareness of straight line & plane.
• Rotations
• Out of round.
• Eccentricity.
• Run out.
• Periodical axial slip.
• Camming.
• Movement of all the working components.
• Spindle test for
• Concentricity.
• Axial slip.
• Accuracy of axis and position.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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STRAIGHTNESS MEASUREMENTS
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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• Types of Straightness Measurements,
1. Straight edge or Spirit level
2. Auto collimator
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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1. STRAIGHT EDGE OR SPIRIT LEVEL
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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2. AUTO COLLIMATOR
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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SQUARENESS MEASUREMENT•Very often, two related parts of a machine need to meet perfect
squareness with each other.
• In fact, the angle 90° between two lines or surfaces or their
combinations, is one of the most important requirements in engineering
specifications.
• For instance, the cross-slide of a lathe must move at exactly 90° to the
spindle axis in order to produce a flat surface during facing operation.
• Similarly, the spindle axis of a drilling machine and a vertical milling
machine should be perfectly square with the machine table.
•From a measurement perspective, two planes, two straight lines, or a
straight line and a plane are said to be square with each other when
error of parallelism in relation to a standard square does not exceed a
limiting value.
•The standard square is an important accessory for conducting the
squareness test. It has two highly finished surfaces that are
perpendicular to each other to a high degree of accuracy.Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC
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SQUARENESS MEASUREMENT
•Two surfaces need to have a high
degree of squareness. The base of a
dial gauge is mounted on one of
the surfaces, and the plunger is
held against the surface of the
standard square and set to zero.
•Now, the dial gauge base is given a
traversing motion in the direction
shown in the figure, and deviation
of the dial gauge is noted down.
• The maximum deviation
permissible for a specific
traversing distance is the error in
squareness.
Dr. J.Jeevamalar, M.E., Ph.D. / EGSPEC