ME C40-3
Computer Integrated Manufacturing
- Manufacturing Automation -
LABORATORY EXERCISE #2
LASER INTERFEROMETRY
I. OBJECTIVES:
1. To become familiar with the principles of laser interferometry.
2. To learn about laser interferometric measurement methods for machine alignment, machine and sensor calibration, and dimension and form measurements.
3. To apply interferometric measurements for assessing machine tool accuracy (velocity, position, and angular errors) and to calibrate a Magnetic Ball-Bar system and/or assess part flatness.
II. BACKGROUND:
Laser interferometric measurement methods are among the most accurate and frequently the only choice for manufacturing tasks aimed at high accuracy and precision. They are used in several different ways: (a) as an integral part of a piece of machinery or equipment by constituting the position feedback sensing system (e.g., machinery for IC manufacture, ultra-precision machine tools, and CMMs), (b) for the assessment of a machine's accuracy and provision of calibration data (e.g., calibration of machine tools for CNC software compensation), (c) for the calibration of various less accurate sensing systems (scales, ball-bars, etc.), (d) as metrology instruments for dimensional measurements, form measurements, etc.
We will explore the principles of operation, implementation issues, and the advantages and disadvantages of laser interferometry for some of the tasks listed above.
III. EQUIPMENT:
- Hewlett-Packard 5528A Laser Measurement System
- Measurement Display
- IBM Personal Computer
- Dimensional Metrology Software
- A variety of optics, including interferometers and retroreflectors
- Linear Slide
- Magnetic Ball-Bar
A brief description of the characteristics of the laser system is given below.
The 5518A Laser Head you will be using houses the laser tube which produces the laser beam used in making measurements. It also contains the measurement receiver into which the laser beam is returned by the measurement optics.
The 5508A Measurement Display
1) provides the power to operate the laser head,
2) converts measurement information received from the laser head into a number that represents a unit of length or seconds of arc of an angle,
3) provides the control and display interface for the operator, and
4) provides an interface for any optional devices.
You can think of the measurement display’s front-panel keys as being organized into four groups:
INDICATORS: Display measurement values, beam strength, and laser status.
MEASUREMENT MODE KEYS: Allow four different measurements to be made.
ENTRY KEYS: Allow manual setting of Set-up keys or inputting of measurement data.
SET-UP KEYS: Allow manipulation of measurement values by providing velocity-of-light (VOL) compensation, thermal expansion compensation, preset calibration numbers, different resolutions, smoothed data, and different sign conventions.
IV. ASSIGNMENT AND REPORT FORMAT:
This exercise will consist of two tasks of the three listed below (depending on availability of equipment), representing different uses of the laser interferometer.
1. Error Motions of a Linear Machine Slide. Using the laser measurement system and the assorted optics, setup a machine tool slide to take measurements of distance traveled. Move the slide a specific displacement and compare this distance to the actual distance recorded by the laser system. Reset the optics for other measurements and establish velocity and angular errors. Report on discrepancies and trends in error.
Perform the experiments for each of the three measurements described above (distance, velocity, angular error). For each set of runs, report on the deviation. Using the Dimensional Metrology software, you will be able to store all of the runs in memory. At the Output Method Menu, choose the "Display/Print all Runs" option and print out all the runs of each measurement (Positioning A and B, Velocity, and Angular A and B). Then choose the "Display/Print Averages only" option to print out the averages of each measurement. Use these plots as part of your report.
2. Ball-Bar System Calibration. Using the laser easement system and the assorted optics, calibrate a Magnetic Ball-bar System. Develop appropriate calibration equations.
Finish up your laboratory report by commenting on any deviations you may have found. Hypothesize on the reasons for these deviations. Report your theories and include any suggestions you may have for future measurements.
V. PROCEDURE:
Note: The procedure of this handout is separated into distinct subsections (A, B,C, D, and E). Each subsection can stand alone as a measurement procedure. All are included here to act as a reference for any future measurements you might make.
PROCEDURE A:
DISTANCE MEASUREMENTS
Interferometer Assembly:
A distance measurement is made using two retroreflectors and one interferometer. The interferometer is placed in the path between the laser head and the two retroreflectors, as shown in Figure 1(a). In actual practice, one of the retroreflectors will be physically attached to the interferometer and the other one will be allowed to move with respect to the interferometer. When planning your setup, it is important to note that the "tail" end of one of the arrows on the interferometer’s label must be toward the laser head, and the "head" of each of the arrows must point toward a retroreflector, whether attached or moving. When the measurement you want to make is along the laser beam, your interferometer assembly will look like Figure 1(b). When the measurement you want to make is along an axis at right angles to the laser beam, your interferometer assembly will look like Figure 1(c). Note that each of the views in Figure 1 is a side view. Attach one of the retroreflectors to the interferometer as shown in Figure 1(b), using the two small knurled screws included. In actual practice, you set up for a measurement perpendicular to the laser beam the same as shown in Figure 1(b), except you rotate the interferometer until the arrows point in the directions you need.
Important Considerations:
1. The interferometer assembly must be located between the laser head and the retroreflector in the laser beam.
2. The beam from the laser head must enter the interferometer at the "tail" of one of the arrows on its label.
3. Vibrations and loose connections must be minimized by proper mounting.
4. The laser beam must be returned to the bottom port on the laser head’s turret.
5. The optics must be aligned to the laser beam well enough to keep the cosine error at an acceptable level.
6. The optics must be aligned to the laser beam well enough to keep the beam strength indicator in the green region along the entire optical path.
7. The laser head turret ring should be set to "OTHER".
Description:
1. You will initially position the optics around the laser beam while they are at the near end of travel using the procedures below.
2. Next, you will adjust the laser head to track the optic’s progression along the travel path, while maintaining the beam’s near-end-of-travel position.
3. Finally, you will check your alignment to insure the "Important Considerations" #5 and #6 have been fulfilled.
Figure 1. Interferometer Assembly for Distance and Velocity Measurements
Procedure:
1. Move the moveable part of your machine as close to the laser head as possible.
2. Visually align the laser head as well as you can parallel to the direction of travel and position it at an appropriate height.
3. Decide where you will position the optics so that:
- the interferometer is between the reflector and the laser head.
- one optic is where the tool mounts and the other is where the workpiece mounts.
- the optics are at the "near end of travel".
4. Attach the interferometer and the retroreflector to a height adjuster to accommodate the positions you chose in step 3.
5. Select the small opening for the laser head’s exit port, and rotate the target into place over the laser head’s bottom port.
6. Move the interferometer in the laser beam while watching the front of the laser head. Position the interferometer or the laser head so the return beam is centered on the laser head return port’s target.
7. Secure the entire assembly to the machine.
8. Position the retroreflector as closely as possible to the interferometer. Look at the front of the laser head and adjust the retroreflector until its return beam also hits the bottom port’s target. Block the laser beam path between the interferometer and the retroreflector to distinguish between the two returning beams. (The dot that remains on the front of the laser head is the interferometer’s return beam. It may be helpful to start by lining up the edges of the retroreflector with those of the interferometer.)
9. Secure the reflector assembly to the machine.
10. Attach the targets to the interferometer and retroreflector, so that
- the hole in the interferometer’s target is centered around the beam, and
- the crosshairs on the retroreflector’s target are also centered on the beam.
11. You are now ready to align the laser to the machine’s travel.
Gunsight Alignment:
1. Verify that you have attached targets to the optics as described above.
2. Move the retroreflector away from the laser. Stop movement when the laser beam is about to move off the retroreflector’s target surface, or when the optics reach the end of travel.
3. Now make a series of adjustments to the laser head until the beam returns to where it was originally on the reflecting optic or its target.
a. Rotate (turn) the laser head to move the beam back toward the crosshairs or etched line on your reflecting optic. As soon as you do this, the laser beam will be partially or fully blocked by the interferometer’s target hole.
b. Translate the laser head vertically and horizontally until the beam again goes through the hole in the interferometer’s target. If the laser beam is not now hitting the correct point on the reflecting optic, perform again the process of turning and translating the laser head.
4. Continue this process of moving the reflecting optic and then adjusting the laser head as many times as necessary until the end of travel is reached. At this point, the laser will be aligned to the table and to the optics.
Checking Alignment for Beam Strength:
1. Verify that you have attached the laser head to the optics as described above.
2. Open both laser head ports to their largest openings.
3. Move the optics over their full travel length while watching the BEAM STRENGTH meter. Any reading in the meter’s green area indicates sufficient beam strength.
4. If the meter’s reading goes into the red area at any time, return the optics to their "near-end-of-travel" position and reposition them so their return dots overlap on the laser head’s crosshair target (after you rotate the target into position at the return port and rotate the small aperture into position at the exit port). Then repeat both alignment checks.
Checking Alignment for Cosine Error:
1. Remove the optic’s targets, if you used them. Make sure that the exit port’s small aperture is selected, and the return port’s target is in place.
2. Observe two dots on the laser head’s return port target. The dots may be overlapped completely (thus appearing as a single dot).
3. Move the machine you are measuring over its full length of travel.
4. Observe how much motion occurs between the two dots. Note that it’s the change in spacing between the dots, not the original spacing between them that’s important. One dot should not move, depending on which optic is stationary. If there is any motion, cosine error is present.
5. Calculate the amount of cosine error as follows:
(a) Judge the amount of motion between the dots. The smallest motion you are likely to perceive is about 0.25 mm (0.010 inch). Let this distance be "S" in the formula below.
(b) Determine the length of machine (optic) travel. Let this be "D" in the formula below.
(c) Your cosine error (E) will then be:
E = S2 / 8D2, in parts-per-million.
6. If the cosine error in your setup is within the limits you need for your measurement, you are finished. If the cosine error is larger than you can tolerate, realign the optics and laser head to reduce any motion between the dots.
Measurements Along a Perpendicular Axis:
When a measurement axis is perpendicular to the laser beam, mount the interferometer in line with the laser, and at the end of the axis you will be measuring. See Figure 2. Be sure to rotate the interferometer so the arrows on its side line up with the laser beam and the measurement axis.
Measurement Display Settings and Keys:
DISTANCE: Push the distance key to make distance measurements.
Figure 2. Three-axis Positioning of Optics
V.O.L.: This is the velocity-of-light key. You must calculate the V.O.L. compensation number using the following section. The default value for V.O.L. is 728.8. This corresponds to an air temperature of 20 C, an air pressure of 760 mm, and relative humidity of 50%.
MATL TEMP: Measure the average material temperature by some means and enter it by pressing XX.XX, followed by the MATL TEMP key. The default value is 20 C.
PRESET: Enter a preset number if you want one used. Zero is the default.
DIR SENSE: Determine which direction you want to be positive, and use this button to make sure it happens.
EXP COEFF: Enter the EXPansion COEFFicient for the material whose temperature you are measuring. Enter the value in parts-per-million-per-degree. For steel, the expansion coefficient is 11.7 ppm-per-degree. You should enter 11.7 then press the EXP COEFF key. Be sure you are using the correct units!
RESOL: Determine the resolution you need from the accuracy you want. Enter the number of places you want, and then press the RESOL key. Resolution extends to five places for millimeters and to six places for inches.
What is the V.O.L. Compensation Factor?
The laser measurement system works by counting wavelengths of the laser beam as the various measurement optics are moved. The wavelength, frequency and the velocity of light are related as follows:
wavelengths (per cycle) = velocity / frequency
The velocity of light is constant in a vacuum, but varies in air as a function of the air’s temperature, pressure and humidity. Since the frequency of the laser is held constant, the wavelength of its light will vary as the light’s velocity varies, and this variation in wavelength will affect your measurements. A one-part-per-million variation in the velocity of light can result from any one of the following:
- a 1-degree C change in air temperature,
- a 2.5 mm of mercury change in air pressure,
- an 80% change in relative humidity.
The distance shown on the measurement display unit at any time is equal to the product of the laser wavelength times the number of wavelengths counted since RESET was last pressed. In practice, this product operation is done in two steps. First, the number of wavelengths counted is multiplied by the compensation factor, and this result is then multiplied by the vacuum wavelength of the laser light. That is,
D = N x CF x Wv
where
D = distance
N = number of wavelengths of motion
CF = the compensation factor.
The compensation factor has the format "0.999abcd" where "abcd" is the four-digit compensation number you enter for V.O.L.. The compensation factor represents the ratio of the wavelength of light in air to the wavelength of light in vacuum.
For example, for an air temperature of 25 degrees C, air pressure of 762.0 mm, and relative humidity of 50%, this ratio is equal to 0.9997329. For the operating environment specified for the laser, no change will ever occur in the first three digits of the ratio; therefore you will have to enter only the last four digits of the value, in the format "abc.d" (in this case, "732.9").
This value would be entered manually as "732.9" followed by the V.O.L. key.
System Checks:
1. Make sure both laser head ports are switched to their large apertures.
2. The laser head turret must be set to "OTHER".
3. The laser head’s "READY" indicator must be lighted steadily, i.e. not blinking.
4. Make sure the laser measurement system is properly interfaced with other instruments, as needed to record your data. If you record your data manually, no interfacing is necessary. For formatted automatic records, the HP Dimensional Metrology Analysis Software is available to record your data automatically. Instructions on its use will be discussed in your laboratory section.
Procedure:
1. Push the RESET key on the measurement display or on the remote control unit connected to the measurement display. (Remember to do this only when the optics are as close together as possible to prevent "deadpath error".)
2. Move one of the optics a predetermined distance.
3. Press the RECORD button on the remote control unit. One measurement is made each time you press this button.
PROCEDURE B:
VELOCITY MEASUREMENTS
Assembly, Installation, and Alignment of Optics:
For each of these setups, the procedures are exactly the same as for those for distance measurements. No additional setup is necessary.
Measurement Display Settings and Keys:
VELOCITY: Push the velocity key to make velocity measurements.
V.O.L.: This is the velocity-of-light key. You must calculate the V.O.L. compensation number as described under Procedure A above. The default value for V.O.L. is 728.8. This corresponds to an air temperature of 20 C, an air pressure of 760 mm, and relative humidity of 50%.
MATL TEMP: Measure the average material temperature by some means and enter it by pressing XX.XX, followed by the MATL TEMP key. The default value is 20 C.
PRESET: Enter a preset number if you want one used. Zero is the default.
DIR SENSE: Determine which direction you want to be positive, and use this button to make sure it happens.
EXP COEFF: Enter the EXPansion COEFFicient for the material whose temperature you are measuring. Enter the value in parts-per-million-per-degree. For steel, the expansion coefficient is 11.7 ppm-per-degree. You should enter 11.7 then press the EXP COEFF key. Be sure you are using the correct units!
RESOL: Determine the resolution you need from the accuracy you want. Enter the number of places you want, and then press the RESOL key. resolution extends to five places for millimeters and to six places for inches.
System Checks:
1. Make sure both laser head ports are switched to their large apertures.
2. The laser head turret must be set to "OTHER".
3. The laser head’s "READY" indicator must be lighted steadily, i.e. not blinking.
4. Make sure the laser measurement system is properly interfaced with other instruments, as needed to record your data. If you record your data manually, no interfacing is necessary. For formatted automatic records, the HP Dimensional Metrology Analysis Software is available to record your data automatically. Instructions on its use will be discussed in your laboratory section.
Procedure:
1. Push the RESET key on the measurement display or on the remote control unit connected to the measurement display. (Remember to do this only when the optics are as close together as possible to prevent "deadpath error".)
2. Setup the measurement display to make measurements at specific time intervals (i.e., "on the fly"). If you are interfacing to a controller, you should probably do this through its programs. Enter the time interval you want between measurements (0.05 to 12 seconds). Push the AUTO RECORD key. This will start the automatic acquisition of data.
3. Move one optic along the full measurement path. A measurement is made automatically every so many seconds until you press the AUTO RECORD key again.
4. Press the AUTO RECORD key when the end of travel is reached. This will turn off the AUTO RECORD, and stop the recording of measurements.
PROCEDURE C:
ANGULAR MEASUREMENTS
Important Considerations:
See Figures 3 and 4.
1. The angular interferometer must be located between the laser head and the angular reflector in the laser beam.
2. The beam from the laser head must enter the angular interferometer (a) through the single opening on one side for an in-line measurement, or (b) through the opening in the bottom for a measurement along an axis perpendicular to the laser beam.
3. Vibrations and loose connections must be minimized by proper mounting
4. The laser beam must be returned to the bottom port on the laser head’s turret.
5. The optics must be aligned to the laser beam well enough to keep the cosine error at an acceptable error.
6. The optics must be aligned to the laser beam well enough to keep the beam strength indicator in the green region along the entire optics’ path.
7. The laser head turret ring should be set to "OTHER".
Description:
1. You will initially position the optics around the laser beam while they are at the near end of travel using the procedures below.
2. Next, you will adjust the laser head to track the optic’s progression along the travel path, while maintaining the beam’s near-end-of-travel position.
3. Finally, you will check your alignment to insure the "Important Consideration" #5 has been fulfilled.
Procedure:
1. Move the moveable part of your machine as close to the laser head as possible.
2. Visually align the laser head as well as you can parallel to the direction of travel and position it at an appropriate height.
3. Decide where you will position the optics so that:
- the interferometer is between the reflector and the laser head.
- one optic is where the tool mounts and the other is where the workpiece mounts.
- the optics are at the "near end of travel".
4. Attach the angular interferometer and the angular reflector to a height adjuster to accommodate the positions you chose in step 3.
5. Select the small opening for the laser head’s exit port, and rotate the target into place over the laser head’s bottom port.
Attach the target to the angular interferometer. The target should be attached to the angular interferometer opening that is directed toward the laser head, and in such a way that the small hole is above the crosshair. Make sure the target is positioned as squarely as possible relative to the edges of the optic.
Figure 3. Attaching Alignment Target to Angular Interferometer
Figure 4. Attaching Alignment Target to Angular Reflector
7. Move the angular interferometer (or translate the laser head) so the laser beam goes through the target hole.
8. Secure the entire assembly in such a way that the interferometer is as square as possible relative to the incoming beam.
9. Remove the target from the interferometer.
10. Position the reflector as closely as possible to the interferometer. Look at the front of the laser head and adjust the reflector until the return beam hits the laser head bottom port’s target. This establishes the "near end of travel". It may help to start by visually lining up the reflector’s edges with the edges of the interferometer.
11. Secure the reflector assembly to the machine so it is square relative to the incoming beam and so that it is not out-of-square in the "roll" direction by more than +/- 1 degree.
12. Reattach the targets to the interferometer and reflector, except now attach them so the hole in the interferometer’s target is centered around the beam, and the crosshairs on the reflector’s target are also centered on the beam. Review Figure 4.
13. You are now ready to align the laser to the machine’s travel.
Gunsight Alignment:
1. Verify that you have attached targets to the optics as described above.
2. Move the retroreflector away from the laser. Stop movement when the laser beam is about to move off the retroreflector’s target surface, or when the optics reach the end of travel.
3. Now make a series of adjustments to the laser head until the beam returns to where it was originally on the reflecting optic or its target.
a. Rotate (turn) the laser head to move the beam back toward the crosshairs or etched line on your reflecting optic. As soon as you do this, the laser beam will be partially or fully blocked by the interferometer’s target hole.
b. Translate the laser head vertically and horizontally until the beam again goes through the hole in the interferometer’s target. If the laser beam is not now hitting the correct point on the reflecting optic, perform again the process of turning and translating the laser head.
4. Continue this process of moving the reflecting optic and then adjusting the laser head as many times as necessary until the end of travel is reached. At this point, the laser will be aligned to the table and to the optics.
Checking Alignment for Beam Strength:
1. Verify that you have attached the laser head to the optics as described above.
2. Open both laser head ports to their largest openings and remove any targets.
3. Move the optics over their full travel length while watching the BEAM STRENGTH meter. Any reading in the meter’s green area indicates sufficient beam strength.
4. If the meter’s reading goes into the red area at any time, return the optics to their "near-end-of-travel" position. Select the small aperture for the laser head’s exit port, and the target for the return port. Adjust the optics to overlap their return dots on the laser head’s return port target. Switch back to the large exit port aperture and the fully open return port. Check again for beam strength. If still red, then repeat both alignment checks.
Measurements Along a Perpendicular Axis:
When a measurement axis is perpendicular to the laser beam, mount the angular interferometer in line with the laser, and at the end of the axis you will be measuring. See Figures 5 and 6. Be sure to rotate the angular interferometer so the bottom opening lines up with the laser beam and the side with two openings faces the moving retroreflector..
Measurement Display Settings and Keys:
Your angular measurements are displayed in units of "arc-seconds", regardless of the setting of the measurement display’s rear-panel "English/Metric" switch.
ANGLE: Push the ANGLE key to make angular measurements.
PRESET: Your measurement data can be multiplied by a value from "0" to "2" before it is displayed. This key allows you to specify what the multiplier value will be. 1.0 is the default multiplier.
DIR SENSE: Determine which tilt direction you want to be "positive" and use this button to make sure it happens.
RESOL: There are only two choices for this key in this measurement mode. Resolution can be extended only to 0.1 arc second. Therefore, push 1 and the RESOL key for "tenths" resolution, or push 0 and the RESOL key for "units" resolution.
System Checks:
1. Make sure both laser head ports are switched to their large apertures.
2. The laser head turret must be set to "OTHER".
3. The laser head’s "READY" indicator must be lighted steadily, i.e. not blinking.
4. Make sure the laser measurement system is properly interfaced with other instruments, as needed to record your data. If you record your data manually, no interfacing is necessary. For formatted automatic records, the HP Dimensional Metrology Analysis Software is available to record your data automatically. Instructions on its use will be discussed in your laboratory section.
Note: Two different measurement methods are available. You can have your system make measurements (a) only at points you specify, or (b) automatically, at the time interval you specify, without regard to the location of the optics.
Measurements at Specific Physical Locations:
1. Push the RESET key on the measurement display or on the remote control unit connected to the measurement display.
2. Move one of the optics a predetermined distance.
3. Press the RECORD button on the remote control unit. One measurement is made each time you press this button.
Figure 5. Three Axis Positioning of Optics for Pitch Measurements
Figure 6. Three Axis Positioning of Optics for Yaw Measurements
- or -
Measurements at Specified Time Intervals:
1. Push the RESET key on the measurement display or on the remote control unit connected to the measurement display.
2. Setup the measurement display to make measurements at specific time intervals (i.e., "on the fly"). If you are interfacing to a controller, you should probably do this through its programs. Enter the time interval you want between measurements (0.05 to 12 seconds). Push the AUTO RECORD key. This will start the automatic acquisition of data.
3. Move one optic along the full measurement path. A measurement is made automatically every so many seconds until you press the AUTO RECORD key again.
4. Press the AUTO RECORD key when the end of travel is reached. This will turn off the AUTO RECORD, and stop the recording of measurements.
PROCEDURE D:
CALIBRATION OF A MAGNETIC BALL-BAR
Introduction:
Due to its high accuracy, laser interferometric measurements are quite often the standard used in calibration of other measurement devices. One measurement device often used in robotics and machine-tool accuracy assessment is the magnetic ball-bar. The ball bar is comprised of two precession spheres connected by a linear variable differential transformer (LVDT). The LVDT can either expand or contract, resulting in a voltage proportional to the distance moved. In this section, we will use the laser interferometer and data analysis tools in MATLAB to calibrate the ball-bar to within ±10 microns.
Procedure:
Set up the required optics on the ball-bar for linear distance measurements, and align the optics taking care to minimize (or at least estimate) the cosine error. Take at least 25 readings at equal intervals throughout the ball-bar's range of motion. At each interval, record the ball-bar output (the digital bit value) and the distance measurement from the laser. After the measurements are complete, we will analyze the data using MATLAB. Ideally, the relationship between the bit value and distance would be linear, so we will try to fit a straight line to the data. This will be the calibration curve of the ball-bar. Sometimes, however, the best straight line is not a good enough fit of the data. You might need to make higher order curve fits depending on the data and your acceptable error. Do whatever is necessary to make sure that the residual error (the difference between what the calibration equation predicts and what the actual distance is) is less than 10 microns. Turn in a plot of the calibration curve superimposed on the raw data.
PROCEDURE E: ! NOT INCLUDED 1996/97 !
FLATNESS MEASUREMENT
See Appendix.
Use the procedure described in the Appendix to determine the flatness of the granite surface plate used in your metrology assignments.
PROCEDURE SUMMARY:
PROCEDURE A: Position Measurements
a) Program the machine slide to move 500 mm (from position 0 to position 500) in 10 mm increments. Take measurements after every increment. The TA will help you on the programming. Repeat this 2 times. (2 RUNS)
b) Program the machine bed to move 500 mm continuously. Take 250 measurements at regular time intervals. Repeat this 3 times for a low speed, 3 times for a medium speed, and 3 times for a high speed. (9 RUNS)
PROCEDURE B: Velocity Measurements
Program the machine bed to move 500 mm continuously. Take 250 measurements at regular time intervals. Repeat this 3 times for a low speed, 3 times for a medium-low speed, 3 times for a medium speed, 3 times for a medium-high speed, and 3 times for a high speed. (9 RUNS)
PROCEDURE C: Angular Measurements
a) Program the machine bed to move 500 mm (from position 0 to position 500) in 10 mm increments. Take measurements after every increment. The TA will help you on the programming. Repeat this 2 times. (2 RUNS)
b) Program the machine bed to move 500 mm continuously. Take 250 measurements at regular time intervals. Repeat this 3 times for a low speed, 3 times for a medium speed, and 3 times for a high speed. (9 RUNS)
PROCEDURE D: Ball-Bar Calibration
Take at least 25 readings at equal intervals within the measurement range of the ball-bar system. Develop a suitable calibration curve for the system..
PROCEDURE E: Flatness Measurement
Determine the flatness of the granite surface plate in the laboratory.