Handbook Of Shaft Alignment Episode 1 Part 10 pot

about 1.5 mm (approximately 60 mils) in diameter as it exits the diode and is collimated (i.e., ‘‘focused’’), since only one side of the diode actually allows the light to exit. After exiting the diode, if the light beam was in a pure vacuum, the beam would stay focused for long distances. However, since there are small molecules of water vapor in the air we breathe, How semiconductor junction diode lasers work Battery positive (+) Battery negative (−) n-Type semiconductor Current must be high enough for electrons to move from a higher to a lower energy level in the junction p-Type semiconductor Hole+ Hole+ Electron- Electron - Junction Partially reflective facets on both sides of the edge of the “chip” act as an optical resonance chamber Battery Photon Photon Photon Photon Collimated light beam Glass lens Cap Heat sink Laser diode Monitor PIN photodiode Stem Laser “beam” • The chemical composition of the semiconductor determines the wavelength of light emitted from the laser. • Near infrared lasers used for alignment measurement devices are made from gallium–aluminum–arsenide (620–895 nm). • Visible red lasers are made from g allium–indium–phosphorous (670 nm). Cross-sectional structure of a 670 nm GaInP semiconductor laser p-GaAs (cap layer) n-GaAs (backing) p-(Ga 1−x Al x ) 0.5 I 0.5 P Ga 0.5 I 0.5 P n-(Ga 1−x Al x ) 0.5 I 0.5 P GaAs n-GaAs substrate Confining layer Active layer Buffer layer Confining layer FIGURE 6.27 How semiconductor laser diodes work. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 240 26.9.2006 8:51pm 240 Shaft Alignment Handbook, Third Edition the light from the laser is diffracted as it passes through each molecule of water vapor diffusing the beam. Typically, the useable distance of laser is somewhat limited to 30 ft due to the diffraction of the beam. Since the laser beam is around 60 mils in diameter as it exits the diode, the measurement accuracy would only be 60 mils (i.e., about 1=16th of an inch) if just the laser beam were solely used as the measurement device. This accuracy is just fine for laser levels when constructing buildings, for example, but since we are looking for accuracies of measurement at 1 mil or better, another device is needed in concert with the laser to attain this measurement precision. That device is the beam detector target. Laser–detector systems are also semiconductor photodiodes capable of detecting electro- magnetic radiation (light) from 350 to 1100 nm. When light within this range of wavelengths strikes the surface of the photodiode, an electrical current is produced as shown in Figure 6.28. Since the laser beam is emitting light at a specific wavelength (e.g., 670 nm), a colored translucent filter is positioned in front of the diode target to hopefully allow only light in the laser’s wavelength to enter. Otherwise, the detector could not tell whether the light that was striking its surface was from the laser, overhead building lighting, a flashlight, or the sun. As shown in Figure 6.29, when light strikes the center of the detector, output currents from each cell are equal. As the beam moves across the surface of the photodiode, a current imbalance occurs, indicating the off-center position of the beam. Most manufacturers of laser–detector shaft alignment systems use 10 Â 10 mm detectors (approximately 3=8 sq. in.); a few may use 20 Â 20 mm detectors. Some manufacturers of these systems use bicell (unidirectional) or quadrant cell (bidirectional) photodiodes to detect the position of the laser beam. An unidirectional photodiode measures the beam position within the target area from left to right only whereas a bidirectional photodiode (Figure 6.30 and Figure 6.31) measures the beam position in both axes, left to right and top to bottom. Therefore, laser– detector systems measure the distance the laser beam has traversed across the surface of the detector by measuring the electrical current at the beam’s starting position and the electrical current at the beam’s finishing position. 6.2.12 CHARGE COUPLE DEVICES The CCD was originally proposed by Boyle and Smith in 1970 as an electrical equivalent to magnetic bubble digital storage devices. The basic principle of their device was to store information in the form of electrical ‘‘charge packets’’ in potential wells created in the semiconductor by the influence of overlying electrodes separated from the semiconductor Cathode Anode CathodeAnode Photodetector Actual size 20 ϫ 20 mm 10 ϫ 10 mm FIGURE 6.28 How photodiodes work. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 241 26.9.2006 8:51pm Shaft Alignment Measuring Tools 241 by a thin-insulating layer. By controlling voltages applied to the electrodes, the potential wells and hence the charge packets could be shifted through the semiconductor (Figure 6.32). The potential wells are capable of storing variable amounts of charge and can be intro- duced electrically or optically. Light impinging on the surface of the charge-coupled semi- conductor generates charge carriers, which can be collected in the potential wells and afterward clocked out of the structure enabling the CCD to act as an image sensor. Laser Detector Cathode Anode CathodeAnode Laser beam (1.5 ϫ 1.5 mm) Differential current measured across anode and cathode pins to determine beam position FIGURE 6.29 Laser–photodiode operation. − + − + − + − + Numerator Denominator Divider R 2 R 3 R 1 Transimpedance amplifier Difference amplifier Sum amplifier Transimpedance amplifier R 1 R 2 R 2 R 3 0.1 µF 15 V ∆X L /2 R 2 FIGURE 6.30 Typical single axis photodiode circuit. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 242 26.9.2006 8:51pm 242 Shaft Alignment Handbook, Third Edition A considerable amount of effort was put forth in the 1960s in developing optical imagers that utilized matrices of photodiodes that effectively became undone by the development of the CCD. The rate of progress in CCD design through 1974 was so astonishing that Rodgers demonstrated a 320Â512 bit CCD sensor that could be used for 525 line television imaging just 4 years after the CCD was invented. CCDs have found their way into everyday life in video cameras and in high technology fields such as astronomy where large area CCDs capture images in telescopes both in orbit and on Earth. With the recent pace of introducing electronic measurement sensors in the arena of alignment, it seems odd that no one has incorporated the CCD as a measurement sensor. The only known application of CCDs for use in alignment was presented as a doctoral thesis by Brad Carman and a research project at the University of Calgary (see references). 6.2.13 INTERFEROMETERS It is suggested that one has to study Figure 2.10 through Figure 2.12 to get a basic under- standing of amplitude and frequency. Although the discussion in Chapter 2 for these figures ∆X L /2 ∆X L /2 − − − − − − − + + + Numerator Denominator Divider R 2 R 3 R 1 Difference amplifier R 1 R 2 + + + + Numerator Denominator Divider R 2 R 3 R 1 Difference amplifier Sum amplifier R 1 R 2 R 2 R 2 R 3 R 2 V+ V− 0.1 µF 0.1 µF Anode Bias adjustment Bias adjustment FIGURE 6.31 Typical dual axis photodiode circuit. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 243 26.9.2006 8:51pm Shaft Alignment Measuring Tools 243 centers around vibration, the same principles can also be applied to sound or light. Also Figure 6.26 explains the electromagnetic spectrum. Interferometers are instruments that utilize monochromatic (i.e., single wavelength) beams of light to measure distance by utilizing the principle of interference of waves. When two signals of the same frequency combine and are in phase, the amplitude of the combined signal intensifies. However, when two signals of the same frequency combine and are exactly 1808 out of phase, the two signals cancel each other out. This is referred to as constructive or destructive interference and is the basis of the field of interferometry. Since the wavelength of light is very small, small amounts of distance can be measured very accurately with these devices. Linear resolutions of 0.0059 min. (0.15 nm) and angular resolutions of 0.005 arc seconds can be measured with these systems. Not only can these systems measure distance, but using the Doppler effect, they can also measure the speed of the object. Distance measuring interferometers work on two principles: 1. Homodyne interferometers count fringes. A fringe is defined as one full cycle of light variation, that is, from light to dark and back to light again, a full 3608 phase shift in the two signals. 2. Heterodyne interferometers measure the change in optical phase of the known frequency of a reference signal to the known, but different frequency of a measurement signal at defined time intervals. Although interferometers are not used in the area of shaft alignment, they are frequently used in the field of metrology. Figure 6.34 shows the basic operating principles of a Michelson interferometer. Electrons A CCD is a multilayered silicon chip. In one layer, an array of electrodes divides the surface into pixels. Each electrode is connected to leads, which carry a voltage. The image forms on the silicon substrate. Light particles pass through the CCD freeing electrons in the silicon substrate. The voltage applied to the leads draws freed electrons together in special areas in the silicon substrate, called photo sites. The number of gathering electrons at the photo site is dependent on the intensity of the light striking in that area. The CCD transfers captured electrons, one by one, to an analog to digital converter, which assigns each site a digital value corresponding to the number of electrons a site holds. The number of electrons at each site determines how light or dark each pixel in the image is. Photo site Electrode Silicon substrate Lead Electrode layer CCD FIGURE 6.32 How a charge-coupled device (CCD) works. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 244 26.9.2006 8:51pm 244 Shaft Alignment Handbook, Third Edition 6.3 SWEEPING 908 ARCS TWICE TO MEASURE A MISALIGNMENT CONDITION To determine where a centerline of rotation of a shaft is, a bracket or holding fixture is attached to one of the shafts. A beam attached to that bracket spans across the gap between the two shafts and holds a precision measuring device (e.g., a dial indicator). The measuring device is positioned to observe the other shaft’s position by hand rotating the shaft, bracket, and attached measuring device through a full rotation (i.e., 3608) around the surface of the observed shaft. As the sweep is made, the shaft, bracket, and attached measuring device are temporarily stopped at 908 intervals and a measurement is recorded on the observed shaft. View from video camera Light “ fringe” Light “fringe” Shaft A Shaft B Fringe image on shaft BFringe image on shaft A The video camera “sees” the two fringe images in these two mirrors Basic procedure Since the relative mirror positions are unknown during setup, a reference line is obtained by placing a straight cylinder (possessing a continuous straight fringe line) in front of the two mirrors establishing a reference line (and reference fringe positions). An image of the actual shaft fringes is then compared to the reference fringe lines to determine the relative dis p lacements and slo p es between the two shafts. Light source Mirror viewing shaft B Top mirror Bottom mirror Shaft A Shaft B Top view Video camera (CCD) Image sent to computer for fringe position evaluation Mirror viewing shaft A Light “fringe” Light “fringe” When light strikes a cylindrical object a “fringe” line appears that is parallel to the centerline of rotation FIGURE 6.33 Using a CCD to detect light fringes on shafts. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 245 26.9.2006 8:51pm Shaft Alignment Measuring Tools 245 If the centerline of rotation of the shaft, bracket, and attached measuring device is directly in line with the centerline of rotation of the observed shaft where the measuring device has been placed, there will be no observed displacement in the measurement device. If the centerline of rotation of the shaft, bracket, and attached measuring device is not directly in line with the centerline of rotation of the observed shaft where the measuring device has been placed, there will be observed displacement in the measurement device. Monochromatic light source Fixed mirror Moveable mirror Detector Beam splitter Distance measured Combined beam from fixed mirror and moveable mirror Reference beam from fixed mirror Measurement beam from moveable mirror Reference beam from fixed mirror Measurement beam from moveable mirror 180Њ Out of phase Intense light from reference and measurement beams when in phase No light when reference and measurement beams are 180Њ out of phase What the detector “sees” FIGURE 6.34 How an interferometer works. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 246 26.9.2006 8:51pm 246 Shaft Alignment Handbook, Third Edition In horizontally mounted rotating machinery, we are trying to determine if the observed centerline of the shaft appears to be higher or lower than that of the shaft the bracket is attached to. We are also trying to determine if the observed shaft appears to be to the left or right of the shaft the bracket is attached to. When the measuring device traverses from the top to the bottom of the observed shaft, the amount and the direction of the measured displacement tell us whether the centerline of the observed shaft is higher or lower than the shaft we have attached to and how high it is or how low it is at that plane of measurement. Therefore we are looking for two pieces of information from this measurement, which way is the shaft? (i.e., is it high or low?) and how far off it is? (i.e., how much high or low?). In other words, this is a vector problem. We need both an amount and a direction. Similarly, when the measuring device traverses from the left side to the right side of the observed shaft, the amount and the direction of the measured displacement tells us whether the observed shaft is to the left or right with respect to the shaft it is attached to and how far to the left or right it is. Since several alignment methods require that these measurements be taken from both shafts, it is recommended that compass directions (i.e., north, south, east, west) be used when recording the side measurements rather than left or right or three o’clock and nine o’clock to eliminate some possible confusion on which way is which. If you are working on a seagoing vessel, then port, starboard, fore, and aft would be appropriate. One popular convention is to stand at the outboard end of the driver looking toward the drive system referencing everything to your left and right from that vantage point. That works fine until you encounter a multiple element drive train where the driver shaft is rotating machinery on both ends of the driver. Where is the outboard end then? Top, bottom, left, and right does not work very well when we are aligning vertically oriented shafts either but compass directions do. Anyway the orientation is designated as just fine as long as you stay consistent. Figure 6.35 and Figure 6.36 show rim measurements taken at 908 intervals from a pump shaft to a motor shaft. Figure 6.35 shows a dial indicator placed at the top dead center position and plunged down approximately half of its total stem travel. This is the usual starting point of the sweep and it is convenient to zero the indicator at this position. It is FIGURE 6.35 Dial indicator positioned at twelve o’clock and zeroed. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 247 26.9.2006 8:51pm Shaft Alignment Measuring Tools 247 noticed that there is a dual spirit level attached to the pump shaft and one of the two levels has been centered here. This dual spirit level is used to stop the rotation at fairly precise 908 arcs to record the measurements at each 908 location. Figure 6.36 through Figure 6.38 show mea- surements taken at the remaining three other 908 locations. The measurement sweep taken from the pump to the motor shown in Figure 6.35 through Figure 6.38 is not an enough information to determine where both shafts are however. Another measurement must be taken to ascertain where the centerlines of each shaft are located. FIGURE 6.36 Pump shaft with bracket and indicator rotated 908 to side of motor shaft, stopped, and indicator reading recorded. FIGURE 6.37 Pump shaft with bracket and indicator rotated 908 to bottom of motor shaft, stopped, and indicator reading recorded. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 248 26.9.2006 8:51pm 248 Shaft Alignment Handbook, Third Edition 6.4 WHY MEASUREMENTS ARE TAKEN AT 908 INTERVALS Invariably the question arises as to why readings are taken at the twelve-, three-, six-, and nine o’clock positions on rotating machinery shafts. In horizontally mounted rotating equipment, adjustments are made to the machinery cases to align the shafts in two planes, the up and down plane to correct the misalignment in the vertical position and the side-to-side plane to correct the misalignment in the sideways or lateral position. Vertical adjustments made to horizontally mounted rotating machinery casings are based on the top and bottom measurements (i.e., twelve o’clock and six o’clock). Lateral adjustments are made to horizontally mounted rotating machinery casings based on the north and south or east and west measurements (i.e., three o’clock and nine o’clock). In other words, when adjusting the height or pitch of the machinery cases, the side readings (three o’clock and nine o’clock) do not mean anything, only the top and bottom readings indicate the vertical position. Likewise, when adjusting the side-to-side positions of the machinery casings, the top and bottom readings are not regarded, only the side readings are considered. Shaft positional measurements are taken in the planes that define the directions of movement the machinery casings will undergo to correct the misalignment condition. In vertically oriented rotating machinery, however, it becomes obvious that there will not be any ‘‘top’’ and ‘‘bottom’’ measurements. In this case, one must determine what the planes of movement or translation will be on the machinery cases and capture the measurements in those planes. Examples of aligning vertically oriented shafts will be covered later in the book. 6.5 ROTATING BOTH SHAFTS TO OVERRIDE A RUNOUT CONDITION Chapter 5 covered information on measuring runout on rotating machinery. A runout condition will affect the accuracy of the alignment measurements and certain precautions need to be taken to insure that the alignment measurement process only finds the centerlines of rotation of the shafts and ignores any runout that may be present. If you have dial FIGURE 6.38 Pump shaft with bracket and indicator rotated 908 to other side of motor shaft, stopped, and indicator reading recorded. Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 249 26.9.2006 8:51pm Shaft Alignment Measuring Tools 249 [...]... 0.03407 417 3 71 −0.03407 417 3 71 −0.0999004225 −0 .15 8 918 6226 0.20 710 67 811 9 −0.2 411 809549 −0.258 819 04 51 −0.258 819 04 51 −0.2 411 809549 −0.20 710 67 811 9 −0 .15 8 918 6226 −0.0999004225 −0.03407 417 3 71 0.03407 417 3 71 0.0999004225 0 .15 8 918 6226 0.20 710 67 811 9 0.2 411 809549 0.258 819 04 51 ROROCOS 1. 07 313 218 5 1. 1645246646 1. 3032253728 1. 5907702752 2.9 318 516 526 1 0.3 410 813 774 0.62862627974 0.76732698798 0.858 719 467 61 0.9 318 516 5258... 26.9.2006 8:51pm Shaft Alignment Handbook, Third Edition 0/360 10 _ 0 + 10 10 20 10 30 30 40 40 40 30 20 20 30 30 50 15 10 20 20 + 10 _ 0 _ 0 + 40 10 20 _ 30 0 + 10 20 30 50 50 40 + 10 0 + 10 20 50 50 30 _ 0 10 30 _ 30 20 40 40 50 + 10 20 50 40 30 10 20 40 0 20 _ 40 40 40 10 30 20 30 20 30 40 40 30 20 + 10 _ 0 30 30 + 10 _ 0 10 20 40 10 50 20 40 30 30 40 _ 50 10 10 50 40 30 20 40 10 50 _ 0 + 40 30 10 40 20... + 10 30 _ 0 + 10 _ 0 10 20 30 40 10 50 20 40 30 30 40 30 10 30 20 20 20 50 _ 0 + 10 10 40 30 20 50 40 40 10 10 _ 0 + Right 50 _ 0 + 10 40 40 10 40 40 10 50 20 50 20 30 30 30 30 _ 0 + 10 90 20 20 20 30 20 30 30 Left _ 30 40 50 40 _ 30 20 + 10 40 50 20 40 30 20 40 10 30 30 _ 0 + 10 20 50 50 40 0 + 10 _ 20 30 40 10 20 30 10 40 20 + 10 _ 0 20 40 10 0 20 50 40 10 40 10 30 30 40 30 20 30 20 20 30 50 + 10 ... −0.86602540378 −0.70 710 67 811 9 −0.5 −0.258 819 04 51 sin A2 0.258 819 04 51 0.5 0.70 710 67 811 9 0.86602540378 0.96592582629 1 0.96592582629 0.86602540378 0.70 710 67 811 9 0.5 0.258 819 04 51 1.2246467991e -16 −0.258 819 04 51 −0.5 −0.70 710 67 811 9 −0.86602540378 −0.96592582629 1 −0.96592582629 −0.86602540378 −0.70 710 67 811 9 −0.5 −0.258 819 04 51 −2.4492935983e -16 sinA2−sinA1 0.258 819 04 51 0.2 411 809549 0.20 710 67 811 9 0 .15 8 918 6226 0.0999004225... 45 60 75 90 10 5 12 0 13 5 15 0 16 5 18 0 19 5 210 225 240 255 270 285 300 315 330 345 A2 15 30 45 60 75 90 10 5 12 0 13 5 15 0 16 5 18 0 19 5 210 225 240 255 270 285 300 315 330 345 360 sin A1 0 0.258 819 04 51 0.5 0.70 710 67 811 9 0.86602540378 0.96592582629 1 0.96592582629 0.86602540378 0.70 710 67 811 9 0.5 0.258 819 04 51 1.2246467991e -16 −0.258 819 04 51 −0.5 −0.70 710 67 811 9 −0.86602540378 −0.96592582629 1 −0.96592582629... 0 + 10 40 20 20 40 50 30 40 40 30 50 20 + 10 30 _ 0 + 10 _ 0 10 20 30 40 10 50 20 40 30 30 40 30 10 30 20 20 20 50 _ 0 + 10 10 40 20 30 30 20 40 10 40 50 40 40 10 40 40 50 50 10 _ 0 + 10 90 20 30 30 30 30 20 10 _ 0 + Left 50 20 10 _ 0 + 30 20 20 30 Right 20 Starting radius of rotation 40 _ 40 40 30 50 _ 0 40 30 20 + 10 20 50 40 50 20 40 30 20 40 10 30 30 _ 0 + 10 20 30 50 40 10 0 + 10 _ 20 30 40 10 ... 40 20 30 40 10 50 50 90 20 30 Right Left _ 0 + 10 _ 0 + 40 10 10 50 30 20 30 40 20 20 30 40 30 _ 0 + 40 20 10 20 30 20 30 40 20 20 _ 40 30 40 10 50 40 40 _ 30 30 40 50 20 40 50 40 30 20 40 30 + 10 30 20 40 30 50 50 40 10 0 + 10 _ 20 30 40 10 20 30 40 20 + 10 _ 0 20 40 10 20 + 10 30 0 20 10 20 50 20 _ 0 20 30 40 30 + 10 _ 0 20 30 0 + 10 40 Bottom 10 270 50 0 + 10 40 Top Starting radius of rotation 50... Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 259 26.9.2006 8:51pm 259 Shaft Alignment Measuring Tools 0/360 15 30 10 _ 0 + 10 10 20 30 20 30 30 40 30 40 40 30 10 20 20 + 10 _ 0 10 _ 0 + 20 50 40 10 20 _ 20 30 50 40 + 10 20 50 30 40 10 30 30 + 10 _ 0 20 50 _ 0 + 10 0 10 20 _ 40 40 40 10 30 20 30 20 30 40 50 Indicator stem is getting pushed in here (i.e., going positive) 0 + 10 ... measurements into the equations Piotrowski / Shaft Alignment Handbook, Third Edition DK4322_C006 Final Proof page 2 61 26.9.2006 8:51pm 2 61 Shaft Alignment Measuring Tools 0/360 15 10 _ 0 + 10 10 20 + 10 _ 0 20 30 30 30 30 40 40 10 20 40 30 10 _ 0 + 20 20 50 40 10 20 _ 20 30 20 30 40 50 50 40 20 50 30 40 10 30 30 + 10 _ 50 20 + 10 + 10 _ 0 20 0 10 0 _ 40 40 40 10 30 20 30 Indicator stem is retracting outward... 30 40 20 + 10 _ 0 20 40 10 30 10 30 30 40 50 20 20 20 40 10 30 50 + 10 _ 0 20 30 0 + 10 40 40 Bottom 40 270 50 50 _ 40 40 0 + 10 40 Top 50 50 40 30 40 30 20 20 10 _ 0 + 10 50 30 20 10 _ 0 + 10 40 40 40 30 20 30 30 30 20 20 10 _ 20 10 _ 0 + 10 0 + 10 Dial indicator measurement 18 0 Neutral axis Angular “lag” 0 90 18 0 Angular position 270 360 FIGURE 6. 51 Plotting the measurements for a misalignment condition . the 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 2 0 30 + _ 10 40 2 0 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 20 3 0 + _ 1 0 4 0 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 2 0 3 0 + _ 1 0 4 0 2 0 3 0 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0/360 15 30 90 18 0 270 Indicator. the 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 2 0 30 + _ 10 40 2 0 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 20 3 0 + _ 1 0 4 0 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 2 0 3 0 + _ 1 0 4 0 2 0 3 0 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0/360 15 30 90 18 0 270 Indicator. the 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 2 0 30 + _ 10 40 2 0 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 20 3 0 + _ 1 0 4 0 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 5 0 1 0 4 0 2 0 3 0 + _ 1 0 4 0 2 0 3 0 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0 50 10 40 20 30 + _ 10 40 20 30 0/360 15 30 90 18 0 270 Indicator