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A novel method for construction of a point coordinate measuring instrument using ultrasonic waves
Measurement 44 (2011) 539–548
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A novel method for construction of a point coordinate measuring instrument using ultrasonic waves A. Mirahmadi ⇑, A. Mansourzadeh Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 11 July 2009 Received in revised form 8 September 2010 Accepted 17 November 2010 Available online 23 November 2010 Keywords: Coordinate measuring instrument Measuring 3D surface Ultrasonic waves Phase-locked loop
a b s t r a c t Point coordinate measuring instruments are applied in the geometric measurement of parts. In this instrument, ultrasonic waves are used for measuring distances using a method similar to the time-of-flight method. For improvement of the measurement resolution, an accurate value of the speed of sound is enhanced by using a phase-locked loop (PLL) circuit to generate a reference signal; this signal is dependent on the variation of the speed of sound. To measure the coordinate of a point, an ultrasonic signal is produced with a wireless transmitter on the surface of a part. The waves are received by a set of three ultrasonic receivers located at the corner of the room. By counting the pulses of that signal within a transmit-to-receive period, the distance between each pair of transducers can be determined. By increasing the coefficient of the frequency divider in the PLL, the output frequency increases and the resolution improves. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Coordinate measuring instruments are applied for measuring the coordinates of components in 3D space. These devices are able to generate CAD models of mechanical parts and transfer them to computers. Various methods and devices such as Coordinate Measuring Machines (CMM) and 3D scanners can implement point scanning of surfaces. CMMs are accurate but slow, whereas 3D scanners are rapid but are not as accurate as CMMs. According to recent research, using sound in coordinate measuring instruments in 3D space is a novel method that has not yet been applied in metrology. Most of the research using sonic fields has been limited to detecting obstacles [1], detecting the angle and direction of sound sources [2] or simulating human hearing [3]. Other research in 3D space is aimed at tracking a moving sound source [4]. These methods are not accurate because of reverberation errors and environmental noises.
⇑ Corresponding author. E-mail addresses: [email protected] (A. Mirahmadi), Mansourzadeh @iust.ac.ir (A. Mansourzadeh). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.11.011
Certainly, there are existing methods that can be used to compensate for the reflection of sound in a closed room [5,6] and that increase the accuracy and decrease the operation range to few centimeters [7]. It is therefore necessary to conduct research on an instrument that measures a part by applying ultrasonic waves to its surface. In general, there are two basic methods for measuring distance by means of ultrasonic waves. The first is the phase-shift method and the second is the time-of-flight (TOF) method [8,9]. The TOF method calculates the period of time that passes between transmission of a signal and reception of that signal by the receiver. In this paper, a method similar to the TOF method is employed; successful implementation of this method requires an accurate value of the speed of sound. Of course, there are several ways to estimate this speed [10], but none are sufficiently accurate. Here, we offer an innovative method that uses a phaselocked loop (PLL) circuit [11] to overcome inaccuracies in measurement of the speed of sound. In this method, a pair of sonic transmitters and receivers is positioned with constant relative distance as part of a PLL circuit in a resonance condition. The circuit produces a signal whose frequency changes are linearly dependent on variation in the sound speed; we call this the reference signal. The reference
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signal produced by the PLL is then used as a reference for determining any unknown distances. A phase-locked loop (PLL) is a control system that generates a signal that has a fixed relation to the phase of an input signal. A PLL circuit responds to both the frequency and the phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase. The method used in this instrument works as follows. A transmitter emits an ultrasonic signal from the workpiece to the receiver, located in a fixed position far from the workpiece. By using the reference signal and measuring the time elapsed from the transmitter to the receiver (and calibrating the device), the exact distance between the two locations can be measured. A point cannot be fully defined in 3D space by a single distance from a specific point: two other coordinatedefined points are required to locate it uniquely in space. Therefore, by measuring three distances from an unknown point to three coordinate-defined points and using simple geometric relations, the coordinates of the unknown point can be determined. Since the waves must be emitted from the target point, and the point must be on the surface of the part, it is not practical to use one emitting wave, because the ultrasonic waves in our transducers do not propagate spherically and the contacted transmitter on the part surface cannot emit waves correctly. Therefore, as shown in Fig. 1, we have built a set of transmitters that includes two ultrasonic transmitters at a specific distance from each other. The tip of this set is considered as the measured point. Each transmitter emits waves to three receivers separated by a short delay, thus six distances will be measured. Using geometric relations, the coordinate of the probe tip can be measured.
To sample a point in 3D space, the point should be in contact with the tip of probe. When the start command key is pressed, the IR transmitter sends a signal to the receiver set and simultaneously, the first ultrasonic transmitter and, afterwards, the second transmitter, send a signal to receiver. In the receiver set, when the IR signal is received, the microcontroller starts counting the number of pulses in the reference signal and stops counting when it receives the ultrasonic signal from the transmitter. It is evident that the number of pulses within the period is proportional to the distance between each pair of transmitters and receivers. The resolution of measurement will be higher if the frequency of the reference signal is greater. In this paper, we first introduce the theory of propagation of sound in air and describe selection of a suitable frequency for the ultrasonic transducers. Then, the geometry used for determining the coordinate of a point in space and relevant equations are derived. The PLL will be explained and the novel method for determination of the speed of sound will be introduced. The specific elements and circuits used in the built instrument will be explained at the end. 2. Sound propagation in air The differential equation of a 3D wave in a homogeneous and viscous fluid is represented by the Stockes equation [12]:
r2 p
1 @2p 4l 2 @p þ r ¼0 c2 @t2 3qc2 @t
ð1Þ
where c is the speed of sound in fluid, p is the dynamic pressure, l is viscosity, and q is the density of fluid. The solution to this equation can be assumed as follows [13]:
p ¼ p0 ejðxtkxÞ
Fig. 1. Geometry of transmitters and receivers in the built instrument.
ð2Þ
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541
where x is frequency and k is a complex number that is related to x. By substituting Eq. (2) in Eq. (1), we obtain k as a function of b and a:
x
k ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ b ja c 1 þ j 34qxcl2
ð3Þ
where a and b express the wave attenuation and changes in the speed of the wave, respectively. By substituting Eq. (3) in Eq. (2), we obtain the answer:
p ¼ p0 ejðxtðbjaÞxÞ ¼ p0 ejðxtbxÞ eax
ð4Þ
To study wave attenuation in one-dimension, a time-independent expression p0eax is assumed. In standard conditions for air, the values l = 19 105 kg/m s, c = 346 m/s and q = 1.184 kg/m3 can be used [14]. By substituting these values into Eq. (3), the value of a can be obtained, a = 2.58 1012x2. By assumption, p0 = 1, in which case the attenuating amplitude p0eax can be written as
p0 eax ¼ e2:5810
12
x2 x
Fig. 3. Geometric method for determination of the coordinate of point P.
X 2 þ PX 2 ¼ r 2O By combining Eqs. (6) and (7) and eliminating PX:
ð5Þ
L2x r 2x þ r 2O 2Lx
As shown in Fig. 2, by increasing the frequency, the effective distance of the wave from its source decreases. The amplitude of a 40 kHz wave located 10 m from the origin attenuates by less than 5%, while that of a 400 kHz wave declines approximately to zero. Therefore, in this paper, a 40 kHz frequency is suitable for triggering and running the ultrasonic transducers.
X¼
3. Geometric method for determination of the coordinate of a point in 3D space
Z¼
As shown in Fig. 3, there are three receivers located at O (origin), A (on the x axis) and B (on the y axis), with the specific distances for A and B being Lx and Ly from the origin, respectively. Assume point P is a transmitter located at distances rO, rx and ry from receivers O, A and B, respectively. The goal here is to find the coordinates X, Y and Z of point P. In the AXP and OXP triangles:
4. Point coordinate measuring instrument
ðX Lx Þ2 þ PX 2 ¼ r 2x
ð6Þ
ð7Þ
ð8Þ
similarly, for Y:
Y¼
L2y r 2y þ r 2O 2Ly
ð9Þ
and for Z:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2O X 2 Y 2
ð10Þ
The main concept in this system is measurement of the distance between the transmitter and receiver by counting the pulses within the reference signal. Fig. 4 shows a block diagram of this instrument. There are two ultrasonic transmitters with specific distances to each other in the transmitter set. Three ultrasonic receivers with specific distance and angle together deliver the ultrasound signals from these two transmitters, separated by a short delay. This delay prevents the interference of two transmitted waves. By counting the number of pulses in the reference signal within the transmitted signal throughout the delivery period, the distance between each pair of transducers can be determined. The reference signal is produced by a PLL circuit, which is introduced here as a novel method for determining the speed of sound. The coordinate of the tip of the transmitter set with respect to the origin of the receiver can be calculated using geometric relations. Software was written and developed to analyze and show the results. 4.1. Elimination of the dependency of the speed of sound on temperature
Fig. 2. Wave attenuation in air in various frequencies.
The speed of sound is proportional to the p temperature ffiffiffiffiffiffiffiffiffi of environment. According to the relation c ¼ cRT , where R is the gas constant, c is specific heat ratio and T is absolute temperature, to eliminate the instrument dependency
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Fig. 4. General block diagram of the instrument.
on the speed of sound, a fast process must measure the temperature. Temperature-induced variations in the speed of sound cause errors in the measured distances. In order to prevent the influence of these variations on the measured distances, an innovative circuit is designed whose output frequency varies with the changes in the speed of
sound. As shown in Fig. 5, a sonic transmitter is positioned at a constant distance in front of a sonic receiver in a plastic chamber. The output signal from the receiver is sent to the phase detector of a PLL circuit and the difference in frequency between it and the divided output of a voltage-controlled oscillator (VCO) is fed into a VCO after
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in the sound chamber and the virtual kPLL are used as a reference for measuring any unknown distance. In this circuit, the instrument dependence on the speed of sound and its relation to temperature is eliminated. Finally, the reference frequency fPLL will be fed into the receiver circuit and used as a reference for measuring the distances between ultrasonic transducers. The relation between wavelength and frequency is represented as follows: Fig. 5. Block diagram for elimination of the sound speed dependency on temperature.
filtering. The output frequency of the VCO is proportional to the difference frequency. Therefore, this control loop always generates a frequency that has the same phase as the frequency sent by the sonic receiver. In order to increase the output frequency of the VCO and increase the resolution of instrument, the ‘‘divide by n’’ block divides the output frequency of the VCO. In this case, the divided frequency is compared with the receiver frequency in the phase detector and the VCO is forced to generate a virtual frequency that maintains this stable condition. It is evident that the VCO frequency must be multiplied by the coefficient of the divider. Therefore, this virtual frequency is n-times the frequency in the sound chamber. The transmitter and receiver in the sound chamber work in a resonance condition and are in phase. Therefore, there are many full waves occurring between them. In this condition, the sound frequency in the chamber changes when the speed of sound changes and, accordingly, the control loop changes the reference signal until the output frequency from the transmitter and the delivered frequency detected by the receiver are in phase again. Therefore, under any condition, the reference signal is proportional to the speed of sound. According to Fig. 6, in the resonance condition, suppose that the reference distance D in the sound chamber spans several wavelengths k. Because of the presence of the divider block, the output frequency of the PLL has a virtual wavelength kPLL that is proportional to k. Therefore, to measure an unknown distance x from point A to point B, it is clear that the distance comprises an integer number N of wavelengths kPLL. N is thus the number of counted pulses that will occur between a pair of transmitter and receiver signals. In other words, the reference distance D
Fig. 6. Virtual kPLL for measuring the unknown distance x.
c ¼kf
ð11Þ
where k is the wavelength, f is the frequency and c is speed of wave propagation. Since the frequency fPLL is multiplied by the divider block coefficient, fPLL will be equal to n f. Assuming that the speed of sound is constant, from Eq. (11) it is concluded that:
kPLL ¼
k n
ð12Þ
Eq. (12) shows that by raising the coefficient n, the virtual wavelength becomes smaller and thus the resolution of measurement is increased. For example, suppose the speed of sound is 340 m/s. If the frequency in the sound chamber is 20 kHz, the wavelength k is 17 mm. To have a resolution equal to 1 lm in measurement, according to Eq. (12), the coefficient n must be equal to 17,000. 4.1.1. PLL equations This instrument uses a phase-locked loop circuit to generate the signal used as a reference for determination of the speed of sound in air. This control loop is widely used in many applications such as signal detectors, data synchronizers and tracking filters. According to Fig. 7, the main element of this loop is the voltage-controlled oscillator. It is assumed that an input alternating signal Vin with a frequency near the frequency of the VCO is fed to a phase detector. The phase detector generates an alternating signal such that its frequency is related to the difference in frequency between Vin and VO. This difference in frequency is amplified and passes through a low-pass filter. The output signal from the filter is carried on a direct voltage from the amplifier. This filtered signal is fed to the VCO for control of the frequency of VO related to the voltage of Vc. Therefore, the control voltage Vc causes a change in the frequency of VO to lock with the frequency of Vin, and generates the same frequency as Vin. Changes in the frequency of Vin, result in
Fig. 7. General view of a PLL circuit.
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changes of the voltage of Vc and allow the frequency of VO to be used to track the frequency of Vin [15]. Fig. 8 shows the control block diagram of a phaselocked loop with the coefficient n of the divider block equal to one. Since the phase detector is a multiplier, the output signal from it can be written as follows [16]:
v p ðtÞ ¼ v i ðtÞ v o ðtÞ
ð13Þ
vp(t) passes through the filter and the passed signal is:
v f ðtÞ ¼ F filter ðv p ðtÞÞ
ð14Þ
The output frequency of the VCO is a function of its input vf(t):
xo ðtÞ ¼ xf þ g v v f ðtÞ
ð15Þ
where gv(Hz/v) and xf(Hz) are the VCO sensitivity and free running frequency, respectively. Therefore, the output signal of the VCO can be written as follows:
v o ðtÞ ¼ Ao cos
Z
t
xo ðsÞds ¼ Ao cosðxf t þ uðtÞÞ
ð16Þ
0
where,
uðtÞ ¼
Z
t 0
g v v f ðtÞds
ð17Þ
We can assume that the input signal is sinusoidal as follows:
v i ðtÞ ¼ Ai sinðxi tÞ
ð18Þ
By combining Eqs. (13), (16), and (18), the phase detector then has an output as follows:
v p ðtÞ ¼ Ai sinðxi tÞ Ao cosðxf t þ uðtÞÞ
ð19Þ
Using the trigonometric identity, Eq. (19) can be rewritten into sum and difference components:
v p ðtÞ ¼
Ai Ao sinðxi t xf t uðtÞÞ 2 Ai Ao þ sinðxi t þ xf t þ uðtÞÞ 2
ð20Þ
As an approximation to the behavior of the loop filter, we may consider only the difference frequency that is passed with no phase change, which enables us to derive a small-signal model of the phase-locked loop. If we can consider xf xi, according to Eq. (20), the output signal from the phase detector can be rewritten as:
v p ðtÞ ¼
Ai Ao Ai Ao sin uðtÞ þ sinð2xi þ uðtÞÞ 2 2
ð21Þ
v f ðtÞ
Ai Ao uðtÞ 2
The phase-locked loop is said to be locked in this case and the output of the filter is a linear function of u(t).
4.2. Transmitter set When the command key in the transmitter set is pushed, an infrared (IR) transmitter sends a short signal at 38 kHz to the receiver set to initiate the microcontroller to start counting the pulses within the reference signal. At the same time, one of the ultrasonic transmitters sends an ultrasonic signal at 40 kHz to the receiver set. Counting of the pulses of the reference signal will be stopped when the receiver receives the ultrasonic signal from transmitter. Accordingly, the number of counted pulses within this period is proportional to the distance between each transmitter and receiver. According to Fig. 9, after about 50 ms, the same procedure will be repeated for the second ultrasonic transmitter. The delay prevents the emitted ultrasonic waves from influencing each other. The IR transmitter emits a start signal to the receiver simultaneously with both of the ultrasonic transmitters. Six distances will be measured for each pair of transducers. Measurement of the coordinate of a point on a part in 3D space requires that the point be in contact with the tip of the probe. The distances between any two transmitters and the tip of the probe are definitive. Since the coordinates of these three points are fixed with respect to each other, the coordinates of the probe tip cab be determined by simply measuring the coordinates of each transmitter. A long probe is useful for sampling inaccessible points, such those not in front of the receivers or points within in cylinders and in the deep holes of parts. Fig. 10 shows the transmitter set. The transmitter set is powered by a small 9-volt battery. Therefore, it is totally wireless and virtually weightless. To increase the operation range of the ultrasonic transmitters, a MAX232 chipset is used. This IC increases the operational voltage of the transmitters from 0–5 V to ±12 V. In addition, the microcontroller of the transmitter circuit generates six pulses at 40 kHz, which is the resonance frequency of the transducers. To prevent the influence of environmental lights and ambient noises on the IR transducers, a modulated signal with 38 kHz is also transmitted. This signal will be demodulated in the receiver when delivered.
As the low-pass filter blocks high frequencies, the output of the filter can be rewritten as:
Fig. 8. Control block diagram of a PLL.
ð22Þ
Fig. 9. Sequence diagram of emitted signals.
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Fig. 10. Transmitter set.
4.3. Receiver set As shown in Fig. 11, the three ultrasonic receivers in the receiver are positioned such that the distances and angle between them are specified. One of them is located at the origin, and two others are on the x and y axes. One infrared receiver is positioned in the middle of the set, and can receive IR signals in front of the receiver. For arranging the measurement setup, the receiver set must be positioned and fixed in place a reasonable distance in front of the measured workpiece. In the receiver set, after receiving the IR signal from the transmitters, the microcontroller starts counting the pulses of the reference signal. Simultaneously, the ultrasonic signal is sent, but it travels with the speed of sound and stops the pulse counting when received by each of the ultrasonic receivers. Ultrasonic signals are amplified and fed into a microcontroller interrupt after arriving at each receiver. The reference signal is also connected to the external counter of the microcontroller. The microcontroller counts the number of pulses within the period of flight for each pair of transducers. Hence, the distances between each pair can be determined. These data are sent to the computer through a serial port. The receiver set is connected to the
Fig. 11. Receiver set.
receiver box containing the circuits and power supply. Fig. 12 shows an internal view of the receiver box, reference signal generator and sonic loop chamber. Transfer of data from the receiver circuit to the computer is established via communication with the RS232 protocol. In order to analyze the delivered data, software has been developed in Visual Basic to receive data from the receiver and perform calculations such as determination of the origin point of the work table and the part, as well as determination of the geometric specification of circles, spheres, angles and intersection of lines and planes, etc. It can also sample from free-form surfaces and generate a point file for transfer to other software. Figs. 13 and 14 show the main form and flowchart of this software, respectively. 5. Error analysis One of the unavoidable error sources in mechanical systems is manufacturing error. For example, the distance between the two ultrasonic transmitters and the probe tip and the distance between the ultrasonic receivers must be accurate. According to derived Eqs. (8)–(10), any errors in the positions and manufacturing distances in the transmitters or receivers result in an increase in the error when determining the coordinates of the probe tip. The X coordinate of one of the transmitters with respect to the receiver origin can be calculated with Eq. (8). The total error of each error source is approximately equal to the differential of X [17]:
DX DX
@X @X @X DLx þ Dr x þ Dr O @Lx @r x @r O L2x þ r 2x þ r 2O 2L2x
DL x
rx rO Dr x þ Dr O Lx Lx
ð23Þ
Lx that is the distance between receivers is constant. By measuring Lx accurately, the manufacturing error DLx can be eliminated. In this case, the first term of the in error X will be omitted as follows:
Fig. 12. Internal view of receiver box and the sonic loop chamber.
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Fig. 13. View of the main form of the software.
DX
rx rO Dr x þ Dr O Lx Lx
ð24Þ
The error in Eq. (24) can be calculated by substituting the appropriate values. The maximum errors Drx and DrO, related to the measurement process, are equal to the resolution. The resolution is the smallest change in the input value that will produce an observable change in the output. Therefore, we can assume Eq. (24) to be the resolution of the instrument and Drx and DrO to be the resolution of the measurements between a transmitter and receiver pair. It is reasonable to set them equal to each other. Eq. (24) can be rewritten as follows:
DX
rO rx Dr x ¼ k Dr x Lx
ð25Þ
where k is a constant value. Eq. (25) shows that the resolution DX is proportional to the resolution Drx with coefficient k. The resolution Drx, the resolution of measurement between a pair of transducers, is equal to the virtual wavelength kPLL. Therefore, Eq. (25) can be rewritten:
DX k kPLL
ð26Þ
By combining Eqs. (12) and (26):
DX k
k n
ð27Þ
Therefore, by increasing the coefficient n in the divider block of the PLL circuit, the resolution of measurement will be increased. Fig. 15 shows the value of the normalized DX/ k versus n. As shown in this figure, by the raising coefficient n, the resolution can be decreased to very fine values. The air temperature is not always uniform throughout the test room. If the temperature near the receiver is different from that near the transmitter, an error due to the variation in sound speed will occur. Assume the temperature
Fig. 14. The flowchart of the software.
distribution is linear. By estimation, we suppose the speed of sound is linear as well. Therefore, the travel time between transducers with constant distance x from other will be 2x/(c1 + c2), where c1, c2 are the sound speeds near that transmitter and receiver, respectively. The error will be:
x x ðc2 þc1 Þ=2 c1 c1 c2 ¼ error ¼ x c 1 þ c 2 c
ð28Þ
1
pffiffiffiffiffiffiffiffiffi According to the relation c ¼ cRT , the speed of sound is proportional to the square root of the absolute temperature. For a DT = 1 °C in T1 = 20 °C, the error in the distance measurement will be obtained as follows:
pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi T 1 T 2 293 294 error pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 0:085% 293 þ 294 T1 þ T2
ð29Þ
Eq. (29) shows that the error due to temperature differences will be increased if this difference increases. Fig. 16
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Fig. 15. The value of normalized DX/k versus coefficient n.
Fig. 16. Error of measurement due to temperature difference.
shows the error versus the temperature difference in three initial temperatures. To eliminate this error, a temperature sensor can be installed in the transmitter set, which can continuously report the air temperature around the transmitter to the receiver to compensate for this type of error. 6. Conclusion According to current research, construction of an instrument for measuring a point coordinate in 3D space using ultrasonic waves has not yet been introduced. Measurement of distances by ultrasonic waves with a method similar to the time-of-flight method does not achieve reasonable accuracy because the speed of sound changes with temperature. In this paper, we offer an innovative method that uses a PLL circuit to eliminate the sound speed dependence on temperature in order to measure the speed of sound accurately. Then, the construction of an instrument that measures the coordinate of points in 3D space was explored. This instrument can measure free-form surfaces and generate a point file that can be converted to solid models in 3D modeling software. In this instrument, the resolution of the measurement can be improved by increasing the frequency of the reference signal by mere changes in the
coefficient of the divider block in the PLL circuit, thus enabling the frequency to be raised several times over, if able to overcome the problem of undesirable noises. To decrease the errors in large-scale applications, such as measurement of a car in a room or control of a welding structure, more receivers can be used. In the presence of temperature differences, the probe can be equipped with a temperature sensor to report its temperature to the receiver. The ultrasonic transducers used in this project are of the piezoelectric type. The effective travel distance of the transmitter is proportional to the trigger voltage. In this case, the amplitude of the generated ultrasonic signal also increases with trigger voltage. Since the instrument has the capability for higher resolution, it can compete with other measuring instruments in its class. In addition, it has benefits over other methods in that it is lightweight, inexpensive, wireless and portable. Therefore, it can be used in general applications and in various industries. Since the transmitter is handheld, this instrument can be applied in a point-to-point measuring application such as the primary assembly of a car body, welding structure control, in-process control of workpieces, and for other applications. Application of this method will improve the accuracy and speed of the quality control process.
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[8] R. Queirós, P.S. Girão, A. Cruz Serra, Cross-correlation and sine-fitting techniques for high resolution ultrasonic ranging, in: Proceedings of the IEEE Inst. Meas. Tech. Conference, Sorrento, April, 2006, pp. 552– 556. [9] F.E. Gueuning, M. Varlan, C.E. Eugène, P. Dupuis, Accurate distance measurement by an autonomous ultrasonic system combining timeof-flight and phase-shift methods, IEEE Transactions of the Institute of Measurement 46 (6) (1997). [10] B. Barshan, Fast processing techniques for accurate ultrasonic range measurements, Measurement Science Technology 11 (2000) 45–50. [11] R. Best, Phase-Locked-Loops: Design, Simulation, and Applications, McGraw-Hill, New York, 2007. [12] D. Blackstock, Fundamentals of Physical Acoustics, John. Wiley & Sons, Ltd., 2000. [13] L. Ziomek, Fundamentals of Acoustic Field Theory and Space-time Signal Processing, CRC Press, Hardback, 1995. [14] C.T. Boehnlein, Air Density Tables, University of Minnesota, Institute of Technology, 1940. [15] J. Oleksy, Practical Solid-State Circuit Design, H.W. Sams, 1981. [16] L. Meiners, Introduction to phase-locked loop system modeling, Analog Applications Journal (2000) (Texas Instruments Incorporated). [17] J.F.W. Galyer, C.R. Shotbolt, Metrology for Engineers, Cassell Publishers Ltd., London, 1990.
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Measurement journal homepage: www.elsevier.com/locate/measurement
A novel method for construction of a point coordinate measuring instrument using ultrasonic waves A. Mirahmadi ⇑, A. Mansourzadeh Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 11 July 2009 Received in revised form 8 September 2010 Accepted 17 November 2010 Available online 23 November 2010 Keywords: Coordinate measuring instrument Measuring 3D surface Ultrasonic waves Phase-locked loop
a b s t r a c t Point coordinate measuring instruments are applied in the geometric measurement of parts. In this instrument, ultrasonic waves are used for measuring distances using a method similar to the time-of-flight method. For improvement of the measurement resolution, an accurate value of the speed of sound is enhanced by using a phase-locked loop (PLL) circuit to generate a reference signal; this signal is dependent on the variation of the speed of sound. To measure the coordinate of a point, an ultrasonic signal is produced with a wireless transmitter on the surface of a part. The waves are received by a set of three ultrasonic receivers located at the corner of the room. By counting the pulses of that signal within a transmit-to-receive period, the distance between each pair of transducers can be determined. By increasing the coefficient of the frequency divider in the PLL, the output frequency increases and the resolution improves. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Coordinate measuring instruments are applied for measuring the coordinates of components in 3D space. These devices are able to generate CAD models of mechanical parts and transfer them to computers. Various methods and devices such as Coordinate Measuring Machines (CMM) and 3D scanners can implement point scanning of surfaces. CMMs are accurate but slow, whereas 3D scanners are rapid but are not as accurate as CMMs. According to recent research, using sound in coordinate measuring instruments in 3D space is a novel method that has not yet been applied in metrology. Most of the research using sonic fields has been limited to detecting obstacles [1], detecting the angle and direction of sound sources [2] or simulating human hearing [3]. Other research in 3D space is aimed at tracking a moving sound source [4]. These methods are not accurate because of reverberation errors and environmental noises.
⇑ Corresponding author. E-mail addresses: [email protected] (A. Mirahmadi), Mansourzadeh @iust.ac.ir (A. Mansourzadeh). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.11.011
Certainly, there are existing methods that can be used to compensate for the reflection of sound in a closed room [5,6] and that increase the accuracy and decrease the operation range to few centimeters [7]. It is therefore necessary to conduct research on an instrument that measures a part by applying ultrasonic waves to its surface. In general, there are two basic methods for measuring distance by means of ultrasonic waves. The first is the phase-shift method and the second is the time-of-flight (TOF) method [8,9]. The TOF method calculates the period of time that passes between transmission of a signal and reception of that signal by the receiver. In this paper, a method similar to the TOF method is employed; successful implementation of this method requires an accurate value of the speed of sound. Of course, there are several ways to estimate this speed [10], but none are sufficiently accurate. Here, we offer an innovative method that uses a phaselocked loop (PLL) circuit [11] to overcome inaccuracies in measurement of the speed of sound. In this method, a pair of sonic transmitters and receivers is positioned with constant relative distance as part of a PLL circuit in a resonance condition. The circuit produces a signal whose frequency changes are linearly dependent on variation in the sound speed; we call this the reference signal. The reference
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signal produced by the PLL is then used as a reference for determining any unknown distances. A phase-locked loop (PLL) is a control system that generates a signal that has a fixed relation to the phase of an input signal. A PLL circuit responds to both the frequency and the phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase. The method used in this instrument works as follows. A transmitter emits an ultrasonic signal from the workpiece to the receiver, located in a fixed position far from the workpiece. By using the reference signal and measuring the time elapsed from the transmitter to the receiver (and calibrating the device), the exact distance between the two locations can be measured. A point cannot be fully defined in 3D space by a single distance from a specific point: two other coordinatedefined points are required to locate it uniquely in space. Therefore, by measuring three distances from an unknown point to three coordinate-defined points and using simple geometric relations, the coordinates of the unknown point can be determined. Since the waves must be emitted from the target point, and the point must be on the surface of the part, it is not practical to use one emitting wave, because the ultrasonic waves in our transducers do not propagate spherically and the contacted transmitter on the part surface cannot emit waves correctly. Therefore, as shown in Fig. 1, we have built a set of transmitters that includes two ultrasonic transmitters at a specific distance from each other. The tip of this set is considered as the measured point. Each transmitter emits waves to three receivers separated by a short delay, thus six distances will be measured. Using geometric relations, the coordinate of the probe tip can be measured.
To sample a point in 3D space, the point should be in contact with the tip of probe. When the start command key is pressed, the IR transmitter sends a signal to the receiver set and simultaneously, the first ultrasonic transmitter and, afterwards, the second transmitter, send a signal to receiver. In the receiver set, when the IR signal is received, the microcontroller starts counting the number of pulses in the reference signal and stops counting when it receives the ultrasonic signal from the transmitter. It is evident that the number of pulses within the period is proportional to the distance between each pair of transmitters and receivers. The resolution of measurement will be higher if the frequency of the reference signal is greater. In this paper, we first introduce the theory of propagation of sound in air and describe selection of a suitable frequency for the ultrasonic transducers. Then, the geometry used for determining the coordinate of a point in space and relevant equations are derived. The PLL will be explained and the novel method for determination of the speed of sound will be introduced. The specific elements and circuits used in the built instrument will be explained at the end. 2. Sound propagation in air The differential equation of a 3D wave in a homogeneous and viscous fluid is represented by the Stockes equation [12]:
r2 p
1 @2p 4l 2 @p þ r ¼0 c2 @t2 3qc2 @t
ð1Þ
where c is the speed of sound in fluid, p is the dynamic pressure, l is viscosity, and q is the density of fluid. The solution to this equation can be assumed as follows [13]:
p ¼ p0 ejðxtkxÞ
Fig. 1. Geometry of transmitters and receivers in the built instrument.
ð2Þ
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where x is frequency and k is a complex number that is related to x. By substituting Eq. (2) in Eq. (1), we obtain k as a function of b and a:
x
k ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ b ja c 1 þ j 34qxcl2
ð3Þ
where a and b express the wave attenuation and changes in the speed of the wave, respectively. By substituting Eq. (3) in Eq. (2), we obtain the answer:
p ¼ p0 ejðxtðbjaÞxÞ ¼ p0 ejðxtbxÞ eax
ð4Þ
To study wave attenuation in one-dimension, a time-independent expression p0eax is assumed. In standard conditions for air, the values l = 19 105 kg/m s, c = 346 m/s and q = 1.184 kg/m3 can be used [14]. By substituting these values into Eq. (3), the value of a can be obtained, a = 2.58 1012x2. By assumption, p0 = 1, in which case the attenuating amplitude p0eax can be written as
p0 eax ¼ e2:5810
12
x2 x
Fig. 3. Geometric method for determination of the coordinate of point P.
X 2 þ PX 2 ¼ r 2O By combining Eqs. (6) and (7) and eliminating PX:
ð5Þ
L2x r 2x þ r 2O 2Lx
As shown in Fig. 2, by increasing the frequency, the effective distance of the wave from its source decreases. The amplitude of a 40 kHz wave located 10 m from the origin attenuates by less than 5%, while that of a 400 kHz wave declines approximately to zero. Therefore, in this paper, a 40 kHz frequency is suitable for triggering and running the ultrasonic transducers.
X¼
3. Geometric method for determination of the coordinate of a point in 3D space
Z¼
As shown in Fig. 3, there are three receivers located at O (origin), A (on the x axis) and B (on the y axis), with the specific distances for A and B being Lx and Ly from the origin, respectively. Assume point P is a transmitter located at distances rO, rx and ry from receivers O, A and B, respectively. The goal here is to find the coordinates X, Y and Z of point P. In the AXP and OXP triangles:
4. Point coordinate measuring instrument
ðX Lx Þ2 þ PX 2 ¼ r 2x
ð6Þ
ð7Þ
ð8Þ
similarly, for Y:
Y¼
L2y r 2y þ r 2O 2Ly
ð9Þ
and for Z:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2O X 2 Y 2
ð10Þ
The main concept in this system is measurement of the distance between the transmitter and receiver by counting the pulses within the reference signal. Fig. 4 shows a block diagram of this instrument. There are two ultrasonic transmitters with specific distances to each other in the transmitter set. Three ultrasonic receivers with specific distance and angle together deliver the ultrasound signals from these two transmitters, separated by a short delay. This delay prevents the interference of two transmitted waves. By counting the number of pulses in the reference signal within the transmitted signal throughout the delivery period, the distance between each pair of transducers can be determined. The reference signal is produced by a PLL circuit, which is introduced here as a novel method for determining the speed of sound. The coordinate of the tip of the transmitter set with respect to the origin of the receiver can be calculated using geometric relations. Software was written and developed to analyze and show the results. 4.1. Elimination of the dependency of the speed of sound on temperature
Fig. 2. Wave attenuation in air in various frequencies.
The speed of sound is proportional to the p temperature ffiffiffiffiffiffiffiffiffi of environment. According to the relation c ¼ cRT , where R is the gas constant, c is specific heat ratio and T is absolute temperature, to eliminate the instrument dependency
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Fig. 4. General block diagram of the instrument.
on the speed of sound, a fast process must measure the temperature. Temperature-induced variations in the speed of sound cause errors in the measured distances. In order to prevent the influence of these variations on the measured distances, an innovative circuit is designed whose output frequency varies with the changes in the speed of
sound. As shown in Fig. 5, a sonic transmitter is positioned at a constant distance in front of a sonic receiver in a plastic chamber. The output signal from the receiver is sent to the phase detector of a PLL circuit and the difference in frequency between it and the divided output of a voltage-controlled oscillator (VCO) is fed into a VCO after
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in the sound chamber and the virtual kPLL are used as a reference for measuring any unknown distance. In this circuit, the instrument dependence on the speed of sound and its relation to temperature is eliminated. Finally, the reference frequency fPLL will be fed into the receiver circuit and used as a reference for measuring the distances between ultrasonic transducers. The relation between wavelength and frequency is represented as follows: Fig. 5. Block diagram for elimination of the sound speed dependency on temperature.
filtering. The output frequency of the VCO is proportional to the difference frequency. Therefore, this control loop always generates a frequency that has the same phase as the frequency sent by the sonic receiver. In order to increase the output frequency of the VCO and increase the resolution of instrument, the ‘‘divide by n’’ block divides the output frequency of the VCO. In this case, the divided frequency is compared with the receiver frequency in the phase detector and the VCO is forced to generate a virtual frequency that maintains this stable condition. It is evident that the VCO frequency must be multiplied by the coefficient of the divider. Therefore, this virtual frequency is n-times the frequency in the sound chamber. The transmitter and receiver in the sound chamber work in a resonance condition and are in phase. Therefore, there are many full waves occurring between them. In this condition, the sound frequency in the chamber changes when the speed of sound changes and, accordingly, the control loop changes the reference signal until the output frequency from the transmitter and the delivered frequency detected by the receiver are in phase again. Therefore, under any condition, the reference signal is proportional to the speed of sound. According to Fig. 6, in the resonance condition, suppose that the reference distance D in the sound chamber spans several wavelengths k. Because of the presence of the divider block, the output frequency of the PLL has a virtual wavelength kPLL that is proportional to k. Therefore, to measure an unknown distance x from point A to point B, it is clear that the distance comprises an integer number N of wavelengths kPLL. N is thus the number of counted pulses that will occur between a pair of transmitter and receiver signals. In other words, the reference distance D
Fig. 6. Virtual kPLL for measuring the unknown distance x.
c ¼kf
ð11Þ
where k is the wavelength, f is the frequency and c is speed of wave propagation. Since the frequency fPLL is multiplied by the divider block coefficient, fPLL will be equal to n f. Assuming that the speed of sound is constant, from Eq. (11) it is concluded that:
kPLL ¼
k n
ð12Þ
Eq. (12) shows that by raising the coefficient n, the virtual wavelength becomes smaller and thus the resolution of measurement is increased. For example, suppose the speed of sound is 340 m/s. If the frequency in the sound chamber is 20 kHz, the wavelength k is 17 mm. To have a resolution equal to 1 lm in measurement, according to Eq. (12), the coefficient n must be equal to 17,000. 4.1.1. PLL equations This instrument uses a phase-locked loop circuit to generate the signal used as a reference for determination of the speed of sound in air. This control loop is widely used in many applications such as signal detectors, data synchronizers and tracking filters. According to Fig. 7, the main element of this loop is the voltage-controlled oscillator. It is assumed that an input alternating signal Vin with a frequency near the frequency of the VCO is fed to a phase detector. The phase detector generates an alternating signal such that its frequency is related to the difference in frequency between Vin and VO. This difference in frequency is amplified and passes through a low-pass filter. The output signal from the filter is carried on a direct voltage from the amplifier. This filtered signal is fed to the VCO for control of the frequency of VO related to the voltage of Vc. Therefore, the control voltage Vc causes a change in the frequency of VO to lock with the frequency of Vin, and generates the same frequency as Vin. Changes in the frequency of Vin, result in
Fig. 7. General view of a PLL circuit.
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changes of the voltage of Vc and allow the frequency of VO to be used to track the frequency of Vin [15]. Fig. 8 shows the control block diagram of a phaselocked loop with the coefficient n of the divider block equal to one. Since the phase detector is a multiplier, the output signal from it can be written as follows [16]:
v p ðtÞ ¼ v i ðtÞ v o ðtÞ
ð13Þ
vp(t) passes through the filter and the passed signal is:
v f ðtÞ ¼ F filter ðv p ðtÞÞ
ð14Þ
The output frequency of the VCO is a function of its input vf(t):
xo ðtÞ ¼ xf þ g v v f ðtÞ
ð15Þ
where gv(Hz/v) and xf(Hz) are the VCO sensitivity and free running frequency, respectively. Therefore, the output signal of the VCO can be written as follows:
v o ðtÞ ¼ Ao cos
Z
t
xo ðsÞds ¼ Ao cosðxf t þ uðtÞÞ
ð16Þ
0
where,
uðtÞ ¼
Z
t 0
g v v f ðtÞds
ð17Þ
We can assume that the input signal is sinusoidal as follows:
v i ðtÞ ¼ Ai sinðxi tÞ
ð18Þ
By combining Eqs. (13), (16), and (18), the phase detector then has an output as follows:
v p ðtÞ ¼ Ai sinðxi tÞ Ao cosðxf t þ uðtÞÞ
ð19Þ
Using the trigonometric identity, Eq. (19) can be rewritten into sum and difference components:
v p ðtÞ ¼
Ai Ao sinðxi t xf t uðtÞÞ 2 Ai Ao þ sinðxi t þ xf t þ uðtÞÞ 2
ð20Þ
As an approximation to the behavior of the loop filter, we may consider only the difference frequency that is passed with no phase change, which enables us to derive a small-signal model of the phase-locked loop. If we can consider xf xi, according to Eq. (20), the output signal from the phase detector can be rewritten as:
v p ðtÞ ¼
Ai Ao Ai Ao sin uðtÞ þ sinð2xi þ uðtÞÞ 2 2
ð21Þ
v f ðtÞ
Ai Ao uðtÞ 2
The phase-locked loop is said to be locked in this case and the output of the filter is a linear function of u(t).
4.2. Transmitter set When the command key in the transmitter set is pushed, an infrared (IR) transmitter sends a short signal at 38 kHz to the receiver set to initiate the microcontroller to start counting the pulses within the reference signal. At the same time, one of the ultrasonic transmitters sends an ultrasonic signal at 40 kHz to the receiver set. Counting of the pulses of the reference signal will be stopped when the receiver receives the ultrasonic signal from transmitter. Accordingly, the number of counted pulses within this period is proportional to the distance between each transmitter and receiver. According to Fig. 9, after about 50 ms, the same procedure will be repeated for the second ultrasonic transmitter. The delay prevents the emitted ultrasonic waves from influencing each other. The IR transmitter emits a start signal to the receiver simultaneously with both of the ultrasonic transmitters. Six distances will be measured for each pair of transducers. Measurement of the coordinate of a point on a part in 3D space requires that the point be in contact with the tip of the probe. The distances between any two transmitters and the tip of the probe are definitive. Since the coordinates of these three points are fixed with respect to each other, the coordinates of the probe tip cab be determined by simply measuring the coordinates of each transmitter. A long probe is useful for sampling inaccessible points, such those not in front of the receivers or points within in cylinders and in the deep holes of parts. Fig. 10 shows the transmitter set. The transmitter set is powered by a small 9-volt battery. Therefore, it is totally wireless and virtually weightless. To increase the operation range of the ultrasonic transmitters, a MAX232 chipset is used. This IC increases the operational voltage of the transmitters from 0–5 V to ±12 V. In addition, the microcontroller of the transmitter circuit generates six pulses at 40 kHz, which is the resonance frequency of the transducers. To prevent the influence of environmental lights and ambient noises on the IR transducers, a modulated signal with 38 kHz is also transmitted. This signal will be demodulated in the receiver when delivered.
As the low-pass filter blocks high frequencies, the output of the filter can be rewritten as:
Fig. 8. Control block diagram of a PLL.
ð22Þ
Fig. 9. Sequence diagram of emitted signals.
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Fig. 10. Transmitter set.
4.3. Receiver set As shown in Fig. 11, the three ultrasonic receivers in the receiver are positioned such that the distances and angle between them are specified. One of them is located at the origin, and two others are on the x and y axes. One infrared receiver is positioned in the middle of the set, and can receive IR signals in front of the receiver. For arranging the measurement setup, the receiver set must be positioned and fixed in place a reasonable distance in front of the measured workpiece. In the receiver set, after receiving the IR signal from the transmitters, the microcontroller starts counting the pulses of the reference signal. Simultaneously, the ultrasonic signal is sent, but it travels with the speed of sound and stops the pulse counting when received by each of the ultrasonic receivers. Ultrasonic signals are amplified and fed into a microcontroller interrupt after arriving at each receiver. The reference signal is also connected to the external counter of the microcontroller. The microcontroller counts the number of pulses within the period of flight for each pair of transducers. Hence, the distances between each pair can be determined. These data are sent to the computer through a serial port. The receiver set is connected to the
Fig. 11. Receiver set.
receiver box containing the circuits and power supply. Fig. 12 shows an internal view of the receiver box, reference signal generator and sonic loop chamber. Transfer of data from the receiver circuit to the computer is established via communication with the RS232 protocol. In order to analyze the delivered data, software has been developed in Visual Basic to receive data from the receiver and perform calculations such as determination of the origin point of the work table and the part, as well as determination of the geometric specification of circles, spheres, angles and intersection of lines and planes, etc. It can also sample from free-form surfaces and generate a point file for transfer to other software. Figs. 13 and 14 show the main form and flowchart of this software, respectively. 5. Error analysis One of the unavoidable error sources in mechanical systems is manufacturing error. For example, the distance between the two ultrasonic transmitters and the probe tip and the distance between the ultrasonic receivers must be accurate. According to derived Eqs. (8)–(10), any errors in the positions and manufacturing distances in the transmitters or receivers result in an increase in the error when determining the coordinates of the probe tip. The X coordinate of one of the transmitters with respect to the receiver origin can be calculated with Eq. (8). The total error of each error source is approximately equal to the differential of X [17]:
DX DX
@X @X @X DLx þ Dr x þ Dr O @Lx @r x @r O L2x þ r 2x þ r 2O 2L2x
DL x
rx rO Dr x þ Dr O Lx Lx
ð23Þ
Lx that is the distance between receivers is constant. By measuring Lx accurately, the manufacturing error DLx can be eliminated. In this case, the first term of the in error X will be omitted as follows:
Fig. 12. Internal view of receiver box and the sonic loop chamber.
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Fig. 13. View of the main form of the software.
DX
rx rO Dr x þ Dr O Lx Lx
ð24Þ
The error in Eq. (24) can be calculated by substituting the appropriate values. The maximum errors Drx and DrO, related to the measurement process, are equal to the resolution. The resolution is the smallest change in the input value that will produce an observable change in the output. Therefore, we can assume Eq. (24) to be the resolution of the instrument and Drx and DrO to be the resolution of the measurements between a transmitter and receiver pair. It is reasonable to set them equal to each other. Eq. (24) can be rewritten as follows:
DX
rO rx Dr x ¼ k Dr x Lx
ð25Þ
where k is a constant value. Eq. (25) shows that the resolution DX is proportional to the resolution Drx with coefficient k. The resolution Drx, the resolution of measurement between a pair of transducers, is equal to the virtual wavelength kPLL. Therefore, Eq. (25) can be rewritten:
DX k kPLL
ð26Þ
By combining Eqs. (12) and (26):
DX k
k n
ð27Þ
Therefore, by increasing the coefficient n in the divider block of the PLL circuit, the resolution of measurement will be increased. Fig. 15 shows the value of the normalized DX/ k versus n. As shown in this figure, by the raising coefficient n, the resolution can be decreased to very fine values. The air temperature is not always uniform throughout the test room. If the temperature near the receiver is different from that near the transmitter, an error due to the variation in sound speed will occur. Assume the temperature
Fig. 14. The flowchart of the software.
distribution is linear. By estimation, we suppose the speed of sound is linear as well. Therefore, the travel time between transducers with constant distance x from other will be 2x/(c1 + c2), where c1, c2 are the sound speeds near that transmitter and receiver, respectively. The error will be:
x x ðc2 þc1 Þ=2 c1 c1 c2 ¼ error ¼ x c 1 þ c 2 c
ð28Þ
1
pffiffiffiffiffiffiffiffiffi According to the relation c ¼ cRT , the speed of sound is proportional to the square root of the absolute temperature. For a DT = 1 °C in T1 = 20 °C, the error in the distance measurement will be obtained as follows:
pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi T 1 T 2 293 294 error pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 0:085% 293 þ 294 T1 þ T2
ð29Þ
Eq. (29) shows that the error due to temperature differences will be increased if this difference increases. Fig. 16
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Fig. 15. The value of normalized DX/k versus coefficient n.
Fig. 16. Error of measurement due to temperature difference.
shows the error versus the temperature difference in three initial temperatures. To eliminate this error, a temperature sensor can be installed in the transmitter set, which can continuously report the air temperature around the transmitter to the receiver to compensate for this type of error. 6. Conclusion According to current research, construction of an instrument for measuring a point coordinate in 3D space using ultrasonic waves has not yet been introduced. Measurement of distances by ultrasonic waves with a method similar to the time-of-flight method does not achieve reasonable accuracy because the speed of sound changes with temperature. In this paper, we offer an innovative method that uses a PLL circuit to eliminate the sound speed dependence on temperature in order to measure the speed of sound accurately. Then, the construction of an instrument that measures the coordinate of points in 3D space was explored. This instrument can measure free-form surfaces and generate a point file that can be converted to solid models in 3D modeling software. In this instrument, the resolution of the measurement can be improved by increasing the frequency of the reference signal by mere changes in the
coefficient of the divider block in the PLL circuit, thus enabling the frequency to be raised several times over, if able to overcome the problem of undesirable noises. To decrease the errors in large-scale applications, such as measurement of a car in a room or control of a welding structure, more receivers can be used. In the presence of temperature differences, the probe can be equipped with a temperature sensor to report its temperature to the receiver. The ultrasonic transducers used in this project are of the piezoelectric type. The effective travel distance of the transmitter is proportional to the trigger voltage. In this case, the amplitude of the generated ultrasonic signal also increases with trigger voltage. Since the instrument has the capability for higher resolution, it can compete with other measuring instruments in its class. In addition, it has benefits over other methods in that it is lightweight, inexpensive, wireless and portable. Therefore, it can be used in general applications and in various industries. Since the transmitter is handheld, this instrument can be applied in a point-to-point measuring application such as the primary assembly of a car body, welding structure control, in-process control of workpieces, and for other applications. Application of this method will improve the accuracy and speed of the quality control process.
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