ISSN 1068-7998, Russian Aeronautics (Iz.VUZ), 2016, Vol. 59, No. 3, pp. 426–432. © Allerton Press, Inc., 2016. Original Russian Text © V.M. Grechishnikov, O.V. Teryaeva, 2016, published in in Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2016, No. 3, pp. 122–128.

AIRCRAFT INSTRUMENTS AND INSTRUMENTATION COMPUTER COMPLEXES

Fiber-Optical Converters of Onboard Position Sensors for Aircraft Mechanization Devices V. M. Grechishnikov* and O. V. Teryaeva** Samara University, shosse Moskovskoe 34, Samara, 443086 Russia *e-mail: [email protected], **e-mail: [email protected] Received September 26, 2014

Abstract—The paper describes the design concepts, a brief theory, and analysis of the power and metrological characteristics of the fiber-optical digital-to-analog converters as the elements of multiplexing the data from onboard position sensors in aircraft instruments and systems. DOI: 10.3103/S1068799816030211 Keywords: digital-to-analog converter, analog-to-digital converter, structural design, conversion function, optical attenuators, influence coefficient, errors, power loss.

INTRODUCTION Among instrumentation applied on board, the binary converters (end position) is a significant group working in the various systems of the aircraft (wing high-lift devices, chassis, limiting system, etc.) [1, 2]. As a rule, the sensors are located in areas with harsh environmental conditions (temperature difference, electromagnetic interference) that reduces the accuracy of the information obtained from them. Furthermore, the presence of individual communication channels for each sensor impairs the mass and dimension parameters of onboard instrumentation. In this regard, an urgent task is creating a multiplexed fiber optic displacement sensors of shutter type by means of fiber-optic digital-to-analog displacement converters (FODADC) [3, 4]. APPLICATION OF FODADC AS PART OF ONBOARD SYSTEMS OF DATA ACQUISITION FROM THE POSITION SENSORS OF AIRCRAFT MECHANIZATION DEVICES A generalized block diagram of a data acquisition system from limit switches is shown in Fig. 1. P0

x0

FD

FODADC

OLSG xn–1

PΣ

Pn–1

u0 iΣ Ampli uΣ ADC fier un–1

Fig. 1.

The system incorporates an optical logic signals generator (OLSG) that converts the data on the end positions x0 , x1 ... xn −1 of structural elements of the measurement object in a corresponding set of optical logic signals p0 , p1 ... pn −1 . OLSG is a set of mechanical elements that performs the function of interrupting the optical radiation when the end position is attained by the element being controlled. 426

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427

In FODADC, the input optical signals p0 , p1 ... pn −1 are multiplied by the respective weighting coefficients and using a Y-coupler are converted into the output optical fiber to a common signal pΣ . Thus, FODADC realizes the function of ‘‘weight’’ multiplexing of channels, and creates the possibility of transferring the sum signal at very long distances via a monofilament or knotted fiber. To restore parallel format of signals in electrical form, a sum signal is fed to a photodetector (FD), increases by the amplitude of the amplifier and is digitized by the ADC, from the output of which the electrical logic signals u0 , u1 ...un −1 are removed, the values of which are uniquely related to the values of the input signals x0 , x1 ... xn −1 . As electronic DAC, the optical DAC can be realized by the schemes with the summation or

multiplication of weighting coefficients. Further, we will consider the principles of construction and analysis of summarizing FODADCs [4---6], in which the interruption of optical radiation occurs through using the movable shutters in the gaps between the transmit and receiving optical fibers. PRINCIPLES OF FODADC CONSTRUCTION BASED ON SUMMATION OF THE WEIGHTING COEFFICIENTS In the ideal ODADC with the addition of weighting coefficients, the output optical signal is equal to n

Pq = ∑ ai ηin ,

(1)

i =0

where ηin is the nominal value of the weight coefficient of the ith channel of summing; ai is the value of the number in the ith digit of the input optical code. Taking into account the passive nature of the optical system, the values of the weighting coefficients ηin cannot take the values greater than one, so for FODADC a sequence of numbers 2 − i is used. Noting

{ }

this the equation of FODADC transformation is represented as follows

PΣ = p0

i =0

∑

i = n −1 j = n −1− i

(

)

a j 2 − i = p0 a0 2 − ( n −1) + a1 2 − ( n − 2) + … + an −1 20 .

(2)

After normalization (2) with respect to the quantization step p0 , we get PΣ∗ =

i =0

∑

i = n −1 j = n −1− i

(

)

a j 2 − i = a0 2 − ( n −1) + a1 2 − ( n − 2) + … + an −1 20 .

(3)

Generally, the parallel FODADC should perform two operations, namely, assignment of weight to each digit and summing the weights being selected by bit numbers. Weights are assigned by optical attenuators being a part of FODADC. The operation principle of the optical attenuator (OA) may be based on such effects as geometrical variation of optical fiber (macrobendings), changes in internal stresses of optical fiber (microbendings), changes in relative position of optical fiber ends, and introduction of additional elements setting a diaphragm between the ends. The simplest and most technologically advanced are optical attenuators based on the axial misalignment of fibers and application of elements setting a diaphragm. Let us present structural designs of FODADC based on the axial misalignment of fibers (Fig. 2a) and a set of diaphragms (Fig, 2b). In the device (see Fig. 2a), the optical radiation Pr from one or several emitters is fed to the transmission optical fibers, the output ends of which are disposed at the distance of the working clearance Ri from the ends of the corresponding receiving optical fibers of an optical multiplexer Y (i is the channel number). Working clearances are chosen so that the transmission coefficients between the corresponding transmit and receiving optical fibers conform to a numerical series 2 − i . As a result of

{ }

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summarizing the signals of receiving optical fibers in the Y-coupler, the analog quantized optical signal is formed proportional to the input optical code that is determined in its turn by the state of limit switches. R = const Pr

x0

x0

2°

Pr

GLr1

2° GLtr1

R0 = hт Pr

x1

a Pq

21

Y

x1 Pr

GLr2

b 21 GLtr2

Pq Y

R1 Pr

xn–1

2n–1

xn–1

Pr

GLr (n–1)

2n–1 GLtr(n–1)

Rn–1 (a)

(b) Fig. 2.

Unlike the second option of the FODADC circuit, the first one is characterized by identical working clearances between the optical fibers working in all channels as well as the weighting coefficients ηi implemented through a set of slit diaphragms D0 … Dn with different ratios Si/S0, where Si and S0 are areas of transparent areas in the diaphragms with the sequence number i and 0. A feature of the second optical scheme is the weak dependence of the radiation transmission coefficient between the two radiation graded-index cylindrical lenses GLri and GLtri on the clearance value Ri . According to [6], for small divergence angles of the collimated radiation (usually 5 –10 mrad) a margin of error of radiation transmission coefficient is caused by small fluctuations of working clearances γ Ri ≈ 0 . This determines the possibility of forming the weighting coefficients by the use of slit

diaphragms, the areas of transparent areas Si of which are correlated as Si = S0 2 − i , where S0 is the area of the diaphragm opening in the senior digit. As in the first structure, the optical quantized signal is formed proportional to the input optical code at the output of the second coupler. MATHEMATICAL MODELS OF FODADC ATTENUATORS Structural design of an attenuator based on the axial misalignment of optical fibers for the i th decade is shown in Fig. 3. R Ri i

шторка Shutter

Передающий световод Transmitting optical fiber

2r2r

Θ

hhTt

ΔRRii

Fig. 3.

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Receiving fiber Приёмныйoptical световод 2r 2r

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The radiation transmission coefficient η0 value through the technological clearance ht designed for the movable shutter moving therein, without radial and angular misalignments of optical fibers is determined by the known equation [7]

r2

η0 =

[r

+ ht NA]

2

,

(4)

where r is the radius of the optical fiber; NA = sin Θ is the numerical aperture. Taking into account the availability of technological clearance, the radiation transmission coefficients in the ith digit can be defined as ηi n = η0 2 − i . (5)

On the other hand, the value of the transmission coefficient in the i th digit taking into account the total working clearance Ri by analogy with expression (4) is equal to r2

ηi =

[r + Ri NA]

2

.

(6)

By equating expressions (5) and (6) and solving the equation obtained with taking into account (4), we obtain a computational formula for Ri

(

)

r 2 0.5i − 1 + 20.5i ht . (7) NA When the values of Ri are found by formula (7), the normalized equation of FODADC transformation Ri =

takes the following form 2

⎛ r + ht NA ⎞ (8) P = ∑ ai 2 = ∑ ai ⎜ ⎟ . i =0 i =0 ⎝ r + Ri NA ⎠ As is evident from formula (7), the parameters Ri are dependent on the radius of the fiber, numerical ∗

n −1

−i

n −1

aperture and technological clearance. Since the axial clearance Ri directly affects the energy loss in each channel, it is reasonable to establish the scale of the weighting coefficients using the lowest possible clearances. One way to solve this problem, as can be seen from (7), is the use of optical fibers with a maximum numerical aperture, for example, silica fibers ( n ≈ 1,46 ), in which the shell is air ( na = 1 ). The results of calculating the working clearances of the 8-bit FODADC by formula (7) at NA = 0.2 and ht = 20 µm for different radii of the optical fibers are presented in table. Table Number of digit i 0 1 2 3 4 5 6 7

Radius of the optical fiber r = 5 µm; Ri,25, µm 20 81 165 285 455 695 1035 1515

r = 50 µm; Ri,50, µm 20 132 290 514 830 1277 1910 2805

r = 100 µm; Ri,50, µm 20 235 540 971 1580 2442 3660 5383

It is evident from table that as the radius of the optical fiber increases, the range of variation of working clearances grows.

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Energy losses Bi introduced by each of the attenuators, depend on the size of working clearances and the parameters of the elements of the optical system r2 Bi = 10 l o g ηi n = 10 l o g (9) 2 ⎡⎣r + Ri ( NA ) ⎤⎦ and, depending on the number of the digit, they change in a range from 0.17 dB in the high digit to 22 dB in the low one, which corresponds to a change in the power attenuation coefficient in the range from 1.1 to 300. To provide the output characteristic value of the quantum of 500 nW of optical power of input signal in the low digit should be at least 150 µW, the total capacity of the power source supplying the first Y-coupler should be proportional to the number of FODADC digits. However, practice shows that due to the influence of technological losses, when introducing radiation into the Y-coupler, the unevenness of its division between the output poles, imperfections of processing the fiber ends, inaccuracies of their relative position and other factors, the actual required power of the radiator in some cases, should be much higher than the calculated one. Structural design of an attenuator based on slit diaphragms with various coefficients of optical transmission is shown in Fig. 4. Shutter x GLtri

GLrec

Pr d

Transmitting optical fiber

Prec i

Receiving optical fiber

(a)

Si ai

2R ai (b)

Fig. 4.

Optical radiation Pr from the transmitting monofilament optical fiber through the collimating selfoc GL tr i is transmitted through the working clearance d , which has a movable shutter, to the entrance of focusing selfoc GL rec i (Fig. 4a). At the input end of a receiving selfoc a round diaphragm with a square hole (Fig. 4b) is installed, the side of which is equal to ai . Areas of the diaphragm holes Si are chosen according to formula Si = S0 2 − i . Obviously, the transmission coefficient of the radiation in the ith channel is equal to

Si = 2 − i , and the conversion function of such FODADC takes the form S0 n −1

n −1

i =0

i =0

p∗ = ∑ ai 2 − i = ∑ ai

Si , S0

(10)

where ai is the value of the i th digit; S0 is the transparent area in the top (zero) digit ANALYSIS OF TOLERANCES OF FODADC ATTENUATORS MANUFACTURING To calculate the tolerances of manufacturing of optical attenuators, we use the formula for the optimal determination of tolerances γ i by the criterion of minimum cost of manufacturing the apparatus obtained in [6]

γi =

γ lim n

bi ∑ bi i =1

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,

(11)

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where γ lim is the limit value of this error of full scale; bi is the coefficient of influence of ith component of the resultant error. In addition, the values of the coefficients of the errors influence of individual factors are calculated by the formula

bi =

∂p∗ xinom , ∗ ∂xi Pmax

(12)

where depending on the FODADC design, x is either the value of the working clearance Ri or the diaphragm area Si . For FODADC with axial mismatch of optical fibers, the formula for influence coefficients takes the form

bi =

∂p∗ Ri nom ∗ ∂Ri Pmax

.

Taking into account that n

∗ pmax = ∑ ai 2 − i i =0

{ai }=1 =

2n − 1 , 2n

we get the formula for the influence coefficients in the form

bi∗ =

⎤ NA ⎡ r 1 − 0.5i +1 ⎥. i +1 ⎢ 2 ⎢⎣ 2 ( r + ht NA ) ⎥⎦

(13)

Calculations performed for the absolute values of the clearance deviations from the nominal values by the formula ΔRi = γ i Ri nom with NA = 0,2 and the fiber of 25, 50 and 100 µm and γ lim = 2 − n showed that the tolerance values in the top digit weakly depend on the fiber radius and the digit number and have approximately the same value of 0.9 µm. However, as the fiber radius and the digit number increase, tolerances increase to 593 µm at r = 25 µm up to 2175 µm at r = 100 µm . For FODADC based on slit diaphragms, in view of expression (10), the formula for the coefficients of influence takes the form 2 n −1 bi = 2 − i n . (14) 2 −1 In accordance with expression (11), taking into account formula (14), tolerances γ i were calculated for 8-digit FODADC for three values of the GL diameters (3, 4, and 5 mm). For the case a0 = b0 (Fig. 2b), the values of the maximum deviations of diaphragms holes squares from the nominal values are determined by the following formula ΔSi = Si γ i = 2 − i S0 γ i . (15) Here S0 = a02 , where a0 is a side of the square hole of the diaphragm in the top digit, inscribed into a circle, equal to the GL diameter (Fig. 4b). Tolerance on linear sizes in diaphragm manufacturing is calculated as follows Δai = ai − ai2 − ΔSi .

(16)

The calculation results show that the tolerances on linear sizes of diaphragm holes, unlike the previous version of FODADC, reduce as digits increase. Thus, at the values of the GL diameters taken above, tolerances lie in the range from 8 to 15 µm for at the high-order digit and in the range from 0.73 to 1.28 µm at the low-digit order. The energy loss is determined by the expression

Bi = 10 l o g

2 πRGL Si

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and, as shown by the calculations, are in the range from 1.96 to 23 dB, which almost coincides with the ranges of losses of FODADC with axial mismatch of optical fibers. At the same time, there are various trends of dependencies of tolerances on linear sizes for the options considered. In the first case, the tolerances increase monotonically with digit increasing. In the second case, they remain constant. This creates the possibility of reducing the requirements for precise manufacturing and an overall increase in the digit by creating hybrid designs of FODADC in which the low-order digits are performed according to the scheme on the basis of the diaphragm, and the high-order digits-----on the basis of axial misalignment of optical fibers. CONCLUSIONS The FODADC designs considered can be used for creating a multiplexed system for data acquisition from binary sensors of aircraft mechanical devices (wing high-lift devices, landing gear, limiting system). We obtained analytical expressions and established the relationship between the optical-geometric, metrological, and power characteristics, the combination of which defines the technical possibilities of using FODADC in design of a multiplexed system of binary sensors for aircraft mechanical devices. Calculations have shown that the modern hardware and technology in the field of fiber optics allows multiplexing eight to ten channels of end positions of aircraft mechanical devices using the FODADC systems. Through the use of fiber-optic communication lines with FODADC, it is possible to reduce the weight of onboard channels for transmission of data from binary sensors by an order of magnitude as compared to their wire counterparts. REFERENCES 1. Koshevoi, N.D., Kostenko, E.M., Oganesyan A.S., and Tsehovskoi, M.V., Aircraft System for Measuring the Angular Deflections of Control Surfaces, Izv. Vuz. Av. Tekhnika, 2013, vol. 56, no. 4, pp. 71–73 [Russian Aeronautics (Engl.Transl.), vol. 56, no. 4, pp. 418–422]. 2. Malyutin, D.M. and, Malyutina, M.D., Information-Measuring and Control System of Unmanned Aerial Vehicles Based on High-Accuracy Micromechanical Sensitive Elements, Izv. Vuz. Av. Tekhnika, 2014, vol. 57, no. 2, pp. 39–43 [Russian Aeronautics (Engl.Transl.), vol. 57, no. 2, pp. 162–168]. 3. Grechishnikov, V.M. and Zelenskii, V.A., RU Patent no. 2029428, Byull. Izobret., 1995. 4. Zelenskii, V.A. and Grechishnikov, V.M., Binarnye volokonno-opticheskie preobrazovateli v sistemakh upravleniya i kontrolya (Binary Fiber Optic Converters in Control and Monitoring Systems), Samara: Izd. SNTs RAN, 2006. 5. Grechishnikov, V.M. and Teryaeva, O.V., Data Acquisition Device Based on the Fiber-Optic Digital-toAnalog Converters, Materialy 17-oi mezhdunarodnoi nauchnoi konferentsii “Reshetnevskie chteniya”, (Proc. 17th Int. Sc. Conf. ‘‘Reshetnev Readings’’), Krasnoyarsk: SibGAU, 2013, part 1, pp. 221---223. 6. Grechishnikov V.M. and Konyukhov, N.E., Optoelektronnye tsifrovye datchiki peremeshchenii so vstroennymi volokonno-opticheskimi liniyami svyazi (Optoelectronic Digital Displacement Sensors with Built-in FiberOptic Communication Lines), Moscow: Energoatomizdat, 1992. 7. Butusov, M.M., Galkin S.L., Orobinskii, S.P., and Pal, B.P., Volokonnaya optika i priborostroenie (Fiber Optics and Instrument Design), Butusov, M.M.,. Ed., Leningrad: Mashinostroenie, 1987.

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