Non-Invasive Monitoring of the Technical Condition of Power Units Using the FAM-C and FDM-A Electrical Methods

Abstract

This article presents the selected results of analytical and structural work conducted at the Air Force Institute of Technology (pl. ITWL) in the field of building a measuring apparatus for non-invasive monitoring of the technical condition of aircraft power units. Presented innovative FAM-C and FDM-A methods allow for observation of frequency modulation parameters as well as identification and diagnostic classification of particular mechanical subassemblies supplying the on-board generator and thus enable non-invasive monitoring of technical condition of the aircraft power unit and the aircraft propulsion system. The main purpose of this article is to present the measurement apparatus errors that occur in the signal conditioning system in the FAM-C and FDM-A methods. In spite of the fact that the measuring instrument was built on the basis of digital technology and that it uses typical solutions of electronic frequency measurement, due to the specificity of the applied diagnostic method there occur specific measuring errors which are presented in this article.

1. Introduction

Diagnostics exerts a positive influence on improving and upgrading the operation and maintenance of technical facilities. Its purpose is the assessment, origin and prediction of the technical condition of the facility without disassembling it and using the widely used direct research methods [1]. Optimal operation and maintenance of a technical facility requires precise damage localization and control of operation and maintenance processes based on changes in available diagnostic signals [2]. The aircraft engine consists of many complex assemblies and elements [3]. Since changes in the technical condition of the power unit are caused by every single change or a change group in the technical condition of the elements of the power unit, it can be concluded that the number of signals is infinite. Operational practice shows that the probability of the simultaneous occurrence of two or more reasons for non-operationality is rare during aircraft operation [4,5]. Therefore, it is not necessary to take into account the change in the technical condition of the aircraft caused by the simultaneous occurrence of several reasons. In detecting and identifying damages, the comparison method of a diagnostic model with the diagnostic model of a particular defect is used in complex technical facilities. Non-invasive monitoring of the technical condition of aircraft power units using the FAM-C and FDM-A (F—frequency, A—alternate current, C—degree of progression of the method at the time of patenting [6]) and FDM-A (D—digital current, A—degree of progression of the method at the time of patenting [7]) is a modern approach to diagnosing defects in the aircraft engine without interfering with the structure of the power unit. The method mentioned above was invented at the Air Force Institute of Technology (pol. ITWL) and it enables us to describe the kinematic disturbance in the selected pairs of aircraft power units based on analyzing and assessing the change dynamics in the frequency modulation of the output voltage of aircraft on-board generators. Consequently, it also allows us to detect and classify defects of particular subassemblies of the on-board generators. To illustrate how the FAM-C method works, the example of the AC generator was used with the predefined number of poles. A detailed description of the author’s FAM-C and FDM-A methods in the measurement path (power unit generator) in the aircraft engine was described in other papers by Prof. A. Gębura on the supervision of the technical condition of power units, while this article focuses mainly on errors in the measuring apparatus in the signal conditioning system. This paper is arranged as follows: Section 2 describes the FAM-C and FDM-A methods used in aircraft powerplant diagnostics based on the fundamental laws of physics. Section 3 presents the results of the research of the developed methods (FAM-C, FDM-A) on the example of measurements carried out on MiG-29 and Mi-24 aircraft. Section 4 introduces the measurement errors resulting from the adopted methodology and the measurement track used. Concluding remarks are given at the end of Section 5.

2. FAM-C and FDM-A Methods in Non-Invasive Monitoring of the Technical Condition of Aircraft Power Units

To illustrate the essence of the FAM-C method, which uses the feedback of instantaneous frequency changes in the electromotive force generated in an on-board generator, the simplified mathematical model was assumed, which describes the dynamical phenomena in the selected kinematic pair installed in the aircraft power unit.

-

For the driving element:

$$J_1 {\epsilon }_1\left(t\right) + D_1 {\omega }_1\left(t\right) = C_1 \left[R_2 {\alpha }_2\left(t\right) - R_1 {\alpha }_1\left(t\right)\right] + M_{SL}$$

(1)

-

For the driven element:

$$J_2 {\epsilon }_2\left(t\right) + D_2 {\omega }_2\left(t\right) = C_2 \left[R_1 {\alpha }_1\left(t\right) - R_2 {\alpha }_2\left(t\right)\right]$$

(2)

where:

J₁, J₂—moments of inertia of the driving and driven element;

D₁, D₂—damping coefficients of the driving and driven element;

${\epsilon }_1, {\epsilon }_2$—angular acceleration of the driving and driven element;

${\omega }_1, {\omega }_2$—angular velocity of the driving and driving element;

C₁, C₂—rigidity coefficients of the driving and driven element;

R₁, R₂—radius vectors of the driving and driven element;

${\alpha }_1, {\alpha }_2$—angular position of the driving and driven element;

M_SL—torque.

In the notation depending on the angular velocity, the above relationships can be presented as follows:

-

For the driving element:

$$J_1\frac{d}{dt}{\omega }_1\left(t\right) + D_1 {\omega }_1\left(t\right) = C_1 \left[R_2\int {\omega }_{1}d\left(t\right) - R_1\int {\omega }_2\left(t\right)dt\right]+M_{SL}$$

(3)

-

For the driven element:

$$J_2\frac{d}{dt}{\omega }_2\left(t\right) + D_2 {\omega }_2\left(t\right) = C_2 \left[R_1\int {\omega }_1\left(t\right)d\left(t\right) - R_2\int {\omega }_2\left(t\right)dt\right]$$

(4)

On the right side of Equation (4), there are parameters that force a rotational movement of particular elements of the kinematic pair (expressed by the torque M_SL, transferred to the aircraft engine, and the mutual interaction of the rotational elements, depending on the instantaneous Δt of angular positions α₁(t) and α₂(t) characterized by rigidity coefficients C₁[α₁(t)], C₂[α₂(t)] and radius vectors R₁[α₁(t)], R₂[α₂(t)]). On the left side of Equation (4), some parameters oppose rotational movement (expressed by the moments of inertia J₁ and J₂ and damping coefficients D₁[ω₁(t)] and D₂[ω₂(t)] in the developed version). In the specialist literature it was assumed that any change in structural components (change in mass and dimensions) would have an impact on the change in the inertia moment of the given rotational element (J_i). The change in bearings will reflect the change in damping coefficient (Di), the change in meshing will reflect the change in rigidity coefficient (C_i), and the change in the geometry of the element installation will reflect the change in radius vectors (R_i) of the driven elements.

The analysis of the mathematical model shows that changes in any coefficient parameters in Equations (3) and (4) have an impact on the instantaneous angular velocity of the driven element [8]. It should be mentioned that the on-board generator shaft as the output element of the aircraft power unit is the driving element in the adopted model. The influence of the disturbance of the instantaneous angular velocity of the AC generator shaft on the electromotive force generated in it can be expressed as follows:

$$sem\left(t\right) = -\frac{d\Phi \left(t\right)}{dt}=-\frac{dB\left(t\right)}{dt}·S·\mathit{cos}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]+B\left(t\right)·S·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]$$

(5)

For $B\left(t\right)=B$:, we have:

$$sem\left(t\right) = B·S·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]=K_{\Phi }·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]$$

(6)

where:

sem—SEM induced voltage;

$\Phi$—stream of the magnetic field;

B—induction of the magnetic field;

S—closed surface in the magnetic field;

${\omega }_{WP}$—angular velocity of the generator rotor;

$K_{\Phi }$—magnetic permeability coefficient;

T—measurement time.

Using the theoretical relations between angular velocity and frequency:

ω(t) = 2nπf(t)

(7)

where:

n—the number of pole pairs in the generator:

$$ft=\frac{\omega \left(t\right)}{2n\pi }=\frac{1}{2n\pi }·\omega \left(t\right)$$

(8)

Equation (8) is used to obtain the instantaneous frequency of the electromotive force produced in the generator with the instantaneous angular velocity of the generator shaft [9]. Equation (8) shows that the disturbance of the instantaneous angular velocity of the generator shaft has an impact on the instantaneous frequency of the electromotive force produced. And conversely, by measuring the instantaneous frequency of the electromotive force, a diagnostic signal is received, which contains information on disturbances of rotational movement in the tested power unit. The analysis of this signal helps in identifying the primary disturbance sources and assess of health of the entire power unit. However, it should not be forgotten that measurement is a research problem, and it is difficult to determine the instantaneous frequency of the electromotive force with the appropriate accuracy [10].

By analyzing Relation (6), the instantaneous angular velocity can be defined (with methodical error) based on the measurement of the instantaneous electromotive force from the following relation:

(a) By averaging the frequency of the electromotive force generated:

$$sem\left(t\right) = K_{\Phi }·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right] = K_{\Phi }·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{\omega }_{ŚR}·t\right]$$

(9)

$${\omega }_{WP}\left(t\right)=\frac{sem\left(t\right)}{K_{\Phi }·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]}=\frac{sem\left(t\right)}{K_{\Phi }·\mathit{sin}\left[{\omega }_{śr}·t\right]}$$

(10)

where:

${\omega }_{śR}$—averaged angular velocity of the generator rotor.

(b) By adopting the method of averaging an amplitude of the produced electromotive force:

$$sem\left(t\right) = K_{\Phi }·{\omega }_{WP}\left(t\right)·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right] = K_{\Phi }·{\omega }_{ŚR}·\mathit{sin}\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]$$

(11)

$${\omega }_{WP}\left(t\right)= \frac{sem\left(t\right)}{K_{\Phi }}·arcsin\left[{{\displaystyle \int }}_0^T{\omega }_{WP}\left(t\right)dt\right]$$

(12)

The angular velocity of the generator in the FAM-C method is calculated on the basis of counting when an armature passes through the magnetic neutral axis:

$${\omega }_{cal}(t_{k)}=2\pi ·f_{cal}\left(t_k\right)$$

(13)

where:

$f_{cal}$—frequency calculated in the FAM-C method.

The frequency f_cal in the FAM-C is:

$$f_{cal}\left(t_k\right)=\frac{1}{2\pi \left(t_k^0-t_{k-1}^0\right)}$$

(14)

where:

$t_k^0=t\left[sem\left(t_k\right)=0\right]$;

$t_{k-1}^0=\left[sem\left(t_{k-1}\right)=0\right]$.

Looking for disturbances in aircraft power units, the generator shaft speed expressed by the Laplace operator is as follows:

$${\omega }_{WP}\left(s\right)=G\left(s\right)·{\omega }_{WE}\left(s\right)$$

(15)

where:

${\omega }_{WE}\left(s\right)$—Laplace transform of the angular velocity of the rotor driving the generator;

$G\left(s\right)$—transmittance of the measurement path.

The potential disturbance is hidden in the angular velocity of the rotor driving the generator (${\omega }_{WE}$) expressed by the following formula:

$${\omega }_{WE}\left(t\right)={\omega }_{WE}\left(0\right)+\mathsf{\Delta }{\omega }_{WE}·\sin \left(2\pi f_{WEZ}·t+{\phi }_{WE}\right)$$

(16)

where:

${\omega }_{WE}\left(0\right)$—constant speed of the shaft of the driving element;

$\mathsf{\Delta }{\omega }_{WE}$—amplitude of disturbance of the driving element;

f_WEZ—frequency of disturbance of the driving element.

The same approach must be adopted to define measurement errors resulting from the measuring apparatus. The instantaneous angular velocity of the generator shaft can be described as a combination of many functions:

$${\omega }_{WP}\left(t\right) = f \left[ {\omega }_1\left(t\right), {\omega }_2\left(t\right), \dots , {\omega }_n\left(t\right) \right]$$

(17)

Adopting a linear model of the impact of disturbance and their transmissions in the kinematic path of the examined power unit, relation (16) can be illustrated by using the transmittance of the kinematic path in the following form:

$${\omega }_{WP}\left(s\right) = G_1\left(s\right)\circ {\omega }_1\left(s\right) = G\left(s\right)\circ {\omega }_{SL}\left(s\right)$$

(18)

The analysis of the influence of disturbance sources is done using the so-called characteristic sets (Figure 1), which are the sets of the frequency deviations of the generated electromotive force (characterizing deviations of the instantaneous angular velocity of the generator shaft from the mean value), expressed as the frequency of their changes (equivalent to the spectrum in the Fourier analysis).

The main difference between the Fourier distribution and the distribution of the characteristic set is that in the Fourier distribution, every stria represents the average disturbance value. The FFT (Fast Fourier Transform) method cannot record a separate disturbance and in the distribution of characteristic sets, every point of the set represents a particular disturbance in the angular velocity of the generator shaft. It enables one to determine the statistical parameters of this disturbance (e.g., average value, maximum value, standard deviation and variance), which are essential to assess the risk of a given disturbance which could cause the deterioration of the technical condition of the examined power unit. The frequency of the determined deviations in the characteristic set simultaneously describes the frequency of their changes in the examined kinematic path and enables one to identify disturbance sources. This identification consists in finding kinematic defects in the kinematic path that affect the generated rotational movement with the same frequency as the frequency of deviations in the determined characteristic set.

The General Description of the FAM-C and FDM-A Method for the Voltage from the AC and DC Generators

The FAM-C and FDM-A methods are applied to diagnose bearing supports [11,12,13,14,15] and other aircraft subassemblies. These methods use data contained in frequency modulation [3,8] for localization and diagnostic classification of mechanical components that were damaged in the examined power unit [16,17]. Primary diagnostic signal processing, i.e., the change in frequency modulation of the instantaneous angular velocity of the mechanical subassembly (when its elements were damaged) has two phases:

• Primary sampling done by the on-board generator, called generator-converter (analog sampling);
• Secondary sampling—done by the signal conditioning system with a counter card (digital sampling).

The generator-converter is an integral part of the power unit. It transfers the primary diagnostic signal (generated in the form of angular velocity modulation by defective kinematic pairs of the examined power unit) into modulation of the output voltage frequency. In the next phase, the output voltage generator signal is prepared to the standard form in terms of processing on the counter card. The signal conditioning system is used to do it. It enables to generate impulses in the TTL (transistor–transistor logic) standard that opens and closes the calculation process in time increments [18,19].

Due to the specificity of the electronic preparation of these pulses, various errors of time displacement and zero level detection errors are created when the sinusoidal signal passes through the zero level [20]. The counter card is a source of errors, such as, e.g., the stability error of a quartz clock. The pulse bundles, collected in the counter card buffer, are stored on the PC disc, where they create measurement files. The sets of measurement files are processed into time lines f_i = f(t) and characteristic set ΔF = f(f_p). The structure of a single-channel measurement system is described in Figure 2 [15]. At the input, there is a standardization block of the voltage signal. First, the sinusoidal sine wave is truncated (to 0.1 0.6 V), allowing us to adjust the input signal to TTL. Due to this, the noise level is reduced. Then, instantaneous frequency measurement is done with the indirect method [12]. It is indispensable to calculate the average frequency if we want to obtain characteristic sets. In the next step, the characteristic sets are virtually created from the output voltage of the on-board generator (which is implemented by the deviation extreme search block and deviation duration calculation block). After that, the height of the characteristic sets obtained in the measurement is automatically compared with the benchmark parameters (the diagnostic signal development block does it by the semiautomatic tester or the authorized diagnostician). The final stage is data archiving and visualization of results. Data archiving occurs by saving data in the internal memory of the tester or the external PC database. Visualization takes the form of signaling the diagnostic classification of the most worn mechanical subassemblies along with the identification (assigning to particular mechanical subassemblies). Transcribing data from the internal memory of the tester to a stationary database of the user enables tracking permanent wear trends of particular kinematic pairs of the aircraft. Diagnostic classification of particular subassemblies enables the user to immediately decide whether to permit the flight of an aircraft or helicopter or, in justified cases, suspend the departure and take current remedial measures, e.g., exchange of a subassembly or the entire power unit. In the FAM-C and FDM-A methods, similarly as in TTM (Tip Timing), secondary sampling is performed by an electronic signal conditioning system and the counter card time base clock [18]. It is a classical sampling method described in many articles focused on TTM. In radio engineering, the measurement of signal return time (radio altimeter and pulse rangefinder) is performed in a similar way. In an electrotechnical environment, there are studies concerning digital sampling, e.g., generator voltage, and, if need be, digital processing of its amplitude. In this case, various error parameters are considered, e.g., error shape of the recorded signal, errors resulting from radio interference, etc. By implementing the FAM-C and FDM-A methods, the object of interest is not the shape of the amplitude changes of the generator voltage, but its frequency, and precisely, the change in time increments between successive movements of the rotor of the generator-converter passing the magnetically neutral stator zone [21,22]. Reflection of the history of the next location enables a secondary, digital processing of changes in the angular velocity of particular kinematic links of the tested power unit. Due to the specificity of obtaining and processing the input signal (waveform of the generator voltage) on the instantaneous frequency waveform, Figure 2 illustrates the methods of electronic signal processing, taking into account the systematic and apparatus errors committed during secondary sampling.

Secondary sampling is carried out with indirect frequency measurement [11,12,13,14,15,23] by counting the number of n pulses of the time base clock f_z during the period or half-period of the sinusoidal voltage signal (generator-converter). The generator-converter (in primary sampling, e.g., in electrical machinery) earlier discretized the spectrum of changes in mechanical modulation of the tested power unit and coded them as changes in time increments of passing through the zero level. Electromechanical sampling has many advantages, the most important of which is the synchronism of mechanical and electrical phenomena [17,24,25,26,27,28,29]. Secondary sampling is used to determine the size of these changes and to transpose them in a way that is understandable for the operating unit. Currently, a time base generator is applied in secondary sampling (‘generator’ block), which produces a constant pulse sequence with permanent frequency. The sequence of these pulses is not synchronized with the frequency modulation and waveform phase of the voltage obtained from the generator-converter coupled with the examined mechanical power unit; thus, the following equation is used:

$$f_i=\frac{f_z}{n}$$

(19)

where:

f_i—subsequent frequency of the measured signal;

f_z—generator frequency of benchmark signal;

n—number of pulses measured during the duration of the measured signal.

3. Results of Non-Invasive Monitoring of the Technical Condition of Aircraft Power Units Using FAM-C and FDM-A Methods

3.1. Measurement Results of the Voltage Frequency for the Rupture of the Generator Shaft in the MiG-29 Aircraft

The waveform of the angular velocity of the generator rotor recorded by rupture of a mechanical connection of the unidirectional clutch of MiG-29 aircraft was presented in Figure 3. The angular position of the rotor for one phase A (i.e., rupture of the bond with the power unit) and for one phase B (i.e., engaging bond with the power unit) was illustrated in the time function. Successive (even) angular positions have been set at the entrance of the selected kinematic pair on the vertical axis of the graph. On the horizontal axis, one can notice uneven successive increments of the time sections. They are called the increments of successive half-periods of the quasi-sinusoidal waveform of the generator output voltage. These time increments are not uniform—they depend on changes in the angular velocity of the generator rotor.

3.2. Example of Disturbance Observability Board for the Aircraft Power Unit of the Mi-24 Helicopter

The design and structure of the measuring apparatus in the FAM-C method enables one to simplify the measurements, i.e., simultaneous or successive measurement in three channels (A, B, C) separately for the left and right GT-40PCz6 generator (Figure 4). Separate measurements for each of both AC generators are necessary due to significant differences in the function and magnitude of mechanical loads of the drive paths for each generator. The drive seat of the left GT 40PCz6 generator also plays the role of a rotation axis of the Z30 gear wheel in the accessory gearbox (AGB), which transfers mechanical power to the tail rotor. The increased circumferential clearance between the Z30 and Z70 wheels can result in problems with maintaining the flight direction (due to the unequal rotational speed of the tail rotor), but disconnecting these gear wheels can terminate in a helicopter crash. Therefore, apart from the measurement paths {A, B, C}, there is also a fourth channel, which measures the phase displacement between frequencies of the generated current from on-board generators. This channel compares the measurement signals. This configuration allows for a detailed observation of the mutual angular movements of Z30 gear wheels between generators.

The measuring instrument is attached to any electrical connector in a given electric circuit (1 × 115 V, 400 Hz; or 3 × 200 V, 400 Hz; or 3 × 47 V, 800 Hz), which is electrically connected to a given generator, located at a safe distance from the place posing a threat to staff.

In the case of the Mi-24, a simultaneous measurement in three following channels was taken:

• Single-phase measurement channel: 1 × 115 V, 400 Hz—mechanical frequency range f_p = 2–250 Hz, which allows for observability of characteristic sets;
• Three-phase measurement channel: 3 × 200 V, 400 Hz—mechanical frequency range f_p = 180–1200 Hz, which allows for observability of characteristic sets;
• Three-phase measurement channel of the pilot exciter (taken from the diagnostic connector of the voltage regulator block): 3 × 48 V, 800 Hz—mechanical frequency range f_p = 580–2500 Hz, which allows for the observability of characteristic sets;

Characteristic sets (along with their frequencies f_p) can be presented in the following diagram (Figure 5), where the observability bands of particular generators are indicated with colored lines. These generators are included in a wide frequency range f_p = 2–7000 Hz, ensuring the monitoring of the most important mechanical elements of the Mi-24 power unit.

It should be noted that the mechanical signals of angular movement modulation in the presented frequency range are processed into characteristic sets, which expose the defects of particular subunits and allow for quick and precise assessment and diagnostic classification. By observing how the above-mentioned observability bands of given measurement channels are assigned, the observed phenomena of the movement dynamics of mechanical subunits of Mi-24 power unit, can be divided into three groups according to the frequency bands of the mechanical process:

• Slowly-changing—f_p = 2–60 Hz;
• Middle-changing—f_p = 60–640 Hz;
• Fast-changing—f_p = 640–7000 Hz.

(Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11) The following Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 are presented the test results of power units of Mi-24 helicopter for different voltages.

4. Detection Errors—Study of the Effect of Changing the Amplitude of a Sinusoidal Signal on the TTL Signal

The test results revealed the influence of the change in signal amplitude on the duty cycle of the TTL signal (high level H and low level L) [21,30,31]. For a given input channel, the impact of the signal duty cycle on the amplitude of the input voltage was calculated from (20). The impact of signal frequency imaging (sum of high level H and low level L) was calculated from Equation (20).

$$Q_{A\_TTL\_H}\left[\%\right]=\frac{\mathsf{\Delta }b+\mathsf{\Delta }t}{T}\ast 100=\frac{{470}^{-9}s+{30}^{-9}s}{{10}^{-3}s}\ast 100=0.005\%$$

(20)

$$Q_{A\_TTL}=Q_{A\_TTL\_H}+Q_{A\_TTL\_L}=0.005 \%+0.0049\%=0.0099\%$$

(21)

The calculated impact of the amplitude change of the input signal on the duty cycle of the TTL signal is shown in the following (Figure 12, Figure 13, Figure 14 and Figure 15).

The above diagrams show that the increase in the voltage amplitude of the measured signal results in the decrease of the measurement error. For higher frequencies of the input signal, this relation is very similar. The differences in error values between measurement channels arise mainly from the different switching times of the galvanic insulation system. It is a constant delay introduced by the opto-isolator. The smallest mapping error is the duty cycle with an amplitude in the range from 18–24 V (nominal or higher voltage). The mapping error of the duty cycle of the low level QL of the TTL signals is analogous.

4.1. Investigation of the Response Delay of the TTL Signals

To reduce the zero level detection error, the study was conducted for voltage waveform of a rectangular shape, voltage of 18 V and duty cycle of 50%.

Using an oscilloscope, measurement of the delay time of the TTL signal was taken compared to the benchmark signal (Figure 15). By changing the frequency of the generated benchmark waveform, the frequency range was determined, in which the response delay of the system is constant. The test was done for the output of the TTL signal and a negated value. This test was repeated for all measurement channels: A, B, C.

The tests exposed that the system delay for a rectangular signal in the frequency range from 1 Hz up to 200 kHz is constant and equals approximately 690 ns for all channels.

The time of the half-period was calculated from relation (22). Values of time T for frequencies are 50 Hz, 400 Hz, 10 kHz, 0.01 s, 0.00125 s and 0.00005 s respectively.

$$T=\frac{1}{2f}=\frac{1}{2\ast 50 \mathrm{H}\mathrm{z}}=0.01 \left[s\right]$$

(22)

Duty cycle Q of H and L levels for frequency 50 Hz calculated from Equation (23).

$$Q_H\left[\%\right]=\frac{\left(\mathsf{\Delta }{t}_2-\mathsf{\Delta }{t}_1\right)}{T}\ast 100=\frac{756.8 \mathrm{n}\mathrm{s}-672.4 \mathrm{n}\mathrm{s}}{10 \mathrm{\mu }s}\ast 100=0.000876\%$$

(23)

Diagrams of duty cycles Q_H of TTL signals and a negated value were presented in the following (Figure 16 and Figure 17).The magnitude of signal delay in the frequency range (1 Hz–200 kHz) is constant. However, the increase in frequency results in shortening the T time T of half-periods. The above shows the increase in the error of duty cycle Q_H. The error is similar in the case of the duty cycle of levels Q_L.

4.2. Investigation of the Detection System of the Common Part of Adjacent Phases (Three-Phase Operation)

Investigation of the detection system of the common part of adjacent phases was conducted according to the measuring apparatus (Figure 18). Using a generator, the waveform of two rectangular characteristics with phase shift φ = 90°, voltage of 18 V and duty cycle of 50%. Signals from the generator were connected to channels A and B.

The delay time between a trigger point and half of the value of the 3F _ TTL signal voltage as well as the 3F _ TTL signal-off delay (Figure 19) were measured using oscilloscope cursors. By changing the frequency of the generated benchmark waveform frequency range was determined, in which system response delays for leading edge and trailing edge signals are constant.

The conducted tests show that delay of the phase comparison system for a rectangular signal in the frequency range from 1 Hz to approximately 180 kHz is constant and is on average 690 ns for all channel pairs. The error of the duty cycle of H and L level of the TTL output signal was calculated in the same way as in 4.1.

Diagrams including the errors of Q_H duty cycle of 3F _ TTL signals and a negated value are exhibited below (Figure 20). The magnitude of the signal delay in the frequency range (1–180 kHz) is constant, but as the frequency increases, the time of half-periods decreases, which results in increasing the impact of the error of the duty cycle Q_H. In the case of the duty cycle of Q_L levels, the error is analogous.

5. Conclusions

In this paper, a possible solution on how to improve test results during FAM-C and FDM-A testing has been given. Research results presented in this article indicate that the smallest error of the zero-crossing detection system of the voltage waveform occurs for nominal input or higher voltages. The impact of the change in signal amplitude is affected by the error, which is due to the slope angle of the measured signal and the magnitude of interference. Phase shift errors that are constant in the whole measured frequency range can be ignored for the performed measurements, taking into account a full repetition period of a single- or three-phase signal. However, the zero level detection error, which, for frequencies 50 Hz, 400 Hz and 10 kHz amounts to 560 ns, 78 ns and 5 ns respectively, should be taken into consideration. These errors can be eliminated by applying the appropriate filters at the system input. In the case of frequencies based on half-period signals, phase shift errors resulting in the change of the duty cycle of the TTL signal should also be considered. It has been proven that errors of the counter card, the frequency of clock f_z should be selected so that the values of the counted pulses are close to the maximum value of the applied counter. Additionally, there are also other errors in the measuring apparatus, such as accuracy error of the generator-sensor, phase asymmetry, disturbance caused by the instruments that perform measurements (the power transmission system provides power to mechanical devices) and stability of the benchmark generator used in the counter card. The article is also addressed at metrological issues related to the operation of generator-converter (doing primary electromechanical sampling) and measurement of time increment (secondary electronic sampling), which may be another way of increasing the reliability of FAM-C and FDM-A methods in diagnosing aircraft power units.