Methodology for assessing reliability of stand-bed systems in testing liquid throat engines

Low- thrust rocket engines (LRE) are currently widely used in motion control systems for spacecraft (SC). They provide orientation, correction and stabilization of the spacecraft in flight, and also create the necessary impulse overloads when starting the propulsion systems of upper stages that carry out the launch of spacecraft into specified orbits. [ 1; 2 ] .

LREs represent a special class of liquid propellant rocket engines. This feature is expressed with the overall and mass characteristics, the specifics of mixture formation and combustion processes in the engine chamber, the absence (in most cases) of active cooling of engine elements. The use of micro motors as control actuators of orientation and stabilization systems imposes strict requirements on their design and characteristics, since each motor becomes a link in the control system and, as an executive link, is described by the transfer function between the command electrical signal and the developed control force [3; 4].

The design of the LRE provides for multiple engine starts with different duration (from several hundredths of a second to seconds) and frequency of starts while meeting the requirements for high efficiency in terms of fuel consumption. The efficiency of these engines directly affects the mass of fuel stored on board the spacecraft (SC) for control, and affects its mass characteristics.

An important feature of LRE is a large total number of operation cycles (up to a million starts) with service life in autonomous mode as part of a spacecraft (SC) in orbit of 10 years or more.

A characteristic difference of LRE is the non-stationarity of its mode of operation. With an increase in engine thrust at the time it enters the mode and with a decrease in thrust at the time of shutdown, the processes of mixture formation, combustion and exhaustion occur in off-design conditions, the engine efficiency is significantly reduced. The specific impulse in such modes is lower than in continuous: I si <  I rp ; reduction can be up to 50% [4; 5].

The specifics of operating conditions establish increased requirements for maintaining energy characteristics when changing in a wide range of input pressures and temperatures of rocket fuel components, since fuel is supplied to them according to a displacement scheme, i.e. due to the pressure created in the service tanks of the spacecraft propulsion system.

It should be noted that in order to achieve the required LRE reliability indicators it is necessary to ensure bench tests of the engines being created at the main stages of design and development work as well as during serial production of items.

Research problem statement

In the process of experimental development of the low-thrust engine great attention is paid to the methodology of bench tests, the technical equipment of benches that simulate the impact of the physical conditions of outer space as well as the use of diagnostic methods and equipment for various physical studies and measurements.

Certified low-thrust engine test procedures and test equipment must ensure that test results are obtained with the required accuracy characteristics and ensure that the required test conditions are reproduced with rated accuracy [3; 6].

Methods and means of metrological testing support including measurements of the parameters of the engine under test, influencing factors, test equipment and test modes, must ensure that test results are obtained with the required accuracy and reliability.

Since the number of low-thrust engine tests in full-scale operating conditions (flight tests) is very limited and in most cases it is generally excluded due to their high cost therefore it is necessary to achieve the maximum efficiency of their ground testing. The efficiency of ground (bench) testing is ensured by simulating the conditions of full-scale tests and taking into account the influence of all operational factors affecting the reliability of the assessment of reliability indicators during design testing in ground conditions. A special place in the issues of ensuring the effectiveness of tests is occupied by the requirements for ensuring the accuracy and reliability of test results.

Low-thrust engine fire test stands are subject to specific requirements. The main of them are: achieving the degree of compliance with high-altitude conditions (environment rarefaction); creation of identity or dynamic similarity of characteristics of low-thrust engine power supply systems with fuel components, including matching of inertial, wave and hydraulic characteristics of supply lines; ensuring compliance with the laws of change in inlet pressures to the engine, pressures in the combus- tion chamber; ensuring within the specified limits the temperature values of the fuel components (both negative and positive).

The short duration, increased danger and high cost of LRE fire tests cause special requirements for the level of reliability of the bench systems [7; 8].

When determining the reliability indicators of the bench systems it is necessary to introduce such characteristics as the output effect of the system and the quality of operation. In this case the output effect should be considered a useful result obtained during the operation of the system for a given time interval and the characteristic of the quality of functioning is a quantitative assessment of the quality of the functioning of the system in its certain state when performing this task.

As a result of failures of some elements of a complex bench system the quality of functioning deteriorates and accordingly the probability of successful execution at a given time of certain functions that determine the output effect of the system decreases.

Therefore the task of assessing the reliability of the stand for firing tests of a rocket engine systems is reduced to to elucidate the influence of failures of elements on the quality of functioning and the output effect of each system [9].

Theoretical factors for ensuring the reliability of bench systems

At the first stage of determining the reliability indicators of the system it is necessary to clearly formulate the goals and objectives facing this system, which it is advisable to number in order of importance ( j' = 1,2..., where m is total number of tasks). Further taking into account the concrete specifics, the complex system should be divided into elements and the elements should be assigned numbers ( i = 1,2..., where n n is the total number of elements) [9].

We represent the mathematical model of the system functioning as a time-varying vector ^Z(y) .

Then in the whole state of the system can be described by the following formula:

■ X1( t) ■ Z(t) = Xn( t) Y1( t) . Ym( t). where Xi(t) is the state of each element that takes values: 1, if i-th element is operational; 0, if i-th element is operational; Yi(t) is the need to complete each j-th task, in this case it is accepted: 1, if there is a need to complete the task; 0 if there is no such requirement.

The characteristic of the functioning quality is defined as a random function ^F z ^(t) = F [ z(y) ] which like the vector changes in time. The mathematical expectation of the random function F z ( t ) time t is an indicator of the system functioning quality.

K(t) = MFz(t).

In the working state of the test bench system all components of the vector Z(y) describing the states of the elements of the system are equal to one.

Obviously each implementation of the random function Fz(t) corresponds to the output effect W z [ 0, t ] as a useful result of the system operation in the considered time interval [ 0, t ]. The indicator of the output effect of the bench system should be considered a mathematical expression:

U [ 0, t ] = M-W [ t ] .

Calculating the indicators K o (t) and U o [ O, t] for an ideal (absolutely fail-safe) system, we define the reliability of bench systems as the ratio of the performance quality indicators and the output effect of the real system to the corresponding indicators and the ideal:

P ( t ) = K ⁽ tP ( t ) = U (° tУит,^ K _.0( t ), U _.0 (0, t ) .

The ambient pressure, dynamic processes in the fuel lines of the stand and the current thrust value and the nature of its change over time are the most significant elements that determine the reliability of the results obtained during fire tests of a low-thrust engine.

Most low-thrust engines operate at very low ambient pressures and therefore a significant amount of testing during their development should be carried out on stands equipped with vacuum systems. When determining traction characteristics and characteristics by specific impulse in a vacuum chamber (with an engine installed in it for testing), a predetermined pressure value is provided for the continuous outflow of gas from the nozzle.

The dynamic processes that occur in the fuel lines for supplying fuel components depend on many factors determined by the properties of the fuel components, the pneumohydraulic circuit and the low-thrust engine operation cycle. It is known [10] that the nature of dynamic processes in highways has a significant impact on engine parameters which is especially relevant for a low-thrust engine since operation in pulsed modes that cause dynamic processes is one of the most typical features of such engines. Therefore in order to reliably determine the characteristics of the engine during testing it is necessary to ensure that the dynamic processes that occur in the bench lines correspond to the processes that occur in the supply fuel lines in propulsion systems (PS) with a low-thrust engine.

Technological test tools

Based on the analysis of the results of the studies carried out, recommendations were developed on the composition of the technological and measuring equipment of low-thrust engine test benches with simulation of high-altitude conditions. The structure of such a stand includes: a pressure chamber, vacuum pumps, a system for measuring vacuum and engine parameters, control systems for the engine and elements of the stand [10].

The pressure chamber and a set of vacuum equipment are selected based on the operating conditions of the tested engines, pressure and temperature in the pressure chamber, the required performance of the stand etc.

The specified test conditions must unambiguously determine the technical characteristics of the test stand including the pressure chamber and vacuum equipment. When testing a low-thrust engine in pulsed modes the pressure in the pressure chamber of the stand at the end of a series of pulses should not exceed the pressure at which the gas flow can be separated from the wall of the engine nozzle.

Before the start of fire tests, the required residual pressure (vacuum) in the thermal vacuum chamber is created by a cascade of vacuum pumps formed by a certain set of mechanical, steam-oil and other types of pumps. The nomenclature of the set is determined by the requirement to ensure pressure in the pressure chamber close to the lower Р н limit.

In the interval (0, t 1 ), the system is in an equilibrium state which is provided by operating vacuum pumps the number of which can be a certain fraction of all vacuum pumps of the test bench [11; 12]. This number is determined by the degree of tightness of the pressure chamber or the level of leakage of the atmospheric medium into the pressure chamber. The pressure level is maintained in the pressure chamber close to the lower Р н permissible limit. At time t1, the engine is started.

In the interval (t 1 , t 1 ), when the engine is running, combustion products enter the pressure chamber. Denoting the total mass per second consumption of fuel components, we write an expression for determining the mass of combustion products that entered the pressure chamber during engine operation,

X t 2

rm _s ( t ) dt

Taking with some assumption the gas mixture in the form of a mixture of ideal gases, we write the equation of state for the time t 2 when the engine is turned off,

PV.

a бар

^{= M} бар ^R пс ^T бар

where R пс is gas constant, T бар is gas mixture temperature, M бар is the mass of combustion products located in the pressure chamber when working with a vacuum pump.

From this equation we find an expression for calculating the optimal value of the pressure chamber volume:

^M бар ^R пс ^T бар

V бар =

Pв

A significant drawback of the obtained formula is the accepted assumption that the functional dependence of the consumption of fuel components is known while in practice this is not always the case. Such dependence can only be obtained by conducting a series of tests with a sufficient degree of reliability, while it is possible to evaluate the optimal volume of the pressure chamber using known statistical values of the parameters that affect this volume. These parameters are: the average values of the total consumption of fuel components and the performance of the vacuum system in the range of permissible pressures in the pressure chamber from Р в to Р н .

When evaluating the dynamic characteristics of a low-thrust engine operating in pulsed modes, the inertial forces arising in the thrust measuring device (TMD) can introduce significant errors in the estimation of the parameters that determine the dynamic characteristics [13]. The error in measuring these parameters increases when the pulsed frequency of the low-thrust engine being tested is in the natural frequency range of the TMD due to the resonance effect. Therefore, when creating a TMD, it is necessary to ensure a significant excess of the natural frequency f tdm over the frequency of the pulsed mode f .

According to well-known recommendations the ratio of these frequencies should be at least 25–30, i.e., f tmd = (25–30)· f , which minimizes the measurement error. As according to statistics, the frequency f of the low-thrust engine pulse mode does not exceed 2 Hz taking into account the condition f tmd = (25–30)· f design maximum permissible value of the natural frequency of vibrations of moving parts TMD f 0пр = 60 Hz .

Pulse modes of low-thrust engine operation initiate transient (low-frequency) processes of movement of fuel components in pipelines. Optimization of low-thrust engine fire testing processes requires solving the problem of ensuring the dynamic similarity of the characteristics of the engine supply systems with fuel components on the bench and in the propulsion system, including the correspondence of the hydraulic inertial and wave characteristics of the supply lines [14].

To exclude the phenomenon of resonance which causes negative (from the point of view of similarity) non-stationary processes the natural frequency of the mains f 0 must differ significantly from the frequency of forced oscillations excited by the pulsed mode of operation of the tested low-thrust engine. We can accept the following dependence of the frequency f 0 and the maximum frequency of forced oscillations f дв max, taking into account the safety factor

• f 0 ^D n дв max ,

where n is stability factor, which is determined empirically based on the results of low-thrust engine bench tests. Taking into account the recommendations [14; 15] when developing a test procedure, we take n = 10.

Thus the length of the bench line should be such that its natural frequency is at least 10 times higher than the maximum frequency of the low-thrust engine pulse mode during testing.

Improving the accuracy of measurements and the reliability of test results

Assessment of measurement accuracy is necessary at the stages of planning, bench testing and analysis of LRE test results [16]. Determining the measurement error of parameters during bench tests is an important component of the development of the product as a whole.

Particular importance is given to the definition and evaluation of instrumental errors which are due to the error of the measuring instruments used. The analysis of instrumental errors in the measurement of parameters in steady-state operating modes during engine testing is carried out. The following main tasks of the methodology for calculating these errors are formulated:

• –    regulate the procedure for obtaining reliable data on instrumental errors in measuring parameters;

• –    to minimize metrological circuits for measuring parameters using modern sensor-forming equipment;

• –    introduce corrective information into the design documentation of products at the final stage of their development.

The initial data for calculating errors are the metrological characteristics of measuring instruments and sensor-converting equipment used in testing products, as well as the test program and specifications for testing.

The pressure of steady-state parameters during engine testing is measured by primary pressure measuring instruments (sensors) of various operating principles (inductive, vibration-frequency, potentiometric, tensometric, etc.). When using inductive pressure sensors calibration is preliminarily carried out as part of the stand with the number of points to be checked in the measurement range. The result of such a calibration is the dependence:

, where А0, А1, А2, А3 are coefficients of the equation calculated by the least squares method, ΔUi is deviation of the output signal of the sensor measuring channel:

A Ui = (Ui - U0), where Ui are recorder readings at the current measurement point; U0 are recorder readings at zero point.

The instrumental error in pressure measurement is determined by the expression :

, where Рmax is the upper limit of measurement by the sensor, Па; Рож is expected pressure value, this value is laid down by the preliminary program for testing; δРосн is the main error of the pressure measuring channel, obtained as a result of a preliminary calibration:

$PocH = 5сл + 5пр + ^пр.рег + 5эт , where δсл is random sensor error obtained during calibration; δпр is the main error of the intermediate converter; δпр.рег is the main error of the transducer-registrar; δэт is working standard error. The instrumentally reduced error of the pressure measuring channel by vibration-frequency, potentiometric and strain gauge sensors was calculated by the formula

5 Р и = P ax ( 5™ + 8 пр.рег ) ,

Pож where δПИП is systematic error of the measuring instrument used. When measuring pressure by several duplicating equal-precision measuring channels the error was determined by the expression

- ^{5 Р} И

^{5 Р} .К , К = (2—4).

One of the difficult problems of engine testing is to determine the thrust force of the engine, since tests are carried out in a pressure chamber [17]. The thrust force in a vacuum (pressure chamber) is determined by an indirect method based on the results of direct measurements of force, pressure in the combustion chamber, atmospheric pressure, residual pressure in the pressure chamber, the geometric dimensions of the nozzle exit area and critical section. Direct measurement of force is carried out using a force-measuring device (FMD) equipped with devices of a vibrofrequency, resistive principle of operation [18]. The output signal from the FMD is fed to the intermediate converting equipment and then to the converter-recorder. Measurement of pressure in the pressure chamber is carried out by pressure sensors. The cross-sectional areas of the critical section and the nozzle exit are known from the engine passport. The traction force within the stand is determined by the expression:

Pn = P + RДОП , where Р is force of thrust measured by a force-measuring device; RADD is additional force of thrust of the product, depending on the residual pressure RДОП = FА ∙PН, where FА is exhaust exit area, PН is residual pressure in the pressure chamber. The force-measuring device is calibrated for at least three “load-unload” cycles, the results are recorded in the FMD passport. After testing the product, another “load-unload” cycle is carried out to control the calibration characteristics. The instrumental error in measuring the traction force of a product in a void is calculated from the error in direct measurement of the traction force of the SIS and the error in the additional value of the traction force which depends on the residual pressure in the pressure chamber. Instrumental reduced error of the measuring channel for direct measurement of the FMD force:

8RИ = Pmax (8 Сиу )осн, ож where Рmax is the upper limit of force of thrust measurement; Рож is expected thrust value; (δсиу)осн is the main error of the measuring channel of the FMD force, obtained during calibration:

(8Сиу )осн   (8Сиу )сл +8пр +8пр.рег +8эт , where (δСиу)сл is random error of FMD, obtained by calibration; δпр is the main error of the intermediate converter; δпр.рег is the main error of the transducer-registrar; δэт is working standard error.

In turn the instrumental error of the additional component of the thrust force R ДОП is caused with the error in measuring the outlet section of the nozzle and the error in measuring the residual pressure in the pressure chamber.

Duplicate systems for calculating the traction force of the product are created on the stand. When this happens the measured value of the pressure in the combustion chamber, the thrust coefficient in the void and the area of the critical section are used. This method is available in the case of a known void thrust coefficient which is determined from the results of the FMD values of previous tests. [19].

Estimation of the instrumental error in measuring the mass flow rates of the fuel components depends on the test modes and can be measured in various ways. In the case of continuous operation of the engine the flow is measured by 2–3 turbine flow sensors (TFS) installed in series in the pipeline main with volumetric flow rates and subsequent conversion to mass flow, or Coriolis-type mass flow meters. Calibration of sensors is carried out on the water. The instrumental reduced error is determined by the formula

• — q ^{max   ТРД}

• ⁸ ^ И = “     7р⁺⁸пр.рег ⁺⁸ р ,

q ож к K qож is expected consumption of the component during testing; δТРД is the largest basic error of one of the flow sensors obtained during calibration; К is number of flow sensors; δпр.рег is the main error of the transducer-registrar; δр is relative component density error.

The temperature during testing is measured by thermometers which according to their purpose, are divided into surface and medium, and according to the principle of operation – into resistance thermometers and thermocouples (thermoelectric thermometers). Absolute measurement error with a resistance thermometer :

AtИ = AtТ.С. + Atпр.рег , where ΔtТ.С. is absolute error of the resistance thermometer; Δtпр.рег. is absolute error of temperature measurement by the transducer-registrar. Similarly, the error is calculated when determining the instrumental measurement error by a thermocouple.

It is advisable to measure torques with a TS-1 type sensor which is previously calibrated as part of the stand, the instrumental error is calculated by the formula

( о \     M кр.тах        \

°кр )и =          (°кр-осн), кр.ож where Мкр.max is upper limit of torque measurement; Мкр.ож is expected torque, where (δкр.осн) is the main error obtained during the calibration of the sensor is calculated by the formula

($КР )осн = ($КР )сл + $ПР + ^пр.рег + $изм.г.в + $эт , where (δкр)сл is random error of the torque sensor obtained during calibration; δпр is the main error of the intermediate converter; δпр.рег is the main error of the transducer-registrar; δизм.г.в is the main measurement error of the geometric values of the arm; δэт isworking standard error.

The angles of rotation of the drive shaft are usually measured with a standard potentiometer while the instrumental error in measuring the angles of rotation of the drive shaft is calculated by the formula

5аи   а    (5эл.пр +§л +5пр.рег), аож where αmax is upper limit for measuring the angles of rotation of the drive shaft; αож is the expected value of the rotation angles of the drive shaft; δэл.пр is the main error of the potentiometer of rotation of the drive shaft; δЛ is relative error of the potentiometer from the backlash value of the electric drive shaft; δпр.рег is the main error of the transducer-registrar.

A scientifically based and experimentally proven method for assessing the accuracy of measurements contributes to the reliability of test results [20].

Conclusion

Based on theoretical and experimental studies a methodology for assessing the reliability of bench systems when testing low-thrust liquid-propellant rocket engines has been developed. The technique for estimating the frequency characteristics of bench hydraulic lines is presented in a general form. Taking into account the results of low-thrust engine tests recommendations have been developed for calculating the internal volume of the pressure chamber and the performance of the bench vacuum system. The analysis of instrumental errors in the measurement of parameters was carried out. Recommendations have been developed to improve the accuracy of measuring parameters in steady-state operating modes of a low-thrust engine during bench tests.