CC BY
24
UDC 621.01
Sibirskii Gosudarstvennyi Aerokosmicheskii Universitet imeni Akademika M. F. Reshetneva. Vestnik Vol. 17, No. 4, P. 964-974
ASSESSMENT OF SPACECRAFT SOLAR ARRAY RELIABILITY DURING GROUND EXPERIMENTAL DEVELOPMENT TEST
S. A. Zakharov
JSC "Information satellite system" named after academician M. F. Reshetnev" 52, Lenin Str., Zheleznogorsk, Krasnoyarsk Region, 662972, Russian Federation E-mail: szaharov@iss-reshetnev.ru
The increase of available power and the lifetime up to 15 years for modern telecommunications satellites significantly actualize the challenge of improving large-sized foldable solar arrays (LF SA) reliability. The reliability of any equipment to be implemented onboard of a spacecraft depends mainly on the quality of their ground experimentaJ test development (GTD). To ensure high quality GTD it is important to accept the correct concept of SA reliability validation, taking into account the specifics of the SA design and the real capabilities ofthe test facilities.
The paper describes constituent parts ofthe concept allowing validating the large-sized foldable solar arrays reliability at the phase of ground experimental test development. There has been obtained the system of differential equations which describes SA deployment using the off-loading system and, as a result, solving ofthe differential equations system to estimate errors introduced to the SA elements motion dynamics by the test equipment is given. "Yamal-401" spacecraft SA mechanism reliability has been calculated. The stresses impacting SA mechanism elements during deployment under zero gravity, used during calculation and design of "Yamal-401" spacecraft SA have been defined.
The developed methodologies of numerical tests have allowed validating the reliability of all large-scale SA structure elements, under all extreme cases, with regard to the available test facilities. This approach allows performing experimental test development of any large-size SA under development for new generation spacecrafts using existing experimental test facilities and equipment.
The results of the research have been used by JSC "Information satellite systems named afteracademician M. F. Reshetnev" at the phase of ground experimental test of large foldable SA structures for"Express-AM5", "Yamal-401" spacecrafts and other spacecraft types.
Keywords: a solar array, a gravity off-loader, differential equations, a panel, a hinge, ground experimental development test, zero-gravity facility, probability, reliability, spacecraft.
Вестник СибГАУ Том 17, № 4. С. 964-974
ОЦЕНКА НАДЁЖНОСТИ СОЛНЕЧНЫХ БАТАРЕЙ КОСМИЧЕСКИХ АППАРАТОВ ПРИ НАЗЕМНОЙ ЭКСПЕРИМЕНТАЛЬНОЙ ОТРАБОТКЕ
С. А. Захаров
АО «Информационные спутниковые системы» имени академика М. Ф. Решетнёва» Российская Федерация, 662972, г. Железногорск Красноярского края, ул. Ленина, 52
E-mail: szaharov@iss-reshetnev.ru
Увеличение энерговооруженности и срока активного существования современных телекоммуникационных космических аппаратов до 15лет значительно актуализирует проблему повышения надежности крупногабаритных трансформируемых солнечных батарей (КТ БС). Надёжность любого оборудования для применения в составе космических аппаратов определяющим образом зависит от качества их наземной экспериментальной отработки (НЭО). Для обеспечения высокого качества НЭО важно принять правильную концепцию подтверждения надежности БС с учётом специфики построения БС и реальных возможностей экспериментальной базы.
Предлагаются составляющие концепции для подтверждения надёжности КТ БС при НЭО. Получена система дифференциальных уравнений раскрытия БС на стенде обезвешивания, и в результате её решения приведена оценка погрешностей, вносимых стендовым оборудованием в динамику движения элементов БС. Выполнен расчет надёжности МС БС космического аппарата «Ямал-401». Определены силовые факторы, действующие на элементы МС БС в процессе раскрытия в невесомости, использованные при расчётах и проектировании БС космического аппарата «Ямал-401».
Разработанные методики численных испытаний позволили подтвердить надёжность всех составных частей крупногабаритных конструкций БС при воздействии всех экстремальных ситуаций, применительно к имеющейся экспериментальной базе. Такой подход позволяет проводить экспериментальную отработку любых разрабатываемых крупногабаритных БС для новых перспективных космических аппаратов на существующей экспериментальной базе и оборудовании.
Результаты исследований использованы в АО «Информационные спутниковые системы» имени академика М. Ф. Решетнёва» при наземных экспериментальных отработках крупногабаритных трансформируемых конструкций БС космических аппаратов класса «Экспресс-АМ5», «Ямал-401» и других типов.
Ключевые слова: солнечная батарея, устройство обезвешивания, дифференциальные уравнения, панель, шарнирный узел, экспериментальная отработка, стенд обезвешивающий, вероятность, надёжность, космический аппарат.
Introduction. The current state of space communication drives the need for powerful telecommunication satellites (SC). So, "Express-AM5" and "Yamal-401" satellites built by JSC "Academician M. F. Reshetnev "Information satellite systems" were launched on December, 26th, 2013, and on December, 15th, 2014, accordingly [1-3]. The satellites are built on the basis of Express-2000, a unified, not sealed satellite Platform providing approximately 15 kW power [4]. Ex-press-2000 Platform Solar Arrays wings span is more than 33 meters.
The importance of the paper. The requirements for the increased power and the extended lifetime of the abovementioned satellites drive the need to improve the reliability of onboard equipment and, especially, of large-sized foldable solar arrays (LFSA).
The equipment available in the industry does not allow to perform a full ground development test for Large Foldable Solar Arrays (LFSA) representing the intended space environment affecting the LFSA during spacecraft launch into orbit and deployment of LFSA into deployed configuration. To validate reliability of actuation of all LFSA components it is required to have appropriate justification and an individual approach, which takes into account the capabilities of available test ground equipment and the rationale on decomposition of critical components of Large Foldable Solar Array structures.
The concept of the solar array reliability validation at the phase of GDT. LFSA mechanism structure components strength and reliability is determined considering the effect of loads applied during manufacturing, of spacecraft launch loads and LFSA in-orbit deployment from folded to deployed configuration. During LFSA structure design activities the required maximum strength and reliability of all mechanical devices and minimal weights and sizes should be in mind [5-7]. The ways to minimize the loads affecting LFSA components must ensure an openwork design of LFSA sections.
An analysis is performed and all loads affecting SA hinges and components are defined considering the forces in synchronization system elements, deformation momenta in cables routed through the hinges, deployment drives momenta. The obtained results are the inputs for definition of loads affecting the SA components, subas-semblies and devices and are the inputs for designing of gravity off-loader to be used for the SA drive mechanism testing during ground development test.
The analysis of LFSA operation reliability is made to define the most critical elements. The LFSA operation reliability analysis reveals that the main single point failures are panels locks and panels hinges and the booms the redundancy of which in a design is not possible to implement.
The decomposition method is applied to validate the operational reliability of all solar array elements under various factors, which replaces the solution of a single reliability problem by separate simple solutions for each LFSA unit or element.
Considering the dimensions of objects under test and capabilities of the existing test equipment the following sequence of experimental development test is applied: unit experimental development test; assembly experimental development test; complex experimental development test at the level of LFSA mechanical deployment system. As a part of a test assembly the SA hinge is assembled from the elements reproducing operation conditions at the level of LFSA (cable bundles, contact gauges, synchronization system simulators, etc.) during manufacturing.
Hinges stand-alone deployment testing under extreme temperatures is performed, during the testing actual resistive torque (or resulting driving torque) in SA hinge is measured. SA mechanisms are subjected to the required phases of ground test development and to the test loads [8], and after the testing their main performance, the capability to transfer all components of SA mechanism from folded to deployed configuration and to securely lock that position is verified [5-7].
The description of the research object. Fig. 1 depicts as an example of "Yamal-401" SA wing structure.
"Yamal-401" spacecraft solar array structure consists of two wings symmetrically accommodated with regards to (wrt) the spacecraft body. The wing is maintained in the folded configuration with five locks.
SA boom frame is fixed to the SA drive mechanism flange with the root hinge. SA boom root hinge and SA boom end hinge are interconnected with the synchronization system.
SA boom motion for deployment in the hinge is done with the help of spring drives using the electromechanical drive. The electro-mechanical drive maintains the hinges deployment rate by the synchronization system. The root panel, the intermediate panel, the end panel and the lateral panels are deployed with the help of spring drives.
Fig. 1. "Yamal-401" SA wing in deployed configuration: 1 - SA boom end hinge; 2, 11 - lateral panels; 3, 10 - lateral panel hinges; 4 - intermediate panel; 5, 8- SA lateral panels deployment restrain subassemblies; 6 - end panel hinge; 7 - end panel; 9 - intermediate panel hinge; 12 - root panel; 13 - electro-mechanical drive; 14 -SA boom frame; 15 - synchronization system; 16 - SA boom root hinge; 17 - SA boom root flange
The synchronization system ensures smoothness of SA elements deployment and locking of the elements in the deployed configuration in the specific sequence from the boom root hinge to the end panel hinge. The collision of the wing elements and spacecraft structure during deployment is avoided, mutual interference of wing elements inertia moments to SA deployment dynamics is minimized. The disturbing torques affecting the spacecraft as a whole which potentially can impact the spacecraft attitude are also minimized.
In each hinge it is necessary to provide a secure excessive driving torque over the total resistive torque, which results in increasing inertia loads for the structure during hinges locking. "Yamal-401" SC Solar Array drive mechanism contains the electro-mechanical drive, which is on the one hand by being a restraining device provides controlled deployment angular rates for the sections, and on the other hand is a back-up source of the driving torque in case of contingency.
The use of special equipment at the phase of SA GDT. SA panels deployment check is done at different phases of spacecraft design development test, usually after environmental tests. SA mechanical drive complex test is done at the phase of spacecraft design test development on an Engineering model or as a part of Flight Model spacecraft after environmental tests using gravity off-loader.
Special gravity off-loader is used during SA wing deployment under gravity, the gravity off-loader compensates for weight of each mobile section during SA deployment.
Such test provide validation of deployment rate and torque stability, validation of maintenance of the integrity of the structure elements including those ones for which the access is difficult when the SA panels are locked in the folded configuration. The gravity off-loader equipment shall have minimal effect to SA mechanism deployment rate and torque stability [9].
Specific test setups and test methods are developed for each newly developed large SA design structure. But at the same time decomposition methods for such structures are also developed to justify the possibility to perform their ground development test using previously developed set-ups and equipment.
The concept of SA mechanical strength. Verification of SA structure strength during deployment is done by comparison of the following results:
- calculation of loads existing during deployment under space environment;
- calculation of loads existing during deployment when gravity off-loader is used;
- calculation of equivalent static loads considering known power performances of the spring drives;
- performance of SA wing equivalent static load testing with validation of specified strength margins including with creation of the required special test equipment ensuring calculated loading reproducing calculated deployment rates.
To assess the impact of test equipment to the confidence of the measured results of multiple section mechanism parameters it is required to do the following:
- to obtain the equations characterizing SA system motion at the test equipment together with its elements;
- to compute SA mechanism motion parameters;
- to assess the error of measured SA mechanism motion parameters wrt the motion parameters in real space environment (simulated conditions). SA mechanism design options depend on the spacecraft application.
Derivation of the differential equations system of SA deployment with the off-loading system. The important step of preparation for SA complex deployments at the phase of GTD is calculation which defines errors introduced to the SA mechanism dynamics by the support equipment [10; 11]. As an example I propose to review a typically used SA mechanism folded like an accordion and having additional lateral panels.
After a signal is sent to pyros the deployment of SA panels is done in the following sequence: the hold-down system is actuated and under the impact of spring drives the SA panel packets are deployed at 120°. The achievement of 115° during the packets deployment anticipates the release of the end panels which are deployed by the spring drives at 180° angle. Till root hinge latch (at 120°) the deployment of root and end panels occurs simultaneously. After end panels are 180° deployed, the lateral panels are released and deployed.
During analysis of SA system motion it is convenient to flow down the deployment process into four sequential phases:
Phase I: Deployment of root panel while the end panel is not deployed yet (here in after SA panels packet) till 115° angle.
Phase II: Simultaneous deployment of root and end panels.
Phase III: Deployment of end panel after the root panel is locked.
Phase IV: Deployment of lateral panels.
Computational scheme of SA root and end panels deployment at the test facility is given in fig. 2.
Differential equation system describing the motion of SA panels packet and slewing booms packet at phase I of the motion is the following:
I j„ -Ф1 = МдВЛ - MдоП.„-МаЭр.„ - мсл,
IЛ.б *ф1б = Мдв.б - Мдоп.б - Мс.б -
(1)
inertia of slewing boom packet; cp15 - angular acceleration of slewing boom packet; Mgon5 is the tension load torque of the off-loader cable; Mc5 - root slewing boom hinge resistive torque; MgB5 - slewing boom packet driving torque.
Computational scheme of SA mechanism second phase motion (simultaneous deployment of root and end panels) are given in fig. 3. SA mechanism motion equations are derived from Lagrange equations.
Substituting the corresponding derivatives found expressions into the equations (1) we obtain a set of second order differential equations describing SA mechanisms motion at phase II:
Ф1 =-
22 ' с 11 а12 ' с12
а11 ' а22 а
12 22
Ф 2 =-
а11 ' с 12 а21 ' с11
11 22
а^о а о * а.
12 21
where:
(2)
ап = m * Т|2 + Joc1 + m2 *12-2 * m2 * А * 12 * C0s Ф2 + m2 * Ь
12
= m2 * ¡2 -m2 * A * ¡2 * C0s Ф2;
c11 = -2 * m2 * A* ¡2 *<P1 *ф 2 *sin Ф2 -m2 * A*12 *<P2 *sin Ф2 +
+ ^^дв.кор.й ^^доп.кор.й M^с.кор.п '
22
= Jос2 + m2 *
where Jn - moment of inertia of SA panels packet concerning a rotation axis; cpx - angular acceleration of SA panels packet; Ma3p„ is aerodynamic resistive torque; MgBn is driving torque of panel spring drive; Mgonn
is an additional resistive torque, caused by the test set-up; Mcn is resistive torque of packet hinge; Jn£ - moment of
a21 = m2 • 42 ~m2 • A • l2 •cosP2;
C12 = m2 • A ]2 •(p1 •<P2 •sin P2 - Maon.K.„ - Mc.K.„ + MflB.K.„ ,
m1 is the mass of the root panel; m2 is the mass of the end panel; Joc1 is the intrinsic moment of inertia of the root panel; Joc2 is the intrinsic moment of inertia of the end panel; MgB.Kn is the driving torque of the end panel. Mgon.Kn are additional torques resisting the motion of the root and end panels due to the test set-up.
1 Y
Fig. 2. SA root and end panels deployment computational scheme
Fig. 3. Root and end panels deployment computational scheme
Similar to the abovementioned we obtain a set of equations describing motion of the root and end panels at phase II:
916 =
9 26 =
a22 • C1 -a162 • c6 c12
a161 • a22 - a162 ' ' a21 '
a161 • c6 c12 -a21 • c6
ah • a22 -a162 • a21
where:
a6i = m16 • 4 + J
i6
+ m
26
•4 -
2 .
- 2 • m26 • A 6 • l26 • cos 926 + m26l26 I a162 = m26 • 4 - m26 • ^16 • l26 •cos 926 I cfi = -2 • m26 • Li6 • l26 • 916 • 926 • sin 926 + + m26 • L16 • l26 •(P26 -916 •sin 926 + + m26 • L16 • l26 •<PL •sin 926 -
"^^gon.Kop.6 "M^c.Kop.6 + "M^gB.Kop.6 '
a21 = m26 4> - L16 • m26 • l26 • cos 926 I
6
(3)
a22 _ Joc26 + m26 ' l26 :
c12 = m26 • L16 • l26 •(P16 -926 •sin 926 -
- Mgon.K.6 -Mc.K.6 + M«B.K.6 -
here m16 is the mass of the root slewing boom: m26 is the mass of the end slewing boom: Jo1ce is the intrinsic moment of inertia of the root slewing boom: Jo2ce is the intrinsic moment of inertia of the end slewing boom: MgB.Kop.6.- MgBK.6 are the driving torques of the root and end slewing booms: Mgon.Kop.6, Mgon.K.6 are additional torques resisting the motion of the root and end slewing boom due to the test set-up.
9K.n MgB.K.n ^^gon.K.n ^^asp.K.n: 'K.n 9K.n — ^^gon.K.6 + ^^£B.K.6 '
(4)
The equations describing the motion of end panel and the end boom at phase III of SA system motion are the following:
li
where JK.n is the moment of inertia of the end panel wrt the motion axis: Ma3p.K.5 is aerodynamic torque resisting the motion of the end panel.
The equation describing end panel motion in the reference frame is the following:
J096n = Mnp - M«on - Masp - Mc - (5)
where: J0 is the panel moment of inertia wrt the hinge axis: Mnp is the driving torque of the spring drive: Mgon is an additional resistive torque due to the test set-up: Masp is aerodynamic torque resisting the motion of the lateral panel.
Integration of a set of differential equations consisting of (1)-(4) and (5) was done by Runge-Kutta method with constant integration step of At = 0.01 s.
To assess the impact of the test equipment elements to the motion parameters- SA mechanism motion computation was done under real conditions (the tension forces are equal to 0- suspensions tension forces are equal to 0- air density is equal to 0, for the case when the object is securely fixed) and- then- at the test facility with gradual test equipment adjustment error accumulation within the allowable limits.
The results of the calculations. The built test equipment allows to perform SA mechanism test at the phase of ground development test of complete LFSA and to assess motion parameters with 10-11 % estimation errors.
During preparation of the test equipment for the performance of test it is required to additionally define actual mass and moments of inertia of the test equipment slewing booms, and to perform additional calculations to define driving torques in the booms hinges, to define more
precisely SA mechanism motion parameters while it is at the test equipment.
The calculation results show that the motion parameters errors (deployment duration, SA panel angular rates at the instant of latching) of SA system wrt SA system motion parameters in real environment are 17.21 %; -23.45 % for panel packets and 17.7 %; -22.2 % for end panels, accordingly.
The utmost error is introduced to the motion parameters by slewing booms mass and moments of inertia, so it is necessary to install into the booms hinges some devices which create driving torques ensuring monitoring of the SA panel motion by the slewing booms.
The field of implementation of the research results. The developed mathematical tool and the method of calculation of SA mechanism motion parameters allow to rapidly perform an assessment of test equipment performances.
Decomposition method allows to perform test to validate reliability of all components of large SA structure including under vacuum and under extreme temperatures using the available ground test equipment.
SA mechanism reliability calculation. SA mechanism reliability analysis was done for the structure depicted in Figure 1. SA mechanism functions are the following:
1) installation of SA panels wings and fixation of SA panels and booms in the folded configuration at satellite level;
2) SA panels and booms release from fixation in the folded configuration;
3) booms and panels transfer to deployed configuration.
During operation SA mechanism is subjected to the
following:
a) mechanical loads seen during transportation, lift-off, launch, separation of LV stages, SA deployment;
b) ground climatic conditions;
c) hot and cold temperatures of launch and orbit phases;
d) vacuum, radiation.
Inadvertent actuation of hold-down locks which potentially can occur due to inadvertent pyrounits actuation due to electrostatic discharge is eliminated by grounding of the structure.
SA mechanism primary items survival is ensured by design, these items are designed with the required strength margins considering the worst combination of loads during transportation, lift-off, launch, LV stages separation.
In-orbit, during SA panels transfer from folded to deployed configuration, the mechanism is in deployment mode and performs functions 2, 3. Functions 2, 3 may be carried out under the following conditions:
a) SA mechanism primary items survival is ensured by the required strength margins provided for the items taking into account the loads occurring during deployment.
b) Events of ny, Cf ..., Cf , C2, C3, C4 occur if the forces (torques) providing subassemblies actuation are higher than the forces (torques) resisting the actuation. Where C[ is actuation of i-th SA panel hold-down lock; C2 is electro-mechanical drive performance; C3 is boom frame, root panel, intermediate panel, end panel motion; C4 is lateral panel motion; ny is a pyrounit actuation.
SA mechanism performance reliability is calculated by the following equation:
p(mc EC) = p2 (ny) ■P2( C1) ...p2( C5)p2(c2)p2(c)p4(c4), (6)
where P(MC EC) is SA mechanism performance reliability;
P( C1).....P( C5), P(C2), P(C3), P(C4) are the probabilities
of occurrence of Cj, ... Cf, C2, C3, C4 events; P(ny) is a probability of ny event occurrence.
Reliability of SA mechanism sub-assemblies actuation
(a probability of occurrence of (Cf..... Cf , C2, C3, C4)
events is characterized by a probability of excess of driving torque (driving force) over resisting torque (resisting force).
The definition of probabilities P( C1).....P C5), P(C3),
P(C4) comes to the solution of the equation P^yHK = Bep(XflB > Y),
where XgB, Yc are random values (driving force or driving forces moment, resisting force or resisting forces moment).
It is understood that distribution of random values XgB, Yc comply with normal low.
In this case
p^k = Bep(X<B > Yc) = ®(U),
where ®(U) is normal distribution function.
XgB, Yc random values distributions are trimmed, so that Xmn > Y™x , so
gB c
P^K = Bep(xmin > icmax) - 1.
Hence, the margin of driving torque shall be at least 200 % (3:1 rate) for each hinge under worst case resistance.
Assessment of reliability of a pyrounit actuation.
Pyrounit structure maintains operational capability while at least one pyro is actuated. Reliability of a pyrounit actuation is defined by the formula
P(ny) = 1 - (1 - PJ2. (7)
By previous experience, reliability of a pyro actuation is Pm = 0.99999. The reliability will be P(ny) = = 0.9999999999.
Assessment of reliability of a SA panel hold-down lock actuation. Detailed analysis performed for hold-down lock scheme showed that the margin on driving torque of the lock rotatable items is not less than 3, the lock actuation reliability is not lower than 0.9999999, probabilities P( C1) = P( C? ) = = P ci) are not less than 0.999999.
Assessment of reliability of boom frame, root, intermediate and end panels motion during SA deployment. Simultaneous motion of SA boom in the SA root boom hinge, of the root panel in the boom end hinge, of intermediate and end panels is done by spring drives with the use of electro-mechanical drive, installed in the boom end hinge and operating in deployment restraining mode (in push mode, if needed), and by the synchronization system connecting boom hinges and SA panels hinges.
The force relation can be missing in the synchronization system cable rods because the cable rods are loose at the final stage of deployment of the boom, the root, the intermediate and end panels while the hold-down items are active.
As a result, while the hold-down items are active, the reliability P(C3) at deployment stage is characterized by the excess of minimal driving torque over the maximum resistive torque separately in each hinge of SA mechanism.
Each of two springs in the boom root hinge is 2.3+0,3 N-m pre-loaded in the deployed configuration = 90°). In accordance with the spring diagram the minimal torque M^foO varies from 4.98 N-m at 91 = 0° to 4.6 N-m at 9! = 90°. Dependence of M^™"^) on motion angle 9! is linear.
Torque M2gB(92) in the boom end hinge (root panel hinge) is provided by two springs. In the boom end hinge each of two springs is 1.65+0,2 N-m pre-loaded in the deployed configuration (92 = 180°). In accordance with the spring diagram the minimal torque M2flBmm(92) varies from 4.98 N-m (9 = 0°) to 3.3 N-m (92 = 180°). Dependence of M2gB(92) on motion angle 92 is linear.
Torque M1c(91) in the boom root hinge at 0° < 91 < 90° is defined by the formula:
M1C(91) = M1m(91) + M1K(91) + 2M1Kp + Mu, (8)
where M1m(91) is friction torque in the boom root hinge; M1K(91) is resistive torque of the cable in the boom root hinge; M1Kp is resistive torque while the hold-down hook is actuated in the boom root hinge at 72° < 91 < 90°; M1g is resistive torque while the detector shaft is down at 80° < 91 < 90°.
Torque M1m(91) is defined by the formula
M1m(91) = (R^ + R^-frm, (9)
where R1m1, R1m2 are responses at the bearings in the boom root hinge; f is friction coefficient; rm is the radius of bearing slip surface in the hinge assembly.
Torque M1Kp is defined by the formula
M1Kp = Qkp'LK, (10)
where
Qkp = Mnp max-cos(90° - 9k)/L1, (11)
QKp is resisting torque under pressure onto the hook; Mnpmax is the maximum torque created by the hook spring; L1 is the arm of force QKp wrt the hook motion axis; LK is the distance from hook motion axis to the axis of the root hinge; 9K is the hook skew angle in degrees.
As per the requirements, the resistive torque in hinge 1 including the resistive torque of the cable M1K(91) in not more than 1.1 N-m.
Torque M1g is defined by the formula
M« = 01^, (12)
where Q1g is the torque of the spring biasing the detector shaft in the boom root hinge; L1g is the arm of force Q1g wrt the boom root hinge axis.
Torque M2c(92) in the boom end hinge at 0° < 92 < 180° is defined by the formula
M2c(92) = M2m(92) + M2k(92) + MKP + 2M2g, (13)
where the characteristics of M2c(92) additives correspond to M1c(91) additives as per formula (8) for angle 92, under
the following peculiarities: M2Kp is the resistive torque when the hold-down hook is actuated in the boom end hinge at 164°< 92 <180°; M2g is the torque resisting the detector shaft downing at 170°< 92 <180°.
Torque M2m(92) is defined as M1m(91) by formula (9), given that responses in the boom end hinge bearings R2m1, R2m2 are used instead of R1m1, R1m2.
The calculation shows that:
- M™ (91) exceeds M^* (91) by not less than 3 times at 0° < 93 < 90°;
- M™ (92) exceeds M™x (92) by not less than 3
times at 0° < 92 < 180°.
Motion of the intermediate panel in the hinge is done by spring drives in two hinge joints.
Reliability is defined by the exceed of the minimal driving torque M3™n (93) in the driving hinge over maximum
torque M3T (93) resisting the motion. Torque M3™n (93)
in intermediate panel hinge is provided by two springs. In the hinge the springs are 1.65+0,2 N-m pre-loaded in the deployed configuration (93 = 180°).
In accordance with the spring diagram the minimal
driving torque M3™n (93) varies from 4.98 N-m at 93 = 0°
to 3.3 N-m at 92 = 180°. Dependence of M3gB(93) on motion angle 93 is linear.
Torque M3c(93) in the intermediate panel hinge at 0° < 93 < 180° is defined by the formula
M3c(93) =M3m(93)+M3K(93)+2M3Kp+M3g, (14) where the characteristics of M3c(93) additives correspond to M1c(91) as per formula (8) for angle 93, under the following:
- M3Kp is resistive torque when the intermediate panel hinge hold-down hook actuated at 165° < 93 < 180°;
- M3g is resistive torque when the detector shaft is downed at 171° < 93 < 180°.
Torque M3m(93) is defined as M1m(91) by formula (9), given that responses in the boom intermediate hinge bearings R3m1, R3m2 are used instead of R^, R1m2.
As per the requirements, the resistive torque in the intermediate panel hinge (including the resistive torque of the cable) is not more than 0.95 N-m.
M3Kp is the resistive torque when the hold-down hook is actuated, it is defined the same way as M1Kp by formulas (10), (11).
Torque M3my(93) equals to the difference between the minimal driving torque in hinge 3 and maximal allowable resistive torque.
The calculation shows that:
- M3mBn (93) exceeds M^ (93) by not less than 3
times at 0° < 93 < 180°.
Motion of the end panel in hinge 4 during deployment is done by spring drives in two hinge joints. Reliability is defined by the exceed of the minimal driving torque M™ (94) in the driving hinge over maximum torque
M4Cx (94) resisting the motion.
Torque M4gB(94) in the end panel hinge is provided by two springs. In the hinge the springs are 1.65+0,2 N-m pre-loaded in the deployed configuration (94 = 180°).
In accordance with the spring diagram the minimal driving torque M™ (ф4) varies from 4.98 N-m at ф4 = 0° to
3.3 N-m at ф4 = 180°. Dependence of M4™n (ф4)
on motion angle ф4 is linear.
Torque М4с(ф4) in the end panel hinge at 0° < ф4 < 180° is defined by the formula
М4с(ф4) = М4ш(ф4) + М4к(ф4) + 2М4Кр + М4Д + 2М3, (15) where the characteristics of М4с(ф4) additives correspond to М1с(ф1) additives as per formula (8) for angle ф4, under the following:
М4кр is resistive torque when the end panel hinge hold-down hook actuated at 165° < ф4 < 180°;
М4Д is resistive torque when the detector shaft is downed at 171° < ф4 < 180°;
М3 is resistive torque when lateral panel retaining assembly is actuated at 170° < ф4 < 180°.
Torque М4ш(ф4) is defined as М2ш(ф2) by formula (9), given that responses in the end panel hinge bearings Л4ш1, Я4шг are used instead of R1in1, Л1ш2.
Resistive torque in end panel hinge (considering the resistive torque of the cable) shall be not more than 0.75 N-m.
Torque М4кр is defined as M1p by formulas (10), (11),
Torque М3 is defined by formula:
Мз = Q4зад^Lз,
where @4зад = (Mnp/L4 + T-L2/L4) is the force resisting the motion of lateral panel deployment retaining hook; Мпр is the torque of the spring retaining the hook; Т = QKnf is friction torque occurring when the hook is moved along the axis at lateral panel; QKn = (M5™x (ф^/L + Qnp) is the
force impacting the hook from the lateral panel; Qnp - is the force of the spring biasing the shaft of the lateral panel displacement detector; L2 is the arm of force Т wrt the hook motion axis; L4 is the arm of force силы Q43ag wrt the hook motion axis; L3 is the arm of force силы Q43ag wrt the end panel axis; M5™x (ф5) is the torque in the lateral panel hinge.
The calculation shows that М4ДВ (ф4) exceeds M™ (ф4)
by not less than 2.7 times at 0° < ф4 < 180°.
The drive ensures the specified output performances while the external torque towards the deployment is from 0 to 25 N-m. The torque due to the spring drives impacting the electro-mechanical drive equivalent to the boom end hinge is not more than 13.7 N-m. The resistive torque margin is not less than 1.8.
To overcome static resistance at the initial instant after the locks release the SA contains pushers ensuring the panel wings displacement.
The requirement that during deployment the boom, intermediate, end, lateral panels driving torques exceed the resistive torques by 3 is met, which ensures that the reliability P(Q) is not less than 0.999999.
Assessment of reliability of a lateral panel motion. Motion of a lateral panel in hinge 5 (hinge 6) is done by spring drives in two hinge joints. Reliability Р(С4) is defined by the exceed of the minimal driving torque M5™n (ф5) driving hinge over maximum torque M™ (ф5) resisting the motion.
Torque M5flB(95) in the lateral panel hinge is provided by two springs. In the hinge the springs are 1.15+01 N-m pre-loaded in the deployed configuration (^5 = 180°). In accordance with the spring diagram the minimal driving torque M5™n (^5) varies from 3.96 N-m at = 0° to 2.3 N-m
at 95 = 180°. Dependence of M5™n (^5) on motion angle 95 is linear.
Torque M5c(95) in the lateral panel hinge at 0° < < 180° is defined by the formula
M5C(^5) = M5J95) + M5K(^5) + 2M5Kp + M5g,
where the characteristics of M5c(^5) additives correspond to M1c(^1) additives as per formula (8) for angle under the following; M5Kp is resistive torque when the lateral panel hinge hold-down hook actuated at 152° < < 180°; M5g is resistive torque when the detector shaft is downed at 171° < 95 < 180°.
Torque M5m(^5) is defined by the formula
M5m(^5) = 2-R5m-f-rm, where R5m is the response in the bearing in the lateral panel hinge; rm is the radius of bearing slip surface in the hinge assembly; fis friction coefficient;
R5m = M5„(q>5)/L5,
where M5„(^5) is the torque of the spring depending on angle of the lateral panel motion; L5 is the arm of spring force application.
As per the requirements, the resistive torque in the hinge of the lateral panel (including the resistive torque of the cable) is not more than 0.7 N-m.
Torque M5Kp is defined as M1Kp by formulas (10), (11).
The calculation shows that Ml™ fa5) exceeds M«™"
by not less than 3 times.
Assessment of reliability of SA drive mechanism
performance. The probability of electro-mechanical drive failure-free performance is not less than 0.9999. SA mechanism performance reliability P(MC EC) calculated by formula (1) is not less than 0.9997.
Calculation of forces and moments, affecting SA mechanism elements during deployment using SA wing mathematical model. Development of the mathematical model, describing dynamics of the solar array panels deployment, and calculation on its basis the dynamic parameters of all links is the major step of preparation for GTD [12-17].
To define maximum duration of SA transfer (see fig. 1) from folded to deployed configuration a calculation was done for the case with maximum resistive torque Mc in the hinge and minimum angular rate of electromechanical drive output shaft (3 °/s).
To define maximum loads to the SA mechanism structure occurring in the hinges, the computation was done for the case of the minimum resistive torque (Mc = 0) and maximum angular rate of electro-mechanical drive (7 °/s). To compute the loads 1.3 safety margin was assumed. ADAMS 2005 was used for the computation.
SA panel wing mathematical model was built on the basis of design documentation and technical description of the mechanism under review including its ground support equipment. The mechanism is a combination
of three dimensional mechanisms and sections having kinematic links (hinge joints), elastic-damping items (structural stiffnesses) and drives, and control and monitoring items (hold-down detectors, logic converters), etc.
The model section masses correspond to the masses of structure items of fig. 1. Hinge or kinematically constrained node is assumed to be a flexible joint consisting of several sections. The boom and panel hinges are rotating pairs having a single degree of freedom (rotation wrt the specified axis).
Geometry model is the base for creation of dynamical model and calculation of mass and moments of inertia of the mechanism parts, and is used later on during creation of kinematic relations and force actions.
During creation of an idealistic model all active forces impacting moving systems are identified:
- deployment mechanisms actuating force;
- hinge joints friction forces;
- moments in hinges due to the force in the synchronization system cable rod.
All active forces are described in the model as load-bearing elements with the corresponding reference data. After the model was created different combinations of the model were made to study its operation in different operation modes. The modelling predicts how the model will behave considering the selected fixations and loads impacting the consistent parts on the model and in the real structure of SA mechanism.
During modelling the following was done:
1) definition of the corresponding motion equations, based on classical mechanics, simulating model sections movement under the impact of a set of forces and restrictions;
2) solving of the equations within the required accuracy under the motion of the mechanism elements (rate and acceleration, applied forces and reaction forces).
During the modelling of the mechanical system its motion was controlled, for this purpose modelling algorithm was created, the algorithm ensured the specified SA panel wing deployment logic. The dynamic modelling was with accuracy 1.0E-006.
The results of the calculation. The results of computation of deployment time for different combination of input data: resistive torques in the hinges (Mc) and the rotation speed of the electro-mechanical drive output shaft (ranp) are given in tabl. 1. The intrinsic times of SA panel elements deployment are the following:
- boom (hinge 1) (25-59.8) s;
- root panel (hinge 2) (25.7-60) s;
- intermediate panel (hinge 3) (23.9-59.2) s;
- end panel (hinge 4) (23.8-56.7) s;
- lateral panel 1 (hinge 5) (8.1-8.5) s;
- lateral panel 2 (hinge 6) (6.8-9.0) s;
The total time of SA panels deployment is (31.9-65.7) as per tabl. 1.
The result of computation of maximum moments in the hinges of the structure deployable elements are given in tabl. 2.
For the panels the total bending moment is given for two hinges.
The maximum force in the synchronization system for hinge 1 - hinge 2 (SA boom) is 1750 N, for hinge 2 -hinge 3 (root panel) is 2000 N, for hinge 3 - hinge 4 (intermediate panel) is 1200 N.
Tabl. 3 gives forces and moments impacting SA drive mechanism during SA panels deployment.
Table 1
Time of SA panels deployment
Hinge Deployment time, s
Mc = 0, ro^ = 7 °/s Mc = max, ronp = 3 °/s
Boom root hinge (hinge 1) 25.0 59.8
Boom end hinge (hinge 2) 25.7 60.0
Boom end hinge (hinge 2) 23.9 59.2
Intermediate panel hinge (hinge 3) 23.8 56.7
End panel hinge (hinge 4) 31.9 65.2
Lateral panel hinge (hinge 5, hinge 6) 30.4 65.7
Table 2
Maximum bending moments in hinges during deployment
Hinge My, N-m
Boom root hinge 300
Boom end hinge 290
Intermediate panel hinge 160
End panel hinge 90
Lateral panel hinge 200
Table 3
Forces and moments impacting SA drive mechanism
Fx, N Fy, N Fz, N Mx, N-m My, N-m Mz, N-m
+100 +45 +50 +200 +300 0
The SA wing frequency in deployed configuration is 0.12 Hz (according to SA wing finite-element model computation with MSC.Nastran).
Conclusion. Calculation and reliability validation methodology for large-sized foldable solar array at GEDT has been developed.
The developed methodology of numeric testing allowed to confirm reliability of all constituent parts of large Solar Arrays structure under the impact of all extreme conditions having both static and dynamic nature considering ground test equipment available. Such approach allows to perform experimental development test of any large Solar Arrays being developed for new advanced spacecrafts.
The calculations performed have allowed to define errors introduced to the movement parameters by the support equipment, and to find the ways to reduce these errors.
The results of the study have been implemented in JSC "Academician M. F. Reshetnev "Information satellite systems" during ground experimental development test of large foldable SA structures of "Express-AM5" and "Yamal-401" spacecrafts type and other types.
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© Zakharov S. A., 2016
