A NOVEL 6 DOF THRUST VECTOR CONTROL TEST STAND

Original scientific paper This study proposes an innovative test stand design to accurately measure rocket motor thrust vector during its operation. Test stand design is clearly presented as well as procedure and mathematical model for its calibration. A method of processing data obtained from the experiments and the results of the jet tab system for thrust vector control are presented in detail. Experiments have shown that the test stand is highly functional and the results obtained have excellent repeatability and matching with the results of the other authors who have used different construction test stands for measurement of the same or a similar mechanism for thrust vector control.


Introduction
Most vehicles used for launching spacecraft require some guidance or steering to ensure that the required flight trajectory will be achieved.In addition, steering is needed to compensate for flight disturbances (winds) and for vehicle imperfections (misalignment of thrust and center of gravity).To provide steering solid propellant rocket motors are equipped with a TVC system [6].
TVC systems are classified primarily by nozzle type, either fixed or movable, and secondly by the method of providing actual thrust vector control [1].
Mechanical systems are based on different mechanical obstacles, which are used to modify flow around obstacle and/or in the nozzle and thus pressure distribution.Both aerodynamic and mechanical techniques have been used to redirect the motor thrust and provide steering forces.Aerodynamic techniques have demonstrated very rapid response rates, but also suffer motor thrust losses at large TVC vector angles.The higher losses with the aerodynamic jet tab, jet vanes and bleed control concepts are a result of the physical creation of side force by creating a shock pattern in the exit cone thrust i.e. the higher the TVC angle required, the larger the percentage of thrust involved.Jet tabs or vanes have been used for rapid thrust vector control steering, especially early in flight when missile speeds are too low to achieve effective control with external aerodynamic fins.These systems usually require tungsten or refractory metal components to minimize the erosion from the solid particles in the hot exhaust gas.The jet tab TVC system has low torque, and is simple for missiles with low-areratio nozzles.Its thrust loss is high when tabs are rotated at full angle into the jet, but is zero when the tabs are in their neutral position outside of the jet.On most flights the time-averaged position of the tab is a very small angle and the average thrust loss is small.Jet tabs can form a very compact mechanism and have been used successfully on tactical missiles.Four tabs, independently actuated, rotated in and out of the motor's exhaust jet during rocket motor operation provide control of a vehicle's pitch, yaw and roll motions [2,8,9].Side forces and roll torques are usually relatively small compared to the main thrust and the pitch or yaw torques.Their accurate static test measurement can be difficult, particularly at low vector angles.Multi-component test stands employing multiple load cells and isolation flexures are needed to assure valid measurements.Solid rocket motor is defined in mechanical terms as a rigid body with six degrees of freedom and the forces and moments produced by them are external forces.Rocket motor is tested on the test stand, which is a standalone assembly or part of a more complex experiment installation.By attaching a rocket motor to the test stand the experimental measurement of forces and moments is realized by movement simulation of one or more degrees of freedom.In doing so by design it is achieved that all elements and generated links meet the requirements of a virtual movement under the action of external (generalized) forces.Thereby test stand meets the requirements of linear operator in the unitary space and allows the forces and moments of rocket motor to be defined by the measured reactions.
Test stands are of different designs, but the most common is the one in which the rocket motor is connected to the basement by the rods (Fig. 1) [5].
In the rods, which are called arms, are placed the force sensors.Arranged arms follow layout of the Descartes coordinate system.Connections arm-motor and arm-stand are spherical in a static sense; design solutions of joint are bearings and flexures.The coordinate system is set so that one axis coincides with the axis of the rocket motor.
In this paper is presented a novel design of 6 degree of freedom thrust vector control test stand.Its verification is performed on measuring thrust vector angle deflection and thrust losses of jet tab TVC configuration in static conditions and results as a function of nozzle exit area blockage percentage are presented.

Test stand design
As can be seen in Fig. 2 lower plate of test stand is connected to the basement by the rigid connections-bolts.The upper plate is connected to the lower plate by six rods attached to both plates by the spherical plain bearings.In that way they can only transfer loads along their axis.In this case external loads will be thrust components of rocket motor which is fastened to the upper plate.The system for motor connection with the upper plate also ensures positioning of jet tab always in the same position, perpendicular to the Y axis.Rods used for upper to lower plate connection have on the ends plain spherical bearing, for connection to the plates, and load cell in the middle capable to measure loads in both directions (compression and tension) which enable the measure test stand response on external loads.Adjustable nuts are used for rod length setting and position locking (Fig. 3).In order to calculate applied forces and position of act onto test stand, the system must be fully calibrated which means calibration upon forces along X, Y and Z axes as well as upon the moment around those axes M x , M y and M z .In that way is obtained 6×6 calibration matrix Our task now is to solve system of 6 simultaneous linear equations using matrices. where , and S is matrix of test stand response (values from load cells The solution to the system of equations is given by: where A -1 is inverse matrix of matrix A, A preliminary analysis of the system was performed by usage of software package NASTRAN. By applying different loads we can obtain reactions on those loads and thus build our calibration matrix A (Fig. 4).As mentioned earlier for measuring jet tab TVC system we will use 4 load cells.This analysis will help to make a choice of the best possible location for load cells.Obviously, three load cells have to be placed symmetrically around the Z axis (rods 1,3 and 5; or 2,4 and 6).Here, the first combination will be used, so the last fourth load cell could be placed in positions 2,4 and 6.In order to determine which position is the best, first calibration matrices have to be calculated for all three cases, after which their condition numbers will be calculated.Condition number of some matrix A is the product of two matrix norms.
Condition number measures the sensitivity of a linear system solution to errors in input vector.A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.This number clarifies how accurate is expected the vector x to be, when solving a system of linear equations Ax=b.So, in solving the equation Ax=b, the relative error in the solution, divided by the relative error in the right-hand-side vector is given by the condition number of A. The following rule of thumb is a useful way to express the above estimate.It states that if  = log 10 (())then m is the number of digits accuracy lost in solving the system of equations Ax=b.There is typically additional error due to the many calculations needed in solving the equations.The estimate for additional losses is given by log 10 () if the matrix A is n×n.From above results it is obvious that placement of loads cell on position 2 will lead to inaccurate calculation and placement of load cell on positions 4 or 6 will lead to results of the same accuracy.In order to accurately calculate forces and moments it is necessary to perform precise calibration of the test stand.Because of that special attention was paid to the introduction of the dead-weight loads on the test stand.Load in Z direction was applied on the test stand over real nozzle mounted on the test stand in the same way as it was during firing test (Fig. 6a).Loads in X (Fig. 6b) and Y (Fig. 6c) direction were applied on the test stand over special pulleys system on two different elevation, along Z axis.
In measuring jet tab TVC system 4 load cells were used and for that reason calibration was performed for two forces F z and F y , and two moments M x and M y .To accomplish that task it is necessary to perform total of five calibrations, one for F z and two for each moment (calibration of F y is already in M x ) on different elevations from the nozzle (first calibration on the nozzle exit level and second calibration is elevated by approximately 105 mm).Miniature, stainless steel universal load cells, with capability to measure in both tension/compression directions, were built in test stand rods.Maximum capacity is 5000 N and accuracy is 0,25 % FSO linearity, hysteresis, repeatability combined.In the following figures some examples are shown of test stand calibration (positive sign is for compression).
After all five calibrations we are able to form calibration matrix of our test stand using reciprocal values of slopes.This matrix represents reaction in rods (load cells) for applied unity forces (here positive sign is for tension according to the adopted coordinate system, see Fig. 2).Now it is possible to create matrix A for calculation of applied forces.

Rocket motor
Rocket motor (RM) used for testing, was of a slotted propellant grain configuration.Length of slots was tailored to provide neutral burning (pressure and thrust versus time are almost without changes -neutral).Graphite nozzle throat was used in order to eliminate throat erosion.Exit diameter of nozzle is 47 mm, the expansion ratio is 5 and half divergent angle is 20 degrees.It is possible to attach different obstacles (tabs) to the exit nozzle surface in order to block desired percentage of exit area.Tabs are made from molybdenum to withstand high thermal loads.Propellant used in test is thermo-plastics composite propellant with 1,5 % of aluminum powder.Total pressure in nozzle was also measured during motor burning time.

Test results
First test was without any tab.This test will be used as a benchmark, to compare these results with other tests results in which variant percentage of the nozzle exit area was blocked A eb .It is also known that, in this first test, side force must be zero.Thus if some other result was to be obtained that would be a signal that something went wrong for sure.Results are presented in the following Fig. 14 and Fig. 15.
Test stand is of vertical type, thus consumed propellant mass has influence on results and has to be incorporated in calculation [7].Measuring of pressure vs. time will help us in that.First the characteristic velocity needs to be calculated by formula: After that it is possible to calculate how much propellant mass is consumed over any time interval by using formula: Consumed mass from time zero up to current time in calculation should be to the value of Z force in that moment to get a real force in Z direction, so called F ztotal .Total impulse of side force is negligible so it can be claimed that the observed system works correctly in this case.From the measured axial F z and side F y forces we can calculate main parameters for judging the performances of our jet tab TVC system.Of great importance are: absolute loss of thrust ∆F, relative loss of axial force ∆F zrel. ,relative side force F yrel. , and deflection angle α.

Conclusion
Regardless of the fact that for measurement of presented single and not movable jet tab TVC system it is not necessary to have test stand with more than 2 DOF (because position in space of jet tab is known and remains invariable) up to 4 load cells were used.The reason for that is to validate results and to prove the concept.By comparing the obtained results to the other published results [4] and some theoretical models [3], as well as by performing analysis of results it can be concluded that it is possible to use this type of the test stand for accurate measuring of the rocket motor thrust in space with all 6 degrees of freedom.Although this study only outlines the results of tests with jet tab, this test stand can be used for testing other TVC's systems in both static and dynamic conditions.Excellent results of testing domed deflector TVC system in dynamic conditions were obtained.Design and manufacturing of presented test stand is very simple and does not require special precision.Even an inaccurate symmetry of the test stand (all rods are not at the same angle to the bottom or/and upper plate) does not present a problem, because by calibration the exact test stand response can be obtained, and that is the only thing important.

Notice
Version of this paper has been presented and published in "Proceedings of 2 nd International Conference on Manufacturing Engineering & Management 2012" [10].Also, the paper "has been awarded the ICMEM 2012 best paper award" (signed by chairperson of the Scientific and Conference Committee).

Figure 1
Figure 1 Schematic representation of classic 6DOF test stand design

Figure 2
Figure 2 Test stand design

Figure 3
Figure 3 Rod design

Figure 4
Figure 4 Reactions in rods upon applied load

Figure 5
Figure 5 Test stand assembled in laboratory 3 Test stand calibration

Figure 9
Figure 9 Nozzle exit surface and used tabs geometry

Figure 14 Figure 15
Figure 14 Pressure vs. time

Figure 16 X
Figure 16 X position of result thrust vs. time

Figure 18 Figure 19 Figure 20 Figure 21
Figure 18 Thrust and side force vs. time for Aeb= 5 %

Table 1
Calibration matrix Ap2 with load cell placed on position 2

Table 5
Calibration matrix for calculation

Table 6
Inverse matrix of calibration matrix for calculation

Table 7
Summary results Figure 26 Test results as a function of relative nozzle exit area blockage