This paper presents a hierarchical and simultaneous gravity unloading method. An air bearing gravity unloading facility for two-orthogonal-axis antenna pointing mechanism (APM) is designed based on this method. This method is proposed based on the characteristics analysis of the two-orthogonal-axis APM and air bearings. The mechanism of the hierarchical and simultaneous gravity unloading method is described in detail. It solves the coupling problem of two axes and unloads the gravity of both joints hierarchically and simultaneously. The air bearing gravity unloading facility which is a structure mechanism with two layers based on this method is designed with planar air bearing and air spindle. The structure of the facility is described in detail. The dynamic models of the APM with its load in space environment and on the air bearing gravity unloading facility are derived respectively. With the analysing of the driving torques and vertical forces of the APM joints in both models, the results demonstrate that the gravity unloading facility can simulate the microgravity environment successfully. This conclusion is also proved by the dynamic simulation with ADAMS software. The simulation also provides some optimization targets for the gravity unloading facility. At last, the gravity unloading facility is established and some experiments are done. The dynamic models, the simulation results and the experiments all show the effectiveness of the hierarchical and simultaneous gravity unloading method.
Tracking and Data Relay Satellite (TDRS) (Zou, 2011; Shaw et al., 2015) is called the satellite of satellites. The TDRS can provide data relay and measurement services for satellites and other spacecraft. It not only is a fundamental solution for the monitoring and control, high coverage communication problems, but also solves the problems of high-speed data transmission and multi-objective monitoring and control. TDRS is usually equipped with one or two large inter-satellite link antenna (Zhai and Baoyin, 2008). The antenna is driven by two-axis antenna pointing mechanism (APM) to get its exact direction for the acquisition and tracking of targets. Usually the TDRS's antenna is very large and needs high tracking accuracy (Jinpeng et al., 2006), so there are higher requirements for the pointing mechanism with its capacity of driving performance, pointing accuracy and reliability. It is necessary to test the performance of the antenna pointing mechanism before launching a TDRS to ensure that the APM meets these requirements. So a gravity unloading facility is needed to test the APM on the ground. The facility unloads the gravity of artificial load (which is designed to replace the antenna on the facility) and the APM parts hierarchically and simultaneously to test the performance while the joints of APM are rotating.
Current methods to build a microgravity environment on the ground include the followings (Zhu and Yuan, 2013): microgravity tower (drop tubes) (Sato and Wakabayashi, 2001), air bearing simulator (Hal, 2003), neutral buoyancy simulator (Atkins et al., 2002; Yao and Mei, 2008), suspending simulator (Yangsheng et al., 1992; Jagannathan et al., 1995), etc. Among those methods, air bearing simulator is used widely because of its higher level of microgravity, lower cost, simpler structure and wider adaptability. Some countries have established air bearing simulators such as United States (Chernesky, 2001; Schwartz and Hall, 2004; Chung, 2007; Jung and Tsiotras, 2007; Scharf et al., 2010), Japan (Umetani and Yoshida, 1989), Britain (Sandor et al., 2007), Germany (Zhang and Cao, 2006), China (Xu, 2010; Zheng et al., 2010; Qi et al., 2011) and so on. However, most of current simulators are designed for the whole satellite model or robot arms which consist of parallel joints to compensate its gravity and simulate the microgravity environment. Those simulators which based on the overall satellite model can test the dynamic performance of the whole satellite model instead of the performance of the parts inside the satellite model because the gravity effect between the parts is not eliminated by the gravity unload method applied. The gravity unloading facility based on parallel joints robot arms models can only test the performance of certain robot arms with parallel joints.
The APM of TDRS is a two-orthogonal-axis structure and the performance of both joints should be tested, so those gravity unloading facilities above are not applicable. Two joints of APM must be unloaded respectively while they are rotating. The unload componests of rear joint may act as the load of front joint, so there is a coupling problem when designing the gravity unloading facility. The most important thing is that the APM must not be modified to mount the unloading facilities and measure equipment, so the difficulty is increased further. In this paper, a hierarchical and simultaneous gravity unloading method is proposed and many problems are solved for the gravity compensation of two-axis antenna pointing mechanism. These problems includes the gravity unload method, the configuration of the gravity unloading facility, the coupling problem, the design of the artificial load of the antenna, the protection of the APM, the non-contact measurement of joints angular, the measurement of torque and residual gravity torque.
Following the introduction in Sect. 1, Sect. 2 describes the gravity compensation method in detail. In Sect. 3, two dynamic models of the pointing mechanism are derived in space environment and on the gravity unloading facility respectively. The gravity unloading facility is proved to compensate gravity successfully by the comparison of two dynamic models. Section 4 shows the simulation of the air bearing gravity unloading facility with ADAMS software. After that, some experiments are done with the facility built and the last section gives the conclusion.
The antenna pointing mechanism is fixed on the satellite in space to drive the antenna which fixed on the output interface. The antenna pointing mechanism consists of two orthogonal joints, a vertical joint and a horizontal joint as shown in Fig. 1. The vertical joint rotor and the horizontal joint stator are fixed together firmly. Thus the pointing mechanism can be divided into three parts: (1) the vertical stator which is fixed on the satellite, (2) the vertical rotor which is also called the horizontal stator because they are fixed firmly, (3) the horizontal rotor. The antenna is fixed on the output interface of the horizontal rotor. The gravity of three parts and antenna (the antenna is replaced by an artificial load on the gravity unloading facility) should all be compensated to test the driving performance of APM on the ground. What's more, the APM can't support the weight of the antenna in the gravity field on the ground or else it may be destroyed by the gravity of the antenna. Thus, a gravity unloading facility is needed on the ground to test the APM, because one main characteristic of space environment is microgravity. The facility should offer two rotational degrees of freedom (DOFs) for the joints of APM with artificial load mounted.
The antenna pointing mechanism.
The gravity of two joints of APM and the artificial load must be unloaded and two joints should rotate freely while unloading the gravity. A hierarchical and simultaneous gravity unloading method is proposed.
The artificial load is mounted on the horizontal joint and rotates around the horizontal axis, so an unload facility is need to unload the gravity and offer a rotational DOF around the axis of horizontal joint. Besides, the horizontal joint and artificial load should rotate around the vertical axis together when the vertical joint is rotating. Thus the horizontal joint, the artificial load should all have the vertical rotational DOF around the vertical axis of the APM while the horizontal joint gravity is unloaded. What's more, the vertical joint gravity should also be unloaded and have the rotational DOF around the vertical axis. So the unloading of the vertical joint gravity and offering vertical rotational DOF can be done by the same component (such as planar air bears or spherical air bearings). The unloading components of horizontal and vertical joint may couple with each other, so the structure must be designed specially and carefully. The APM is designed to run in space, so the APM on the gravity unloading facility cannot support the gravity of the antenna. The facility must offer protection structure to avoid the destruction of the APM by the gravity of artificial load and the unloading parts.
The gravity must be compensated on the ground to simulate microgravity environment. One method is using air bearings to unload gravity because of its low viscous resistance without direct contact. Currently, there are three kinds of air bearings: planar air bearing, spherical air bearing and air spindle. Their characteristics are shown in Table 1. Planar air bearings and spherical air bearings must be mounted on the horizontal plane while the air spindle can be mounted vertically or horizontally.
Three kinds of air bearings.
Structure of the gravity unloading facility.
The gravity unloading facility for the antenna pointing mechanism should have two DOFs of rotation: a vertical and a horizontal rotation. The whole horizontal joint also rotates around the vertical one when the APM vertical joint is activated.
Both the spherical air bearing and air spindle can be used for the horizontal joint according to the analysis of the pointing mechanism gravity unloading facility. Because only one DOF of rotation is needed, the air spindle is chosen to unload the gravity of horizontal joint taking the structural stability and maintainability. The vertical joint must use several planar air bearings to balance the gravity because the APM and artificial load are not asymmetry around the APM vertical axis. There are air films in the air bearings, so there is not direct contact between the rotor and stator of the air spindle, so as to the planar air bearings and the granite platform. A frameless motor is chosen also because there is not direct contact between the rotor and stator. The frameless motor is used to offer extra torque which is caused by the cable of the antenna when the TDRS runs in space. With a thick cable, the torque between the APM and the antenna cannot be ignored when the joint of APM is rotating. There is not any cable between the artificial load and the APM on the gravity unloading facility, so the frameless motor is applied to simulate the torque on the facility (shown in Figs. 2 and 3).
3-D model of the gravity unloading facility.
The gravity unloading facility consists of the granite platform, a frame on the granite platform to mount the APM, two adjustable spring mechanisms, a guide and block pair, the APM (the red one in Fig. 2), air spindle, planar air bearings, artificial load, frameless motor, the flatbed and other connecting components and measuring devices (shown in Fig. 3). The granite platform supports all the other components through the planar air bearings and the frame on the platform. The APM is fixed on the block of the guide and block pair which is fixed on the frame on the granite platform. Adjustable spring mechanism-2 is fixed between the APM and the frame on the granite platform. The rotor of the air spindle and artificial load is mounted on the horizontal rotor of the APM (on the end interface of the APM). The frameless motor's rotor is fixed on the end of the artificial load while the stator is fixed on the flatbed. Adjustable spring mechanism-1 is mounted between the vertical rotor of APM and the flatbed to support the gravity of the APM vertical joint's rotor. Three planar air bearings are mounted under the flatbed and supported by the granite platform via the air films between the air bearings and the platform.
The gravity unloading facility is designed with two layers (shown in Fig. 4). The bottom layer consists of three planar air bearings placed as a triangle while the upper layer is the air spindle. Three planar air bearings are mounted under the support flatbed while the air spindle is fixed on the top of the flatbed. The facility can be divided into three parts to unload the gravity (shown in Fig. 4).
Gravity unloading method.
Firstly, the air spindle bears the gravity of part 1 (including horizontal
axis's rotor, the artificial load and the frameless motor's rotor, shown in
Fig. 4) by the force
Secondly, the gravity of horizontal axis's stator and vertical axis's rotor
is compensated by the spring mechanism-1 (spring force
Thirdly, the gravity of part 3 (vertical axis's stator, shown in Fig. 4) is
unloaded precisely by adjustable spring mechanism-2 (a spring which is also
connected to an adjustable structure). The adjustable structure can offer the
force
The gravity unloading facility offers two DOFs of rotation around vertical and horizontal axes with the gravity compensation method described above. Especially, the unloading is working no matter these two axes rotate one after another or together. Three planar air bearings are placed on the same plane to ensure the rotation around vertical axis while unloading part 2. The air spindle can still unload part 1 while it is rotating around horizontal axis. With air films, both axes rotate with extremely low air viscous resistance. Thus the APM runs in the environment of microgravity just as running in space.
Schematic diagram of gravity unloading facility.
As shown in Fig. 5a, part 1 is the guide and block pair to set free of vertical movement, part 2 is the APM, part 3 is the air spindle while part 4 is the planar air bearings. During the initialization process of the gravity unloading facility, the balance of the air films and the gravity is accomplished with vertical movement in extremely small range, so there are slider joints in the air spindle and planar air bearings.
There are three processes during the performance test of the APM: the initialization process after pressing the start button, the testing process and the ending process when the test is over. During the initialization process, the schematic diagram is shown in Fig. 5a. The air spindle and planar air bearings all move upward while the slider joint in part 1 is also move upward. The air films in the air spindle and planar air bearings are accomplished with high stiffness. Then during the testing process, the slider joints in air spindle and air bearings do not move at all with stable high pressure air supply. There is not any upward movement, so those slider joints can be replaced by firmly fixed connection shown in Fig. 5b. The slider joint in part 1 is not replaced just to protect the APM from being damaged by extra force. After the test, the high pressure air supply is cut off. The schematic diagram is changed back to the structure shown in Fig. 5a. The slider joints in parts 1, 3, 4 all move downward to eliminate the air films in air spindle and planar air bearings.
Two dynamic models of the APM with artificial load in space environment and on the gravity unloading facility are built respectively. They are compared to verify the effectiveness of the facility mentioned above. Air bearings are used to balance the gravity on the facility, so the dynamic model is also changed with the change of mass distribution. There are also some extra unloading forces on the gravity unloading facility when it is working, so the dynamic model with the unloading force must be derived specially. Newton-Euler is used to derive the dynamic models taking the extra unloading forces into consideration. So both dynamic models are derived with Newton-Euler method. The torque and vertical force of APM links are chosen to proof the effectiveness of the gravity unloading method. This is because that the torque is the output of the APM to drive the antenna and the vertical force is influenced by the gravity. The gravity unloading method is effective if the torque and vertical force of APM links are the same between the models in space and on the facility.
The gravity unloading facility is designed to test the performance of the antenna pointing mechanism, so the interaction between the pointing mechanism and the satellite is ignored. The APM is mounted on a fixed base. The model of pointing mechanism in space environment is shown in Figs. 6 and 7 with its coordinates and parameters. No gravity acceleration is considered in space.
The vertical joint's stator is the base (link 0). The vertical joint's rotor and horizontal joint's stator are link 1 while the horizontal joint's rotor and the artificial load are link 2.
Antenna pointing mechanism in space.
Kinematic sketch with D-H coordinate system.
Antenna pointing mechanism on the facility.
The D-H coordinate system is shown in Fig. 7. The kinematic model is derived with parameters in Table 2.
Link parameters of the model in space.
The dynamic model is derived with Newton-Euler method (shown in Appendix A).
The followings are the driving torque and vertical force of joint 1 and
joint 2 in model without gravity:
The APM don't move in the vertical direction on the guide and block pairs
when the gravity unloading facility running stably. But the slider joint in
part 1 (shown in Fig. 5) is maintained just to protect the APM from being
damaged by extra force. On the facility, air spindle is used to compensate
the gravity of part 3 (shown in Fig. 4). It is considered as a third
rotational joint when deriving the dynamic model, shown in Figs. 5b and 8.
The horizontal joint's rotor, air spindle rotor, the artificial load and
frameless motor's rotor are link 3 while air spindle stator, frameless
motor's stator, support flatbed and planar air bearings are link 4. The
balancing state of link 1, link 2 and link 4 is changed to unload the gravity
of part 3 and part 2. There are extra forces:
The D-H coordinate system is shown in Fig. 8. The kinematic model is derived with parameters in Table 3.
Link parameters of the model on the facility.
The dynamic model equation during the derivation is changed with the extra
force mentioned above, so the equation in Newton-Euler is also changed.
Taking link 2 as an example, there is an extra force
The force and torque formulations of link 1 and link 4 are also changed with
extra force
Thus the followings are torques of three joints:
The last joint (joint 4) is the air spindle which is a passive joint, so the gravity and the torque of three planar air bearings act as its driving torque. The driving torque of joint 4 is neglected. The torque of joint 3 is also changed as follows:
The items of torque of pointing mechanism are different between two dynamic models by comparing torque formulations. The loads of both joints are changed with the application of air bearings on the gravity unloading facility. The air spindle and planar air bearings change not only the distribution of mass but also the structure of load.
Angular velocity of joints.
Horizontal joint torque.
The dynamic model in space includes two rotational joints which are the
joints of the APM.
The dynamic model on the facility includes four joints: three rotational
joints and one translational joint. The air spindle is considered as a third
rotational joint which is a passive joint driven by the torque of support
forces of the planar air bearings and the gravity.
Corresponding torque of APM in tow dynamic models are shown in Table 4.
Vertical joint torque.
Torque of two APM joints in both models.
Calculate forces and torques in Table 2 with values of each item from 3-D
model:
Horizontal joint force.
Vertical joint force.
The 3-D model of the air bearing gravity unloading facility is designed as
described in part 2, shown in Fig. 3. Another 3-D model (Fig. 6) is built to
get the torque and force curves of the APM in space. Then two models are used
in the simulation with ADAMS software. The angular velocity of both joints is
shown in Fig. 9. Figures 10 and 11 are the torque of horizontal and vertical
joints respectively in space environment and on the facility. Figures 12 and
13 are the vertical forces of horizontal and vertical joints respectively in
space environment and on the facility. The angular velocity starts with 0 and
then accelerates to 0.3
The facility.
APM in different position on the facility.
In Fig. 10, the horizontal driving torque on the gravity unloading facility is nearly the same with the one in space environment except the first one has a slight offset down. The offset is cause by the asymmetry of the artificial load of horizontal axis especially after the application of air bearing and other connection parts. Though the balance with the counterweight is considered, the offset still exist because of the precision of software model. In the simulation, the offset can be eliminated by applying an extra force on the counterweight which means that when the real gravity unloading facility is established, the offset can be eliminated by adjusting the counterweight carefully. Besides, to imitate the fundamental modal frequency, the artificial load has a low fundamental frequency which means a low stiffness in the tangential direction of the horizontal axis. So the torque of horizontal axis has fluctuations at the acceleration and deceleration points. The fluctuations attenuate quickly, so the gravity unloading facility works stably.
In Fig. 11, the driving torque on the gravity unloading facility is the same with the one in space environment except the beginning of the vertical joint torque. On the facility, there are two reasons bring the great torque impact at the beginning. Firstly, at the starting point of the whole system with the supply of high pressure air, the planar air bearings have an initial process which brings the impact of the vertical axis. Secondly, springs are used for unloading the gravity (adjustable spring mechanism-1 and 2). During the start of the simulation, there is a balance process with the spring and air bearings stiffness and damping. Compared with the torque of horizontal axis, the torque of vertical axis is smoother except the beginning. Because the stiffness in the axial direction of the artificial load is quite large, the low fundamental modal frequency has no influence on the vertical driving torque.
The points to measure the air films.
Measure the air films in the planar air bearing and air spindle.
Figures 12 and 13 are the vertical forces of horizontal and vertical joints respectively in space environment and on the facility. The vertical forces of both joint in space are zero perfectly. Both the vertical forces of horizontal and vertical joint on the facility include an impact at the beginning with the same reason of the impact of vertical joint torque on the facility in Fig. 11. Both curves of vertical forces of horizontal and vertical joint are zero just as in space except the beginning, which means the facility can unload the gravity sufficiently.
Figures 10 to 13 show that the air bearing gravity unloading facility provides an environment of microgravity successfully. The facility can test the performance of antenna pointing mechanism effectively.
With all the analysis and simulation done above, the gravity unloading facility is built (shown in Fig. 14) based on the method described in part 2.
The APM rotates on the gravity unloading facility freely just as it rotates in space. The following are the pictures that the joints of APM in different position (shown in Fig. 15). Before the APM is connected, the whole parts (over 150 kg) on the granite platform can even be rotated or moved by only one finger which means that those parts are float by the air bearings.
There are two experiments done to illustrate the effectiveness of the gravity unloading method. The first one is to measure the thickness of the air films in the air bearings. This measurement proves that the air bearing do support the load on it to unload the gravity. The second one is the measurement of the torque on the horizontal APM joint. It verifies that the load on the horizontal joint is balance and the joint is just as the state in space because it is so sensitive to the change of torque.
The air film in the air bearings is too thin to be seen directly when the high pressure air is connected, so the thickness of the air film must be measured by dial indicator. The air films in three planar air bearings and the air spindle are measured in 5 points on the gravity unloading facility (shown in Fig. 16). The dial indicator is put on the granite platform and adjusted to 0 before the high pressure air is supplied, then connect and disconnect the high pressure air for several times and record the thickness of air film (the dial indicator is put on the support platform to measure the air film in the air spindle).
Table 5 is the the following is the thickness of air films measured. The result shows that the air bearings are effective when the high pressure air is connected. With the thickness measured, there is high pressure air in the air bearings which means that both joints of APM rotate only with air viscous resistance which is very small and neglectable. So the APM joints rotate just as in space.
The thickness of air films.
The following figure shows the torque of horizontal joint while the high pressure air is connected and disconnected several times. Then two coins (about 3 g) are pasted onto the load of horizontal joint and the torque changes accordingly, shown in the figure. This means that the horizontal joint is sensitive with the change of torque because its gravity is unloaded by the air spindle, which also means that the method is effective.
Torque of horizontal joint
A hierarchical and simultaneous gravity unloading method with air
bearings is proposed for the two-orthogonal-axis antenna pointing mechanism.
The mechanism is described in detail. This method realizes the gravity
unloading of the APM hierarchically and simultaneously and solves the
coupling problem of two joints of APM. The air bearing gravity unloading facility based on the hierarchical and
simultaneous gravity unloading method is designed with planar air bearings
and air spindle. The facility is a structure with two layers which
compensates the gravity of both axes when they rotate one after another or
together. The effectiveness of the gravity unloading method is proved by the
dynamic models and simulation. The dynamic models of the pointing mechanism in space environment and on
the gravity unloading facility are derived respectively. Two models show
that the gravity unloading facility compensates the gravity successfully
after comparing the force and torque formulations. The precision is analysed with the calculation of torques and vertical
forces in both models. The corresponding joint torques and vertical forces of
APM in both models are equal after the calculation with values from 3-D model.
The result means that the gravity unloading facility unloads the gravity
successfully with air bearings and the test result of APM on the facility is
reliable. The simulation in ADAMS also shows that the gravity unloading facility
can provide microgravity environment. The asymmetry of the horizontal axis
load results in the extra torque of horizontal joint. The asymmetry is
brought by the structure of some connection parts which reduces the precision
of the gravity unloading facility. The counterweight of the horizontal load
must be adjusted carefully to eliminate the asymmetry. The gravity unloading facility is established. Some experiments are done
on the facility and verify the effectiveness of the facility.
The data to this paper can be found in the Supplement.
Newton–Euler method used when deriving the dynamic models.
The forces in model of Fig. 7:
The forces in model of Fig. 8:
The authors declare that they have no conflict of interest.
This study was co-supported by the State Key Laboratory of Robotics, Shenyang Institute of Automation Chinese Academy of Sciences and Beijing Institute of Control Engineering. This paper is supported by the project of Control-Capture Integrated Test System (0002546159001). Edited by: L. Romdhane Reviewed by: Z. Affi and one anonymous referee