Magic Semi-Rigid Tether Deployment Damping Experiment

A Demonstration and Optimization of a Nanosatellite‘s
Mechanically Actuated Gravity-Induced Control (MAGIC)
Semi-Rigid Tether Release System and Tip Mass Slow-Down

Mechanism

A Part of the Deployment and Intelligent Nanosatellite

Operations (DINO) Nanosatellite Project

Author:

Timothy Shilling

3/26/04

Based on and Portions From the Work of:

Timothy Shilling

Jeffrey Parker

Michael Martinez

Grayson McArthur

Original Concept:

Anthony Lowery

Colorado Space Grant Consortium

University of Colorado at Boulder

Boulder, CO 80309-0520

    The MAGIC (Mechanically Actuated Gravity-Induced Control) Tether Experiment will serve to test and refine DINO’s (Deployment and Intelligent Nanosatellite Operations) boom deployment and slow-down mechanism system. The experiment will be conducted aboard a NASA KC-135, reduced gravity aircraft. The experiment has been accepted for two days (60 parabolas, 25sec of zero-g per parabola) of testing. With this time, it is hoped that the deployment system for DINO’s boom can be tested and its dynamics understood. The rotational and linear acceleration rates will be collected, as well as the physical reactions of the tether observed, while a simulated DINO is separated. The simulated structure consists of tip mass and primary satellite weighing no more then 50lbs. They are tethered to each other with two 4ft long Stanley tape measures placed face to face. An initial velocity will be induced, separating the two satellites with a relative velocity of approximately 1.7 ft/sec. This velocity will then be damped out over a 4ft deployment. The rate of damping will be controlled by an adjustable spring connected to a pawl and ratchet. Each time the pawl goes over one of the teeth of the ratchet the spring will be compressed. The energy required for this compression will come from the kinetic energy of the two satellites. With this, the satellites motion will be damped and brought to a smooth stop. The experiment will vary the initial displacement of a spring in the slow-down mechanism, x₀, to empirically measure how much energy the slow-down spring dissipates. The purpose of the experiment is to optimize the system such that the tip mass’ motion is critically damped as it reaches the end of the tether, eliminating any recoil. The dynamics of the deployment system are currently poorly understood and roughly predicted. It is the goal of this experiment to gain a better understanding of the deployment systems damping and reactions to different levels of such

1.  
   1. Background
      

DINO’s mission requires the nano-sat to always be nadir pointing. This requirement was derived by science and communication needs. In a desire to alleviate this attitude control from the actively controlled ADCS system, gravity gradient control was desired. To allow for gravity gradient stabilization, DINO will deploy a boom by means of a semi-rigid tether. DINO’s MAGIC (Mechanically Actuated Gravity-Induced Control) boom has been designed to be about six meters long with a 5-kg tip mass at its end. The connection between DINO’s primary 25-kg satellite with the 5-kg tip mass will be made by a stainless steel “tape measure” tether. The boom will be deployed by the Lightband separation system, developed by Planetary Systems Corporation (Figure 1.1). The Lightband system is expected to separate the primary satellite from the tip mass at a relative velocity of 2±0.5 ft/s. At this rate, the boom will be fully deployed after 10 seconds.

Figure 1.1: Lightband Separation System

Once the tether has reached its full deployed extension, it is important that the tip mass come to a gentle stop without recoiling back toward the primary satellite. Any recoil action could result in a collision, but more likely it would result in wild oscillations about the zenith axis, which would be detrimental to DINO’s vital gravity-gradient stabilization requirements. To prevent this, the MAGIC Tether team is designing a slow-down mechanism to bring the tip mass to a gentle stop before it reaches the full six-meter extension. The full dynamics of DINO’s deployment system and the slow-down mechanism cannot be fully tested outside of a micro-gravity environment. Therefore, the MAGIC Tether team has constructed the MAGIC Tether Experiment to demonstrate and test DINO’s tether deployment system and slow-down mechanism on the KC-135. This experiment is not a follow-up of a previous experiment, nor is it a preliminary step to a future experiment. It is an experiment designed to optimize the performance of DINO’s MAGIC Boom and gain a valuable “real world” understanding of the systems dynamics.

1. Experimental Goals
   

The purpose of the MAGIC Tether Experiment aboard NASA’s KC-135 is to demonstrate and test DINO’s boom deployment system and tip mass slow-down mechanism. In an attempt to simulate DINO, a tip mass will be deployed in free-fall aboard the KC-135 on a 4-foot (1.22-m) tether. The tip mass will be accelerate to an initial velocity of approximately 1.7 ft/s as it is deployed with a tip-off rate no more than 1°/s. While the tip mass deploys, a slow-down mechanism will be invoked that will dissipate the energy from the system bringing the separation to a smooth stop. The MAGIC Tether Experiment will include accelerometers and rate gyros to measure the linear and angular accelerations that the system experiences during the full deployment, including the large accelerations experienced during the initial deployment and the subtle decelerations as the tether is reeled out. To better understand the damping, the experiment will vary the initial displacement of a spring in the slow-down mechanism, x₀, to empirically measure how much energy the slow-down spring dissipates. The purpose of the experiment is to optimize the system such that the tip mass’ motion is critically damped as it reaches the end of the tether. Running multiple trials during the reduced gravity flight will result in multiple case data, from which damping trends can be extrapolated and scaled up to DINO’s full length and mass.

1. Objectives
   

1. Measure the large-scale and small-scale dynamics during the deployment, including linear and angular accelerations imparted by the tether as it is deployed.
2. Empirically measure how the energy in the system can be dissipated using the spring force in the slow-down mechanism. The goal is to optimize the system such that the tip mass’ motion is critically damped as it reaches the end of the tether.
3. Demonstrate a successful deployment of DINO’s MAGIC Boom, building substantial confidence in its design. This is very importance since a successful deployment of DINO’s MAGIC Boom is a vital component to DINO’s success.

1. Experimental Deployment System
   

1. General System

The experimental test article consists of two halves, the primary and Tip Mass satellites. The primary satellite is the heaviest at 14.602 kg (32.19 lbs weight) and the Tip Mass is 8.066 kg (17.78 lbs weight). Initially they will be held together, compressing the kick off springs (figure 2.1).

Figure 2.1. Stowed System.

The unit will then be activated, and the two halves will be allowed to separate (figure 2.2).

Figure 2.2 Deployed System

An initial velocity will be imparted on the two satellites. It is this relative velocity that must be damped out of the system. This will be done by repeatedly converting the kinetic energy of the system into spring energy with a ratchet and pawl. The pawl will be attached to a compression spring. The energy required to compress this spring will control the rate of energy dissipation, and will ultimately bring the system to a smooth stop.

1. Kick off Springs
   

When adequately stable, near a zero-g state, the deployment system will be fired. The two halves of the system will be accelerated away from each other by four separation springs (figure 2.3). These springs will serve to simulate Lightband and as such were based on those used by Lightband. Each spring has a spring constant of 22.5 lb/in (3.94 N/mm).

Figure 2.3 The profile of a separation spring.

While in the stowed setup, the springs will be compressed 0.787in (20mm). This will result in an initial combined stored mechanical energy of approximately 3.1 J. It should be noted that this initial stored energy does not take into account that which is stored with in the tape measure tether system itself. The spring constant for the reeled tape measure is unknown, and is one of several system properties that a better understanding of will be obtained through this experiment. For the purposes of initial analysis, this additional stored energy will be assumed (with in an order of magnitude) to be equal to the unaccounted energy dissipation due to friction and drag during the deployment. From these assumptions, conservation of energy was used to find the initial velocity and kinetic energy of the system. It is this initial energy that must be dissipated during deployment.

1. Ratchet and Pawl Damping System
   
2. General Description
   

The ratchet and pawl is the heart of the damping system. The ratchet is directly connected by a shaft to the interconnected spools on which the reels are attached. (figure 2.4).

Figure 2.5 Damper assembly

s unwound and the spools and ratchet rotate. When the ratchet rotates, a spring, connected to the pawl, is compressed once per tooth (figure 2.5). This will dissipate the kinetic energy of the system by converting it to potential spring energy and then to heat.

Figure 2.5 Ratchet and Pawl

As the kinetic energy is converted, the relative velocity of the system will decrease.

1. Energy Dissipation, Spring Sizing
   

The braking ratchet has 42 individual teeth. This means, that for every full rotation of the spool, the spring will compress 42 times. It was found that over the deployment, the spring would compress 366 times. To dissipate the initial 3.1J of energy given to the system by the kick off springs the energy per tooth was found to be (3.1/366) 0.0085J. To determine the spring constant needed to absorb this much energy per tooth, equation 2.1 was used. The needed constants, unique to the experiment, are given in Table 2.1 below.

Equation 2.1

*For a complete derivation of Equation 2.1 and further explanation of Table 2.1, refer to reference 1, The MAGIC Tether Experiment.

From Equation 2.1, Chart 2.1 was generated

Equation 2.1: Slow-Down Spring Sizing

Chart 2.1, plots the number of cogs, n, needed to damp out the total energy of the system for each combination of initial displacement, x₀ and spring constant, k_SS. Knowing that there are only 366 cogs (n = 366) to dissipate the energy, the behavior of the damping system can be explored. If the system were under damped (n > 366), the number of needed cogs would exceed those available (366) and the length of the tether would be exceeded before all energy was dissipated; the system would recoil. If the system were over damped (n < 366) the system would not deploy to its entire length.

From this chart and the available stock of springs from SPEC, the C0180-014-1000 was chosen. This springs properties are shown below.

This spring nominally removes all of the energy in the system after 366 cogs when x₀ is 0.66″. Furthermore, the spring setting can vary from x₀ values of about 0.55″ to about 0.75″ and still remain in an interesting dynamical regime. The mechanical dial shown in Section 2.3.3 has therefore been optimized to provide a travel between about 0.5″ and 0.8″ to explore the full dynamical range of interesting x₀ values.

1. Mechanical Dial
   

The mechanical dial (figure 2.6) will be used to adjust the spring’s initial compression.

Figure 2.6 Mechanical Dial

It was designed to allow for a compression range of .5 to .8 in. During the reduced gravity flight, the initial compression of the spring will be adjusted between tests. In this manor, a plot can be generated showing the relationship of x₀
to n. This would be the plot from which DINO’s needed spring constants could be extrapolated.

1. Testing
   

For the test, the two satellites will only be deployed 4ft. The experiment must me conducted in such a manor as to allow for the system to be scaled to DINO’s full length. To achieve this, the initial spring displacement, hence the required work per tooth, will be adjust. For the first experimental run, the spring will be set to over damp the system (Maximum initial compression). After each test, the spring’s initial compression will be decreased by 0.05in. This will be continued until the system becomes significantly under damped. For each run, the total deployment length will be recorded, along with visual observations. After the first day of testing, the data obtained from the accelerometers and rate gyros will be used to determine ranges of initial compression lengths that are of interest

During the second day of testing, the procedure will be repeated for the previously found areas of interest. Between each run, the spring will again be adjusted, but at a mush smaller displacement increment. This increment will be determined from the previous days experiences and data.

For both days of experimentation, it is expected to obtain 7 to 14 sets of data. The number of runs is subject to the ability of the test crew to perform the experiment and the number of near zero-g experimental runs that can be obtained from the KC-135.

1. Experiment Goal
   

It is the explicit goal of the experiment to determine the feasibility and properties of the MAGIC tether deployment system. Through this experiment, many valuable aspects of the deployment system will be better understood. The experiment will demonstrate the successful deployment of the tether system, measure the deployment dynamics and determine the optimal configuration for DINO’s tether slow-down mechanism. It is critical to DINO, that the deployment of the Tip Mass is proven safe and reliable. DINO’s mission would be at a great risk if the behavior of the Boom system were poorly predicted. If the Tip Mass were to recoil, it could induce uncontrollable rotation, critically disrupting the science objectives. Even worse, the recoil could cause the Tip Mass to collide with the primary satellite, damaging vital components. If the Tether were over damped, and not allowed to deploy its full length, the consequences are far less severe. However, the reduction in gravity gradient stabilization would result in a great hindrance to Science and Communications, whom require strict attitude control.

This experiment is critical to insuring mission success for DINO. A greater understanding of the properties of the deployment system will result in far fewer risks to DINO and its mission. Conducting this experiment and exploring the systems dynamics in a near zero-g environment will led to a far more accurate model of the real deployment system to be flown with DINO and will led to the insured success of its operation.

1. References
   

The MAGIC Tether Team, “Test Equipment Data Package”, CSGC, 3/5/04