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  Figure 1.  Beginning of Oscillation of CMG-4 SMCC

Figure 2.  One single cycle of CMG-4 SMCC

Since the wheel speed remains relatively constant, the wheel speed controller is reacting to real variations in drag torque.  The increases in temperature reported by the thermistors confirmed that increased power is dissipated in the bearing assembly as a result of the oscillations.

Determining the cause of these oscillations has presented many challenges.  There are obstacles to performing on-orbit testing.  Furthermore, testing on the ground is limited by equipment availability,  budget restraints, and inability to simulate environmental conditions comparable to Low Earth Orbit (LEO).

Some have posited that misalignment may be the cause, since there were indications of misalignment in the bearing system of the failed CMG-1 that was returned to earth for analysis.  However, this hypothesis must be rejected for several reasons.

First, the expected signature of misalignment does not match the telemetry data.  Second, there is no credible cause for periodic misalignment that matches the characteristics observed.  Third, testing on the Robust Test Fixture failed to produce any evidence that thermal causes could create sufficient misalignment to impact SMCC.  Fourth, analysis of the torquer motor currents failed to produce any evidence torsional mechanisms are occurring.  Fifth, in all ground testing in which misalignment was induced by direct mechanical means, indications of retainer instability have always occurred simultaneously with increased SMCC.

Therefore, unless we have discovered a new phenomena such as spontaneous misalignment, that theory must be discounted.

The periodic nature of the disturbances implies that the stimulus for the behavior is also periodic (unless there exists a remarkable coincidence that the natural frequency of the system coincides with attitude controller as well as an absence of damping).   Positive feedback is necessary also, since there is reasonable certainty that the stimulus is much smaller in magnitude than the response of the system.

Characteristics

Other characteristics of the oscillations can be observed from telemetry data.  The temperature fluctuation is much larger on the motor-side thermistor than the resolver-side thermistor.  The increased power is dissipated predominately in the motor-side bearing.  (single side effect)

There appears to be no correlation to particular gimbal angles.  Oscillations do not increase or decrease in amplitude because of the particular angular range of motion that the controller exercises.  This observation is startling because the thermal radiation environment inside the CMG cavity is not isotropic.  (angular independence)

The peak periods of radial loading (due primarily to gimbal motion) occur during both the high and low phases of the oscillations.  Additionally, increases in current occur when radial loading is decreasing or minimal.  (radial load independence)

Oscillations occur over all of the temperatures experienced in XPOP.  Also, similar increases have been observed during propulsive attitude control by Russian thrusters at much lower temperatures. (temperature independence)

Initially, the shape of a single cycle typically reflected a slow increase and a relatively fast decrease.  In later periods of XPOP, an initial “overshoot” and rapid decline marked the beginning of many of the oscillations.  This overshoot occurred in nearly half of the cycles. (relief bias and overshoot anomaly)

To summarize, the oscillations seem indifferent to gimbal angles, magnitude of the radial load, and temperature conditions.  We are about to see that the only condition that seems to correlate to the high and low SMCC is the position of contact of the radial load with the bearing housing.

Correlations

With the application of software tools to analyze the telemetry data, the pattern of indifference observed above is shattered to reveal some remarkable correlations.  The increasing phase of the cycle shows definite correlation to direction of radial load as expressed by the Load Compass.  Figure 3 shows an example of the correlation to direction of the radial load indicated by the Load Compass.  In all cases the increase in current coincides with radial load contact on the positive U-axis of the bearing housing.  Furthermore, in all cases, the decrease in current occurs when the load contacts the negative U-axis.  (compass position dependence)

Figure 3.  Correlation of Oscillation to Position of Radial Load on Bearing Housing

Analysis of telemetry from periods of attitude control by propulsive assets (Russian thrusters), even in attitudes other than XPOP, reveals that similar disturbances occur when the radial load changes position around the load compass.  See Figure 4.  It should be noted that only the XPOP attitude controllers cause the periodic motion of the gimbals from positive to negative U-axis in a nearly inertial reference frame. (controller dependence)

Figure 4.  Correlations to Position of Radial Load During Attitude Control by Propulsion

During propulsive attitude control, the magnitude of the current disturbance still reflects insensitivity to the magnitude of radial load.  However, examination of various cases indicates that the characteristic slow rise and fast fall of current can be altered by rapid motion of the radial load around the compass. (compass motion rate dependence)

In all cases, the position of contact with the bearing housing correlates to SMCC variations.  Furthermore, slightly to the right of center in Figure 4, there is a rather unique circumstance.  The position of the radial load changes abruptly to press against the positive U-axis of the bearing housing (indicated by +1.0 on the Load Compass).  The magnitude of the radial load (indicated by the bearing load measured in deg/s) does not change although gimbal motion has stopped (an indication of rotation of the station without gimbal motion).

In this rare instance where only one physical parameter changes, it can be clearly observed that the SMCC shows a distinctly thermal response.

Possible Causes

The set of possible causes that must be considered includes anomalies or unexpected changes in the following:

            Preload System

            Alignment of the two Spin Bearings

            Mechanical Drag (displaced or deformed part)

            Retainer Motion

            Lubricant

            Ball Motion in Raceway

            Bearing Geometry and Radial Play

Model

 It strains the imagination to construct a hypothesis that both explains the observed correlations and is consistent with the independencies.  The important clue regarding positive feedback will prove to be critical.  A model was developed to describe the thermal state of the spin bearing.  The f-function model is based on an inverse-root power demand (inflow) and a linear power drain expression (outflow) from Fourier’s law.

The inverse root power demand component of the model results in positive feedback characteristics.

Model Fit

When the model is applied to the telemetry data from an oscillation cycle, a particularly gratifying result is obtained.  See the following example.

 Figure 5.  Example fit of the F-function Model to a Single Oscillation

That such a good fit to the data can be accomplished is important.  The close fit indicates that the model describes the behavior of the system very well in the region of interest.  The fit was created using an abrupt change in the thermal boundary conditions of the f-function model.  A non-linear least squares routine was performed using MATLAB.  The f-function has an analytical solution, but it cannot be put in the form of an extrinsic solution.  Therefore, it is unwieldy to use for calculations.

Along with the impressive fit of the model, there is even stronger support from the analysis of telemetry using the load tools.  The oscillator behavior of the CMG is explained well by comparing with the result of periodic upset of the thermal boundary conditions of the thermal model.  The hypothesis implied by this analysis follows.

Implied Hypothesis

Since the Inner Gimbal (IG) angle is typically very close to zero, the IG cover that is on the negative U-axis side is more directly exposed to the radiance of the Electronics Assembly (EA).  The absorbed thermal load is about 20 Watts.  The path of heat rejection by conduction is along the T-axis, which is aligned with the IG ring.  There will be a small temperature variation “around the load compass.”  The negative U-axis will be warmer than the positive U-axis.

For purposes of perspective, it is important to note that typical temperature changes at the thermistor are of the order of less than a few tenths of 1 º C per hour.  The periodic motion of the most recently used XPOP controller toggles the radial load back and forth across the load compass at twice orbital frequency (twice-ω˚ ) .  This results in an abrupt change in the thermal interface conditions of the bearing outer race as the region of contact for heat rejection transfers from one side of the U-axis to the other.

The decline is caused by the thermal contact of the bearing being moved away from the +U-axis toward the –U-axis.  The twice-ω˚ XPOP controller accomplishes this movement in about 3 minutes. 

The heating of the outer race by the higher temperature at the –U-axis “relieves” the radial play by slightly expanding the outer race.  This also means that the ΔT across the bearing is decreased and power demand reduces.  In effect, the system is moving “down” the power curve toward lower demand.  The decreased power allows the inner race to cool, decreasing the heat flow to the outer race (and wheel).

The rise is caused by thermal contact of the bearing being moved toward the +U-axis from the –U-axis.  The twice-ω˚ XPOP controller accomplishes this movement in about 9 minutes.

The cooling of the outer race by the lower temperature at the +U-axis “restricts” the radial play by slightly contracting the outer race.  The ΔT across the bearing is increased and the power demand rises.  The system is moving “up” the power curve toward higher power. The increased power heats up the inner race, increasing the heat flow to the outer race (and wheel).

The motor side is predominately affected since it is far more sensitive to temperature changes because it operates at a much higher position on the power curve.  This is supported both by the high motor current and by the large temperature difference between the two bearings.

References

CMG1_Failure_Investigation.doc

 InverseRootPowerDemand.doc

CMG-4Illustrations.ppt

NewTools_1.ppt

Derivation of the Model

A brief sketch of the development may render this more plausible.  The expression for heat in the bearings is

For the angular contact bearing, bearing geometry (especially angle of contact) and radial play are clearly functions of the temperature difference across the bearings.  The usual definition of radial play is

where:

B is the Total Curvature, DW is the ball diameter, and a0 is the angle of contact.

Radial play can be obtained with a simple calculation involving the temperature profile of the bearing.  With the assumption that the temperature of the balls is the average of race temperatures, the calculation (in ºF & inches) would be similar to

 With a little work and a key assumption that friction remains proportional to normal load on the bearing surface, a very simple form of the inflow of power to the bearing is obtained. 

Heat transport within the bearing is complicated, and involves heat transport by the rotating balls and lubricant.  As long as the temperature changes occur slowly enough, Fourier’s law asserts that conduction heat flow will be proportional to the temperature difference that “drives” the flow.  Indeed the previous assumption that the ball temperature is the average of Tinner and  Touter is also dependent on relatively slow changes of the profile.

With the slow change assumption, the temperature difference across the races can be used to measure heat flow out of the bearing. 

Therefore the f-function model is based on an inverse-root power demand (inflow) and a linear power drain expression (outflow) from Fourier’s law.  With an exercise in applied mathematics this can be transformed into the f-function