Hydraulic brake on the carriage house and dome
testing the hydraulic brake system on the carriage house.
07jun01 testing the
hydraulic brake system on the carriage house. (top)
measuring the speed of the carriage with only the brake (no motor).
valve on dome brake clogs while testing.
26jun02 measuring the hydraulic
brake on the dome.
the pointing with the brake on and off.
A hydraulic brake was mounted on the gear of the uphill carriage
house motor (motor 1). When the system moves downhill, the fluid moving
through an orifice resists the motion (going as the velocity squared).
A bypass valve causes no resistance when moving uphill. On 07jun01
the brake was installed and the carriage house was moved from zenith angle
2 up to zenith angle of 19.5. It was then moved back down to 2 degrees.
A preset motion was used for the movement. It moved at maximum velocity
with no feedback on the position (so it wasn't constant velocity). The
torques (motor amps) were measured once a second using the computer. These
torque measurements are by motor without a sign telling the direction of
the force. The plots
show the results of the measurements.
The torque profile moving uphill taken later in the day matches the profile
with the brake installed. This shows that the bypass valve is working correctly.
Figure 1 top shows the position versus time profile for the motion.
Figure 1 bottom plots the torques by motor for the uphill and downhill
motion. Black and red are the two motors moving uphill. Green and blue
are the two motors moving downhill. Brown and pink are an upward
motion from 2 to 8 degrees made later in the day when the brake had been
removed. Without the braking system you would expect the torque needed
to move up to equal the EMF force generated when moving downhill. You can
see that the green/blue traces use vary little torque to start at 19 degrees
since the gravitational force is almost balancing the braking system. As
the system moves farther downhill, the brake resistance remains constant
while the gravitational force decreases by the sine of the za. So the motors
must push harder at lower za.
Figure 2 top has the torques versus za for the first few seconds after
the ch started moving downhill from a stopped position at 19.5 degrees.
The black line is motor 1 with the brake attached. The red line is motor
2. Each * is spaced by 1 second. The torque starts of at 0 (on the right)
and then jumps up to 3 amps. This is needed to hold the ch after the parking
brake is removed. The force is in the upward direction since the velocity
is zero and there is no resistance from the brake fluid. As the ch starts
moving downhill, the torques drop and then climb again. This is the torque
switching directions from pushing uphill to pushing downhill against the
fluid. The motor with the motor attached has a smooth torque profile (at
least at this sampling rate) while the motor without the brake has its
torques oscillating (this is seen in the normal operations without a brake
Figure 2 bottom plots the torque versus velocity while the ch is coming
up to speed.
It would be good to redo the test with a variable velocity so we could
measure the velocity/za where the gravitational force exactly balances
the brakes friction (i.e. the torque will go to zero while the ch is moving).
21jun01 Carriage house speed
with only the brake (no motor). (top)
The hydraulic brake should allow the carriage house to move
safely from zenith angle of 20 degrees down to 0 degrees za with the motor
disconnected. Directly measuring the "free fall" velocity of the
carriage house by removing the motors has its drawbacks (what if we made
a mistake!!). An indirect method was used to do this measurement. The technique
The forces on the carriage house (CH) moving downhill
at zenith angle ZA in the two acceleration sections can be equated to the
mass times the constant acceleration (Accel = .000444 degs/sec^2)
Fmot+ Fgrav(sinza) - Ffriction - Fbrake(v^2)=Mch*Accel
Fmot+ Fgrav(sinza) - Ffriction - Fbrake(v^2)=Mch*(-1)Accel=-K
Fgrav from gravity points downhill and is MassCH * 9.8 met/sec^2
Ffriction is the velocity independent part of the friction. It is probably
a function of the zenith angle depending on how the rack gear and rails
interact with the wheels and drive train.
The Fbrake is from the brake and is proportional to the square of the velocity.
It points opposite to the motion.
FMot is the force applied when the motor is on. It can be be uphill or
Mch is the mass of the carriage house and Accel is the fixed acceleration.
K is a constant.
When we start downhill at 0 velocity there is no resistance from the brake
since the velocity is zero. The motor must push uphill. As the velocity
increases the brake resistance increases and the motor has to push less
uphill. At some point the motor switches from pushing uphill to pushing
downhill. This occurs when:
Start at rest at zenith angle za.
Move downhill for 90 seconds at a constant acceleration going from 0 to
.04 degrees/second (slew speed).
Continue down for another 90 seconds moving at the negative acceleration
in 2. The velocity will go from .04 deg/sec to 0.
Record the position, velocity, and magnitude of the motor torques each
second during this motion.
Fgrav(sinza) - Ffriction - K = Fbrake(v^2)
accel increases abs(vel)
Fgrav(sinza) - Ffriction + K = Fbrake(v^2)
accel decreases abs(vel)
At this point the motor does not have to apply any force.
Any further increase in velocity will require the motor to push downhill.
If we plot the torque of the motor versus velocity, the minimum of the
curve is where the brake resistance balances gravity. This is the
free fall velocity for that zenith angle. The figures
show the results:
vel^2= A0 + A1*za
This is the free fall velocity squared versus za (the fit should be to
sin(za) but the difference is negligible for this za range). The bottom
plot is the velocity versus za with the same fit over plotted. In the upper
left of each plot (above the red line) the motors are always pushing downhill
(against the brake). The lower right portion (below the red line) the motors
are pushing uphill (against gravity). In the later region the motors are
generating energy and the regeneration boards can be activated.
The measurements show the freefall velocity of the ch. At 10 degrees za
it will be moving at .02 degrees per second (half slew). According to the
plot the CH will stop at 2.8 degrees za.
Figure 1 shows the torque versus position for the 16 separate measurements.
4 zenith angles were done twice : 9.2, 12.2, 15.2, and 17.2 degrees. These
show good repeatability of the measurements. The red line is the velocity
*100 in degrees/sec for the 180 second motion. The CH started on the right
of each plot and moved downhill. It reached maximum velocity in the middle
and then started slowing down till it came back to 0 velocity on the left.
The plots in the upper left are at low za while the lower right are at
higher za. At low za the motor has to start pushing immediately downhill
since there is not much gravitational force at low za. For high za
the motors must push hard uphill, decreasing until the balance point is
hit and then must start pushing downhill to reach the maximum velocity
in the middle of the plot. The green line is a 3rd order polynomial fit
to the torques(vel).
Figure 2. At the balance point Fgrav(sinza) = Fbrake(vel^2) (ignoring Ffriction
and K). The upper plot is the velocity squared versus za with a linear
On 21may02 the hydraulic valve on motor 22 clogged
while testing. The plot shows
the torques while the valve clogged. The colored lines are the currents
for the individual motors. Motor 22 had the problem. The dome was at 1.43
degrees and started to move downhill slowly. The dashed red line is the
dome position - 1.43 degrees in .1 degree units. The torque on motor 22
increased until the system shutdown (or was shutdown). The samples were
taken at 1 second intervals.
dome hydraulic brake valve clogs while testing. (top)
The hydraulic brake was installed on 26jun02 for testing.
The brake was on motors 11,12,31,32. A velocity profile of 0 to slew then
back to 0 moving down hill was used. The constant acceleration took 3 minutes
to ramp up to slew speed and then back down. This profile lets us measure
the free fall velocity of the dome (as if the motors were not installed).
See the carriage house brake test
for why this works. The
figures show the torques needed for the dome to move with this velocity
profile against the hydraulic brake.
Fig 1 top: this is the velocity profile used. Slew rate downhill is -.04
deg/sec. This profile was repeated at 16 different zenith angle positions.
Fig 1 Bottom: These are the torques for each of the 8 motors for 3.2,10.2,
and 17.7 degrees za. Negative torque has the motors pushing downhill. Since
the vertex system provides the absolute value of the torque, I switched
the sign when the torque went through zero.
Fig 2,3. These plots show the velocity profiles done at 16 different zenith
angles. Torque versus za is plotted in black. A fit to torque(vel) is shown
in green. The red plot is the absolute value of the velocity * 1000. At
the center of each plot, the dome is moving -.04 deg/second downhill. The
dashed red line is slew, the dashed blue line is 0. At low za the torque
is mostly negative. The motors must push downhill to overcome the brake.
At higher za positive torque is needed to hold the dome until the velocity^2
brake friction equals gravity. Above this velocity the torque becomes negative
and the motors must push downhill. Tests done at 19 deg za moving uphill
(at slew) needed 160 ftlbs. This is a little more than the 150 ftlbs needed
at low za moving downhill at slew rate.
Fig 4. When the motor torque goes through zero, the brake friction (plus
any other friction) equals the gravitational force. The top plot is the
velocity^2 versus za for each of these positions. The linear fit to velocity
squared shows that the brake (which goes as velocity^2) is doing most of
the work against gravity. Extrapolating the line to zero velocity has
the dome stopping at 3 deg za for freefall (no motor). The bottom plot
shows the same curve versus velocity. When the velocity,za position is
above this line, the motors must push downhill. When the velocity,za position
is below the line, the motors are pushing uphill, holding the dome.
the hydraulic brake on the dome. (top)
The current hydraulic brake makes the low za downhill
motion comparable to the high za uphill motion. Most long slews will be
uphill acquiring a source that is coming into the beam. There will be short
slews at low za when moving between on and off positions while position
The source 3C138 (B0518+165) was tracked rise to set
using the cband receiver and the heiles calibration scans. On 02jul02 the
hydraulic brake was installed. On 03jul02 the hydraulic brake was removed.
show the pointing errors for both tracks. The dashed lines are for
rise (when the motors would be pushing against the hydraulic brake) while
the solid line is for set (after transit) where the hydraulic brake should
Top: the zenith angle error versus zenith angle. The dashed black
and red lines are very close together. These should be the ones most affected
by the brake.
Center: the azimuth errors versus za. There seems to be more variation
in these errors than in the za errors.
Bottom: the error difference Brake-noBrake for za errors (black) and az
Checking the pointing with and without the brake on the dome. (top)
The brake does not affect the za errors during rise.
The azimuth errors seem to have more variation. This may be caused by
tiedown motion, or the dome moving horizontally and then jumping back on
the rolling surface (since the rollers are set too loose).