# Hydraulic brake on the carriage house and dome

#### june, 2001

Topics: 07jun01 testing the hydraulic brake system on the carriage house. (top)
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.
1. Figure 1 top shows the position versus time profile for the motion.
2. 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.
3. 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 installed).
4. Figure 2 bottom plots the torque versus velocity while the ch is coming up to speed.
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.
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).
`    processing: x101/010607/ch.pro`

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 was:
1. Start at rest at zenith angle za.
2. Move downhill for 90 seconds at a constant acceleration going from 0 to .04 degrees/second (slew speed).
3. Continue down for another 90 seconds moving at the negative acceleration in 2. The velocity will go from .04 deg/sec to 0.
4. Record the position, velocity, and magnitude of the motor torques each second during this motion.
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       =K
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 downhill.
• 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:

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:

• 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 fit to:
• 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.
`processing: x101/010621/doit.pro`

#### 21may02 dome hydraulic brake valve clogs while testing.  (top)

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.
processing: x101/agc/21may02valveclog.pro

#### 26jun02 measuring the hydraulic brake on the dome.  (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 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 switching.
processing: x101/020626/doit.pro

#### 02jul02 Checking the pointing with and without the brake on the dome.  (top)

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. The plots 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 be bypassed.
• 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 errors(green).

•     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).
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