# Dome weight:Torques vs za

#### july,2002

The vertex system provides a voltage from each motor amplifier that is proportional to the absolute value of the torque. On 19jun02 the dome was moved from 2 degrees za to 19.5 degrees za and back down to 2 degrees za at .02 degrees/second (half slew rate). This motion was then repeated with a velocity of .01 degrees/second. The torques were measured once per second and recorded.
The plots show the torques by motor during the motion (.ps)  (.pdf)
• The motors are numbered 11,12,21,21,31,32,41,42 going uphill to downhill.
• The adjacent pairs (11,12), (21,22) etc. have backlash compensation at low zenith angle.
• The torque units are foot lbs and are computed as:ftlbs=13.3*(dToACnts*10./2047)^.73

This  is a fit to the torque versus voltage done by jon hagen 05jul02 using his torque wrench.
Note: this measurement was done before the hydraulic brake was installed on the dome.

#### Fig 1 torques versus time

The top plot shows the torques for each of the eight motors for za 2->19 (left half) and za 19->2 (right half) going at .02 deg/sec. The data was sampled once a second. The plot has been smoothed and decimated by 7. The purple line is  za/2. There is a large step in torque when it changes directions at 19.5 from going up to going down.
When you go up, the motors must push the weight of the dome plus friction. When coming downhill, the motors must hold the weight of the dome - the frictional force (the frictional force helps the motors rather than opposing them).  The step at 20 degrees za should be twice the frictional force. Since we move at constant velocity, the non frictional force should be the same for moving uphill or downhill (sin(za)*Weight of the dome).
The middle picture is a blowup of the torques around 19.5 deg za where it changed direction. The data is plotted with 1 second resolution. The  purple line is a blowup of the za. The dome sat at 19.5 degrees for about 20 seconds before it started down.
The bottom plot is the sum of the torques for the  8 motors during the turnaround. At 16.350 you can see the torques wandering up while the dome remains stationary. This can happen if there is a small dc offset in the voltage sent to the amplifiers. The integrator will then accumulate this value. A simplified model of the torques needed are:
ForceUp= Fgrav + Ffriction
ForceDown=Fgrav-Ffriction

Half the difference should be the frictional force:
friction=(166-121)/2=22  or 22/166=13% of torque moving upward at 20 degrees.

#### Fig 2 torques versus za.

The upper plot has has the torques versus za moving uphill while the middle plot has the torques moving downhill. The uphill motors (11,21,31,41) have a steeper slope than the downhill motors. When moving downhill they go to zero torque around a za of 7 degrees and then the torque increases. Below 7 degrees the torque is changing direction and the motors are pushing in the direction of motion (while moving downhill).
The bottom plot is the sum of the torques for the 8 motors. Black is moving uphill and red is moving downhill. The torques below 7 za for the uphill motors have had their sign flipped. When moving downhill below za=4.5, the motors must push the dome to keep it moving downhill. The frictional force becomes larger than the gravitational force. The sine of 4.5 is 8%. If the dome weighs 200000 lbs then the frictional force at 4.5 degrees is 16000 lbs.

#### Fig 3 summing uphill and downhill.. weighing the dome.

•  The top plot is the average of the uphill and downhill motion for each motor. If the frictional force reverses going uphill, downhill, then the average should be the weight of the dome times the sine of the zenith angle. The .02 deg/sec and .01 deg/sec runs are over plotted and they lay on top of each other. The average has done a good job of removing any velocity dependent frictional forces.
• The force needed to push the dome uphill = DomeWeight*sin(za) where the za in the center of mass za.
• The encoders report the za of the optic axis.
• the dome  centerline za is  1.1113 degrees downhill from the optic axis za.
• The center of mass of the dome is .7827 degrees downhill from the dome centerline za.
• So the center of mass za is 1.904 degrees downhill from the optic axis za (see reference)
• The center plot divides the mean by sin(zaCenterOfMass).  The motors break into two groups: the uphill motor of each pair, and the downhill motor of each pair.
• The bottom plot sums the average of the 8 motors, divides by 1/sin(zaCenterOfMass) and then multplies by the gear ratio and pinion radius to get lbs.  This should be a constant line that is the weight of the dome. The .02 deg/sec and .01 deg/sec runs are over plotted and agree. This means that we have corrected the velocity dependant frictional forced correctly. There is still a za dependence below 13 degrees za. This may be from the dome Center of mass correction.

#### Fig 4 differencing the uphill and downhill motions.. looking at the friction.

The top plot is a blowup showing the torques versus za. You can see were the torques cross zero. The discontinuities are from dc offsets in the readouts (below za=7 moving down, i negated the torques for the uphill motor pairs).
The center plot is  the difference (torquesUphill-torquesdownhill)/2. The uphill motors go to zero near 7 degrees and then increase.
The bottom plot is the sum of the 8 motors. This should be the frictional force. The black plot is .02 deg/sec and the red plot is .01 deg/sec. There is a small difference between the two velocities so there may be a small velocity dependent frictional force. Above 10 degrees there is a linear or sin(za) dependence in the friction. There is a transition from 10 to 5 degrees below which it levels out.

#### Summary:

1. At high za it take 27% less torque to move downhill than uphill. This implies that friction is 13% of the force needed to move up at high za.
2. When the dome is sitting still, it looks like the PI integrator is not turned off and the torques build up from dc offsets.
3. The pairs of motors (uphill, downhill) have different torque profiles. It is probably the bias compensation to prevent gear backlash that causes this.
4. There is no velocity dependence after summing the uphill and downhill motions.
5. Dividing the mean of uphill,downhill by sin(za) does not give a flat line for the dome weight. Whatever frictional force has not been removed, it is not velocity dependent since the .01,.02 deg/sec runs overlay each other.
6. The weight of the dome at high za is about 208000 lbs.
7. The difference of the uphill,downhill motions give a frictional force that has a linear dependence with za above 10 degrees, a transition, and then a flat level below za=5.
8. The bias and gravity compensation needs to be looked into some more. There is also probably a torque dependent frictional term for the gear box that would differ for the uphill, downhill motions. I've also assumed that the wind load is not a function of za nor direction.
processing: x101/020621/doitgr.pro
 gear ratio 190.07 pinion pitch diameter .2667 meters convert torq values to ftlbs .4031*e-2 optic axis offset uphill 1.1113 +.7827degrees max continuous motor torque 35. ftlbs
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