Dome weight:Torques vs za


       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)

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

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.

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.


  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/
Values used in the calculations
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