Fit Dome Torque vs za (after hydraulic brake)
jun,2013
Terminology
Forces that the motors must
overcome
Fitting the torques
Monthly fits of the torques
Yearly summary of the torque fits
Summary
The hydraulic brake for the dome was
installed 26jun02 (more info).
It guaranteed that an amplifier failure would not allow the dome to
slide down hill. This brake added a velocity ^2 force when the
dome goes downhill. Moving uphill, there should be no added force
required to move.
Back in 2002, the dome motor torques (prior to
the hydraulic brake) were fit and used to the weigh the dome (more
info). This page fits the motor torques after the hydraulic
brake was installed.
Terminology:
 Wgr : gregrorian weight. This includes everything that
moves with the dome (motors, pigs, etc..)
 zaE,zaCm : Zenith angle. (more
info)
 zaE: encoder zenith angle. This is the zenith angle reported
by the encoders.
 It is 1.1113 degrees uphill from the dome centerline
position
 zaCM: the zenith angle of the dome center of mass. This is
.80 degrees downhill from the dome centerline.
 So zaCM= zaE  1.913 degrees. This is zenith
angle that is needed when fitting for the sin(za) term
of the force (gravity).
 Sign of motor force. Let a positive force be uphill.
Forces that motors must overcome:
The forces acting on the dome (after the
hydraulic brake installation) are:
 Wgr * sin(zaCm) . This is the gravitational force.
 zaCm is the zenith angle of the dome center of mass.
 C1 .. i have called this C1 in the fit.
 This force always points downhill (negative).
 C2*vel: This is caused by friction.
 vel will be measured in deg/sec
 C3*accel: This is the force needed to accelerate the dome
 It is measured in deg/sec^2
 C4*vel^2: The resistance provided by hydraulic brake when
moving down hill.
 This term is not used since we limit the motion to uphill
(see below).
The vertex system measures the encoder position
and motor torques once a second:
 The velocity and acceleration are computed by differencing the
position and velocity.
 The hydraulic brake is designed so that the motors must push
downhill above a certain velocity.
 This velocity differs for the 8 motors (because of
torque biasing of pairs of motors).
 The zenith where this occurs differs for different motors.
 The torque measurements return the absolute value of the motor
torque.
 I've limited the fit data set to za > 5deg, vel > .001
deg/sec because:
 we only have the absolute value of the torques
 moving downhill, different motors switch from holding back
the dome, to pushing downhill.
 staying above .001 degs/sec will hopefully stay away from
stiction (static friction).
Fitting the torques:
The fits to the torque were limited to uphill
motion (vel > .001 deg/sec) and za > 5 degrees za.
The fit used was:
 motorTorqueFitFtLbs= C0 +
C1*sin(zaCm) + C2*vel + C3*acceleration
 C0: offset for fit
 C1: The motor torque that is needed for the dome weight
 C2: The motor torque to overcome friction
 C3: the motor torque to handle the acceleration.
Potential problems with
the fit:
 positions and torques are only measured once a second
 The maximum velocity is .04 deg/sec
 The maximum acceleration is .025 deg/sec^2
 With only 1 sec position measurements:
 the velocity and accel are computed by differencing the
positions and then interpolating back to the time of the
torque measurement.
 This will cause errors in fitting the friction and
acceleration portions of the fit.
 The motor torques are returned by the motor amplifier as
a voltage proportional to the torques.
 Jon hagen calibrated a number of these devices and found a
nonlinear response:
 ftLbs=13.3*(A/Dcnts/2047 * 10) ^ .73
 I've used this for the measured ft lbs.
 This was measured back in 200? . It may have changed when
amplifiers were replaced.
 I've tried to avoid sticktion (static friction) grabbing and
then letting loose at low velocities by forcing the vel <
.001 deg/sec
 This may not have been enough given the errors in the
velocity computation.
Monthly fits of the torques
The data for each month was fit. 8 separate
fits were done (one for each motor).
The fit used was :
motorTorqueFitFtLbs=
C0 + C1*sin(zaCm) + C2*vel + C3*acceleration
Each monthly fit plots contain:
 Page 1:
 The x axis has the 8 motors 0.. 7 are
motors:m11,m12,m21,m22,m31,m32,m41,m42
 The red * are the Uphill motors (of each pair)
 The blue * are the downhill motors (of each pair)
 TopFrame: C0: constant term in the fit
 2ndFrame: C1: The dome weight in foot lbs
 See below for converting torque to weight.
 3rdFrame: C2 : The ft lbs needed to overcome friction
(moving uphill).
 The velocity units used are deg/sec (max vel = .041
deg/sec).
 bottomFrame;C3;The ft lbs need for the dome acceleration.
 The acceleration units are deg/sec^2. Max Accel= .025
deg/sec^2
 Page 2:
 Top: The fit errors:
 This is the (data fit) rms for each motor.
 2ndFrame: The fractional error for each coef by motor.
 The x axis is the 4 coef used for the fitting: c0,c1,c2,c3
 The fit values for each motor have been over plotted
(in color).
 This is returned by the fitting routine. Since i didn't
enter any measurement errors, it may not be too meaningful.
 I also divided by the value of the coef. to give a
fractional error.
 This caused coefs close to 0 to blow up the fractional
error.
 Bottom:The 4 fit coef for the 8 motors are printed.
Monthly Notes:
 2013:
 jun13: trouble with dome jun13. motor 22 replaced. (more
info)
 2003:
 july03 was after the hydraulic brake and before alfa was
installed.
processing:x101/agc/mottq/dome/dofittorq.pro
Yearly summary of fits to dome motor
torques
A yearly summary is plotted comparing values from
each month.
The plots containPage 1: The fit coefs plots
 Page 1: The fit coefs for each month over plotted in color,.
 The x axis is the coef: c0,c1,c2,c3
 Top Frame: C0 constant term of fit
 2ndFrame: C1 sin(za) coef. dome weight.
 3rdFrame: C2: frictional coef.
 bottomFrame: C3 acceleration coef.
 Page 2:
 TopFrame: Fit rms for each motor by month:
 rms of (yfit  ydata) for each motor and month.
 The x axis 0..8 are the 8 motors
m11,m12,m21,m22,m31,m32,m41,m42
 Each color is a different month.
 2ndFrame: fractional error in each fit coef.
 the x axis 0..3 are the 4 fit coef.
 Each color is a different motor.
 Each month is over plotted.
 These errors are returned by the fit.
 BottomFrame: Dome weight from the fits:
 For each month, the C1 coef for each motor is added and
then foot lbs is converted to lbs (see below).
Yearly summary dome
torque fits
year

plots

Notes

2013

.ps .pdf


2012

.ps .pdf


Yearly notes:
processing: x101/agc/mottq/dome/yearlyplotfits.pro
Summary:
 What the fits can be used for:
 The measured dome weight
 20122013 had dome weights of for 2012, 2013 of 228232
kips
 the fitted value is stable to within a few percent so we
can probably use it for relative changes.
 comparing the jul03 motor weight to the feb03 weight
from maldonado's measurement, the motor weight could
differ by 5%.
 Changes in the fit coef's may show problems in the system.
 But probably only if the problems are persistent for the
month.
 Comparing a daily fit to the monthly average may help
troubleshoot problems.
 Some of the variations in the fit values may be a function
of the telescope motion that was done that month.
 Eg.a month with lots of galfacts slewing 219 degs at
1/2 slew rate may give different results than a month of
on/off position switching.
 friction:
 The C2 coef for friction is between 1000 1500 ft lbs.
 at .01 deg/sec this is about 1200*.01 * 8=96 footlbs.
 The coef for dome weight is 4*80 + 4*55=540 ftlbs
 So friction is about
96/540= 18% at .01 deg/sec.
 Acceleration :C3
 the sum of C3 for the 8 motors
ranges from 550 to 900 ftlbs
 as and example, used .0125 deg/sec^2 (1/2 the max
acceleration)
 .0125*725=9 ftlbs. This is 10% of what is needed to hold
the dome against gravity at za=10 deg.
 Comparing the dome weights

date

weight (kips)
1kip=1000 lbs

Notes

jun02

208

motor torques
before hydraulic brake

jun02


hydraulic
brake installed 
feb03

215.5

maldonado using load
cells, and jacks.

july2003

225

motor torques

apr04


alfa
installed in dome 
jan12dec12

228233

motor torques

janjun13

230232

motor torques

To convert from motor lbs to lbs of force:
 gear ratio of transmission: 190.07
 radius of pinion: .4375 feet
 Lbs=FtLbs*190.07/.4375
 To get the total weight you need to convert and then sum the
C1 coef from all 8 motors.
home_~phil