IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 8

SIMULATION OF OSCILLATING ARM WIRE MONITOR MECHANICSDRIVEN BY A STEPPER MOTOR
R. Dölling†, Paul Scherrer Institut, Villigen, Switzerland
Abstract
The present oscillating arm wire monitors at HIPA operate with wire speeds of 0.75 m/s. Based on basic dynamic
simulations of mechanics and motor, we discuss possible
variants of this design using stepper motors in open loopcontrol. The results suggest that 4 m/s can be reached with
sufficient position resolution, when using a predefined step
sequence customized to the mechanics. This speed should
be sufficient to measure the full proton beam current in theinjection line.

INTRODUCTION
The majority of profile monitors presently operating in
the 0.87 MeV, 72 MeV and 590 MeV beam lines of HIPA
are wire monitors using an oscillating monitor arm (MA).
A fork at the MA holds the wire, foil, or finger, which ismoved transversely through the beam (Fig. 1) [1, 2]. TheMA is driven via a con-rod (CR) from a crank wheel (CW),
which again is driven via a gear (MG) connected to abrushed DC motor. A bellow at the MA axis of rotation separates the vacuum from the in-air mechanics. Since the bellow needs to bend only ±10°, its lifetime is practically unlimited at the given maximum wire speed of 0.75 m/s. The
wire position is determined by a potentiometer attached tothe MA, while the home position is indicated by a homeswitch (HS) actuated by a cam on the CW.

measure at full beam current of 10 mA, however, with limited dynamic range. Wire monitors with at least approximately four times higher speed could be an alternative. By
using a stepper motor instead of the DC motor, the potentiometer can be eliminated, and the control of the movement is simplified.
In the following we simulate the movement of variantsof the present mechanics driven by stepper motors and conclude to wire speed and error of wire position caused by
the motor characteristics.

MECHANICS
With the present monitor, the inertia of the 20:1 worm
gear and the DC motor is high. We look at three alternatives
with stepper motor and the same dimensions of CW-CRMA connection (Fig. 1, right):
1. Only motor replaced. Worm gear reduction 20:1.
The range of unidirectional CW movement is
CW = 151.2° to 568.8°. The long travel allows asofter acceleration. Wire speed 0.75 m/s unchanged.
2. Whole mechanics replaced by a moderately less-inertia variant (Fig. 2c). No potentiometer. Spur gear reduction 3:1. Range CW = 151.2° to 568.8°.
Wire speed 4 m/s.
3. Ditto, but gear reduction 1:1 (direct drive, Fig. 2a) andRange CW = 180° to 540°.

Figure 2: Lower-inertia setups (schematic).

Figure 1: Present MA wire monitor. Wire crosses beamaxis at CW = 90° and 270°. HS not shown. The monitor
needs little space in beam direction. Horizontal and vertical
MA are only 20 mm apart.
In the 0.87 MeV beam line and a few locations in the72 MeV beam line, the power density at full proton beam
current is too high to let the wire or foil survive at the givenspeed. Beam induced fluorescence monitors installed in 10of 32 monitor locations in the 0.87 MeV line allow to___________________________________________† doelling@protonmail.com, rudolf.doelling@psi.ch

03 Transverse Profile and Emittance Monitors

In cases 2, 3, the wire position is determined by counting
steps with respect to the HS switching positions. We assume a Baumer precision switch [3], pressed face on by theupper part of the MA. In order not to exceed the specification for the maximum approaching speed, the HS must bepositioned not too far from the axis of rotation of the MA.
Together with the play of the mechanism, this introduces awire position error at beam axis of the order of 100 m.
Alternatively, the wire position can be determined bycounting steps between the centres of the forward andbackward measured beam profiles (if the beam has notshifted in between).
A brake is not needed. The MA is kept in the parking
position against gravity by the CR, then in one line with theCW axis. Even the small holding torque of the currentless
motor is sufficient for this.
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12th Int. Beam Instrum. Conf.
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12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 8

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SIMULATION PROCEDURE
Moments of inertia are estimated for motor, worm or
spur MG or direct coupling, CW, CR and the complete MA.
The masses of both halves of the CR are assumed to beconcentrated in the connection points CW-CR and CRMA. The actual MA angle is calculated from the CW angle
analytically with the simplifying assumption that the connection point between CR and MA moves along the dottedline in Fig. 1 right.
The simulation is split into three runs, each done in time
steps of t = 0.2 s. In the first run, we define the ‘preset
trajectory’ of the whole system by presetting over time oneof the three ‘input characteristics’ a) rotor angular speedrot_pre, b) rotor angular acceleration rot_pre, c) used fractionof pullout-torque fracDpre. With the inertias, gear ratios, energy conservation (no losses are assumed in this run) and apreset dependency of pullout-torque on rotor angular speed
Dpullout_pre(rot), from each of the three ‘input characteristics’ a), b), c), the other two can be derived, together withthe rotor angular position rot_pre and the actual motor
torque Dpre over time and many other parameters.
In the second run, the time dependent angular position ofstator field and stator current phase stat_cur_pre is calculated
via the phase difference tooth_pre = stat_cur_pre - rot_pre,which results from the assumed ‘cosine potential’ condition fracDpre = sin(tooth_pre nteeth), with nteeth the number ofteeth at the rotor. Optionally, tooth_pre = 0 can be used instead in this step (‘tooth_pre ignored’). However, this lack ofadaptation will lead to significant deviations of the resulting trajectory from the ‘preset trajectory’, especially ifthese are not smooth as, e.g., the linear ramps often used.
Furthermore, the phase shift diff_induct_pre between stator
voltage stat_volt_pre and stator current stat_cur_pre is calculated
from the actual change of current, the inductance and resistance of stator coils and 50 m cable, and the available
DC voltage (of the actual needed polarity).
(In this way, also the actual motor current could be calculated, which results in a sinusoidal time dependence forhigh DC voltage or low rotor angular speed, and in triangular time dependence for low DC voltage or high rotor
angular speed. Integrating over a half period of same sign
results in a charge which depends very similar on angularrotor speed as the pullout-torque given by the manufacturer, however with significant lower DC voltages thanspecified. We did not use this to calculate Dpullout_pre(rot),
but use the dependency given by the manufacturer.)
With this, we get the angular position of stator voltage
stat_volt_pre, i.e., the ‘phase’ set by the motor driver. It ischanged not continuously, but, more realistic, only in fullmicrosteps. To reproduce realistic driver properties, we assume that each microstep needs a minimum time of 2 s.
Further we assume stat_volt_pre is updated to the actual microstep only in time intervals corresponding to the pulsewidth modulation (PWM) frequency fPWM = 40 kHz of thedriver.
Optionally, all microsteps corresponding to fullstep frequencies below, e.g., fstart,fs = 500 Hz can be suppressed.

This resembles the fullstep start frequency of linear ramps
used in many drivers.
The third run starts from the microstep sequence represented by stat_volt_pre. To this, a phase error is added, corresponding to the error of full-step positions due to manufacturing inaccuracies of the teeth of the rotor. The error is
statistically distributed to the teeth within boundaries
err_bound = ±0.025°. It is assumed that the error between
one fullstep and the next changes linearly over half a fullstep. An offset is added to all errors to bring the error of thefullstep of the starting position to zero. In general, it isstarted at rest, hence this position is reached exactly.
diff_induct is again calculated as above to get stat_cur. From
the difference tooth to the actual rot results the used fraction of pullout-torque fracD = sin(tooth nteeth), and with theactual pullout-torque kweak Dpullout(rot) we derive thetorque D. Optionally, with kweak different from 1, here 0.9,
we account for the fact that the pullout-torque may differ
from the specification.
The difference dtooth/dt of angular speeds of stator current stat_cur and rotor rot causes a viscous drag, leading toa torque Dloss = hloss dtooth/dt, which leads to a damping of
eventual oscillations of the rotor angular position in the‘cosine potential’ of the teeth (OICP). hloss = 0.003 Js/rad2
is roughly estimated from the damping of oscillations after
a single step starting from rest. Optionally, no damping canbe assumed. (Microsteps are assumed to instantaneously
change tooth, not slowed by inductance, which is taken into
account only summarily via diff_induct. In time steps, wherea microstep is executed, this leads to unrealistic large values of Dloss, depending on the length of time steps. Thiscancels out over a microstep and is not critical for the overall trajectory. For a decent plotting, depending parameters
are averaged over a microstep or fullstep. Only every
1000th time step is plotted.)
With the inertias, gear ratios, energy conservation andDpullout(rot), from the total torque, the change drot/dt is
calculated, and from this the positions, speeds and kinetic
energies of all the other parts and the torques between
them, i.e., the ‘resulting trajectory’ of the system. In thispart, an efficiency gear of the gear between motor and CW
can be considered, which is useful in the case of a worm
gear. (This option cannot be used together with Dloss, since
its momentarily unrealistic large values would not cancelout and would cause an unrealistic large overall gear loss.)
In the resulting trajectory, OICP are visible. This is more
prominent in the rotor angular speed and acceleration,
fracD, and other parameters. The excitation is caused bythe ‘disturbing conditions’ introduced above (printed inblue), but also by not well adapted ‘input characteristics’,
especially if in the second run, tooth_pre is ignored.
Further parameters of the trajectory are calculated, as position xwire, speed vwire and acceleration awire of the wire at
the height of the beam, the wire position increment dxwire
corresponding to a fullstep, the deviation xwire_dev2pre of wire
position against the preset trajectory, and also
xwire_dev2pre_corr, the same corrected for the predictable partof the effects of PWM and, in case, ignoring tooth_pre.

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12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 8Figure 3: Case 2: Spur gear reduction 3:1, 50 motor teeth, hloss = 0.003 Js/rad2, fstart,fs = 0 Hz, 6400 microsteps/revolution,
err_bound = ±0.025°, fPWM = 40 kHz, kweak = 0.9. Column A: a) Pullout-torque characteristic, only used part shown (black:preset trajectory, blue: resulting trajectory), b) total inertia seen by the motor, c) wire position change per fullstep depending on wire position. Column B, C, D: a) Rotor speed over time, b) used fraction of actual pullout-torque, c) phase in‘cosine potential’ (grey: deviation due to manufacturing inaccuracies, yellow: due to inductance), d) deviation of wire
position (red: to preset trajectory, grey: ditto, corrected, blue: compared to bottom of ‘cosine potential’), e) torques ofmotor and at CW due to MG (green) and MA (yellow). Due to the larger CW inertia (Fig. 2c versus 2b), the torque
DCW_byMG of CW to MG changes its sign distant from the beam axis (arrow), thereby minimizing the effect of gear play
to the measured profile shape at Column C, D. f) Preset step sequence (time difference between microsteps). At Column
C the few adapted microstep intervals at the limits of the ramps are visible. Columns B, C, D present simulations fordifferent input characteristics, ranging from ‘badly adapted’ to ‘well adapted’. The two variants at bottom left illustratethat it depends on details, how ‘badly adapted’ input characteristics interfere with the eigenfrequency of OICP. This isless critical with ‘well adapted’ smooth input characteristics.

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SIMULATION RESULTS

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
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IBIC2023, Saskatoon, CanadaJACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 1 8Figure 4: Case 3: Direct drive 1:1. Parameters as in Fig. 3 caption. Additional information compared to Fig. 3: Rotoracceleration, motor power, deviations of rotor phase by PWM (green) and against preset (red) and ditto corrected (grey),energies of parts of the mechanism, wire velocity and CW angular position, wire acceleration.
The example of case 2 (Fig. 3) and further simulations
imply that OICP are reduced by (in this order)• taking into account tooth_pre• providing a (preferentially smooth) input characteristic, not interfering with the eigenfrequency of OICP
• the presence of damping hloss >0 Js/rad2• microstepping at least at lower speeds• small other disturbing conditions• reduced motor current, if torque is abundant.
Thereby the accuracy of wire movement is improved, andthe used fraction of pullout-torque reduced.
With an adapted input characteristic and parameters assumed to be realistic, the simulations suggest that for cases
2 and 3 (Fig. 4), a wire speed of 4 m/s is well in reach.
Electronics able to provide a microstep sequence from alook-up table to the step-direction input of a commercial
driver is required for this. The predicted accuracy of wire
movement, defined as band width of xwire_dev2pre_corr, issomewhat better at gear ratio 3:1 (~50 m) than at 1:1(~150 m). With lower wire velocity the accuracy does notimprove. Here, a higher gear ratio can provide better accuracy. With 20:1 (case 1) ~3 m is predicted, which issmaller than the effect of the to be expected mechanicalplay of the mechanism.
An ultimate limit for maximum wire speed is given by
the available motor torque. However, OICP will lead to aloss of synchronisation already at somewhat lower speeds.
This is described by the simulation (Fig. 3 bottom left). For
quantitative predictions, at least, a more precise determination of hloss is required. Experimental tests are needed tocheck the predictions of the simulation. A simple test casecan be a motor loaded with an additional inertia.

OUTLOOK
A test stand is under preparation [4] to evaluate the performance of monitor setups as the ones discussed here. Furthermore, other aspects, as the lifetime of the bellows, thestiffness of the MA and wire vibrations will be studied.

ACKNOWLEDGEMENTS
Thanks to Oliver Dölling for preparing Fig. 2.

REFERENCES[1] L. Rezzonico, “Beam diagnostics at SIN”, in Proc. CYCLOTRONS’86, Tokyo, Japan, Oct. 1986, paper I5-05, pp. 457460.
[2] L. Rezzonico, M. Olivo, “Profile measurements of high intensity-low energy ion beams”, Rev. Sci. Instrum., vol. 67,
no. 3, pp. 1246-1248, 1996.
doi:10.1063/1.1146687[3] https://www.baumer.com[4] Stuart Warren, PSI, personal communication.

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