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A simple air-bearing pulley
NUCLEAR
INSTRUMENTS
A N D M E T H O D S 77
(I97O) 329-33o;
© NORTH-HOLLAND
PUBLISHING
CO.
A S I M P L E AIR-BEARING P U L L E Y
D. M. BINNIE and A. DUANE
Imperial College Department of Physics, London, England Received 8 September 1969 Experience with a simple pulley for floating-wire measurements to less than 1 part in 10a is described. There has recently been interest in the use of airsupported pulleys for floating wire measurements1'2). Such measurements rely on the theorem that a thin, flexible, weightless wire carrying a current i and under a tension T takes the same path through a static magnetic field as a charged particle of magnetic rigidity T/i. A standard weight provides a known vertical tension simply. For applications where the path is horizontal, the pulley used to change the direction usually causes a significant loss in accuracy. Several solutions to this problem have been proposed and applied; we offer a variant that appears to combine accuracy, ease of construction and simplicity of use. In connection with the Imperial College/Southampton University physics programme at Nimrod, we had to set up the momentum spectrometer sketched in fig. 1 to cover 0.7 to 4.0 GeV/c. A and B are at conjugate planes of the quadrupole doublet QtQ2 for the nominal momentum; between A and B there is magnification in the horizontal plane. Momenta of particles within a range of __+1% from the nominal were determined from the sum of the displacements of the particle in A and B relative to the spectrometer axis. The aims of the floating wire measurement were to calibrate the dipole field and to match the quadrupole and dipole fields. One end of the wire (0.12 mm Be Cu) was mounted in A and the other end passed over the pulley whose centre was 1 m from B.The tension was 100gm
weight. It was found necessary to shim all the magnets. Fig. 2 shows the pulley. It consisted essentially of a hollow brass axle into which were drilled two sets of eight holes spaced regularly round the axis, and an aluminium alloy disc of diameter 20 cm pressed onto a brass boss. A groove 0.12 mm deep was cut in the rim of the disc but in practice this proved unhelpful. (We observed the wire directly and so had no need to locate it precisely on the rim.) The axle and wheel were turned on a standard lathe. The gap between wheel and axle is not critical as a second wheel with internal diameter 0.15 mm greater than the axle was also satisfactory. The final accuracy of the pulley depends on the concentricity of the hole and the rim of the wheel. The pulley was based on a prototype bearing which consisted of the axle and the brass cylinder. Fig. 2b shows an enlarged view of part of the bearing and illustrates the principle behind the design. Air at an initial pressure Po flows through the small holes in the axle to the inner surface of the cylinder, where the average pressure is Pi, then in the narrow gap between axle and cylinder and finally in the relatively wide gap between cheek and cylinder where the average excess pressure is AP. The design aims were: 1. that Pi be approximately half of P0, with AP small, 2. that to provide lift reasonably efficiently, the impedance between top and bottom via path " a " should be large compared with the other impedances, 08 M OUADRUPOLES B
1'5M
DIPOLE
SCALE ~
?
,2
METERS
Fig. 1. The momentum spectrometer. Quadrupoles Q1 and Q2 have an aperture of 20 cm and are standard apart from the addition ot cylindrical shims at the ends of the poles. A and B represent conjugate planes of unit horizontal magnification for the central momentum. The trajectories sketched in illustrate this on a somewhat exaggerated scale. The floating wire is used to give an absolute momentum calibration of the dipole field as monitored by an NMR probe and also to set the quadrupole currents correctly at the central momentum. 329
330
D . M . B I N N I E AND A, D U A N E
3. that the two sets of holes operate to some extent independently, thereby providing a restoring couple if necessary, 4. that the small excess AP, sensitive to the gap between cheek and cylinder, should provide a centering force along the axle. F-,.- A 0-25ram 8" HOLES
~"IW
I/
~
I
~
i---I["~--
\IL -
0.25ram
IIHI
i,t
-
Sect. A-A RADIAL CLEARANCE
SCALE i0 i
~ i
i
UA
I5crn
Fig. 2a. A scale drawing of a cross section of the bearing. Most of the aluminium disc has been omitted.
The relative dimensions of the hole and the gap were estimated on the assumption of simple streamlined flow. However, this assumption would lead to a maximum velocity well into the supersonic region and is probably much too naive. This view is supported by a measurement of the total flow of gas (14 litres/min at atmospheric pressure), about a tenth of the predicted value. After care was taken to remove burrs, the pulley floated satisfactorily with Po = 1.4 kg/cm 2 though 2.0 kg/cm 2 was used during the floating wire measurements. It was balanced by adding pieces of sticky tape to the disc and tested by loading with approximately equal weights on both sides and noting the differential weight needed to produce clear movement in either direction at any orientation of the pulley. The differential was _+ 10 m g m at 100 gm weight tension. We met no significant problems when using the pulley in practice. The air pressure was not critical and the slight flow from the bearing did not disturb the measurements. We found no need to introduce any extra damping in the system; typically we waited about half a minute after displacing the pulley before reading the wire position. This experience contrasts with that reported in ref. 1). No investigation of damping in our system was made. At most of the momenta studied it sufficed to examine 5 trajectories spanning the 18 cm useful aperture of Q1 in the median plane. The envelope of these trajectories extrapolated to the focus was typically 0.7 m m at the nominal momentum, corresponding to an equivalent m o m e n t u m spread of _+2.5 x l0 -4, and the longitudinal focus position could be located to _+2 cm. A significant hysteresis was found in the quadrupole currents which was overcome by cycling the current around the final value. There appears to be no reason why, given sufficient care, absolute m o m e n t u m measurements should not be made to a few parts in 104 using the floating wire technique. At present we have no check on our accuracy in this respect, however, we hope to make some tests using known reaction thresholds. We thank Mr. R. F. Hobbs who constructed the pulley. The assistance of the Rutherford Laboratory engineering staff is also gratefully acknowledged.
Fig. 2b. An illustration of the essentials of the bearing. Any displacement from equilibrium of the cylinder with respect to the axle results in forces or couples tending to restore the equilibrium.
References 1) V. R. W. Edwards and A. E. Osborne, Rev. Sci. Instr. 38, no. 6 (1967) 806. 2) H. Bichsel, Proc. Intern. Syrup. Magnet technology (1965) p. 467.
INSTRUMENTS
A N D M E T H O D S 77
(I97O) 329-33o;
© NORTH-HOLLAND
PUBLISHING
CO.
A S I M P L E AIR-BEARING P U L L E Y
D. M. BINNIE and A. DUANE
Imperial College Department of Physics, London, England Received 8 September 1969 Experience with a simple pulley for floating-wire measurements to less than 1 part in 10a is described. There has recently been interest in the use of airsupported pulleys for floating wire measurements1'2). Such measurements rely on the theorem that a thin, flexible, weightless wire carrying a current i and under a tension T takes the same path through a static magnetic field as a charged particle of magnetic rigidity T/i. A standard weight provides a known vertical tension simply. For applications where the path is horizontal, the pulley used to change the direction usually causes a significant loss in accuracy. Several solutions to this problem have been proposed and applied; we offer a variant that appears to combine accuracy, ease of construction and simplicity of use. In connection with the Imperial College/Southampton University physics programme at Nimrod, we had to set up the momentum spectrometer sketched in fig. 1 to cover 0.7 to 4.0 GeV/c. A and B are at conjugate planes of the quadrupole doublet QtQ2 for the nominal momentum; between A and B there is magnification in the horizontal plane. Momenta of particles within a range of __+1% from the nominal were determined from the sum of the displacements of the particle in A and B relative to the spectrometer axis. The aims of the floating wire measurement were to calibrate the dipole field and to match the quadrupole and dipole fields. One end of the wire (0.12 mm Be Cu) was mounted in A and the other end passed over the pulley whose centre was 1 m from B.The tension was 100gm
weight. It was found necessary to shim all the magnets. Fig. 2 shows the pulley. It consisted essentially of a hollow brass axle into which were drilled two sets of eight holes spaced regularly round the axis, and an aluminium alloy disc of diameter 20 cm pressed onto a brass boss. A groove 0.12 mm deep was cut in the rim of the disc but in practice this proved unhelpful. (We observed the wire directly and so had no need to locate it precisely on the rim.) The axle and wheel were turned on a standard lathe. The gap between wheel and axle is not critical as a second wheel with internal diameter 0.15 mm greater than the axle was also satisfactory. The final accuracy of the pulley depends on the concentricity of the hole and the rim of the wheel. The pulley was based on a prototype bearing which consisted of the axle and the brass cylinder. Fig. 2b shows an enlarged view of part of the bearing and illustrates the principle behind the design. Air at an initial pressure Po flows through the small holes in the axle to the inner surface of the cylinder, where the average pressure is Pi, then in the narrow gap between axle and cylinder and finally in the relatively wide gap between cheek and cylinder where the average excess pressure is AP. The design aims were: 1. that Pi be approximately half of P0, with AP small, 2. that to provide lift reasonably efficiently, the impedance between top and bottom via path " a " should be large compared with the other impedances, 08 M OUADRUPOLES B
1'5M
DIPOLE
SCALE ~
?
,2
METERS
Fig. 1. The momentum spectrometer. Quadrupoles Q1 and Q2 have an aperture of 20 cm and are standard apart from the addition ot cylindrical shims at the ends of the poles. A and B represent conjugate planes of unit horizontal magnification for the central momentum. The trajectories sketched in illustrate this on a somewhat exaggerated scale. The floating wire is used to give an absolute momentum calibration of the dipole field as monitored by an NMR probe and also to set the quadrupole currents correctly at the central momentum. 329
330
D . M . B I N N I E AND A, D U A N E
3. that the two sets of holes operate to some extent independently, thereby providing a restoring couple if necessary, 4. that the small excess AP, sensitive to the gap between cheek and cylinder, should provide a centering force along the axle. F-,.- A 0-25ram 8" HOLES
~"IW
I/
~
I
~
i---I["~--
\IL -
0.25ram
IIHI
i,t
-
Sect. A-A RADIAL CLEARANCE
SCALE i0 i
~ i
i
UA
I5crn
Fig. 2a. A scale drawing of a cross section of the bearing. Most of the aluminium disc has been omitted.
The relative dimensions of the hole and the gap were estimated on the assumption of simple streamlined flow. However, this assumption would lead to a maximum velocity well into the supersonic region and is probably much too naive. This view is supported by a measurement of the total flow of gas (14 litres/min at atmospheric pressure), about a tenth of the predicted value. After care was taken to remove burrs, the pulley floated satisfactorily with Po = 1.4 kg/cm 2 though 2.0 kg/cm 2 was used during the floating wire measurements. It was balanced by adding pieces of sticky tape to the disc and tested by loading with approximately equal weights on both sides and noting the differential weight needed to produce clear movement in either direction at any orientation of the pulley. The differential was _+ 10 m g m at 100 gm weight tension. We met no significant problems when using the pulley in practice. The air pressure was not critical and the slight flow from the bearing did not disturb the measurements. We found no need to introduce any extra damping in the system; typically we waited about half a minute after displacing the pulley before reading the wire position. This experience contrasts with that reported in ref. 1). No investigation of damping in our system was made. At most of the momenta studied it sufficed to examine 5 trajectories spanning the 18 cm useful aperture of Q1 in the median plane. The envelope of these trajectories extrapolated to the focus was typically 0.7 m m at the nominal momentum, corresponding to an equivalent m o m e n t u m spread of _+2.5 x l0 -4, and the longitudinal focus position could be located to _+2 cm. A significant hysteresis was found in the quadrupole currents which was overcome by cycling the current around the final value. There appears to be no reason why, given sufficient care, absolute m o m e n t u m measurements should not be made to a few parts in 104 using the floating wire technique. At present we have no check on our accuracy in this respect, however, we hope to make some tests using known reaction thresholds. We thank Mr. R. F. Hobbs who constructed the pulley. The assistance of the Rutherford Laboratory engineering staff is also gratefully acknowledged.
Fig. 2b. An illustration of the essentials of the bearing. Any displacement from equilibrium of the cylinder with respect to the axle results in forces or couples tending to restore the equilibrium.
References 1) V. R. W. Edwards and A. E. Osborne, Rev. Sci. Instr. 38, no. 6 (1967) 806. 2) H. Bichsel, Proc. Intern. Syrup. Magnet technology (1965) p. 467.