- Email: [email protected]
A friction drive system for accurate positioning
A friction drive system for accurate positioning J. Bendtsen*
A transmission system for positioning a conventional moving table has been constructed. The gearbox which has been inserted between the lead screw and the driving stepping motor is o f the friction type. The resolution o f the system has been measured to be less than 0.01 Ilm
Keywords. friction drives, position control, spectroscopy The system to be described was constructed to be used as the drive system in a scanning Michelson interferometertype spectrometer. As the position of the moving mirror in the interferometer is measured by means of a He-Ne laser interferometer, the purpose of the drive system is to perform a smooth, well defined movement of the mirror. The mirror is attached to the moving part of a standard machine table made by W. Schneeberger A.G., Roggwil, Switzerland. The mirror is connected to the table through three piezo ceramics clamped to the table. The final positioning of the mirror is performed by driving the piezo ceramics. The requirement originally put on the mechanical syste[n was that the displacement of the table performed by one step of the motor be short compared to the wavelength of the He-Ne laser light. The table is equipped with a lead screw and a nut of the satellite-roll type. One revolution of the lead screw results in 4 mm displacement. The lead screw is driven through a friction gearbox (Fig 1) with a total ratio of 1 : 1249. The gearbox is driven by a stepping motor having 500 steps per revolution. Thus one step performed by the motor results in a displacement of the table of 6.4 nm. This displacement is 100 times less than the wavelength of the He-Ne laser light used in the position measuring system. A conventional gearbox might have been used to obtain the desired reduction between the lead screw and the motor, but a tooth-wheel gearbox has several shortcomings when used for high precision work. It may give rise to vibrations disturbing the measurement with the laser interferometer, and it has a high degree of backlash. Therefore a smooth and backlash-free system had to be constructed.
The friction gearbox The principle of operation has been obtained from a description of a gearbox made by Philips1 . A stepping motor is used to drive a worm gear. The shaft of the drivewheel is springloaded onto a hardened steel wheel. The force causing this wheel to rotate with the shaft is due to friction between the shaft material and the wheel material. In the gearbox to be described this principle has been fully employed. The stepping motor is connected to the input shaft drives the first gearwheel through a spring-loaded input shaft drives the first gearbox through a spring-loaded idler roller. The connection between the components is performed as shown in Fig 2. The wheel and the shaft do not touch each other, but the idler roller is forced into the *Chemical Institute, Aarhus University, DK-8000 Aarhus C, Denmark
PRECISION ENGINEER ING
Fig 1 The gearbox o f the friction drive system gap by a spring. This system is repeated three times. The diameters of the shafts and the drive wheels are 13 mm and 140 ram, respectively, giving rise to a total ratio between the input shaft and the output shaft of 1249. In order to get a smooth movement, the wheels, the idler rollers, and the shafts were hardened, ground to a high degree of diameter accuracy and finally polished. The amount of energy per unit time which can be transmitted through the gearbox is dependent on the force exerted on the idler roller and the coefficient of friction of the materials used. In the present case all components are made of hardened steel. The coefficient of friction for clean steel (unspecified) on steel is 0.58 at 20 °C2. The gearbox is going to work in vacuum, and this is known to enhance the coefficient of friction considerably. The force constant of the springs used is 1500 N m -1 . As each spring is compressed approximately 10 mm the force exerted on the idler roller is about 15 N. The position of the idler roller relative to the wheel and the shaft has been chosen so that the resultant forces keeping the idler in contact w i t h the wheel and the shaft are approximately equal to the force exerted by the springs on the idler roller. By measuring the force necessary to prevent drive wheel rotation while the input shaft was still rotating, the moment of rotation with respect to the output shaft was derived. Equating this moment to the moment calculated with respect to the same axis of rotation at the point of contact between the idler and the drivewheel, the coefficient of friction was determined to be 0.62 -+ 0.05 in agreement with the value given in Ref. 2.
Results Measurements using a Millitron from "FeinpriJf" Feinmessund Pr(Jfger~te GmbH, G6ttingen, F RG, have been performed. With this instrument displacements less than 10 nm are
0141--6359/82/020071--02 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
71
Bendtsen - Friction drive system for accurate positioning Housing
/
/
/
Spring
Idler
Steering plate
J Housing
Steering \,
J
b a detectable. By clamping the gauge to one part of the table every step performed by the motor is detectable on the instrument. The position of the table was measured for each 100 steps over an interval of 40/Jm. The positions were fitted to the number of steps by means of a least squares procedure. From this calculation the average displacement per stepwas determined to be 5.625(2) nm for the clockwise rotation of the shaft (see Fi 9 2(a)) and 6.197(2) nm for the counter clockwise rotation of the shaft. The difference between the two displacements may be explained by the fact that with clockwise'rotation the idler is to some extent thrown out of contact by the small shock from each step of the motor. This effect causes a tiny slip to occur between the idler and the shaft, redacing the effective displacement. When altering the direction of rotation of the motor, about five steps have to be performed before the instrument indicates an opposite translation. Thus the backlash of the system is of the order of 30 nm. One would expect the main part of this backlash to originate from the nut and the lead screw. To get rid of the backlash, the lead screw might be replaced by a traction bar driven by the output shaft of the gearbox as shown in Ref. 1.
72
Fig 2(a) Sideview of the idler roller system. The idler is mounted in the house through ball bearings. The steering plates prevent the idler "walking" out. (b) Front view of the idler roller system
Conclusion The above description has been given in order to demonstrate that ultra-high precision positioning may be performed using ordinary mechanics. The system described is not ideal in that respect, but some modifications could probably make it so.
Acknowledgement This work was performed in cooperation with the technicians V. Langer and P. Strand. The original design was developed through discussions with V. Langer. The final drawings and the production of the gearbox were performed by P. Strand. Their interest in the work and their ability to perform it is outstanding and much appreciated.
References 1. Machine Design, 21, February, 37 2. Handbook of Chemistry and Physics. The Chemical Rubber Company, 57th Edition, p. F 20
A P R I L 1982 V O L 4
NO 2
A transmission system for positioning a conventional moving table has been constructed. The gearbox which has been inserted between the lead screw and the driving stepping motor is o f the friction type. The resolution o f the system has been measured to be less than 0.01 Ilm
Keywords. friction drives, position control, spectroscopy The system to be described was constructed to be used as the drive system in a scanning Michelson interferometertype spectrometer. As the position of the moving mirror in the interferometer is measured by means of a He-Ne laser interferometer, the purpose of the drive system is to perform a smooth, well defined movement of the mirror. The mirror is attached to the moving part of a standard machine table made by W. Schneeberger A.G., Roggwil, Switzerland. The mirror is connected to the table through three piezo ceramics clamped to the table. The final positioning of the mirror is performed by driving the piezo ceramics. The requirement originally put on the mechanical syste[n was that the displacement of the table performed by one step of the motor be short compared to the wavelength of the He-Ne laser light. The table is equipped with a lead screw and a nut of the satellite-roll type. One revolution of the lead screw results in 4 mm displacement. The lead screw is driven through a friction gearbox (Fig 1) with a total ratio of 1 : 1249. The gearbox is driven by a stepping motor having 500 steps per revolution. Thus one step performed by the motor results in a displacement of the table of 6.4 nm. This displacement is 100 times less than the wavelength of the He-Ne laser light used in the position measuring system. A conventional gearbox might have been used to obtain the desired reduction between the lead screw and the motor, but a tooth-wheel gearbox has several shortcomings when used for high precision work. It may give rise to vibrations disturbing the measurement with the laser interferometer, and it has a high degree of backlash. Therefore a smooth and backlash-free system had to be constructed.
The friction gearbox The principle of operation has been obtained from a description of a gearbox made by Philips1 . A stepping motor is used to drive a worm gear. The shaft of the drivewheel is springloaded onto a hardened steel wheel. The force causing this wheel to rotate with the shaft is due to friction between the shaft material and the wheel material. In the gearbox to be described this principle has been fully employed. The stepping motor is connected to the input shaft drives the first gearwheel through a spring-loaded input shaft drives the first gearbox through a spring-loaded idler roller. The connection between the components is performed as shown in Fig 2. The wheel and the shaft do not touch each other, but the idler roller is forced into the *Chemical Institute, Aarhus University, DK-8000 Aarhus C, Denmark
PRECISION ENGINEER ING
Fig 1 The gearbox o f the friction drive system gap by a spring. This system is repeated three times. The diameters of the shafts and the drive wheels are 13 mm and 140 ram, respectively, giving rise to a total ratio between the input shaft and the output shaft of 1249. In order to get a smooth movement, the wheels, the idler rollers, and the shafts were hardened, ground to a high degree of diameter accuracy and finally polished. The amount of energy per unit time which can be transmitted through the gearbox is dependent on the force exerted on the idler roller and the coefficient of friction of the materials used. In the present case all components are made of hardened steel. The coefficient of friction for clean steel (unspecified) on steel is 0.58 at 20 °C2. The gearbox is going to work in vacuum, and this is known to enhance the coefficient of friction considerably. The force constant of the springs used is 1500 N m -1 . As each spring is compressed approximately 10 mm the force exerted on the idler roller is about 15 N. The position of the idler roller relative to the wheel and the shaft has been chosen so that the resultant forces keeping the idler in contact w i t h the wheel and the shaft are approximately equal to the force exerted by the springs on the idler roller. By measuring the force necessary to prevent drive wheel rotation while the input shaft was still rotating, the moment of rotation with respect to the output shaft was derived. Equating this moment to the moment calculated with respect to the same axis of rotation at the point of contact between the idler and the drivewheel, the coefficient of friction was determined to be 0.62 -+ 0.05 in agreement with the value given in Ref. 2.
Results Measurements using a Millitron from "FeinpriJf" Feinmessund Pr(Jfger~te GmbH, G6ttingen, F RG, have been performed. With this instrument displacements less than 10 nm are
0141--6359/82/020071--02 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
71
Bendtsen - Friction drive system for accurate positioning Housing
/
/
/
Spring
Idler
Steering plate
J Housing
Steering \,
J
b a detectable. By clamping the gauge to one part of the table every step performed by the motor is detectable on the instrument. The position of the table was measured for each 100 steps over an interval of 40/Jm. The positions were fitted to the number of steps by means of a least squares procedure. From this calculation the average displacement per stepwas determined to be 5.625(2) nm for the clockwise rotation of the shaft (see Fi 9 2(a)) and 6.197(2) nm for the counter clockwise rotation of the shaft. The difference between the two displacements may be explained by the fact that with clockwise'rotation the idler is to some extent thrown out of contact by the small shock from each step of the motor. This effect causes a tiny slip to occur between the idler and the shaft, redacing the effective displacement. When altering the direction of rotation of the motor, about five steps have to be performed before the instrument indicates an opposite translation. Thus the backlash of the system is of the order of 30 nm. One would expect the main part of this backlash to originate from the nut and the lead screw. To get rid of the backlash, the lead screw might be replaced by a traction bar driven by the output shaft of the gearbox as shown in Ref. 1.
72
Fig 2(a) Sideview of the idler roller system. The idler is mounted in the house through ball bearings. The steering plates prevent the idler "walking" out. (b) Front view of the idler roller system
Conclusion The above description has been given in order to demonstrate that ultra-high precision positioning may be performed using ordinary mechanics. The system described is not ideal in that respect, but some modifications could probably make it so.
Acknowledgement This work was performed in cooperation with the technicians V. Langer and P. Strand. The original design was developed through discussions with V. Langer. The final drawings and the production of the gearbox were performed by P. Strand. Their interest in the work and their ability to perform it is outstanding and much appreciated.
References 1. Machine Design, 21, February, 37 2. Handbook of Chemistry and Physics. The Chemical Rubber Company, 57th Edition, p. F 20
A P R I L 1982 V O L 4
NO 2