- Email: [email protected]
The tribology of precision machines
The tribology of precision machines w.. B A I L E Y *
The Cranfield Unit for Precision Engineering (CUPE) was established in April 1968, at the Cranfield Institute of Technology near Bedford to provide a service to industry in precision engineering. Initially set up with a Ministry of Technology grant, the Unit became entirely self-supporting in its third year and now has a turnover of approximately £270000 per annum. The work of the Unit includes the design and construction of machine tools and instruments of the highest precision together with their controls. Work is currently in hand for major British and European companies and British Observatories.
In the design of a precise machine there are three major principles which must be applied. Abbe's Principle of Collinearity has only indirect influence on the topic of this article, but both of the other two have immediate impact on the design of bearings.
1 The Principle of Kinematic Design The principle demonstrates the minimum number of constraints necessary to define any particular position or motion. This is extended to suggest that no more than the minimum of constraints should be used to control the motion of any moving member.
2 The Principle ofA veraging This principle says that the position defined by some average of several points on a surface has less variance than that of the individual points. Thus if the standard deviation of the position of one contact is o, the standard deviation of the average of n contacts, on = o/x/n-. Instruments, in the past, have tended to be designed according to the Principle of Kinematic Design utilising the minimum number of constraints and thus minimising the stress within the instrument, but requiring the highest accuracy of each constraint. On the other hand, Precision Machines have required the load bearing capacity of multiple contacts and the required accuracy has then been more economically achieved by averaging many contacts over less accurate surfaces. It is only as a result of the historically separate growth of the two crafts that the two schools have arisen, as things apart, to represent the extremes between which the precision engineer can select the best solution to any particular design problem. In making a bearing, either rotary or linear, the designer has several criteria to satisfy including: 1 2 3 4 5
Accuracy of motion required Stiffness across moving surfaces Friction along the moving surfaces Load bearing capacity Affect of bearing design on the remainder of the machine and system
* Cranfield Unit for Precision Engineering, Cranfiel,d Institute Technology, Cranfield, Bedford.
of
6 Temperature considerations 7 Cost of fabrication 8 Life of bearing It will be seen that most of the factors interact with each other in some way but for most people, and particularly for CUPE engineers, considerations of cost must always be paramount. However the cost of fabrication is only a part of that cost and the cost of design time for 'specials' must be considered. The ability to maintain the specified accuracy over long periods of time, possibly in difficult environments, without costly reworking must also weigh heavily in the selection of the optimum bearing. Since the interaction of the above factors to achieve the above criterion is complex and highly specific to a particular problem, it is probably not profitable to consider them in a general way. Each family of bearings is therefore considered separately, ie rolling element, hydrostatic etc, with examples taken from CUPE's experience.
ROLLING BEARINGS
If the roughness of the surface of the guideways is r 1/am, since this is the mean displacement of the surface it c a n approximately be said that the standard deviation of the surface from the average level defined is o 1 = ~2rl, similarly f o r the other surface o 2 = ~2r2 so that the standard deviation of the gap between the surfaces is 3 °12 = 2 - ~ 1 Some 95% of the gaps between the two surfaces will lie within plus or minus two standard deviations of the average gap. If, for the moment, all the balls or rollers are considered to be identical and one of them is caught between two high spots, then it must be compressed by 4o12 to ensure that 95% of the rolling elements are in contact. If, in addition, there is a difference e between the minimum diameter of the smallest element and the maximum diameter of the largest element then the maximum compression
TRIBOLOGY international April 1975 73
required of a single element to ensure the contact of 95% of the balls or rollers is ~2rnax=e+4Ol2=e+6 r@{ The roughness of balls or rollers is usually very much less than that of the bearing surfaces and can be ignored. If typical values are taken for surface roughness, out of roundness and size tolerance of 9 mm diameter steel balls on a linear guideway it is found that a loading of about a third the normal maximum dynamic loading is required to get all the balls into contact. This confirms one's normal experience that on well designed machines the straightness of motion is often better when the machine is fully loaded. This is only true, of course, if the structure is adequate for the loads imposed, which is part of being 'well designed'. Bearing in mind the loadings necessary to achieve good averaging and precision of motion it will be realised that for instrument applications balls rather than rollers are usually the preferred choice. An additional benefit is the greater freedom from damage caused by dirt enjoyed by balls, which tend to sweep the dirt around them whereas rollers trap particles between themselves and the guideway surface. Where the size of a guideway precludes the use of ground ways it will usually be necessary to scrape the ways to achieve a high precision and in this case, rollers must be used to span the hollows between high spots since only the high spots define the surface of the guideway. It will be appreciated that the previous discussion is an ideal design solution. This has been employed in the design of a High Speed Automatic Plate Measuring machine in conjunction with the Cambridge Institute of Astronomy, see Fig 1, where the very good performance that can be achieved provides the most economical solution for an X-Y table o f travel 380 mm X 350 mm. The design is pseudo-kinematic
Fig 1
74
High speed automatic plate measuring machine
TRIBOLOGY international April 1975
Fig 2 Guideways of this large measuring machine use 50 mm balls in V guMeways directly scraped in cast iron in that only one double V way is employed on each guideway with a V and fiat on the other side. Where a truly kinematic design would employ only two balls between the double V and one between the V and fiat, in this design at least 33 balls are in contact on each side so that the permissible error in the surface of the way can be five times greater than for a kinematic design and the cost of manufacture accordingly reduced. Whilst the above example represents the optimunr use of rolling elenrents it is not always possible to achieve this and marly examples of high precision can be found in which only some of the balls or rollers are in contact at the high spots of the surface. This represents a type transitional between the kinematic and elastically averaged way, in which there is some improvement in accuracy of motion compared with a kinematic design but, because of the paucity o f contact, the guideway must be constructed more accurately than the optimum design for a given performance. An interesting example of this latter type of design is the long guideway of a large measuring nrachine seen under construction in Fig 2, with a travel of 4 m along a horizontal axis constructed for the QAD FVE/MOD at Woolwich. The loading is too heavy for balls and hollow crossed rollers of 50 mnr diameter were chosen to run in V guideways directly scraped in cast iron. It was not possible to load all the rollers into contact, indeed some of the load must be taken by spring loaded bearings running on a separate, lower accuracy, track, because of the reduced area of con tact on scraped surfaces and the reduced loading necessary on unloaded surfaces to prevent 'Brinelling'. A structure as large as this must be expected to elastically deform as the carriage moves and the guideway is therefore scraped to a W-form, not straight, but computed to ensure the correct linear motion of the carriage despite the changing shape of the structure as the carriage rolls over it. ( Ref 3). The total error of motion of this carriage weighing 14 tons over 4 metres travel is less than 3 arc seconds in pitch, yaw and cross-wind. This includes both the errors ira the non-linear form scraped into the guideway and the lack of averaging in the rolling contacts, and testifies to the extreme precision which experienced hand-scrapers can achieve.
In conclusion it can be seen that applications of the highest precision can be satisfied using parts basically of commercial tolerance but that the loadings required with these components make this design solution most suited to those applications of relatively slow motion in which the design life is unlikely to be exceeded for a long time. Where considerable motion is required the tolerances on the rolling element and the ways must be tightened up to allow the reduced loading of the ways then possible to extend their life. In these classes of application it will be appreciated that thermal problems do not usually arise since those applications in which a great deal of heat is evolved generally have a limited life. H YDROSTA TIC BEAR INGS
For precision applications hydrostatic bearings are always used in opposed configurations so that the equilibrium position is only slightly dependent on supply pressure. Consequently it is only those configurations which will be considered. The equilibrium position achieved by a bearing pad is such that the rate of fluid flow out of the bearing is equal to the rate of flow into the bearing. The equilibrium pressure over the effective area of the bearing is equal to the sustained load, it can be seen that the position of the bearing pad over the surface is defined by the fluid flow resistance of the gap between the surface and the land area. For any small area the flow resistance along the flow line is given by dP
12dl -
V
r~
wh 3
(where dp is the pressure drop over a length dl and width w of two surfaces separated by a distance h through which liquid of viscosity r7 is flowing at a volume rate V). The total flow resistance of the land is then some combination of the flow resistance of the individual elements. It will be seen that this average flow resistance must take account of the spatial distribution of the area with large gaps and is not merely determined by a statistical distribution of the gaps. The h 3 in the formula for flow resistance means that it is the largest gaps in the separation of the surfaces which dominate the flow resistance shunting the flow around areas of high resistance. Thus if scraped surfaces were used it would be the hollows which hydrostatically defined the surface, rather than the high spots which are, in fact, the surfaces constructed to define a plane. Scraped surfaces are therefore unsuitable for hydrostatic bearing surfaces since only those surfaces which do not control the flow are carefully worked! It has been seen that the position assumed by a hydrostatic bearing pad is such that the average position from the bearing surface is a function of load, the fore-restrictor and the supply pressure. The precise form of the average is difficult to evaluate but the improvements in precision of motion expected from the averaging have been experimentally shown in hydrostatic journal bearings. Thus J. G. C. de Gast (1966) reports a shaft turned to have an out of roundness of 0.1 ~m TIR on a hydrostatic bearing headstock the spindle of which has an out of roundness of 0.7/.tin TIR. In assessing the use of hydrostatic bearings in an application it is necessary to consider carefully the thermal equilibrium
of the bearing. In its expansion through the restrictor and bearing the oil increases its temperature, typically by 1°C/20 atmospheres. If the temperature of the oil entering the forerestrictor is suitably controlled it is possible to arrange that there is no nett transfer of heat energy to the bearing and the oil flow actually improves the thermal stability of the machine. The viscous shearing of the oil in the bearing, particularly at the lands results in a power dissipation in the bearing which is proportional to the square of the velocity, either linear or angular. To remove this heat without excessive temperature rise it is necessary to ensure, by adjusting the land width and gap, that there is sufficient mass flow of oil through the bearing. An important advantage of hydrostatic bearings compared with the externally pressurised gas bearings is the ability to increase the bearing system stifflless by using what de Gast et al call 'Membrane Double Restrictors' or Rowe et al call 'Rowe Valves'. It appears that they were simultaneously and independently invented. In the application of these due regard must be given to the frequency response of the restrictor but this need not be excessively restrictive, as J.J.t' Mannetje's hydrostatic coupling testifies. 'The frequency response characteristic, because of the small deviation (<0.1 btm) hardly measurable, shows only at high frequencies (~500 Hz) very little amplitude rise'. (JJ't Mannetje 1973). Hydrostatic guideways and work head are essential features of the ultra high precision cylindrical grinder (Fig 3) at present under construction in CUPE's temperature controlled laboratory. This machine is intended to produce work of roundness within 0.1 ~m TIR and parallel within 0.1/Jm/ 50 ram, with a minimum of skill on the part of the operator. Absolute dimensions can be reproduced to within 0.2 gin. The very high stiffness of hydrostatic bearings will enable an economical operating cycle to be achieved. The high inherent stiffness of the workhead bearing is augmented by the use of a later modification of the MDR, the Cantilever Double Restrictor (CDR). EXTERNA LL Y PRESSURISED GAS BEARINGS
Where it is found that the viscous heating in a hydrostatic bearing cannot be dissipated without excessive fluid flow or temperature rise then the fluid viscosity must be reduced. The externally pressurised gas bearing is the logical limit to this. Whilst in broad outline the concept of this bearing is similar to the hydrostatic bearing the greatly increased compressibility of the working fluid compared with oil results in reduced stiffness and a tendency to acoustic oscillations; this latter tendency, particularly, places a further restriction on the design in order to achieve stable operation. Provided that these restrictions are properly observed there are very many applications of relatively light loading where externally pressurised bearings present an optimum solution. Thus the motor bearings of the cylindrical grinding machine of Fig 4 are externally pressurised gas bearings to minimise heat generation in this fast rotating component. More typical applications are tile CUPE-Horstmann 1000 mm and 300 mm diameter rotary tables, the wheelhead and guideway bearings of the CUPE surface grinding and dicing machine, Fig 4 (No 32107) and the laser beam scanning unit of the high speed automatic plate measuring machine, Fig 1. The experience of Horstmann and others, eg Goulders, in
TRIBOLOGY international April 1975
75
Fig 4 Hydrostatic guMeways and work head are essential features of this ultra high precision cylindrical grinder
making aerostatic journal bearings l'or rotary tables and spindles shows an accuracy gain in rotational accuracy of between 7 and 15 times. Discussion cannot be exhaustive in the space available for this article and in particular the use o1 gas and liquid hydrodynamic rotary bearings and plain linear bearings have not been described at all despite their use in some machines o1" the highest precision, eg the vertical guideway or Fig 2. Perhaps this reflects the author's opinion tlrat their use is less general than those described, in that the precision o1 location and stitl'ness are a tunction of speed, It will have been seen that tire correct design of the correct type o1" bearings is a very important part ot making precision machine systems, no less so than their exact l'abrication or the design and manul'acturer ot the servo's and control. We
76
TRIBOLOGY international April 1975
Fig 4 The motor beanngs of this cylindrical grinding machine are externally pressurised gas bearings to minimise heat genera tion are lortunate at CUPE in having lacilities, skill and experience in all ol these elements ot precise machines at one location giving us the ability to supply a complete precision machine conceived and made as a whole.
REFERENCES I de Gast, J. G. (7. (1966) "Advancesin Machine luot Designand Research', Proceedings of the 7th International MTDR ('onference Birmingham 1966. Pergamon, Oxford 1967,273 298 2 t'Mannetje, J. J. (1973) Proceedings of International MTI)P, ('onference, Manchester 1973 3 McKeown,P. A. (19731 "Some Aspects of the Design of ttigh Precision Measuring Machines', ('[RP Annuals Vol 22/1, 1973. Proceedings of the 23rd General Assembly or" ('l RP. Bled,Jugoslavia. Sep 1973
The Cranfield Unit for Precision Engineering (CUPE) was established in April 1968, at the Cranfield Institute of Technology near Bedford to provide a service to industry in precision engineering. Initially set up with a Ministry of Technology grant, the Unit became entirely self-supporting in its third year and now has a turnover of approximately £270000 per annum. The work of the Unit includes the design and construction of machine tools and instruments of the highest precision together with their controls. Work is currently in hand for major British and European companies and British Observatories.
In the design of a precise machine there are three major principles which must be applied. Abbe's Principle of Collinearity has only indirect influence on the topic of this article, but both of the other two have immediate impact on the design of bearings.
1 The Principle of Kinematic Design The principle demonstrates the minimum number of constraints necessary to define any particular position or motion. This is extended to suggest that no more than the minimum of constraints should be used to control the motion of any moving member.
2 The Principle ofA veraging This principle says that the position defined by some average of several points on a surface has less variance than that of the individual points. Thus if the standard deviation of the position of one contact is o, the standard deviation of the average of n contacts, on = o/x/n-. Instruments, in the past, have tended to be designed according to the Principle of Kinematic Design utilising the minimum number of constraints and thus minimising the stress within the instrument, but requiring the highest accuracy of each constraint. On the other hand, Precision Machines have required the load bearing capacity of multiple contacts and the required accuracy has then been more economically achieved by averaging many contacts over less accurate surfaces. It is only as a result of the historically separate growth of the two crafts that the two schools have arisen, as things apart, to represent the extremes between which the precision engineer can select the best solution to any particular design problem. In making a bearing, either rotary or linear, the designer has several criteria to satisfy including: 1 2 3 4 5
Accuracy of motion required Stiffness across moving surfaces Friction along the moving surfaces Load bearing capacity Affect of bearing design on the remainder of the machine and system
* Cranfield Unit for Precision Engineering, Cranfiel,d Institute Technology, Cranfield, Bedford.
of
6 Temperature considerations 7 Cost of fabrication 8 Life of bearing It will be seen that most of the factors interact with each other in some way but for most people, and particularly for CUPE engineers, considerations of cost must always be paramount. However the cost of fabrication is only a part of that cost and the cost of design time for 'specials' must be considered. The ability to maintain the specified accuracy over long periods of time, possibly in difficult environments, without costly reworking must also weigh heavily in the selection of the optimum bearing. Since the interaction of the above factors to achieve the above criterion is complex and highly specific to a particular problem, it is probably not profitable to consider them in a general way. Each family of bearings is therefore considered separately, ie rolling element, hydrostatic etc, with examples taken from CUPE's experience.
ROLLING BEARINGS
If the roughness of the surface of the guideways is r 1/am, since this is the mean displacement of the surface it c a n approximately be said that the standard deviation of the surface from the average level defined is o 1 = ~2rl, similarly f o r the other surface o 2 = ~2r2 so that the standard deviation of the gap between the surfaces is 3 °12 = 2 - ~ 1 Some 95% of the gaps between the two surfaces will lie within plus or minus two standard deviations of the average gap. If, for the moment, all the balls or rollers are considered to be identical and one of them is caught between two high spots, then it must be compressed by 4o12 to ensure that 95% of the rolling elements are in contact. If, in addition, there is a difference e between the minimum diameter of the smallest element and the maximum diameter of the largest element then the maximum compression
TRIBOLOGY international April 1975 73
required of a single element to ensure the contact of 95% of the balls or rollers is ~2rnax=e+4Ol2=e+6 r@{ The roughness of balls or rollers is usually very much less than that of the bearing surfaces and can be ignored. If typical values are taken for surface roughness, out of roundness and size tolerance of 9 mm diameter steel balls on a linear guideway it is found that a loading of about a third the normal maximum dynamic loading is required to get all the balls into contact. This confirms one's normal experience that on well designed machines the straightness of motion is often better when the machine is fully loaded. This is only true, of course, if the structure is adequate for the loads imposed, which is part of being 'well designed'. Bearing in mind the loadings necessary to achieve good averaging and precision of motion it will be realised that for instrument applications balls rather than rollers are usually the preferred choice. An additional benefit is the greater freedom from damage caused by dirt enjoyed by balls, which tend to sweep the dirt around them whereas rollers trap particles between themselves and the guideway surface. Where the size of a guideway precludes the use of ground ways it will usually be necessary to scrape the ways to achieve a high precision and in this case, rollers must be used to span the hollows between high spots since only the high spots define the surface of the guideway. It will be appreciated that the previous discussion is an ideal design solution. This has been employed in the design of a High Speed Automatic Plate Measuring machine in conjunction with the Cambridge Institute of Astronomy, see Fig 1, where the very good performance that can be achieved provides the most economical solution for an X-Y table o f travel 380 mm X 350 mm. The design is pseudo-kinematic
Fig 1
74
High speed automatic plate measuring machine
TRIBOLOGY international April 1975
Fig 2 Guideways of this large measuring machine use 50 mm balls in V guMeways directly scraped in cast iron in that only one double V way is employed on each guideway with a V and fiat on the other side. Where a truly kinematic design would employ only two balls between the double V and one between the V and fiat, in this design at least 33 balls are in contact on each side so that the permissible error in the surface of the way can be five times greater than for a kinematic design and the cost of manufacture accordingly reduced. Whilst the above example represents the optimunr use of rolling elenrents it is not always possible to achieve this and marly examples of high precision can be found in which only some of the balls or rollers are in contact at the high spots of the surface. This represents a type transitional between the kinematic and elastically averaged way, in which there is some improvement in accuracy of motion compared with a kinematic design but, because of the paucity o f contact, the guideway must be constructed more accurately than the optimum design for a given performance. An interesting example of this latter type of design is the long guideway of a large measuring nrachine seen under construction in Fig 2, with a travel of 4 m along a horizontal axis constructed for the QAD FVE/MOD at Woolwich. The loading is too heavy for balls and hollow crossed rollers of 50 mnr diameter were chosen to run in V guideways directly scraped in cast iron. It was not possible to load all the rollers into contact, indeed some of the load must be taken by spring loaded bearings running on a separate, lower accuracy, track, because of the reduced area of con tact on scraped surfaces and the reduced loading necessary on unloaded surfaces to prevent 'Brinelling'. A structure as large as this must be expected to elastically deform as the carriage moves and the guideway is therefore scraped to a W-form, not straight, but computed to ensure the correct linear motion of the carriage despite the changing shape of the structure as the carriage rolls over it. ( Ref 3). The total error of motion of this carriage weighing 14 tons over 4 metres travel is less than 3 arc seconds in pitch, yaw and cross-wind. This includes both the errors ira the non-linear form scraped into the guideway and the lack of averaging in the rolling contacts, and testifies to the extreme precision which experienced hand-scrapers can achieve.
In conclusion it can be seen that applications of the highest precision can be satisfied using parts basically of commercial tolerance but that the loadings required with these components make this design solution most suited to those applications of relatively slow motion in which the design life is unlikely to be exceeded for a long time. Where considerable motion is required the tolerances on the rolling element and the ways must be tightened up to allow the reduced loading of the ways then possible to extend their life. In these classes of application it will be appreciated that thermal problems do not usually arise since those applications in which a great deal of heat is evolved generally have a limited life. H YDROSTA TIC BEAR INGS
For precision applications hydrostatic bearings are always used in opposed configurations so that the equilibrium position is only slightly dependent on supply pressure. Consequently it is only those configurations which will be considered. The equilibrium position achieved by a bearing pad is such that the rate of fluid flow out of the bearing is equal to the rate of flow into the bearing. The equilibrium pressure over the effective area of the bearing is equal to the sustained load, it can be seen that the position of the bearing pad over the surface is defined by the fluid flow resistance of the gap between the surface and the land area. For any small area the flow resistance along the flow line is given by dP
12dl -
V
r~
wh 3
(where dp is the pressure drop over a length dl and width w of two surfaces separated by a distance h through which liquid of viscosity r7 is flowing at a volume rate V). The total flow resistance of the land is then some combination of the flow resistance of the individual elements. It will be seen that this average flow resistance must take account of the spatial distribution of the area with large gaps and is not merely determined by a statistical distribution of the gaps. The h 3 in the formula for flow resistance means that it is the largest gaps in the separation of the surfaces which dominate the flow resistance shunting the flow around areas of high resistance. Thus if scraped surfaces were used it would be the hollows which hydrostatically defined the surface, rather than the high spots which are, in fact, the surfaces constructed to define a plane. Scraped surfaces are therefore unsuitable for hydrostatic bearing surfaces since only those surfaces which do not control the flow are carefully worked! It has been seen that the position assumed by a hydrostatic bearing pad is such that the average position from the bearing surface is a function of load, the fore-restrictor and the supply pressure. The precise form of the average is difficult to evaluate but the improvements in precision of motion expected from the averaging have been experimentally shown in hydrostatic journal bearings. Thus J. G. C. de Gast (1966) reports a shaft turned to have an out of roundness of 0.1 ~m TIR on a hydrostatic bearing headstock the spindle of which has an out of roundness of 0.7/.tin TIR. In assessing the use of hydrostatic bearings in an application it is necessary to consider carefully the thermal equilibrium
of the bearing. In its expansion through the restrictor and bearing the oil increases its temperature, typically by 1°C/20 atmospheres. If the temperature of the oil entering the forerestrictor is suitably controlled it is possible to arrange that there is no nett transfer of heat energy to the bearing and the oil flow actually improves the thermal stability of the machine. The viscous shearing of the oil in the bearing, particularly at the lands results in a power dissipation in the bearing which is proportional to the square of the velocity, either linear or angular. To remove this heat without excessive temperature rise it is necessary to ensure, by adjusting the land width and gap, that there is sufficient mass flow of oil through the bearing. An important advantage of hydrostatic bearings compared with the externally pressurised gas bearings is the ability to increase the bearing system stifflless by using what de Gast et al call 'Membrane Double Restrictors' or Rowe et al call 'Rowe Valves'. It appears that they were simultaneously and independently invented. In the application of these due regard must be given to the frequency response of the restrictor but this need not be excessively restrictive, as J.J.t' Mannetje's hydrostatic coupling testifies. 'The frequency response characteristic, because of the small deviation (<0.1 btm) hardly measurable, shows only at high frequencies (~500 Hz) very little amplitude rise'. (JJ't Mannetje 1973). Hydrostatic guideways and work head are essential features of the ultra high precision cylindrical grinder (Fig 3) at present under construction in CUPE's temperature controlled laboratory. This machine is intended to produce work of roundness within 0.1 ~m TIR and parallel within 0.1/Jm/ 50 ram, with a minimum of skill on the part of the operator. Absolute dimensions can be reproduced to within 0.2 gin. The very high stiffness of hydrostatic bearings will enable an economical operating cycle to be achieved. The high inherent stiffness of the workhead bearing is augmented by the use of a later modification of the MDR, the Cantilever Double Restrictor (CDR). EXTERNA LL Y PRESSURISED GAS BEARINGS
Where it is found that the viscous heating in a hydrostatic bearing cannot be dissipated without excessive fluid flow or temperature rise then the fluid viscosity must be reduced. The externally pressurised gas bearing is the logical limit to this. Whilst in broad outline the concept of this bearing is similar to the hydrostatic bearing the greatly increased compressibility of the working fluid compared with oil results in reduced stiffness and a tendency to acoustic oscillations; this latter tendency, particularly, places a further restriction on the design in order to achieve stable operation. Provided that these restrictions are properly observed there are very many applications of relatively light loading where externally pressurised bearings present an optimum solution. Thus the motor bearings of the cylindrical grinding machine of Fig 4 are externally pressurised gas bearings to minimise heat generation in this fast rotating component. More typical applications are tile CUPE-Horstmann 1000 mm and 300 mm diameter rotary tables, the wheelhead and guideway bearings of the CUPE surface grinding and dicing machine, Fig 4 (No 32107) and the laser beam scanning unit of the high speed automatic plate measuring machine, Fig 1. The experience of Horstmann and others, eg Goulders, in
TRIBOLOGY international April 1975
75
Fig 4 Hydrostatic guMeways and work head are essential features of this ultra high precision cylindrical grinder
making aerostatic journal bearings l'or rotary tables and spindles shows an accuracy gain in rotational accuracy of between 7 and 15 times. Discussion cannot be exhaustive in the space available for this article and in particular the use o1 gas and liquid hydrodynamic rotary bearings and plain linear bearings have not been described at all despite their use in some machines o1" the highest precision, eg the vertical guideway or Fig 2. Perhaps this reflects the author's opinion tlrat their use is less general than those described, in that the precision o1 location and stitl'ness are a tunction of speed, It will have been seen that tire correct design of the correct type o1" bearings is a very important part ot making precision machine systems, no less so than their exact l'abrication or the design and manul'acturer ot the servo's and control. We
76
TRIBOLOGY international April 1975
Fig 4 The motor beanngs of this cylindrical grinding machine are externally pressurised gas bearings to minimise heat genera tion are lortunate at CUPE in having lacilities, skill and experience in all ol these elements ot precise machines at one location giving us the ability to supply a complete precision machine conceived and made as a whole.
REFERENCES I de Gast, J. G. (7. (1966) "Advancesin Machine luot Designand Research', Proceedings of the 7th International MTDR ('onference Birmingham 1966. Pergamon, Oxford 1967,273 298 2 t'Mannetje, J. J. (1973) Proceedings of International MTI)P, ('onference, Manchester 1973 3 McKeown,P. A. (19731 "Some Aspects of the Design of ttigh Precision Measuring Machines', ('[RP Annuals Vol 22/1, 1973. Proceedings of the 23rd General Assembly or" ('l RP. Bled,Jugoslavia. Sep 1973