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A thermohydrodynamic analysis of the infinite slider bearing
SYSTEMATIC
due to welding. A method of interpreting laboratory results to give an indication of field performance is suggested. The setting up, recording and assessing of
ABSTRACTS
497
field trials under practical workshop conditions were discussed and illustrated with particular reference to multi-tool applications, precision grinding and metal machining.
4. BEARINGS A Prediction of Some Journal Bearing Characteristics under Static and Dynamic Loading*. R. Horsnell and H. McCallion, University of Nottingham. The journal centre locus and oil flow were predicted for static and cyclic loads on a bearing with oil supplied under pressure to a circumferential groove. equaReynolds’ two-dimensional The tion, which includes terms due to tangential and radial velocity of the shaft centre, was solved by relaxation techniques. By employing the analysis due to Floberg, the boundaries of the oil film were uniquely determined. Numerical integration of the pressure distribution yielded the oil force components and oil flow. A range of parameters was investigated such that the oil force on the shaft in any position within the bearing and with any resultant motion, could be interpolated. This information was then used to find the locus of the shaft centre and the oil flow under given loading conditions. Some Factors Affecting the Whirl Instability of a Journal Bearing*. R. M. Bowman, L. C. Collingwood and J. W. Midgley, The English Electric Co. Ltd, Whetstone. Existing theories and experimental work were briefly reviewed. A test rig built to investigate fundamental aspects of whirl consist essentially of a journal mounted on one end of a slender shaft, the other end of which was rigidly held in a driving chuck. The speed of the onset of whirl found was greater than twice the natural frequency and increased systematically with the oil viscosity and with the shaft length, tending asymptotically to twice the natural frequency as the shaft length was reduced to zero. The importance of the nondimensional ratio, hydrodynamic force/elastic restoring force was emphasized. Dynamic Characteristics of Turbine Journal Bearings *. D. M. Smith, A.E.I. Ltd. The author presented information on the dynamic characteristics of journal bearings for the use of turbine engineers. Influence on vibration was briefly reviewed and related to physical conditions in the oil films and to analytical and experimental work. For small journal movement, the dynamic characteristics were expressed approximately by
linear force-displacement-velocity relations which were not reciprocal and thus different from those in elastic systems. Characteristics were calculated for certain bearing designs and their practical significance was examined. Thermal and Elastic Distortions in Thrust Bearings *. C. Ettles and .4. Cameron, Imperial College, London. The elastic and thermal distortions that affect the performance of thrust pads were studied. Equations were derived for elastic deflections, assuming a circular thrust pad, centrally pivoted with a conical pressure distribution. The thermal distortions were analysed and, under normal operating conditions, were found to be much larger than the elastic deflections. A design method enabling the minimum film thickness to be calculated was given. This analysis was applied to some experimental data for the thrust bearings of the Grand Coulee dam and for a ship. The agreement was most satisfactory. Some modified pad constructions were suggested as a means of limiting pad thermal distortion. A Thermohydrodynamlc Analysis of the Infinite Slider Bearing*. D. Dowson and J. D. Hudson, University of Leeds. A thermohydrodynamic analysis normally considers the basic Reynolds and energy equations. In Part I of this paper an attempt was made to introduce more realistic boundary conditions by considering the question of heat conduction to the stationary and moving surfaces. The basic equations were established and a form of the Reynolds equation which allowed for property variations along and across the film was introduced. Computer solutions were presented which showed the separate and combined effects of density and viscosity changes for constat and equal surface temperatures. The effect of transverse velocity components was also discussed. Heat balances were presented and the influence of the Peclet number was examined. A full thermohydrodynamic analysis based on the method developed in Part I was applied to the parallel surface bearing. The more realistic boundary temperatures resulting from the analysis gave rise to a reversal Wear, 6 (1963) 495-501
498
LITERATURE
AND CURRENT
of the viscosity wedge predictions. It was found that the variation of lubricant properties could not explain the steady state performance of parallel surface bearings.
MinimumPower Loss of Hydrostatic Slipper Bearings for Axial Piston Machines *. N. .‘1. Shute and D. E. Turnbull. An expression for the total of the flon rate and viscous drag losses of a slipper pad bearing, suitable for use in axial piston machines, was derived in terms of bearing area and film thickness. The corresponding values of these quantities which gave a minimum total power loss were obtained and the results were presented in the form of charts showing contours of constant loss. If a machine is to operate over a range of speed or pressure or both then a method of designing the bearing to give a minimum average loss may be used. Measurements of the two components of the losses of a rigidly mounted bearing at various speeds and film thicknesses agreed well with the predicted values, suggesting that the method of analysis should provide a useful guide to bearing design. Water-lubricated Bearings - Initial Studies and Future Prospects in the Power Generation Industry*. S. Hother-Lushington, and 1’. Sellers, C .E.G.B., North Eastern Region, Leeds. Experiments are being conducted to detcrmine the most suitable combinations of materials in such bearings operating under starting or boundary lubrication conditions. The properties required arc : no corrosion ; low coefficient of friction and wear rate when starting or stopping; and the least possible damage to the shaft in bearing failures. 1X/8 stainless steel, Stellite S.Fro, and Siutox or Cwikotr> shafts have been used. Jletallized carbon and P,TPE-filled metallic bearings have proved the most promising. A\ brief review of previous work on this subject was given and the possible applications in the power generation industry \verc discussed. Aerostatic Jackingof aVented,Aerodynamic Journal Bearing *. G. L. Shires and 11. l’antall, L. I<.h.E..\., Reactor 11evelopment Division, \Yinfrith. l>uring the starting of an aerodynamic bearing, the shaft is initially unsupported. The authors gave a method of predicting the load-carrying capacit)r of bearings in which gas from an external source supports the shaft during this critical period and described tests carried out with them. To avoid half-speed \vhirl instabilit)-, the hydrodynamic bearings are often made with a vent at the top. In the combined bearing, as a result of the vent, the shaft is moved upwards. This leads to instability at low speeds
EVEiiTS
and the shaft might even “lock” against the top of the sleeve. From the mathematical model, design criteria were derived for avoiding this “locking-up” of vented aerodynamic journal bearings during aerostatic jacking. Fundamental Theory and Experiments on Hydrostatic Air Bearings*. J. \Y’. Powell, l\l. H. Moye and I’. R. Dwight, l’nivcrsity of Southampton. The authors considcrcd the static load pcrformancc of externally pressurized air bcarings in xvhich the air was fed to the clearance space through feed holes in one of the bearing surfaces. Experimentally-determined load capacity and pressure distributions were compared with the theory, both for flat circular thrust bearings and for journal bearings, and the effects of gas hehaviour were discussed. Recommendations were made regarding the design of bearings. Gas Behaviour and Load Capacity of Hydrodynamic Gas Journal Bearings*. J. \&‘. l’owell, lrniversity of Southampton. The author’s theoretical analysis indicated that, in all practical bearings, the gas condition is close to isothermal. Circumferential pressure and temperature distribution, friction torque and friction heating were measured and no circumferential temperature variation was found around the hearing slccvc; as the compressibility of the bearing was raised, the circumferential pressure tended towards the isothermal asymptotic distribution. Quasistatic loading experiments, using several gases, gave results in close agreement with .4usmans linearized pH solution theory, assuming isothermal gas behaviour. The condcnsation of water vapour was observed in a bearing with a perspex sleeve. The index of air expansion again indicated that the gas behaviour xvas isothermal. Bearings and Gears for Operation in Inert Gases *. H. 1X’. l’ricker, i1.E.E. LVinfrith. In the I)vagox reactor various bearings and gears will rnn in pure helium at rather high temperatures and irradiation levels. Because of the low concentration of chemically active gases, the lack of formation of oxide or other films on the rubbing surfaces would lead to local welding, resulting in high friction and wear. In plain bearing tests with unlubricated metals and ceramics the expected high friction and wear wore encountered. Graphite, or carbon lubricated with molybdenum disulphide, running against hard, well-finished shafts, gave low friction and wear. I’TFE as a lubricant also gave good results at moderate temperature and irradiation. For light duties ball bearings of high-speed tool steel can run dry. Good results were obll’ear,
6 (1gG3) z+gj-jOI
due to welding. A method of interpreting laboratory results to give an indication of field performance is suggested. The setting up, recording and assessing of
ABSTRACTS
497
field trials under practical workshop conditions were discussed and illustrated with particular reference to multi-tool applications, precision grinding and metal machining.
4. BEARINGS A Prediction of Some Journal Bearing Characteristics under Static and Dynamic Loading*. R. Horsnell and H. McCallion, University of Nottingham. The journal centre locus and oil flow were predicted for static and cyclic loads on a bearing with oil supplied under pressure to a circumferential groove. equaReynolds’ two-dimensional The tion, which includes terms due to tangential and radial velocity of the shaft centre, was solved by relaxation techniques. By employing the analysis due to Floberg, the boundaries of the oil film were uniquely determined. Numerical integration of the pressure distribution yielded the oil force components and oil flow. A range of parameters was investigated such that the oil force on the shaft in any position within the bearing and with any resultant motion, could be interpolated. This information was then used to find the locus of the shaft centre and the oil flow under given loading conditions. Some Factors Affecting the Whirl Instability of a Journal Bearing*. R. M. Bowman, L. C. Collingwood and J. W. Midgley, The English Electric Co. Ltd, Whetstone. Existing theories and experimental work were briefly reviewed. A test rig built to investigate fundamental aspects of whirl consist essentially of a journal mounted on one end of a slender shaft, the other end of which was rigidly held in a driving chuck. The speed of the onset of whirl found was greater than twice the natural frequency and increased systematically with the oil viscosity and with the shaft length, tending asymptotically to twice the natural frequency as the shaft length was reduced to zero. The importance of the nondimensional ratio, hydrodynamic force/elastic restoring force was emphasized. Dynamic Characteristics of Turbine Journal Bearings *. D. M. Smith, A.E.I. Ltd. The author presented information on the dynamic characteristics of journal bearings for the use of turbine engineers. Influence on vibration was briefly reviewed and related to physical conditions in the oil films and to analytical and experimental work. For small journal movement, the dynamic characteristics were expressed approximately by
linear force-displacement-velocity relations which were not reciprocal and thus different from those in elastic systems. Characteristics were calculated for certain bearing designs and their practical significance was examined. Thermal and Elastic Distortions in Thrust Bearings *. C. Ettles and .4. Cameron, Imperial College, London. The elastic and thermal distortions that affect the performance of thrust pads were studied. Equations were derived for elastic deflections, assuming a circular thrust pad, centrally pivoted with a conical pressure distribution. The thermal distortions were analysed and, under normal operating conditions, were found to be much larger than the elastic deflections. A design method enabling the minimum film thickness to be calculated was given. This analysis was applied to some experimental data for the thrust bearings of the Grand Coulee dam and for a ship. The agreement was most satisfactory. Some modified pad constructions were suggested as a means of limiting pad thermal distortion. A Thermohydrodynamlc Analysis of the Infinite Slider Bearing*. D. Dowson and J. D. Hudson, University of Leeds. A thermohydrodynamic analysis normally considers the basic Reynolds and energy equations. In Part I of this paper an attempt was made to introduce more realistic boundary conditions by considering the question of heat conduction to the stationary and moving surfaces. The basic equations were established and a form of the Reynolds equation which allowed for property variations along and across the film was introduced. Computer solutions were presented which showed the separate and combined effects of density and viscosity changes for constat and equal surface temperatures. The effect of transverse velocity components was also discussed. Heat balances were presented and the influence of the Peclet number was examined. A full thermohydrodynamic analysis based on the method developed in Part I was applied to the parallel surface bearing. The more realistic boundary temperatures resulting from the analysis gave rise to a reversal Wear, 6 (1963) 495-501
498
LITERATURE
AND CURRENT
of the viscosity wedge predictions. It was found that the variation of lubricant properties could not explain the steady state performance of parallel surface bearings.
MinimumPower Loss of Hydrostatic Slipper Bearings for Axial Piston Machines *. N. .‘1. Shute and D. E. Turnbull. An expression for the total of the flon rate and viscous drag losses of a slipper pad bearing, suitable for use in axial piston machines, was derived in terms of bearing area and film thickness. The corresponding values of these quantities which gave a minimum total power loss were obtained and the results were presented in the form of charts showing contours of constant loss. If a machine is to operate over a range of speed or pressure or both then a method of designing the bearing to give a minimum average loss may be used. Measurements of the two components of the losses of a rigidly mounted bearing at various speeds and film thicknesses agreed well with the predicted values, suggesting that the method of analysis should provide a useful guide to bearing design. Water-lubricated Bearings - Initial Studies and Future Prospects in the Power Generation Industry*. S. Hother-Lushington, and 1’. Sellers, C .E.G.B., North Eastern Region, Leeds. Experiments are being conducted to detcrmine the most suitable combinations of materials in such bearings operating under starting or boundary lubrication conditions. The properties required arc : no corrosion ; low coefficient of friction and wear rate when starting or stopping; and the least possible damage to the shaft in bearing failures. 1X/8 stainless steel, Stellite S.Fro, and Siutox or Cwikotr> shafts have been used. Jletallized carbon and P,TPE-filled metallic bearings have proved the most promising. A\ brief review of previous work on this subject was given and the possible applications in the power generation industry \verc discussed. Aerostatic Jackingof aVented,Aerodynamic Journal Bearing *. G. L. Shires and 11. l’antall, L. I<.h.E..\., Reactor 11evelopment Division, \Yinfrith. l>uring the starting of an aerodynamic bearing, the shaft is initially unsupported. The authors gave a method of predicting the load-carrying capacit)r of bearings in which gas from an external source supports the shaft during this critical period and described tests carried out with them. To avoid half-speed \vhirl instabilit)-, the hydrodynamic bearings are often made with a vent at the top. In the combined bearing, as a result of the vent, the shaft is moved upwards. This leads to instability at low speeds
EVEiiTS
and the shaft might even “lock” against the top of the sleeve. From the mathematical model, design criteria were derived for avoiding this “locking-up” of vented aerodynamic journal bearings during aerostatic jacking. Fundamental Theory and Experiments on Hydrostatic Air Bearings*. J. \Y’. Powell, l\l. H. Moye and I’. R. Dwight, l’nivcrsity of Southampton. The authors considcrcd the static load pcrformancc of externally pressurized air bcarings in xvhich the air was fed to the clearance space through feed holes in one of the bearing surfaces. Experimentally-determined load capacity and pressure distributions were compared with the theory, both for flat circular thrust bearings and for journal bearings, and the effects of gas hehaviour were discussed. Recommendations were made regarding the design of bearings. Gas Behaviour and Load Capacity of Hydrodynamic Gas Journal Bearings*. J. \&‘. l’owell, lrniversity of Southampton. The author’s theoretical analysis indicated that, in all practical bearings, the gas condition is close to isothermal. Circumferential pressure and temperature distribution, friction torque and friction heating were measured and no circumferential temperature variation was found around the hearing slccvc; as the compressibility of the bearing was raised, the circumferential pressure tended towards the isothermal asymptotic distribution. Quasistatic loading experiments, using several gases, gave results in close agreement with .4usmans linearized pH solution theory, assuming isothermal gas behaviour. The condcnsation of water vapour was observed in a bearing with a perspex sleeve. The index of air expansion again indicated that the gas behaviour xvas isothermal. Bearings and Gears for Operation in Inert Gases *. H. 1X’. l’ricker, i1.E.E. LVinfrith. In the I)vagox reactor various bearings and gears will rnn in pure helium at rather high temperatures and irradiation levels. Because of the low concentration of chemically active gases, the lack of formation of oxide or other films on the rubbing surfaces would lead to local welding, resulting in high friction and wear. In plain bearing tests with unlubricated metals and ceramics the expected high friction and wear wore encountered. Graphite, or carbon lubricated with molybdenum disulphide, running against hard, well-finished shafts, gave low friction and wear. I’TFE as a lubricant also gave good results at moderate temperature and irradiation. For light duties ball bearings of high-speed tool steel can run dry. Good results were obll’ear,
6 (1gG3) z+gj-jOI