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Gears
The tilting pad configuration has received renewed attention as a journal bearing assembly for turbo machinery 9 s. The ability of the pads to pivot gives low 'cross stiffness' to the assembly, resulting in the stable operation of flexible shafts in instances where conventional journal bearings give shaft whip. The damping of pivoted pad journal bearings is found to be low but operation is possible at several times the shaft pinned critical speed. Bearings of this configuration are currently under test development by several organizations. C. Ettles
Bearing and rotor dynamics Activity in this field has been intense with four well attended international conferences since 1972. Advances in the state of the art during the past decade have been considerable, particularly in analytical methods, which can be divided into the two broad areas of linear and non-linear methods. In the majority of theoretical investigations it is assumed that the excursion of a journal about its equilibrium position is small so that the oil film force, in each of two perpendicular directions, may be approximated as a linear function of the velocity and displacement from the equilibrium position. The oil film force acting on the journal, for a given bearing configuration and given equilibrium position, is thus determined by eight linearized bearing coefficients usually known as the stiffness and damping coefficients. This concept was well established ten years ago and since then has been much expanded, since it yields linear equations of motion which are amenable to well established techniques of analysis. Some key papers in the last decade on the experimental determination of bearing coefficients are by Glienicke 94 using sinusoidal excitation, Woodcock and Holmes 9 s using rotating unbalance, and Morton 96 for large turbo generator bearings using a method similar to Glienicke. Each method requires the amplitude and phase measurement of the ellipitical journal orbit that results from harmonic excitation. The excitation applied must be sufficiently large to give accurately measurable orbits but small enough to retain the linearised assumption. The monitoring equipment for journal motion must therefore be most accurate if misleading results are to be avoided. The principal uses of bearing coefficients include the calculation of response of rotors to excitation (eg unbalance 9 s) and the calculation of stability. It is possible to treat a number of rotor models, including the stiff shaft, the point mass rotor on a light elastic shaft 94 and the continuous massive flexible shaft. The last model is clearly the most realistic and three basic methods are now in use. These are: (a) The lumped mass method (b) The transfer matrix method (Myklestad-Prohe) (c) The assumed modes method (Rayleigh-Ritz) Of these (b) and (c) have received attention in the last decade. Although the transfer matrix method is similar to (a) it has the advantage that large matrices are not generated. Notable contributions have been made by, for
26 TRIBOLOGY international February 1978
example, Lund and Orcutt 97, Lundga and Dostal e t al 99 The assumed modes method is both elegant and effective and reduces the number of degrees of freedom needed to accurately represent any deflected form of the shaft by summing a suitable set of mode shapes calculable from a simpler situation, for example, pin-pin or free-free. This was first used by Morton I oo and later by Black et al I o 1 For all methods of analysis the stability of the system can be assessed by the magnitude of the eigenvalues of the system in that the real parts should be negative for stability and the imaginary parts can give an indication of natural frequencies. A drawback of linearised methods in general is that they give no information of large amplitude vibration which is often observed in practice, particularly at rotational speeds beyond twice the first pinned critical speed. To examine large amplitude excursions, non-linear methods are used in which the equations of motion are marched out in successive short time steps. Such a method is most expensive in computer time and many investigations have perforce used the short bearing model which has a closed form solution for bearing forces. Recently Holme~ I o 2 developed a fast journal bearing solution combined with the assumed mode method to analyse the stability of a two-rotor four-bearing system. This showed the sensitivity of turbo generators with solid coupled rotors to vertical misalignment of the bearings from the catenary. Here the bearing bore shape is shown to be of critical importance in limiting the amplitude without recourse to damping. It appears that the asymmetry of practical bearings has an important effect on promoting stability or promoting acceptable amplitude if the system is unstable. It is interesting to reflect that current bearing designs evolved from a desire to minimise power loss, giving large feed 'scallops'. Now it appears that asymmetric features have an important and largely unknown effect on stability. Much further work is required on existing bearing designs. Perhaps the most interesting and technically advanced application in the field of rotor dynamics is the inclusion of fracture mechanics for the determination of crack position in a rotor and its growth rate 1 os. The application of such work has allowed the continued running of large turbo-sets with known cracks. Rotor dynamics as a subject is typical of many under the general heading of tribology in that more than one area of expertise is needed to appreciate the whole field. Contributors are often expert in dynamics or in bearings but rarely in both. It is those with this particular combination of talents who have made the most notable advances, and this is likely to be an increasingly important requirement for advances in the future. C. Ettles
Gears The most striking development over the past decade has been the eclipse of the traditional 'soft' gear even in areas such as the marine field where owners are most conservative. The extra safety and compactness of the hardened gear nitrided or carburised and profile ground - has now been C. Ettles, Imperial College o f Science and Technology, London SW7 2BX, UK
accepted by owners and classification societies, who are giving their full backing to such gear designs with appropriate load ratings. Hand in hand with this, production methods have developed to cope with the larger pitches and harder materials now required, and rigid machines capable of high speed cutting of 2 to 3 metre diameter wheels with pitches upwards of 20 module are now available. Profile grinding as the finishing process is accepted as the norm. Carburising and hardening of large wheels with minimum distortion is now coming under control. Fabrication by welding the rim to a plated centre prior to heat treatment has been tried as a means of controlling distortion. A different approach is the actual hobbing by high speed 'skiving' of the gear in the hardened state so as to reduce the amount to be removed in final grinding. Of equal importance, modern mathematical techniques of analysis have led to increased knowledge of stresses and deflections in the gear tooth. With this guidance, national and international standards authorities and classification societies have produced all-embracing rules governing permissible loadings and logical standards of accuracy. Tooth forms of the non-invohite type have persisted in some applications, but interest has waned over the decade and major use of circular arc forms is unlikely to develop. Gear arrangement has received much attention. Epicyclic gears in particular have proliferated, with ingenious means of load sharing. There has been a trend towards simplicity and the straight spur gear has made a successful comeback in some designs. For naval applications great ingenuity has been required in providing gears for diesel engines and gas turbines driving separately or in combination to single or twin propeller shafts. Such designs have required parallel development in the field of overrunning and friction clutches. In the industrial field, gas turbine power generation, and all types of compressor drives have demanded higher powered gears with ever increasing pitch line speeds. Again, modern methods of analysis of distortion and heat dissipation have shown the means to be used to keep temperatures and power losses to a minimum. Scuffing of the teeth, once thought to be a function only of bad tooth design, has called for more attention as a criterion of gear acceptance. Since extreme pressure lubricants are avoided where possible, the advantages of nitriding and providing immunity from scuffing in critical applications are more and more appreciated. Noise reduction is being given more attention and more is now understood of its causes. Limitations in possible noise reduction still exist however and accoustic cladding of boxes is frequently required. Developments in the coming years will certainly include progress in this area to meet legislation. I. 7". Young
L T. Young, GEC Marine and Industrial Gears Ltd., Mill Road, Rugby CV21 1BD, UK
Flexible shaft couplings The main developments in this field have been at the high technology end, where high power and high speed have to be transmitted for long periods with high reliability. The decade has seen a major increase in the industrial application of contoured disc and multiple membrane couplings as replacements for the traditional gear coupling. This increased application has been based on much improved knowledge of the stresses in the critical flexing elements as a function of the operating conditions, torque, speed, and, of particular importance, the axial and angular misalignments. In the case of multiple membrane couplings, fretting between the membranes, and between the membranes and clamping bolts, has been recognised as an inherent performance limiting factor and fundamental work is in progress in this area and should lead to further advances. Fretting cannot occur in contoured disc couplings and this gives more scope for material selection to increase coupling performance, particularly their flexibility; developments in this area, such as the wider use of titanium, are likely. The main practical development of gear couplings has been in the design and manufacture of light weight, high precision couplings with good balance characteristics, to satisfy the trend to increased speed applications. Improved understanding has been built up of how gear couplings work and, in particular, of how the critical tooth contact conditions are influenced by operating conditions and of how they, in turn, limit performance. The detailed tribology of of the tooth contacts is currently receiving attention and may well become a fruitful field for research, leading to developments in tooth surface treatments and materials, and in the method and type of lubrication, to permit higher tooth sliding velocities. For all coupling types the critical effect of relative movement of the connected shaft ends, in response to thermal expansions, and forces on the machines from such things as heavy pipework, is becoming increasingly recognised. This will hopefully result in a major effort to develop and establish practical approximate methods for predicting shaft end movements in different applications, for use at the coupling design stage. The use of coupling for detuning the torsional and lateral critical speeds of machine systems has increased over the last decade. Special coupling ranges with widely variable torsional stiffnesses, based on inserted elastomer blocks or variable geometry links, have become available and it is likely that further advantage will be taken of this convenient facility of the coupling as machine systems increase in speed and complexity. The technology of couptings for high powers and speeds has recently been usefully summarised in an international conference and associated procee dings ~o 4 A.B. Crease
Brakes and clutches Brakes and clutches have to dissipate continually greater energies, particularly with commercial vehicles where speeds
A.B. Crease, Michael Neale & Associates Ltd, 43 Downing Street. Farnham, Surrey GU9 7PH, UK
TRIBOLOGY international February 1978 27
Bearing and rotor dynamics Activity in this field has been intense with four well attended international conferences since 1972. Advances in the state of the art during the past decade have been considerable, particularly in analytical methods, which can be divided into the two broad areas of linear and non-linear methods. In the majority of theoretical investigations it is assumed that the excursion of a journal about its equilibrium position is small so that the oil film force, in each of two perpendicular directions, may be approximated as a linear function of the velocity and displacement from the equilibrium position. The oil film force acting on the journal, for a given bearing configuration and given equilibrium position, is thus determined by eight linearized bearing coefficients usually known as the stiffness and damping coefficients. This concept was well established ten years ago and since then has been much expanded, since it yields linear equations of motion which are amenable to well established techniques of analysis. Some key papers in the last decade on the experimental determination of bearing coefficients are by Glienicke 94 using sinusoidal excitation, Woodcock and Holmes 9 s using rotating unbalance, and Morton 96 for large turbo generator bearings using a method similar to Glienicke. Each method requires the amplitude and phase measurement of the ellipitical journal orbit that results from harmonic excitation. The excitation applied must be sufficiently large to give accurately measurable orbits but small enough to retain the linearised assumption. The monitoring equipment for journal motion must therefore be most accurate if misleading results are to be avoided. The principal uses of bearing coefficients include the calculation of response of rotors to excitation (eg unbalance 9 s) and the calculation of stability. It is possible to treat a number of rotor models, including the stiff shaft, the point mass rotor on a light elastic shaft 94 and the continuous massive flexible shaft. The last model is clearly the most realistic and three basic methods are now in use. These are: (a) The lumped mass method (b) The transfer matrix method (Myklestad-Prohe) (c) The assumed modes method (Rayleigh-Ritz) Of these (b) and (c) have received attention in the last decade. Although the transfer matrix method is similar to (a) it has the advantage that large matrices are not generated. Notable contributions have been made by, for
26 TRIBOLOGY international February 1978
example, Lund and Orcutt 97, Lundga and Dostal e t al 99 The assumed modes method is both elegant and effective and reduces the number of degrees of freedom needed to accurately represent any deflected form of the shaft by summing a suitable set of mode shapes calculable from a simpler situation, for example, pin-pin or free-free. This was first used by Morton I oo and later by Black et al I o 1 For all methods of analysis the stability of the system can be assessed by the magnitude of the eigenvalues of the system in that the real parts should be negative for stability and the imaginary parts can give an indication of natural frequencies. A drawback of linearised methods in general is that they give no information of large amplitude vibration which is often observed in practice, particularly at rotational speeds beyond twice the first pinned critical speed. To examine large amplitude excursions, non-linear methods are used in which the equations of motion are marched out in successive short time steps. Such a method is most expensive in computer time and many investigations have perforce used the short bearing model which has a closed form solution for bearing forces. Recently Holme~ I o 2 developed a fast journal bearing solution combined with the assumed mode method to analyse the stability of a two-rotor four-bearing system. This showed the sensitivity of turbo generators with solid coupled rotors to vertical misalignment of the bearings from the catenary. Here the bearing bore shape is shown to be of critical importance in limiting the amplitude without recourse to damping. It appears that the asymmetry of practical bearings has an important effect on promoting stability or promoting acceptable amplitude if the system is unstable. It is interesting to reflect that current bearing designs evolved from a desire to minimise power loss, giving large feed 'scallops'. Now it appears that asymmetric features have an important and largely unknown effect on stability. Much further work is required on existing bearing designs. Perhaps the most interesting and technically advanced application in the field of rotor dynamics is the inclusion of fracture mechanics for the determination of crack position in a rotor and its growth rate 1 os. The application of such work has allowed the continued running of large turbo-sets with known cracks. Rotor dynamics as a subject is typical of many under the general heading of tribology in that more than one area of expertise is needed to appreciate the whole field. Contributors are often expert in dynamics or in bearings but rarely in both. It is those with this particular combination of talents who have made the most notable advances, and this is likely to be an increasingly important requirement for advances in the future. C. Ettles
Gears The most striking development over the past decade has been the eclipse of the traditional 'soft' gear even in areas such as the marine field where owners are most conservative. The extra safety and compactness of the hardened gear nitrided or carburised and profile ground - has now been C. Ettles, Imperial College o f Science and Technology, London SW7 2BX, UK
accepted by owners and classification societies, who are giving their full backing to such gear designs with appropriate load ratings. Hand in hand with this, production methods have developed to cope with the larger pitches and harder materials now required, and rigid machines capable of high speed cutting of 2 to 3 metre diameter wheels with pitches upwards of 20 module are now available. Profile grinding as the finishing process is accepted as the norm. Carburising and hardening of large wheels with minimum distortion is now coming under control. Fabrication by welding the rim to a plated centre prior to heat treatment has been tried as a means of controlling distortion. A different approach is the actual hobbing by high speed 'skiving' of the gear in the hardened state so as to reduce the amount to be removed in final grinding. Of equal importance, modern mathematical techniques of analysis have led to increased knowledge of stresses and deflections in the gear tooth. With this guidance, national and international standards authorities and classification societies have produced all-embracing rules governing permissible loadings and logical standards of accuracy. Tooth forms of the non-invohite type have persisted in some applications, but interest has waned over the decade and major use of circular arc forms is unlikely to develop. Gear arrangement has received much attention. Epicyclic gears in particular have proliferated, with ingenious means of load sharing. There has been a trend towards simplicity and the straight spur gear has made a successful comeback in some designs. For naval applications great ingenuity has been required in providing gears for diesel engines and gas turbines driving separately or in combination to single or twin propeller shafts. Such designs have required parallel development in the field of overrunning and friction clutches. In the industrial field, gas turbine power generation, and all types of compressor drives have demanded higher powered gears with ever increasing pitch line speeds. Again, modern methods of analysis of distortion and heat dissipation have shown the means to be used to keep temperatures and power losses to a minimum. Scuffing of the teeth, once thought to be a function only of bad tooth design, has called for more attention as a criterion of gear acceptance. Since extreme pressure lubricants are avoided where possible, the advantages of nitriding and providing immunity from scuffing in critical applications are more and more appreciated. Noise reduction is being given more attention and more is now understood of its causes. Limitations in possible noise reduction still exist however and accoustic cladding of boxes is frequently required. Developments in the coming years will certainly include progress in this area to meet legislation. I. 7". Young
L T. Young, GEC Marine and Industrial Gears Ltd., Mill Road, Rugby CV21 1BD, UK
Flexible shaft couplings The main developments in this field have been at the high technology end, where high power and high speed have to be transmitted for long periods with high reliability. The decade has seen a major increase in the industrial application of contoured disc and multiple membrane couplings as replacements for the traditional gear coupling. This increased application has been based on much improved knowledge of the stresses in the critical flexing elements as a function of the operating conditions, torque, speed, and, of particular importance, the axial and angular misalignments. In the case of multiple membrane couplings, fretting between the membranes, and between the membranes and clamping bolts, has been recognised as an inherent performance limiting factor and fundamental work is in progress in this area and should lead to further advances. Fretting cannot occur in contoured disc couplings and this gives more scope for material selection to increase coupling performance, particularly their flexibility; developments in this area, such as the wider use of titanium, are likely. The main practical development of gear couplings has been in the design and manufacture of light weight, high precision couplings with good balance characteristics, to satisfy the trend to increased speed applications. Improved understanding has been built up of how gear couplings work and, in particular, of how the critical tooth contact conditions are influenced by operating conditions and of how they, in turn, limit performance. The detailed tribology of of the tooth contacts is currently receiving attention and may well become a fruitful field for research, leading to developments in tooth surface treatments and materials, and in the method and type of lubrication, to permit higher tooth sliding velocities. For all coupling types the critical effect of relative movement of the connected shaft ends, in response to thermal expansions, and forces on the machines from such things as heavy pipework, is becoming increasingly recognised. This will hopefully result in a major effort to develop and establish practical approximate methods for predicting shaft end movements in different applications, for use at the coupling design stage. The use of coupling for detuning the torsional and lateral critical speeds of machine systems has increased over the last decade. Special coupling ranges with widely variable torsional stiffnesses, based on inserted elastomer blocks or variable geometry links, have become available and it is likely that further advantage will be taken of this convenient facility of the coupling as machine systems increase in speed and complexity. The technology of couptings for high powers and speeds has recently been usefully summarised in an international conference and associated procee dings ~o 4 A.B. Crease
Brakes and clutches Brakes and clutches have to dissipate continually greater energies, particularly with commercial vehicles where speeds
A.B. Crease, Michael Neale & Associates Ltd, 43 Downing Street. Farnham, Surrey GU9 7PH, UK
TRIBOLOGY international February 1978 27