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A design methodology for wheel and rail profiles for use on steered railway vehicles
Wear, I44 (1991) 329-342
329
A design methodology for wheel and rail profiles for use on steered railway vehicles Roy E. Smith RZSCO Engineering,
823 Overlea Court, Kingston, Ontario K7M 628 (Canada]
J. Kalousek National Research Ctnmcil of Canada, Tribologg and Mechanics Laboratory, 3650 We&rook Mall, Vancouver V6S 2L2 (Canada)
Abstract The geometry of the interface between steel wheels and steel rails can create conditions which affect the dynamics of a vehicle, the development of rail and wheel corrugation and noise. It has come to be expected that the worn protlle of the wheel is uncontrollable and must be regularly corrected. This reflects the normal experience with non-steered trucks. Dynamicists have usually chosen a range of cordcities to bound the performance of a vehicle design. Maintenance techniques have then been used to control the conditions occurring in service to be within these bounds. Hunting (instability generated by the self-centrlng action of the coned wheelset) is thereby controlled. Increasing demand for higher performance reduces the range of conlcity allowable (using conventional truck technology). The cost of maintaining that conicity increases. The design technique described here enables wheel and rail profiles to be developed which have a limited range of conicity throughout their life, generate little noise, greatly reduce corrugation and, when used on steered axle vehicles, together with the described techniques of trade geometry control, can be virtually self-perpetuating. These are important benefits for the system operator.
1. The bounds
of the problem
Vehicles with steered axles have a number of dynamic features which are peculiar to the type [ 11. Two of these properties are: (1) such vehicles have greater stability than similar unsteered ones at the medium and high conic&y range (worn wheels); (2) such vehicles can have low frequency instabilities at low conic&y and/or creep coefficient. The design range for the conicity may thus be extended at the high end but may also have a higher limit at the low end. (Note. The only low limit for conicity on non-steered trucks is the point at which flange-flange wandering or “zigzag” motion takes place owing to a lack of self-centring.) Maintaining conformity of the wheel and rail profiles reduces contact stress. If the profiles become too closely conformal, however, two undesirable results arise. Firstly, the effective conicity of the wheelset increases. Hunting instabilities, at frequencies around 11 Hz, were regularly observed in Vancouver 0043-1648l91B3.50
0 Elsevier Sequoia/Printed in The Netherlands
330
at speeds of 80 km h and sometimes less. This demonstrated that conicity in excess of 1 .O had been reached with only 1.5 mm of radial wear on wheelsets which began life with a taper of 1:20! Secondly, as the profile conformity increases, very high frequency localized oscillations can be set up (CCL800 Hz), involving rotation and/or translation of the rail head. The wear patterns produced by these oscillations can result in short wavelength (CCL50 mm) corrugation of the wheel and the rail. These osc~ations are aggravated by the presence of even small amounts of steady state lateral slip in the contact patch. This has also been observed in Vancouver. 2. Design method It has been well known for some time (see Wickens [Z], who further acknowledges Heumann and dePater) that the effective conicity of a wheelset can be given by the function . .
&
conicity= R2_RI tan LY
(1)
where RI is the transverse radius of the rail head, Rz is the transverse radius of the wheel profile and LYis the angle of contact. This expression is actually a simplification of the full relationship which exists between these terms, but it is a useful approximation which enables us to gain insights into the effect of profile geometry upon conicity. The straight tapered wheel runnmg on a rail of finite transverse radius has an effective conicity of tan cy. To obtain moderate or high levels of conicity, the value of (Y must be correspondingly high. This is because R2 is infinite and therefore the quotient R2/(R2-RI) is unity. This is illustrated in Fig. 1. With finite values for Rz the quotient RJ(R, -RI) becomes greater than unity and, in the limit as Rz approaches the value of RI,this value approaches infinity. Evidently it is possible, using curved profiles, to obtain almost any desired value for the conicity while maintaining a small value for CY. Two simultaneous points of contact between the wheel and the rail are highly undesirable. As long as the wheel and rail profiles are each single circular arcs, with R2 > RI,this isavoided. Unfortunately, such profiles generally require too much wheel ~dth.~d/or lateral motion to achieve the extremes of rolling radius difference required in tight curves. To satisfy these requirements, the proties may be designed by combining two or more arc radii. To do this, however, some rules must be formulated so as to avoid two-point contact. Necessary and sufficient conditions at all potential points of contact are that the inclinations to the horizontal of both wheel and rail must be equal and the rail radius must be smaller than the wheel radius at that point. A simple design methodology, for profiles which are to be made up of a series of circular arcs, is as follows.
331
WHEEL
CONICITY
FOR STRAIGHT
CONICITY
?OR CURVED PROFILE
= TANa
TAPER =
RP RL-Rl
TANa
-
v
Fig. 1. Effect of profile curvature on conicity.
ROLLING
RAD. DIFF. CONTACT
EXCURSION
Fig.
2. A proiile using a single circular arc.
(1) For tangent sections and large radius curves choose a wheel transverse radius which will provide the required rolling radius difference within a reasonable lateral excursion. See Fig. 2. (2) Determine the largest rolling radius difference which will be required throughout the operating system. Connect a second circular arc, of smaller radius than the first, to the first one, the tangents at the point of connection being coincident. Choose this radius such that the remaining rolling radius differential is provided within the remaining lateral excursion. See Fig. 3 (3) Create a rail profile which will provide single-point contact with the wheel profile at all times. This is done by selecting rail radii to correspond with each of the wheel radii and then creating a rail profile by connecting arcs of each of these radii. The lengths of the arcs in the rail profile must subtend the same angles at their centres as their mating ones on the wheel. By this means it is ensured that two-point contact can never occur. Beyond the region within which it is intended that wheel-rail contact shall occur, the rail profile may take on the same shape as the root and flange of the wheel. This can be seen in Fig. 4. The limit of expected wheel-rail contact (the working area) is shown in heavier line. Outside this area the rail profile may fall below the line shown and the wheel profile may rise above the line
Fig. 3. A profile using two blended circuIar Fig. 4. Derivation
of the required
ares.
rail profile.
shown, but not vice versa. Any deviation from this can cause a second point of contact to occur, in an area outside the designed one, and this can have undesirable effects upon vehicle behaviour, noise and wear. (Note. Contact occurs in a patch of fimte width and this must be taken into account when establishing the width of the working area on the wheel. Some random lateral excursions from the true curving position are also to be expected in normal operation and these must also be allowed for in the working area of the tread.) The design shown here is a simple one. It was assumed that the system would be divisible into two regimes: the first a high speed one, containing the tangent sections and large curves, in which moderate conicity would be required; the second a low speed one, containing the sharp curves, where high conicity would be allowed. In some instances it may be necessary to subdivide the running regimes further, into three sections for instance, and thus have three radii in the working ranges of both wheel and rail. It is also possible to conceive of profile designs which, in the working zone, are made of a single arc of an ellipse. All that would be required to ensure that the control for s~gle-post contact were met would be to ensure that the aspect ratio (the ratio of minor and major axes) for each of the ellipses (wheel and rail) was the same and that corresponding arcs were used, the rail ellipse being proportionally smaller than that of the wheel. Several other criteria must be taken into account in determining the values of RI, RB, R3, R4, etc., as follows. 2.1. Unbalanced superelevation and l&&al forces Whenever a vehicle is negotiating a curve, if the proper difference between the rolling radii of the inner and outer wheels is to exist, the angles of contact of the two will be different. This means that a net lateral force wilI exist (owing to the unequal horizontal components of the reaction forces at the wheels). See Fig. 5.
333
Fig. 5. Horizontal forces in steady state curving.
There is no friction force available during roiling contact, so this lateral force must be supplied either (a) from lateral motion of the wheel relative to the rail (resulting inevitably in contact with the flange), (b) from an angular misalignment of the wheels with the rails or (c) from unbalanced superelevation or centrifugal forces. Flange contact is highly undesirable if low noise and wear are the objectives. Angular ~s~~ent must be aged for the same reasons. This leaves the superelevation. It is easy to see from Fig. 5 that a deficiency in superelevation will provide a force in the correct sense. There is a limit to the level of unbalanced centrifugal force which can be tolerated by the passengers of a rail car, however. This limit is arrived at in two ways. Firstly, it is usually recommended that p.assengers not be subjected to more than 0.1 g laterally, for comfort and safety. Secondly, unbalanced lateral forces deflect the lateral suspension of the car, bringing the car nearer to its bump stops. A 1 Hz suspension is deflected 1 in (25 mm) by a 0.1 g lateral acceleration. This would be too close to the bump stops for most vehicles at their maximum operating speed. It is therefore reco~ended here that the system be designed for no more than 0.05 g lateral unbalance in the high speed curves. For this to be in equilibrium with the resultant lateral force at the wheels, the difference between the angles of contact should be approximately 3”. This criterion applies for the high speed curves because it is at high speeds that the bump stop clearance is most critical. For lower speed (sharper radius) curves, where the consequences of contact with the bump stops are less severe, a 0.1 g limit can be allowed. This would mean that a difference of 6” could be tolerated. 2.2. Contact patch width, contact an&e, co&city and corrugations Because the contact patch has a finite width, if it has an inclination to the plane of revolution, there is a spin component of the slip within the patch. This comes about because the rolling radius changes across the width of the contact and therefore so does the surface velocity of the wheel relative to the axis of rotation. The slip rate is given by
334
w
s=rotana
(2)
where w is the width of the contact patch, s is the slip rate and r, is the wheel running radius. The slip within the contact patch is linearly proportional to tan a. The width of the contact patch, on the other hand, is proportional to a function of R2, RI and the wheel diameter, such that it increases at a slower rate than R,I(R, - R,). Conicity is determined by eqn. (l), so from all of this it can be seen that, whereas it is inevitable that the slip within the contact patch will increase as conicity is increased, nevertheless, the increase in slip will be less if we obtain higher conicity from reducing R2 -RI rather than from increasing tan cy. A useful “rule of thumb” is that the rolling radius difference from one side of the contact patch to the other should not exceed 0.5% of the wheel diameter. This value can be used to determine the limits of CY,R2 and RI for a given wheel radius and vertical load. A wider contact patch results in lower contact stress values and thus the expectation of lower wear rates. Contrary to this, a wider contact patch can also result in greater slip within the contact patch and thus higher wear. A wider contact patch also creates more noise than a narrower one. 3. Track alignment It has been found that the wheels on steered axle trucks will run consistently on the same contact band. This fact, if unmitigated, can lead to undesirable behaviour, but it can also be taken advantage of as a means to control the effects of wear upon the wheel profile. Non-steered vehicles typically utilize a larger portion of the tread width for running contact and so “smear” the wear over a wide band and avoid close conformity. Track laid to wide gauge tolerances also has this effect. Wider gauge tolerances could be utilized for steered truck operation and this would undoubtedly alleviate the problem of profile conformity to some extent. Wider gauge tolerances, however, have the drawback of introducing larger random inputs to the wheelset and thus deteriorating the ride, and perhaps even the stability. 3.1. Gauge width variation A wiser alternative is to deliberately introduce varied gauge width over continuous lengths of the tangent track, maintaining the gauge tolerance within each length, to spread the contact points over a wide area of the tread without introducing larger random dynamic inputs. By deliberately choosing the proportions of distance run at various contact points on the wheel, the effects of wear can be controlled to maintain the worn profile to be very similar to the original machined profile. Let us examine a case to illustrate the principle.
335
Figure 6 shows a wheel profile which was designed for use with the steered truck on the Vancouver SkyTrain system. There is a wide part of the tread, between points C and D, which has a transverse radius of 300 mm (12 in). This is the section used for all of the mainline track and it operates against a rail with a 150 mm (6 in) crown radius. The area from D to E comes into use in the tight curves of the yard. It has a curvature of 29 mm (19 in), running against the rail shoulder of 20 mm ($8 in) radius. The running section has four points (P, Q, R and S) located at distances 12 mm apart. These are the four points at which contact is designed to occur on various sections of the tangent track. The rail profile, also shown in Fig. 6, has four corresponding points (P’, Q’, R’ and S’). Evidently, these points are 6 mm apart, the ratio of the radii being 2:l. For contact to occur at these corresponding points, the rail profile must be moved relative to the wheel profile so that P’ lines up with P in one track section, Q’ lines up with Q in another section and so on. Clearly then, the rail profile must move 6 mm relative to the wheel profile for each of these steps or, since the wheels are at constant gauge, the two rail profiles must move 12 mm relative to one another for each step. Setting the tangent track selectively at four different gauges throughout the system, - 12 mm, standard, + 12 mm and + 24 mm, will achieve the desired effect. (Note. For each 12 mm that the rail profiles move relative to each other, the contact points move 24 mm relative to each other.) 3.2. Wheel wear In Fig. 7 we see the result of the rail profile wearing itself conformally into the wheel profile at each of the four points. A dashed line is shown to illustrate the desired radius of 300 mm (12 in) for the worn zone. We see that in the middle of the zone the wear can be expected to produce the desired effect. Towards the flange side of the zone the wear will have to remove more metal than it does in the centre to produce the same penetration. This wiIl probably occur naturally because of the angle of contact and the increased contact stress. At the outside of the contact area we see that the penetration must be expected to be less. This is because, as the rail wears into the wheel, the
Fig. 6. Spreading the contact range.
Fig. 7. Wear in the profile with spread contacts. XNURCED DASUD
VUT LlNz
(88)
anOK.
Of CONTACT AREA IL”
(SOown) RADIUS
Fig. 8. Wear in the stepped profile.
contact band widens rapidly, increasing the conformity and reducing the stress. We see that the wear will not maintain the desired wheel profile. This problem can be overcome by undercutting the wheel profile, outside the desired area of contact, so as to equalize the expected depth of wear at each contact. This is shown in Fig. 8, where we see that the predicted worn radius of the wheel is very close to the newly machined profile radius. The “stepped” profile resulting from this technique can provide two other advantages. Firstly, as the wheel wears, the height of the step provides an easily observed “witness mark” to indicate when re-profiling is necessary. Since re-profiling is more likely to occur because of wheel surface deterioration than for hunting, the depth of the step should be determined in practice by
337
the amount of wear which takes place on a particular system before the wheel surface becomes unacceptable. Secondly, in a system where some curves exist which are of substantially smaller radius than the next larger ones (such as in a storage yard), the low rail contact point can be brought out onto the step on those curves, reducing the requirement for excursion up into the throat at the high rail. The “stepped” area can also be increased in inclination, if desired and if sufficient rim material exists, in order to reduce the contact angle difference in these sharp curves. 3.3. Gauge width in curves The above discussion concentrated on the deliberate scattering of contact points in tangent track in order to distribute wear and maintain a profile transverse curvature. For practical reasons only a few finite contact points were chosen, despite the fact that this will have a tendency to produce multiple “grooves” in the tread. The practical problems of maintaining track gauge to give completely uniform scatter of wear would be onerous. This is also unnecessary because, if a system has a substantial number of curves, as most do, there will be sufllcient contact in the intermediate areas between the tangent running contacts to ensure a wear surface without “grooves”. To illustrate this, let us look at data from the SkyTrain system given in Table 1. This table shows the curve distribution for the system and the contact point shift either side of contact point Q (i.e. for rails set at standard gauge) for these curves. It can be seen that 20% of the total track will give contact points 3-5 mm either side of point Q and that a further 4% will spread the wear by 7.5 mm. To create more contacts between points R and S, the lower rail could be profiled by grinding in some curves. Because of the reduced slope in the area from R to S on most profiles, this will probably only be
TABLE 1 Data from the SkyTrain system Range of radii (m)
Percentage of track
Average radius (m)
Rolling radius difference (mm)
Contact point shift (per side) (mm)
Contact angle difference (deg)
70-100 101-200 201300 301-500 501-1000 1000 +
1.34 4.22 12.96 7.17 11.08 6.97
87.33 166.27 260.60 413.86 779.2 1 2311.75
4.04 2.12 1.35 0.85 0.45 0.15
14.28 7.50 4.79 3.00 1.59 0.54
5.512 2.894 1.848 1.158 0.614 0.208
338
necessary in a few instances. Setting the gauge in all curves for contact point Q with the wheelset centred (i.e. standard gauge) will usually provide all the profile “smoothing” required. The treatment in the very sharp yard curves was discussed above. It is not presently proposed to take advantage of the potential for running outside the “step” on yard curves in Vancouver, but it is a possibility for the future. The profile as designed will allow for all the required rolling radius differences, including the 35 m yard curves. Fleet application awaits delivery of a wheel lathe and a rail grinder, both scheduled for 1991.
4. Test results The profiles shown here were tested on Vancouver’s SkyTrain system, on a track section over the new SkyBridge before it opened for service. The increased conic&y substantially reduced body yaw motions following an “S” curve, improving ride comfort overall and especially in that area. A curved profile running on the same, freshly ground, rail contact area as a new 1:20 straight tapered profile showed a 10 dbA reduction (from 74-75 to 64-65 dbA) in in-car noise. A similar curved profile running on a steeper, unused, part of the rail profile showed a 6 dbA reduction (to 68-69 dbA) compared to the straight taper on the freshly ground section. 5. Obtaining the rail profile The rail profile shown in Fig. 6 is considerably different from that which is available commercially. Evidently, the task of producing such a profile could be an onerous one if it were attempted to produce this throughout the system by profile grinding alone. Fortunately, this is not necessary. 5.1. Grinding uncanted rail The profile as shown provides for the complete range of contact points for all the requirements of the system. At no single position in the system, however, do all of these requirements have to be met. Tangent track only uses a range of contact around the centre. The high rail in curves uses a range around the gauge side and the low rail uses a range around the field side. As long as the actual rail does not protrude above the desired surface on either side of the working area for any location, this is sufficient. It may descend below that surface outside the desired working band. Figure 9 shows the maximum grinding required to create the required rail profile from a 115AREA section laid with no cant. The tangent track profile shown is for the extreme case where contact is required on the field side. For other contact points the profile can be “lifted” relative to the baseline, reducing the grinding required. On the high rail of curves it can be seen that very little grinding is required, but for the
339
, r-Ill
I’
LOF
run
Fig. 9. Rail-head-grinding patterns.
NO RAIL
1:20
CANT
RAIL
CANT
Fig. 10. Effect of rail cant in head grinding.
low rail it can be considerable. This is alleviated as much as possible by not grinding the gauge corner. Because, with steered trucks, both axles move out towards the high rail, it is not necessary to clear the flange root on the low rail. (This would not apply for non-steered trucks.) 5.2. Grinding
canted
rail
Laying the rail with sufficient cant angle can substantially reduce the amount of rail grinding required. This is illustrated in Fig. 10. This technique also allows for reversing of the rails and thereby reduces waste of rail head material. The example given here was for a system with very small wheels, so it was possible to achieve the modest rolling radius difference required with a relatively low contact angle. For other systems, greater rolling radius difference and therefore steeper contact angles might be required. If so, greater rail cant might be recommended. In these illustrations the rail head and profile shape were both moved laterally by the amount required to give the correct contact point on the wheel. Profile grinding of the rail head can also be used as a practical technique for changing the apparent gauge without changing the actual gauge face distance of the rails (such as through special trackwork). The desired rail profile simply has to be shifted laterally by the required amount, without shifting the rail head, and superimposed upon it. Clearly this will usually require more grinding. The extra grinding can be reduced in some circumstances by omitting the grinding of the gauge corner. In practical circumstances it will often be found that this is not permissible because of the two-point contact which will then occur during transient lateral excursions of the wheelset. The technique of rail re-gauging (and perhaps canting, if necessary,
340
to reduce grinding) will usually be found to be the most effective and easily maintained. It will also sometimes be found, as is the case in Vancouver, that existing rail with insufficient cant has nevertheless worn to an asymmetrical shape so that it effectively has a properly canted face and only requires minor grinding to produce the required effect. 6. Conclusions A design technique has been described which allows a wheel-rail system to be created to suit steered axle vehicles. Such a system will reduce maintenance costs by being almost self-perpetuating and will reduce the incidence of certain kinds of wheel and rail corrugation. The cost of implementation when the system is built is very low, and alternative techniques have been described which are cost effective for implementation in existing systems. Although the technique which has been described here is particularly beneficial and applicable for use with steered axles, some important aspects of it will also find application in more conventional systems. The use of a “step” in the wheel profile may not be applicable to unsteered trucks and/or heavy haul systems, for instance, because usually in those cases both axles do not seek the high rail as do steered ones. Typically these systems do not have extremely tight curves and the step could promote wheel shelling where the track gauge tolerances are such that contacts on the corner of the step could occur. The rail profile will inevitably wear “flatter”. To maintain the benefits described, a programme of rail profile grinding is necessary, primarily outside the contact area, to regain the rail head shape. The successful prototype testing conducted in Vancouver indicates that there is potential for “system-specific” wheel-rail profile design. Whether the objective is improvement in noise, ride quality, maintenance costs, wheel and/or rail life, tailoring the profiles to the system can go a long way towards achieving these goals. References 1 R. E. Smith and R. J. Anderson, Characteristics of guided steering railway trucks, Vehicle Syst. Dyn., 17 (1988) l-36. 2 A. H. Wickens, The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels, Znt. J. Solids Strut., 1 (1965) 319-341.
Appendix
A: Discussion
Question
of paper
(Dr. Rao): Would gauge widening seriously affect the behaviour
of the profile pair? Answer (Mr. Smith): The gauge variations suggested in the paper cause the worn wheel profile to resemble the new wheel profile more closely than
341
would otherwise be the case. Consequently the behaviour of the profile pair is more consistent over a long running period than would ~onvention~ly be the case. Question (professor Kndhe): Do you think that the methodology which you have proposed would also work for mixed trafllc, e.g. bogies with both steered and unsteered wheelsets on the same track? For example, would the critical gauge variation be allowed under such circumstances? Answer (Mr. Sm~th)~ Clearly the parameters which the system designer could modify would be constrained differently if non-steered trucks were to be operated on the system as well as steered ones. I believe that the technique itself may still be applied in substance but the performance boundaries would be different. Question @r. Grassier: Have you identified the noise mechanisms (e.g. wheel squeal, impact, rolhng noise) associated with the reductions of 10 dB and 6 dB which were found with the change in wheel/rail profiles? Answer (Mr. Smith): No detailed examination of this was undertaken: the measurements were simply recorded and the effects noted. I think that rolling noise would be the principal mech~ism, and that the narrower contact patch brought about by a reduction in conformity of the profiles is the principal reason for the reduction in noise. It should be noted that this vehicle had an unusually direct noise transmission path into the vehicle. The reduction in noise may have been less noticeable in a vehicle with better isolation. Qwestion (ProfessorKalker): Is anything known about the wear behaviour of this new wheel/rail profile? Answer (Mr. Smith): The profiles, as described, are designed to minimise longitudinal and lateral creepages and spin. It is unavoidable that some residual creep wilI occur but this will be less than with conventional wheel/ raiI systems. This is p~cul~ly so for the worn condition as conventional techniques allow closer conformity to deveelop and spin creep to increase. Question (Mr. Sroba): You presented a table showing a desired shift of the contact band e.g. 14 mm in a 70 m curve and 9 mm in shallower curves. Do you actually try to achieve these different shifts in each of the different curves? Answer (MT-. Smith): The wheelset itseIf tends naturally to run at these offsets. Non-steered trucks prevent this from occurring because of the misalignments which they impose. Steered trucks allow proper alignment and the wheelsets (both leading and trailing) seek their proper lateral offset to achieve nearly pure rolling. This has been observed to occur in practice during these tests. @u-W&m (nr. Palhan): Were any running stability tests carried out to assess the ride quality with the new profile?
342
Answer (Mr. Smith): Yes, running stability tests were undertaken with heartening results: the ride indices dropped from 2.8 to 2.4 for tests on the same section of track. Question @fr. Debailk) : At what speed was the noise reduction of 10 dbA measured for the new wheel profile? Answer (Mr. Smith): All of the noise measurements to which I referred were made at 80 km h-l. I should stress that this type of vehicle had a particularly direct noise transmission path from truck to body and that noise measurements were made inside the vehicle.
329
A design methodology for wheel and rail profiles for use on steered railway vehicles Roy E. Smith RZSCO Engineering,
823 Overlea Court, Kingston, Ontario K7M 628 (Canada]
J. Kalousek National Research Ctnmcil of Canada, Tribologg and Mechanics Laboratory, 3650 We&rook Mall, Vancouver V6S 2L2 (Canada)
Abstract The geometry of the interface between steel wheels and steel rails can create conditions which affect the dynamics of a vehicle, the development of rail and wheel corrugation and noise. It has come to be expected that the worn protlle of the wheel is uncontrollable and must be regularly corrected. This reflects the normal experience with non-steered trucks. Dynamicists have usually chosen a range of cordcities to bound the performance of a vehicle design. Maintenance techniques have then been used to control the conditions occurring in service to be within these bounds. Hunting (instability generated by the self-centrlng action of the coned wheelset) is thereby controlled. Increasing demand for higher performance reduces the range of conlcity allowable (using conventional truck technology). The cost of maintaining that conicity increases. The design technique described here enables wheel and rail profiles to be developed which have a limited range of conicity throughout their life, generate little noise, greatly reduce corrugation and, when used on steered axle vehicles, together with the described techniques of trade geometry control, can be virtually self-perpetuating. These are important benefits for the system operator.
1. The bounds
of the problem
Vehicles with steered axles have a number of dynamic features which are peculiar to the type [ 11. Two of these properties are: (1) such vehicles have greater stability than similar unsteered ones at the medium and high conic&y range (worn wheels); (2) such vehicles can have low frequency instabilities at low conic&y and/or creep coefficient. The design range for the conicity may thus be extended at the high end but may also have a higher limit at the low end. (Note. The only low limit for conicity on non-steered trucks is the point at which flange-flange wandering or “zigzag” motion takes place owing to a lack of self-centring.) Maintaining conformity of the wheel and rail profiles reduces contact stress. If the profiles become too closely conformal, however, two undesirable results arise. Firstly, the effective conicity of the wheelset increases. Hunting instabilities, at frequencies around 11 Hz, were regularly observed in Vancouver 0043-1648l91B3.50
0 Elsevier Sequoia/Printed in The Netherlands
330
at speeds of 80 km h and sometimes less. This demonstrated that conicity in excess of 1 .O had been reached with only 1.5 mm of radial wear on wheelsets which began life with a taper of 1:20! Secondly, as the profile conformity increases, very high frequency localized oscillations can be set up (CCL800 Hz), involving rotation and/or translation of the rail head. The wear patterns produced by these oscillations can result in short wavelength (CCL50 mm) corrugation of the wheel and the rail. These osc~ations are aggravated by the presence of even small amounts of steady state lateral slip in the contact patch. This has also been observed in Vancouver. 2. Design method It has been well known for some time (see Wickens [Z], who further acknowledges Heumann and dePater) that the effective conicity of a wheelset can be given by the function . .
&
conicity= R2_RI tan LY
(1)
where RI is the transverse radius of the rail head, Rz is the transverse radius of the wheel profile and LYis the angle of contact. This expression is actually a simplification of the full relationship which exists between these terms, but it is a useful approximation which enables us to gain insights into the effect of profile geometry upon conicity. The straight tapered wheel runnmg on a rail of finite transverse radius has an effective conicity of tan cy. To obtain moderate or high levels of conicity, the value of (Y must be correspondingly high. This is because R2 is infinite and therefore the quotient R2/(R2-RI) is unity. This is illustrated in Fig. 1. With finite values for Rz the quotient RJ(R, -RI) becomes greater than unity and, in the limit as Rz approaches the value of RI,this value approaches infinity. Evidently it is possible, using curved profiles, to obtain almost any desired value for the conicity while maintaining a small value for CY. Two simultaneous points of contact between the wheel and the rail are highly undesirable. As long as the wheel and rail profiles are each single circular arcs, with R2 > RI,this isavoided. Unfortunately, such profiles generally require too much wheel ~dth.~d/or lateral motion to achieve the extremes of rolling radius difference required in tight curves. To satisfy these requirements, the proties may be designed by combining two or more arc radii. To do this, however, some rules must be formulated so as to avoid two-point contact. Necessary and sufficient conditions at all potential points of contact are that the inclinations to the horizontal of both wheel and rail must be equal and the rail radius must be smaller than the wheel radius at that point. A simple design methodology, for profiles which are to be made up of a series of circular arcs, is as follows.
331
WHEEL
CONICITY
FOR STRAIGHT
CONICITY
?OR CURVED PROFILE
= TANa
TAPER =
RP RL-Rl
TANa
-
v
Fig. 1. Effect of profile curvature on conicity.
ROLLING
RAD. DIFF. CONTACT
EXCURSION
Fig.
2. A proiile using a single circular arc.
(1) For tangent sections and large radius curves choose a wheel transverse radius which will provide the required rolling radius difference within a reasonable lateral excursion. See Fig. 2. (2) Determine the largest rolling radius difference which will be required throughout the operating system. Connect a second circular arc, of smaller radius than the first, to the first one, the tangents at the point of connection being coincident. Choose this radius such that the remaining rolling radius differential is provided within the remaining lateral excursion. See Fig. 3 (3) Create a rail profile which will provide single-point contact with the wheel profile at all times. This is done by selecting rail radii to correspond with each of the wheel radii and then creating a rail profile by connecting arcs of each of these radii. The lengths of the arcs in the rail profile must subtend the same angles at their centres as their mating ones on the wheel. By this means it is ensured that two-point contact can never occur. Beyond the region within which it is intended that wheel-rail contact shall occur, the rail profile may take on the same shape as the root and flange of the wheel. This can be seen in Fig. 4. The limit of expected wheel-rail contact (the working area) is shown in heavier line. Outside this area the rail profile may fall below the line shown and the wheel profile may rise above the line
Fig. 3. A profile using two blended circuIar Fig. 4. Derivation
of the required
ares.
rail profile.
shown, but not vice versa. Any deviation from this can cause a second point of contact to occur, in an area outside the designed one, and this can have undesirable effects upon vehicle behaviour, noise and wear. (Note. Contact occurs in a patch of fimte width and this must be taken into account when establishing the width of the working area on the wheel. Some random lateral excursions from the true curving position are also to be expected in normal operation and these must also be allowed for in the working area of the tread.) The design shown here is a simple one. It was assumed that the system would be divisible into two regimes: the first a high speed one, containing the tangent sections and large curves, in which moderate conicity would be required; the second a low speed one, containing the sharp curves, where high conicity would be allowed. In some instances it may be necessary to subdivide the running regimes further, into three sections for instance, and thus have three radii in the working ranges of both wheel and rail. It is also possible to conceive of profile designs which, in the working zone, are made of a single arc of an ellipse. All that would be required to ensure that the control for s~gle-post contact were met would be to ensure that the aspect ratio (the ratio of minor and major axes) for each of the ellipses (wheel and rail) was the same and that corresponding arcs were used, the rail ellipse being proportionally smaller than that of the wheel. Several other criteria must be taken into account in determining the values of RI, RB, R3, R4, etc., as follows. 2.1. Unbalanced superelevation and l&&al forces Whenever a vehicle is negotiating a curve, if the proper difference between the rolling radii of the inner and outer wheels is to exist, the angles of contact of the two will be different. This means that a net lateral force wilI exist (owing to the unequal horizontal components of the reaction forces at the wheels). See Fig. 5.
333
Fig. 5. Horizontal forces in steady state curving.
There is no friction force available during roiling contact, so this lateral force must be supplied either (a) from lateral motion of the wheel relative to the rail (resulting inevitably in contact with the flange), (b) from an angular misalignment of the wheels with the rails or (c) from unbalanced superelevation or centrifugal forces. Flange contact is highly undesirable if low noise and wear are the objectives. Angular ~s~~ent must be aged for the same reasons. This leaves the superelevation. It is easy to see from Fig. 5 that a deficiency in superelevation will provide a force in the correct sense. There is a limit to the level of unbalanced centrifugal force which can be tolerated by the passengers of a rail car, however. This limit is arrived at in two ways. Firstly, it is usually recommended that p.assengers not be subjected to more than 0.1 g laterally, for comfort and safety. Secondly, unbalanced lateral forces deflect the lateral suspension of the car, bringing the car nearer to its bump stops. A 1 Hz suspension is deflected 1 in (25 mm) by a 0.1 g lateral acceleration. This would be too close to the bump stops for most vehicles at their maximum operating speed. It is therefore reco~ended here that the system be designed for no more than 0.05 g lateral unbalance in the high speed curves. For this to be in equilibrium with the resultant lateral force at the wheels, the difference between the angles of contact should be approximately 3”. This criterion applies for the high speed curves because it is at high speeds that the bump stop clearance is most critical. For lower speed (sharper radius) curves, where the consequences of contact with the bump stops are less severe, a 0.1 g limit can be allowed. This would mean that a difference of 6” could be tolerated. 2.2. Contact patch width, contact an&e, co&city and corrugations Because the contact patch has a finite width, if it has an inclination to the plane of revolution, there is a spin component of the slip within the patch. This comes about because the rolling radius changes across the width of the contact and therefore so does the surface velocity of the wheel relative to the axis of rotation. The slip rate is given by
334
w
s=rotana
(2)
where w is the width of the contact patch, s is the slip rate and r, is the wheel running radius. The slip within the contact patch is linearly proportional to tan a. The width of the contact patch, on the other hand, is proportional to a function of R2, RI and the wheel diameter, such that it increases at a slower rate than R,I(R, - R,). Conicity is determined by eqn. (l), so from all of this it can be seen that, whereas it is inevitable that the slip within the contact patch will increase as conicity is increased, nevertheless, the increase in slip will be less if we obtain higher conicity from reducing R2 -RI rather than from increasing tan cy. A useful “rule of thumb” is that the rolling radius difference from one side of the contact patch to the other should not exceed 0.5% of the wheel diameter. This value can be used to determine the limits of CY,R2 and RI for a given wheel radius and vertical load. A wider contact patch results in lower contact stress values and thus the expectation of lower wear rates. Contrary to this, a wider contact patch can also result in greater slip within the contact patch and thus higher wear. A wider contact patch also creates more noise than a narrower one. 3. Track alignment It has been found that the wheels on steered axle trucks will run consistently on the same contact band. This fact, if unmitigated, can lead to undesirable behaviour, but it can also be taken advantage of as a means to control the effects of wear upon the wheel profile. Non-steered vehicles typically utilize a larger portion of the tread width for running contact and so “smear” the wear over a wide band and avoid close conformity. Track laid to wide gauge tolerances also has this effect. Wider gauge tolerances could be utilized for steered truck operation and this would undoubtedly alleviate the problem of profile conformity to some extent. Wider gauge tolerances, however, have the drawback of introducing larger random inputs to the wheelset and thus deteriorating the ride, and perhaps even the stability. 3.1. Gauge width variation A wiser alternative is to deliberately introduce varied gauge width over continuous lengths of the tangent track, maintaining the gauge tolerance within each length, to spread the contact points over a wide area of the tread without introducing larger random dynamic inputs. By deliberately choosing the proportions of distance run at various contact points on the wheel, the effects of wear can be controlled to maintain the worn profile to be very similar to the original machined profile. Let us examine a case to illustrate the principle.
335
Figure 6 shows a wheel profile which was designed for use with the steered truck on the Vancouver SkyTrain system. There is a wide part of the tread, between points C and D, which has a transverse radius of 300 mm (12 in). This is the section used for all of the mainline track and it operates against a rail with a 150 mm (6 in) crown radius. The area from D to E comes into use in the tight curves of the yard. It has a curvature of 29 mm (19 in), running against the rail shoulder of 20 mm ($8 in) radius. The running section has four points (P, Q, R and S) located at distances 12 mm apart. These are the four points at which contact is designed to occur on various sections of the tangent track. The rail profile, also shown in Fig. 6, has four corresponding points (P’, Q’, R’ and S’). Evidently, these points are 6 mm apart, the ratio of the radii being 2:l. For contact to occur at these corresponding points, the rail profile must be moved relative to the wheel profile so that P’ lines up with P in one track section, Q’ lines up with Q in another section and so on. Clearly then, the rail profile must move 6 mm relative to the wheel profile for each of these steps or, since the wheels are at constant gauge, the two rail profiles must move 12 mm relative to one another for each step. Setting the tangent track selectively at four different gauges throughout the system, - 12 mm, standard, + 12 mm and + 24 mm, will achieve the desired effect. (Note. For each 12 mm that the rail profiles move relative to each other, the contact points move 24 mm relative to each other.) 3.2. Wheel wear In Fig. 7 we see the result of the rail profile wearing itself conformally into the wheel profile at each of the four points. A dashed line is shown to illustrate the desired radius of 300 mm (12 in) for the worn zone. We see that in the middle of the zone the wear can be expected to produce the desired effect. Towards the flange side of the zone the wear will have to remove more metal than it does in the centre to produce the same penetration. This wiIl probably occur naturally because of the angle of contact and the increased contact stress. At the outside of the contact area we see that the penetration must be expected to be less. This is because, as the rail wears into the wheel, the
Fig. 6. Spreading the contact range.
Fig. 7. Wear in the profile with spread contacts. XNURCED DASUD
VUT LlNz
(88)
anOK.
Of CONTACT AREA IL”
(SOown) RADIUS
Fig. 8. Wear in the stepped profile.
contact band widens rapidly, increasing the conformity and reducing the stress. We see that the wear will not maintain the desired wheel profile. This problem can be overcome by undercutting the wheel profile, outside the desired area of contact, so as to equalize the expected depth of wear at each contact. This is shown in Fig. 8, where we see that the predicted worn radius of the wheel is very close to the newly machined profile radius. The “stepped” profile resulting from this technique can provide two other advantages. Firstly, as the wheel wears, the height of the step provides an easily observed “witness mark” to indicate when re-profiling is necessary. Since re-profiling is more likely to occur because of wheel surface deterioration than for hunting, the depth of the step should be determined in practice by
337
the amount of wear which takes place on a particular system before the wheel surface becomes unacceptable. Secondly, in a system where some curves exist which are of substantially smaller radius than the next larger ones (such as in a storage yard), the low rail contact point can be brought out onto the step on those curves, reducing the requirement for excursion up into the throat at the high rail. The “stepped” area can also be increased in inclination, if desired and if sufficient rim material exists, in order to reduce the contact angle difference in these sharp curves. 3.3. Gauge width in curves The above discussion concentrated on the deliberate scattering of contact points in tangent track in order to distribute wear and maintain a profile transverse curvature. For practical reasons only a few finite contact points were chosen, despite the fact that this will have a tendency to produce multiple “grooves” in the tread. The practical problems of maintaining track gauge to give completely uniform scatter of wear would be onerous. This is also unnecessary because, if a system has a substantial number of curves, as most do, there will be sufllcient contact in the intermediate areas between the tangent running contacts to ensure a wear surface without “grooves”. To illustrate this, let us look at data from the SkyTrain system given in Table 1. This table shows the curve distribution for the system and the contact point shift either side of contact point Q (i.e. for rails set at standard gauge) for these curves. It can be seen that 20% of the total track will give contact points 3-5 mm either side of point Q and that a further 4% will spread the wear by 7.5 mm. To create more contacts between points R and S, the lower rail could be profiled by grinding in some curves. Because of the reduced slope in the area from R to S on most profiles, this will probably only be
TABLE 1 Data from the SkyTrain system Range of radii (m)
Percentage of track
Average radius (m)
Rolling radius difference (mm)
Contact point shift (per side) (mm)
Contact angle difference (deg)
70-100 101-200 201300 301-500 501-1000 1000 +
1.34 4.22 12.96 7.17 11.08 6.97
87.33 166.27 260.60 413.86 779.2 1 2311.75
4.04 2.12 1.35 0.85 0.45 0.15
14.28 7.50 4.79 3.00 1.59 0.54
5.512 2.894 1.848 1.158 0.614 0.208
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necessary in a few instances. Setting the gauge in all curves for contact point Q with the wheelset centred (i.e. standard gauge) will usually provide all the profile “smoothing” required. The treatment in the very sharp yard curves was discussed above. It is not presently proposed to take advantage of the potential for running outside the “step” on yard curves in Vancouver, but it is a possibility for the future. The profile as designed will allow for all the required rolling radius differences, including the 35 m yard curves. Fleet application awaits delivery of a wheel lathe and a rail grinder, both scheduled for 1991.
4. Test results The profiles shown here were tested on Vancouver’s SkyTrain system, on a track section over the new SkyBridge before it opened for service. The increased conic&y substantially reduced body yaw motions following an “S” curve, improving ride comfort overall and especially in that area. A curved profile running on the same, freshly ground, rail contact area as a new 1:20 straight tapered profile showed a 10 dbA reduction (from 74-75 to 64-65 dbA) in in-car noise. A similar curved profile running on a steeper, unused, part of the rail profile showed a 6 dbA reduction (to 68-69 dbA) compared to the straight taper on the freshly ground section. 5. Obtaining the rail profile The rail profile shown in Fig. 6 is considerably different from that which is available commercially. Evidently, the task of producing such a profile could be an onerous one if it were attempted to produce this throughout the system by profile grinding alone. Fortunately, this is not necessary. 5.1. Grinding uncanted rail The profile as shown provides for the complete range of contact points for all the requirements of the system. At no single position in the system, however, do all of these requirements have to be met. Tangent track only uses a range of contact around the centre. The high rail in curves uses a range around the gauge side and the low rail uses a range around the field side. As long as the actual rail does not protrude above the desired surface on either side of the working area for any location, this is sufficient. It may descend below that surface outside the desired working band. Figure 9 shows the maximum grinding required to create the required rail profile from a 115AREA section laid with no cant. The tangent track profile shown is for the extreme case where contact is required on the field side. For other contact points the profile can be “lifted” relative to the baseline, reducing the grinding required. On the high rail of curves it can be seen that very little grinding is required, but for the
339
, r-Ill
I’
LOF
run
Fig. 9. Rail-head-grinding patterns.
NO RAIL
1:20
CANT
RAIL
CANT
Fig. 10. Effect of rail cant in head grinding.
low rail it can be considerable. This is alleviated as much as possible by not grinding the gauge corner. Because, with steered trucks, both axles move out towards the high rail, it is not necessary to clear the flange root on the low rail. (This would not apply for non-steered trucks.) 5.2. Grinding
canted
rail
Laying the rail with sufficient cant angle can substantially reduce the amount of rail grinding required. This is illustrated in Fig. 10. This technique also allows for reversing of the rails and thereby reduces waste of rail head material. The example given here was for a system with very small wheels, so it was possible to achieve the modest rolling radius difference required with a relatively low contact angle. For other systems, greater rolling radius difference and therefore steeper contact angles might be required. If so, greater rail cant might be recommended. In these illustrations the rail head and profile shape were both moved laterally by the amount required to give the correct contact point on the wheel. Profile grinding of the rail head can also be used as a practical technique for changing the apparent gauge without changing the actual gauge face distance of the rails (such as through special trackwork). The desired rail profile simply has to be shifted laterally by the required amount, without shifting the rail head, and superimposed upon it. Clearly this will usually require more grinding. The extra grinding can be reduced in some circumstances by omitting the grinding of the gauge corner. In practical circumstances it will often be found that this is not permissible because of the two-point contact which will then occur during transient lateral excursions of the wheelset. The technique of rail re-gauging (and perhaps canting, if necessary,
340
to reduce grinding) will usually be found to be the most effective and easily maintained. It will also sometimes be found, as is the case in Vancouver, that existing rail with insufficient cant has nevertheless worn to an asymmetrical shape so that it effectively has a properly canted face and only requires minor grinding to produce the required effect. 6. Conclusions A design technique has been described which allows a wheel-rail system to be created to suit steered axle vehicles. Such a system will reduce maintenance costs by being almost self-perpetuating and will reduce the incidence of certain kinds of wheel and rail corrugation. The cost of implementation when the system is built is very low, and alternative techniques have been described which are cost effective for implementation in existing systems. Although the technique which has been described here is particularly beneficial and applicable for use with steered axles, some important aspects of it will also find application in more conventional systems. The use of a “step” in the wheel profile may not be applicable to unsteered trucks and/or heavy haul systems, for instance, because usually in those cases both axles do not seek the high rail as do steered ones. Typically these systems do not have extremely tight curves and the step could promote wheel shelling where the track gauge tolerances are such that contacts on the corner of the step could occur. The rail profile will inevitably wear “flatter”. To maintain the benefits described, a programme of rail profile grinding is necessary, primarily outside the contact area, to regain the rail head shape. The successful prototype testing conducted in Vancouver indicates that there is potential for “system-specific” wheel-rail profile design. Whether the objective is improvement in noise, ride quality, maintenance costs, wheel and/or rail life, tailoring the profiles to the system can go a long way towards achieving these goals. References 1 R. E. Smith and R. J. Anderson, Characteristics of guided steering railway trucks, Vehicle Syst. Dyn., 17 (1988) l-36. 2 A. H. Wickens, The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels, Znt. J. Solids Strut., 1 (1965) 319-341.
Appendix
A: Discussion
Question
of paper
(Dr. Rao): Would gauge widening seriously affect the behaviour
of the profile pair? Answer (Mr. Smith): The gauge variations suggested in the paper cause the worn wheel profile to resemble the new wheel profile more closely than
341
would otherwise be the case. Consequently the behaviour of the profile pair is more consistent over a long running period than would ~onvention~ly be the case. Question (professor Kndhe): Do you think that the methodology which you have proposed would also work for mixed trafllc, e.g. bogies with both steered and unsteered wheelsets on the same track? For example, would the critical gauge variation be allowed under such circumstances? Answer (Mr. Sm~th)~ Clearly the parameters which the system designer could modify would be constrained differently if non-steered trucks were to be operated on the system as well as steered ones. I believe that the technique itself may still be applied in substance but the performance boundaries would be different. Question @r. Grassier: Have you identified the noise mechanisms (e.g. wheel squeal, impact, rolhng noise) associated with the reductions of 10 dB and 6 dB which were found with the change in wheel/rail profiles? Answer (Mr. Smith): No detailed examination of this was undertaken: the measurements were simply recorded and the effects noted. I think that rolling noise would be the principal mech~ism, and that the narrower contact patch brought about by a reduction in conformity of the profiles is the principal reason for the reduction in noise. It should be noted that this vehicle had an unusually direct noise transmission path into the vehicle. The reduction in noise may have been less noticeable in a vehicle with better isolation. Qwestion (ProfessorKalker): Is anything known about the wear behaviour of this new wheel/rail profile? Answer (Mr. Smith): The profiles, as described, are designed to minimise longitudinal and lateral creepages and spin. It is unavoidable that some residual creep wilI occur but this will be less than with conventional wheel/ raiI systems. This is p~cul~ly so for the worn condition as conventional techniques allow closer conformity to deveelop and spin creep to increase. Question (Mr. Sroba): You presented a table showing a desired shift of the contact band e.g. 14 mm in a 70 m curve and 9 mm in shallower curves. Do you actually try to achieve these different shifts in each of the different curves? Answer (MT-. Smith): The wheelset itseIf tends naturally to run at these offsets. Non-steered trucks prevent this from occurring because of the misalignments which they impose. Steered trucks allow proper alignment and the wheelsets (both leading and trailing) seek their proper lateral offset to achieve nearly pure rolling. This has been observed to occur in practice during these tests. @u-W&m (nr. Palhan): Were any running stability tests carried out to assess the ride quality with the new profile?
342
Answer (Mr. Smith): Yes, running stability tests were undertaken with heartening results: the ride indices dropped from 2.8 to 2.4 for tests on the same section of track. Question @fr. Debailk) : At what speed was the noise reduction of 10 dbA measured for the new wheel profile? Answer (Mr. Smith): All of the noise measurements to which I referred were made at 80 km h-l. I should stress that this type of vehicle had a particularly direct noise transmission path from truck to body and that noise measurements were made inside the vehicle.