ABSTRACT For many years, the North American Railway industry has been interested in the shock and vibration environment of freight cars. Initially this interest was related to the potential damage to cargo. More recently the interest has expanded to enhanced car and component reliability. A recent important subtopic has been the installed resonance frequencies of pneumatic equipment for air brake control valves (CVs). Perhaps the most critical accessory feature of a railcar is the braking system -- a complicated assembly of pneumatic controls and air reservoirs. Millions of pneumatic brake control valves are in service every day in North America. These devices depend on spring-loaded parts moving within very small dimensional clearances to work properly. As pneumatic controls, they are challenged to receive and repeat subtle air difference signals down the length of any train they comprise. Further, they are expected to work in all weather and operating conditions, and for several years at a time without any maintenance or inspection. At this time, the North American rail industry does not have any standards for CV design or mounting that accounts for vibration. The CV builders themselves have put one proposal forward. The industry is currently discussing this proposed design limit -- it would require installed natural frequencies to be above a minimum value. The valves themselves have been studied at length. However an examination of the current variations in both acceptable and “suspect” railcars has not been available thus far. In this paper, variations in resonance for existing attachment methods will be presented, as well as common response modes. In addition, a preliminary method for predicting the severity of vibration levels for different freight cars will be presented. NOMENCLATURE SR Severity Rating of likely field vibration at Control Valve L Location Factor E Empty Weight Factor Z Railcar input vibration, assumed from vertical spectrum found in AECTP-400 V Inertance FRF of the Control Valve, driving point vertical (g/lb, These are the traditional H1 calculations
using no windowing on a 4096-sample records that completely contain the accelerometer response. Data was collected with a 2000 Hz sampling rate using a 48 msec pretrigger.)
Axes In this and most railroad literature, longitudinal is the direction of train travel. Lateral is to the left in the
direction of travel, and vertical is up. Roll, pitch and yaw motions are taken about the longitudinal, lateral, and vertical axes respectively.
Proceedings of the IMAC-XXVIIIFebruary 1–4, 2010, Jacksonville, Florida USA
INTRODUCTION Automatic air brakes were first introduced ion trains in the early part of the twentieth century. Prior to this time brakemen ran perilously atop railcars applying the brakes by hand. The idea and implementation to automate air brakes conceived by George Westinghouse was a major leap forward for the rail industry in productivity and safety. The initial design was a simple air valve on the locomotive that controlled brake cylinder pistons on each car to apply the brakes. The idea quickly exposed its limitations when trains were separated and the cars were without brakes, and cut-off from any control. Westinghouse quickly engineered the solution by developing the “triple valve” to control and store air on each railcar. With the triple valve, the engineer no longer would apply pressure to set the brakes. Instead, a line of compressed air was maintained throughout the train, and the engineer would reduce pressure (the pneumatic signal) to brake. Then each triple valve would respond by using the car’s stored air to apply the brakes. Brake control valves (CVs) operating today still employ this method. This has allowed trains to grow in length, size and tonnage. In 1910, a heavy car was 50,000 lb (22.3 kg) whereas today 290,000 lb (129.5 kg) is common. Also, as loaded capacity has increased, empty (tare) weights have decreased. Today’s 290,000 lb (130 kg) railcar only weighs 45,000 lbs (20.1 kg) when it is empty. For decades, freight car design has been driven by three prime goals: “longer asset life, lighter weight, and higher payload capacity.” [1] Regarding efficiency of the transportation mode, the results have been quite good. However, starting in the early 1990s some in the rail industry began to believe that lighter weight car designs were responsible for a harsher operating environment felt by the accessories mounted on cars [2, 3]. The aforementioned papers were results of extensive tests by the CV (control valve) makers. They outlined modifications of their products to lessen vibration-induced wear. This again restored the CV service life, but the need for optimized mechanical car designs, and greater railroad efficiency (more and faster miles) continues to challenge the hardware. As the CV manufacturers gathered more data and understanding of the problem, they began to focus on the localized supporting brackets used to attach the CV to the freight car. In particular, they have proposed that the supporting brackets and car structure be designed such that its resonance frequency is between 135 and 200 Hz. [2] Railroads aggressively push the limits of braking performance to accommodate today’s heavier trains, and increase productivity while reducing costs. Due to design longevity, many parts within today’s automatic airbrake valves were engineered with the freightcar of the 1970s in mind. Considering the light weight of today’s cars their insensitivity to 21st-century vibrations is still successful. However, recent reliaibliity concerns show that some attention to the supporting structures may be merited. SOURCES OF RAILCAR VIBRATION Some amount of vibration will occur any time a train is moving. Some of the track-based energy is due to random irregularities, having no periodicity. Track designed for higher speeds is inherently smoother due to U.S. government regulations for track quality [4]. However, in general the random inputs get stronger as the train encounters them faster. This leads to a well-known increase in ride roughness with increased train speed. Note that if certain rigid body resonances (pitch, roll, bounce) or kinematic wheelset lateral hunting occur, the response will be an exception to this overall trend of higher speeds leading to rougher ride. In addition to random track roughness, other energy sources can be periodic and speed-dependent, as shown in Figure 1. This shows forcing frequencies versus train speed for three common sources: historical 39-foot (11.9 m) spacing of rail joints, wheel RPM, and sleeper (or crosstie) spacing. The three colored regions bound the fundamental through 3rd harmonic frequency for these common sources of periodic energy. The lowest shaded region in the figure is due to rail joints. If the track is made of jointed rail in North America, most commonly one will find 39.5-ft. pieces of rail. Since the bending strength of the rail is less near a joint, dips in the track can develop over time. Several railcar types tend to respond to these dips by showing rigid body roll (rotation about the X-axis) at 1.9-2.8 Hz, which corresponds to 12-18 mph train operations. This is sometimes called “rock and roll” and is the most common car dynamic issue relative to jointed rail. Car/payload combinations
with higher centers-of-gravity (CGs) exacerbate this. For this reason, the A.A.R. limits the overall car CGs to 98“ (or less) above the top of rail [5].
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Figure 1. Speed-dependent energy sources of railcar vibration. Colored regions bound the fundamental
and 3rd harmonic frequency for three common sources of tonal energy. The next higher shaded region is related to wheel imperfections and RPM. These can be either flat spots (which are tolerable to about 1 sq. inch in area) on a portion of the tread, or out-of-round (which allows runout of up to 0.07” or 1.78mm) wheels. The top shaded region in the plot is due to sleeper (crosstie) spacing. Placement of wooden sleepers varies somewhat, but they are usually spaced along the track at 19.5-inch (0.48m) centers. When directly over a sleeper, the rail is effectively in vertical compression, resting directly on the sleeper below. When a wheel is between two sleepers, the rail is supporting the wheel in bending, as a simply supported beam with a different vertical stiffness. As the railcar rolls, it sees these periodic changes in stiffness as a varying force input. Given the wide variety of track and operating speeds, it is difficult to represent the overall vibration source for rail vehicles. Even so, various North American and EU specifications exist for designing components that will fulfill their service lives on rail vehicles (rolling stock). A long-standing illustration of the broad nature of the energy available can be found in U.S. and NATO military specifications MIL-STD-810F [6], and AECTP 400 [7]. The North American rail spectra are essentially equal in both documents. Regarding vibration, AECTP 400 incorporates much of MIL-STD-810F and is a bit more comprehensive. Figure 2 shows rail vibration profiles specified therein. These are intended to verify that a piece of equipment shipped by rail to a forward staging area will survive the transport. Relative to the CV design issue at hand, the useful features of these plots are the indication of vertical as the most severe axis, and the gradual reduction of source energy above 40 to 80 Hz (depending on the axis). This would indicate that the most robust orientation of design should be vertical, and the least robust orientation should be longitudinal. Also, any longitudinal resonances are subject to energy that begins to fall off above 40 Hz, while reduction in vertical energy is above 80 Hz. This shape of the vertical PSD (power spectral density) will be used as a representative vibration input for a suggested vibration severity rating (SR) later in this paper.
Figure 2. Rail vibration test PSDs as specified for equipment to be transported by rail for NATO, from
document “AECTP 400, Mechanical Environmental Tests.” RAILCAR RESPONSES TO VIBRATION The response amplitudes to vibration can be affected by whether the input energy is close to a natural frequency of the system. A strong source may have little effect on the system if it is far from a resonant frequency. As well, a lesser source may dominant a particular response if it matches some localized resonant condition. With regard to the lowest frequency responses of railcar bodies, the three modes that most commonly are brought to the attention of railroad dynamicist are the car body roll natural frequency, the bounce natural frequency, and hunting activity. The first two are rigid body resonances; the third is a kinematic effect of the tapered wheel profiles. Roll (0.5 to 0.8 Hz) can be excited while traveling 12-20 mph (19-32kph) especially if the rails have out-of-phase vertical irregularities (also called crosslevel deviations). Bounce (1.6-2.2 Hz) can be excited at transient bumps sometimes found near highway (road, or grade) crossings if the car is traveling in the 45-55 mph (72-89kph) range. Hunting (2 to 4 Hz) is a lateral instability of the axles alternatively moving between the left and right wheel flange gaps, and may occur at 45 to 60 mph (72-97kph). Generally above the rigid body modes is flexure of the car structure. These are affected by whether the car is heavily laden or empty. Figure 3 shows typical ranges of the three fundamental flexure modes of six car styles [compiled from ref. 8].
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Tank car
Boxcar
Cov. hopper
Coal car
Gondola
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Typical Range of Flexural Frequencies (Hz, Loaded-to-empty)
VerticalTorsionalLateral
Figure 3. Typical range of flexural frequencies for various fundamental modes of various railcars. (The
fully loaded conditions are shown at the left end of a band, the empty conditions at the right end.)
The bands are representative, but will vary beyond the limits shown for atypical car configurations. Note that the top three car types (Intermodal well cars, gondolas, and coal cars) have open tops, which result in low torsional stiffness and frequencies. Also note that the tank car bodies are generally much stiffer than all other car designs. SURVEY OF FREIGHT CAR CONTROL VALVE MOUNTING Within this paper a control valve (CV) will be considered to be each of two pneumatic portions (containing various ports, pistons, and manifolds) known as the service portion and the emergency portion. Both of these portions are needed, and are mated to either side of a heavy casting known as the pipe bracket. In North America, vendors supply the valves and bracket in both steel/iron and aluminum. Any combination of these valve portions and brackets may be found on any particular railcar in the field due to long service lives and the likelihood of single portion repairs or replacements. The pipe bracket may come in a double-sided or single-sided design. “Double-sided” indicates a pipe bracket that is nominally a rectangular prism with valve portion mounted on opposite vertical faces of the bracket, as shown in Figure 4. (A single-sided bracket uses a much wider manifold with both portions mounted to the same vertical face, but is not the focus in this document.) The stout box-shaped casting of the double-sided pipe bracket causes the important modes of vibration to be rigid unto the assembly itself, but flexural relative to its supporting structure on the railcar. This supporting bracket is often a ½” (12.7mm) plate formed into an inverted “U”-section or a short piece of structural channel. Regardless of the vendor and material, the overall dimensions of the valve assembly are quite consistent (approx. 8 x 22 x 11 inches, or 20x56x28cm). The range of weights for the assembly is approximately 75 lb (34kg, all items aluminum) to 170 lb (77kg, all steel). Thus, all other things equal, an all-aluminum installation could have a 50% higher natural frequency (flexure of the as-mounted assembly) than a steel/iron installation. In practice, many more steel/iron valves than aluminum are found in the fleet. And again these will be the focus within this paper. All valve combinations interface with the overall train brake system via tubular steel air pipes, as shown in Figure 5. Certain unfortunate combinations of the supporting structure and the piping runs have been found to fatigue the pipe flange connections. The pipes are believed to be especially sensitive to low frequency vibrations (due to its attendant greater deflection for a given g-level). The authors have not studied this general view.
Figure 4. A CV (Control Valve) assembly. From left, the emergency portion, the rectangular-shaped pipe
bracket, the service portion.
Figure 5. CV installed on center sill of freight railcar.
COMMON CV SUPPORT HARDWARE AND LOCALIZED RESPONSE MODES This section will show a range of the most common responses found in a survey of about 149 freight cars. The natural frequencies and actual hardware designs were found to be quite variable even within this small population. Regardless, the authors hope to present an incomplete but orderly summary of the analytical and experimental results. For the analytical part of this study, a linear finite element model was created for a typical two-sided valve assembly and supporting “U”-section bracket. The vibrations of the service and emergency portions of the valve have been reported elsewhere by two North American valve manufacturers in an excellent paper [2]. The resonances of the portions themselves were 200-350 Hz (well above the 10-135 Hz band of interest herein). Therefore, this FEA model only represents the appropriate inertia of a two-sided pipe bracket and associated steel hardware. Thus, the CV is represented as the nominal envelope of a valve assembly, but without internal details (and with artificial lightening holes to mimic the suitable overall inertial properties). The focus of the models is not the CV itself, but the support brackets. The resulting generic mode shapes can help show whether natural frequency increases could be made with minor stiffeners, or whether the larger car frame structure is likely to control the response frequency. Further, due to the many small variations in railcar dimensions and larger variations in vehicle lengths and capacity, this model was not calibrated in detail, nor was it tuned using the experimental FRFs collected herein. Rather it was used to show the baseline modes of a CV assembly when fixed to ground, and then to compare the results to typical car installation techniques. The next subsections show the FEA results for the first few flexural modes for several CV boundary conditions assumptions. The results will show that (commonly) the car’s local flexibility tends to dominate the as-installed frequencies. The section of mode shape predictions is organized into four cases: • Case 1: Baseline, CV on rolled “U” channel and fixed to ground • Case 2: CV on pinned-pinned beam (shallow channel), often found hanging under Boxcars • Case 3: CV on rolled “U”, and then to larger plate (with or without stiffening flanges) usually as outrigger at
corner of car, common on some Coal cars, Well cars, and Tank cars (but without vertical leg) • Case 4: CV again on “U” section but welded to more substantial member of car, shown here on the end of the
car’s “backbone” known as the center sill.
Case 1 Figure 6 shows a common mounting style, but fixed to ground. The model shows only 3 modes below 500 Hz, lateral translation, pitch, and vertical. The vertical mode incorporates a small amount of roll due to the slight asymmetry in the location of the CV on the “U”-section. As expected, the frequency of the first mode can be increased significantly with a gusset in the interior, or with additional legs. For example, simple Euler equations show that increasing the “U”-section plate thickness by 50% and adding a third leg will increase this frequency by 70-75%. Both the pitch and vertical modes would also be increased greatly. This suggestion was outlined at an industry conference in 1994 [3]. On more flexible freight cars, such a modification may have less effect however.
Case 1: Baseline, CV on rolled “U” channel and fixed to ground
105 Hz Lateral Translation
256 Hz Pitch
403 Hz Vertical (shown plus some Roll, when not centered on “U”)
Figure 6. Modes for baseline FEA.
Although intended as a hypothetical extreme, effectively this baseline design was assumed to be found on some covered hopper cars where the “U”-section foot welds were made directly on a shear plate that was itself fixed to the car’s “backbone” or center sill. This conclusion is made because the response appeared to duplicate this Case 1 scenario. Lateral translation of the valve assembly occurred with the two legs of the c-shape lozenging (parallelogramming) together at 95-105 Hz. Case 2 Figure 7 is an initial step beyond ground fixation. Case 2 shows a simple and common design for actually supporting a CV on a rail car. Herein, the valve is attached to a longer but shorter portion of channel, and the ends of the channel attached to the railcar frame. This channel is either rolled plate or a structural “C”-shape. Weld patterns found in the field were judged to approximate of a pinned-pinned beam fixation. The first natural frequencies are roll, vertical bounce, and pitch.
Case 2: CV on pinned-pinned beam (shallow channel), common when hanging under Box cars
64.5 Hz Roll
66.2 Hz Vertical (plus some roll,
when non-perfect symmetry)
71.8 Hz Pitch
Figure 7. Modes for pinned-pinned beam support. Regarding experimental results on actual cars, at least seven subfamilies of this Case 2 style were seen. For example, Figure 8 shows three pinned-pinned span designs just inboard of the car’s side sill and between floor supports. Overall for the several boxcars, lowest experimental (pitch and roll frequencies) were measured between 39-58 Hz, with higher (vertical bounce) frequencies at 88-104 Hz. The higher bounce frequencies may indicate fixed-fixed behavior rather than pinned-pinned boundary conditions. When the channel is firmly connected to a significant element of the railcar frame, these frequencies are likely to vary with the dimensions of the channel. Therefore minor design changes are likely to be effective if one or more frequencies are deemed too low. However, in some car designs this hardware is further connected to “outrigger” sections built from structural angles in order to place the valve at the car’s extreme corner to allow for better service and maintenance access. Such is the situation for Case 3. Case 3 Figure 9 shows a merger of Cases 1 and 2, that is, the CV is directly connected to the “U”-section, which then is welded to a shallow wide plate or channel. In turn, this is supported on truss-like elements. The benefit is that the CV is placed out near the extreme corner of a railcar making assembly and service easier. The illustration below shows a vertical leg at the extreme rear (right) corner of the rail car, as found on many coal cars. A similar design but without the vertical leg is found on tank cars. In this case the CV is arranged as a cantilevered assembly with supporting structural angles directed forward and laterally to the more-substantial frame members of the car. In this Case 3, the first FEA mode is at 37.5 Hz with flexure of the underlying plate largely controlling the response. The second are third modes are nearly identical, with pitching motions about slightly different centers. In all three modes, changes to the “U”-section are unlikely to affect the response frequencies significantly. This design was measured on many coal hoppers. Depending on the width and flanges of the plate steel, the fundamental mode was found in a 32-80 Hz range and controlled by the flexural stiffness of the plate. In this case, the c-shape and valve assembly tended to roll together in nearly a rigid-body response.
Further, for the tank car situation (not shown above), lowest cantilever modes have been measured at 12-14 Hz. These occurred when this “outrigger” design was not vertically triangulated as a truss; four such styles are shown in Figure 10. Secondary bending of the support angles resulted in a pitching mode in the 48-52 Hz range. Thus, the strengths of the structural angles are heavily involved in the frequencies. In this scenario, changes to either the “U”-section or the underlying plate are likely to have only secondary effects.
Figure 8. One of many forms of the Case 2 beam support tested for impact FRFs.
Case 3: CV on rolled “U”, and then to larger plate (with or without stiffening flanges) usually as outrigger at corner of car, common on some Coal cars (as shown here), some Well cars, and Tank cars (but without vertical leg).
37.5 Hz Lateral
(controlled by underlying plate flexure, not “U” section)
67.9 Hz Pitch (about forward edge of
“U”, controlled by underlying plate flexure, not “U” section)
71.0 Hz Pitch
(about rear edge of “U”, controlled by underlying plate flexure, not “U” section)
Figure 9. Modes for railcar rear-corner “outrigger” support. This Case 3 design was measured on many coal hoppers. Depending on the width and flanges of the plate steel, the fundamental mode was found in a 32-80 Hz range and controlled by the flexural stiffness of the plate. In this case, the c-shape and valve assembly tended to roll in nearly a rigid-body response. Further, for the tank car situation (not shown above), lowest cantilever modes have been measured at 12-14 Hz. These occurred when this “outrigger” design was not triangulated as a truss; four such styles are shown in Figure 10. Secondary bending of the support angles resulted in a pitching mode in the 48-52 Hz range. Thus, the
strengths of the structural angles are heavily involved in the frequencies. In this scenario, changes to neither the “U”-section nor the underlying plate are likely to have significant effects.
Figure 10. Four of the several styles of tank car outrigger supports tested for impact FRFs. Case 4 Finally Figure 11 is a less common method of mounting the CV to coal cars and covered hoppers (wherein it is mounted more closely to the car’s backbone, known as the center sill). Because of the increased size and mass of the center sill, its vertical and lateral bending modes dominate the lower two natural frequencies for this case, 21.5 Hz vertical bending and 27.2 Hz lateral bending. The third frequency is controlled by the torsional stiffness of the center sill, at 62.9 Hz. For this model, the boundary conditions for the center sill were only roughly estimated. However, actual tests of an operating loaded car were performed at the center sill with peaks in the PSDs at 22.4, 29.3, and 72.8 Hz, showing good agreement with the assumed boundary conditions. Regardless, with reasonable confidence it can be said that a stiffener in the “U”-section is unlikely to change the actual experimental frequencies, although it may beneficially reduce the overall CV deflection. This design will be shown later to have an overall advantage in terms of severity. Unfortunately, service and repair access to the CV is compromised in this location. Case 4: CV again on “U” section but welded to more substantial member of car, shown here as the end of the car’s
“backbone” known as the center sill.
21.5 Hz Vertical bending mode of center sill “backbone” of car
27.2 Hz Lateral bending mode of center sill “backbone” of car
62.9 Hz Higher torsional mode
of center sill, “U”-section participates but does not control.
Figure 11. Modes for railcar “backbone” center sill support.
Other Cases Although also investigated in the field, several other design styles were not included in the FEA analyses. Cantilevered bookend designs (for example, Figure 12), usually hanging from the car’s side sill are found on steel coil gondola cars and some boxcars. This style of support has the widest variation in experimental frequencies of the various hardware families, with fundamental frequencies ranging from 19-95 Hz. The variation is greatly affected by gussets when provided, and by the local stiffness of the car’s side sill. There is no indication that the rail industry is experiencing problems with any of these valves.
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Figure 12. One of many cantilevered bookend style supports tested (left), and wide variety of driving point
inertance FRF magnitudes measured with impact tests (right). Another family of mounting styles includes built-up beams cantilevered off a vertical face of a car end, commonly found on intermodal well cars (for example, Figure 13). These have a wide array of first natural frequencies depending on the existence of additional gussets, and the vertical section size of the cantilevers. For thin or shallow sections (e.g. 6” and under) first frequencies of 34-69 Hz were found (left). For thicker sections, the frequencies increased to between 80-194 Hz (right). The first response mode is usually torsion of the cantilever, which often couples to lateral motion due to the valve assembly center-of-percussion being above the cantilever.
Shallow cantilever style support, 32.7 Hz (considered to be a design of concern) Deep cantilever style support, 80.1 Hz
Figure 13. Two of a few dozen cantilevered built-up beam supports tested for impact FRFs. Finally hybrids between the design styles abound. Figure 14 shows a small sampling. None of these styles are designs suspected of vibration issues.
Wide right-angle plate, 34.1 Hz “U” section of stepped leg length, 66.4 Hz
“U”-section with internal gusset along 50% of legs, 87.4 Hz.
Figure 14. Three of many hybrid support designs and dominant lowest natural frequencies. INHERENT VARIATIONS FOUND WITHIN ONE SERIES OF COAL CARS FRFs were measured on 67 cars from an empty coal train, of which 54 were the Case 3 design and same car series. (This small diversion is presented because of the author’s long-standing interest in how close an FEA model should be tuned to a single test specimen. Perhaps the demonstration is of utility to some readers.) Figure 15 shows these FRFs in a waterfall fashion, and ordered by increasing serial number of the car. The dominant response mode (highest mobility) was at an average frequency of 79.51 Hz. Given this sampling, and assuming a lognormal distribution of this natural frequency, the +/-3 sigma limits for this response are 73.71 to 85.77 Hz. Such a band is approximately +/-7.5% of the mean natural frequency, and would be expected to contain 99.73% of the coal cars of this particular design. This is at the upper extent of the 3-7% variation in natural frequencies found in a previous study which investigated assembly-to-assembly variation of such “non-precision” mechanical assemblies [8].
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PREDICTION OF RAILCAR VIBRATION SEVERITY This final section of the paper will propose a ranking algorithm suggested by the first author. The method is in an initial stage of hypothesis and does not reflect the opinion of the second author, nor the engineering approaches of CN Railway, nor any other members of the North American rail industry. General discussions on CV vibration and infrequent but accelerated wear of valves tend to focus on lightweight aluminum coal gondolas (Case 3, and Figure 13-left, above) and on certain intermodal well cars with shallow-section cantilevered CV supports. The ranking method described herein has heuristically evolved during the project. It has emerged based on the extensive FRF tests of these cars, as well as many trial and error examinations of hammer-to-valve driving point FRFs, hammer-to-car FRFs, and car-to-valve transmissibility’s. Various other methods of discriminating railcars were tried along the way, including frequency of resonance (low vs. high), amplitude of resonance, and effective mass lines. None of these showed results that matched informal industry feedback about frequency of repair or replacement of valves for various car types. The method combines several numerical quantities:
INPUT VIBRATION, Zi The nominal available input vibration at a hypothetical fully loaded railcar is assumed to be as shown by the rail vibration test spectra as shown in Figure 2 (as specified “AECTP 400, Mechanical Environmental Tests” and MIL-STD-810F). The primary axis of consideration is assumed to be vertical due to its larger overall amplitude. The other axes are ignored for simplification. LOCATION FACTOR, L Some car styles mount the CV near the wheels and therefore closer to the track input energy, for example coal cars. Other cars support the CV at mid-span between front and read wheels under the car, such as boxcars. The second style cars receive a reduction in assumed input, via a simple fraction of the car length between the car and the wheels. A multiplier of 1.00 is used for the input spectrum for a CV directly over the wheels; a multiplier of 0.50 is used if the CV is halfway along the car length. This factor is applied across the input spectrum for the car under consideration. EMPTY WEIGHT FACTOR, E As any pickup truck driver knows, an empty truck rides harsher than a loaded truck. The situation is similar with freight cars. Thus, a second multiplier (applied to the assumed input spectrum) is defined by the ratio of sprung weight while fully loaded to the sprung weight while empty (tare). This multiplier can vary from about 4 (for a heavy steel-hauling gondola) to 11 (for a very lightweight aluminum coal gondola). The coal car has a 286,000 lb. gross rail load, and only a 41,400 lb. empty load (of which approximately 17,000 lb. are unsprung). INERTANCE OF THE CONTROL VALVE, Vi The final piece of the rating algorithm is the driving point vertical inertance frequency response function (FRF) of the control valve in (g/lb). To better focus on the ranges of natural frequencies found within the surveyed cars, and the frequencies of greatest interest to the valve manufacturers, this summation is made across a band from 30-135 Hz. SEVERITY RATING, SR The severity rating is calculated by multiplying the assumed available vibration on the car by the magnitude of the driving point FRF at the control valve (on a spectral line by spectral line basis). Then sum this product across the 30-135 Hz band. Finally multiply this scalar by the location factor and the empty weight factor.
Taken together, the above steps are indicated by equation (1) below. The result is an estimated severity rating of field operating vibrations, as made from a single driving point FRF of a given car.
( )∑ •∗∗=135
30VZELSR i (1)
COMPARISON OF CAR SEVERITIES Figure 16 shows the results of the severity rating for a random selection of 20 railcars from the 149 tested. This rating system indeed shows the “suspect” car styles would have the largest severities. That is the 4 highest bars indicate the lightweight coal cars with Case 3 design, and shallow beam cantilever supports on intermodal well cars. The other CV support styles and car types may have shown natural frequencies below 135 Hz, and/or larger peak FRF amplitudes. However, with the employment of the various modification factors and frequency weighting from Equation (1), this method indicates that they do not require further attention by the industry.
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Figure 16. Severity Ratings for 20 of the 149 surveyed cars, based on preliminary equation (1).
CONCLUSION / RECOMMENDATION This paper has attempted to support the authors’ opinions that a proposed design criteria (blanketed across the North American railcar fleet) for 135 Hz as the minimum allowable first mode [2] is not advised. That is not to say that the concept is not a useful ideal. As indicated back in Figure 2, input energy falls away above 40-80 Hz (depending on the axis), and it is a widely accepted rule of thumb that designing brackets for higher natural frequencies is better than lower. Further, this is especially true in typical ground-vehicle random vibration environments. The field survey and FRF measurements for 147 of 149 rail cars do not pass the 135 Hz proposed rule. Many of these cars are accepted and long-standing design styles. Therefore, the authors have continued to seek a simple method to objectively rank designs in terms of likely CV vibration severity during field operating conditions. One method would be recording the vibrations for each car type and mounting style, throughout a several day train trip. This is not feasible due to the many combinations, and the costs involved. The simpler proposed severity rating method was shown to approximate concerns within the industry about certain car types and CV support structures. It yields a single value to help prioritize the railcar fleet from a simple 2-channel driving point FRF. If adopted or developed further, this severity rating could assist the industry with
allocating resources toward the cars of highest interest. Note again, this approach is quite preliminary; therefore the author welcomes reader comments. ACKNOWLEDGEMENTS The authors would like to express gratitude to the AAR Brake Control Valve Task Force for ongoing interest and feedback, and to the Canadian National Railway and the BNSF Railway for providing access to the railcars. REFERENCES [1] Vantuono, W., “Next-generation freight cars take shape,” Railway Age, Sept. 2000. [2] Wright, E., and Troiani, V., “A Study of Vibration Response of DB-60 and ABDX Freight Brake Control Valves
and Recommendations for Installation on Freight Cars,” The Air Brake Assn. Annual Technical Conf. Chicago, IL Sept. 26, 2004.
[3] Hart, J., “Severe Vibration of ABD, ADBW and ABDX Control Valves,” The Air Brake Assn. Annual Technical
Conf. Chicago, IL Sept. 20, 1994. [4] United States Codes of Federal Regulations 49 CFR 213.9, Part 213 Track Safety Standards [5] Association of American Railroads, Interchange Rule 89, Section B, 1, e. [6] MIL-STD-810F, Jan. 2000, Method 514-5 Vibration (Annex B, Engineering Information, paragraphs 2.1.4
Endurance Test, and 2.2 Fatigue Relationship), pg. 514.5B-2 and 514.5B-3. [7] “Mechanical Environmental Tests,” AECTP 400, NATO, 3rd Edition, a subset of STANAG 4370, 2006. [8] Przybylinski, P., and Anderson, G., “Engineering Data Characterizing the Fleet of U.S. Railway Rolling Stock,
Vol. II: Methodology and Data,” Federal Railroad Admin. Report FRA/ORD-81/75.2, Nov. 1981. [9] Shust, W.C., Smith, K.B., "Bounding Natural Frequencies in Structures II: Local Geometry, Manufacturing and
Preload Effects," IMAC-XXII: A Conference on Structural Dynamics, January 2004, Dearborn, Michigan USA, Society for Experimental Mechanics, Inc.
