Proceedings of the ASME 2013 Rail Transportation Division Fall Technical Conference RTDF2013 October 15-17, 2013, Altoona, Pennsylvania, USA

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1 Proceeding of the ASME 0 Rail Tranportation Diviion Fall Technical Conference RTDF0 October 5-7, 0, Altoona, Pennylvania, USA RTDF Toward a Better Undertanding of the Rail Grinding Mechanim Shaodan Zhi PhD tudent: Beiing Jiaotong Univerity, Beiing, China Dr. Allan M. Zarembki PE, FASME Hon. Mbr. AREMA Reearch Profeor and Director of Railroad Engineering Program, Univerity of Delaware, Newark, Delaware USA Dr. Jianyong Li Dean, Profeor, Beiing Jiaotong Univerity, Beiing, China ABSTRACT Rail grinding continue to be one of the mot effective technique for extending rail life, improving wheel/rail contact behavior, and reducing the overall cot of track maintenance. While the ability to more effectively implement improved rail grinding program continue to expand, the undertanding of the grinding mechanim itelf ha not kept pace with the improved implementation. Thu, while railroad engineering and maintenance peronnel have learned to better develop grinding pattern and profile through empirical teting and field evaluation, the fundamental theoretical bae for the improved grinding performance have not kept pace. One uch fundamental area of undertanding i the modeling of the rail grinding proce itelf, both individually, a a function of a ingle grinding motor on the head of the rail, and in the more complex configuration of multiple grinding motor in a range of pattern. Thi paper preent the reult of reearch directly aimed at better undertanding thee mechanim and then utilizing thi better undertanding to develop a detailed rail grinding model that allow for the accurate analyi of not only an individual grinding motor but alo a full grinding train application, a a function of pattern and peed. In the cae of the ingle grinding motor on the head of the rail, thi reearch look at the fundamental mechanim aociated with each cutting abraive grinding grain in the grinding tone, and then expand that mechanim to a full 0 inch diameter grinding wheel a it cut into the rail head at a defined angle and peed. Uing actual rail profile data and grinding data, a theoretical grinding wheel model i developed and then calibrated with wheel tet data and actual grinding (field) data. Thi ingle motor model i then expanded into a full grinding train model, uch a for a 96 tone grinding train with 48 motor per rail, where it i able to analyze the full equence of 48 motor a each motor individually and equentially remove metal from the rail head. The reulting analyi i enitive to uch key factor a grinding peed, and the key pattern parameter of motor angle, equence and power. The model i then calibrated to and compared with actual full cale rail grinding metal removal data from a maor Cla railroad. Such an analyi tool allow railroad to analyze the performance of different grinding pattern in a real world operating etting, to improve their rail grinding practice and take further advantage of new technologie in rail grinding to better manage the grinding proce and improve planning of grinding activitie. INTRODUCTION Rail repreent one of the mot critical and expenive part of the railroad track infratructure and one that i ubect to ignificant level of loading and tre. A uch, it maintenance i of eriou importance to railroad engineering and track maintenance department. However, the pecific type of maintenance available for addreing rail problem, other than imply replacing the rail, are limited. In the area of rail fatigue and urface defect, rail grinding i and continue to be one of the mot effective technique for extending rail life, improving wheel/rail contact behavior, and reducing the overall cot of track maintenance. From a practical implementation perpective, the ability to more effectively implement improved rail grinding program continue to expand. Thi include better

2 undertanding of the wheel/rail interaction mechanim that profile grinding addree a well a the rolling contact and other related urface and uburface fatigue mechanim, alo addreed by rail grinding. However, the undertanding of the grinding mechanim itelf ha not kept pace with the improved implementation. Thu, while railroad engineering and maintenance peronnel have learned to better develop grinding pattern and profile through empirical teting and field evaluation, the fundamental theoretical bae for the improved grinding performance have not kept pace. One uch fundamental area of undertanding i the modeling of the rail grinding proce itelf, both individually, a a function of a ingle grinding motor on the head of the rail, and in the more complex configuration of multiple grinding motor in a range of pattern. At the fundamental level, grinding i performed by individual abraive particle or grain, which are held together by a bonding material and combined to form a grinding wheel or tone. The baic grinding wheel ued in the railroad indutry i the 50 mm (0 ) grinding wheel which contain everal thouand abraive grinding grain of defined ize (the grit ize), held together by a rein type bonding material. Each abraive grain i held by bond pot which hold the individual grain until it i worn out and no longer capable of effectively cutting the rail metal. At that point the worn out grain i releaed to expoe a freh abraive grain particle []. A production type grinding train can have 96 uch grinding tone with 48 motor per rail, with each wheel (and correponding grinding motor) operating a defined angle (which adut the poition on the rail head) and power level. Thi combination of motor or pattern repreent the baic approach ued in modern profile grinding []. By undertanding the grinding proce from the bottom up, i.e. through initial undertanding of the cutting proce of individual abraive grinding particle or grain, it i poible to better define the more global grinding proce that i achieved through the application of dozen of grinding wheel, each coniting of thouand of grinding grain. In particular, it i poible to look at the key metal removal rate, that i achieved by a grinding train, from the point of view of metal removal at the individual abraive grain level and the individual grinding wheel level ( with each wheel containing thouand of individual grain). Thi paper preent the reult of reearch directly aimed at better undertanding how thee mechanim interact, and in particular how the application of thouand of grinding grain reult in the development of a ground rail profile. Thi reearch build on baic cutting theory [,4,5] and more recent reearch into the mechanim of cutting and chip formation, at the individual cutting grain lavel [6,7,8,9] and applie thee theorie better undertand the rail grinding proce. Thi undertanding i then utilized to develop a detailed rail grinding model that allow for the accurate analyi of not only an individual grinding motor but alo a full grinding train application, a a function of pattern and peed. GRINDING MECHANISMS Baic grinding mechanim and determination of depth of cut at the abraive grain level The rail grinding proce i the proce by which a mall amount of rail metal i removed from the urface of the rail head uing rotary grinding motor []. Properly applied, thi proce i a gentle proce, carefully removing a fraction of a millimeter of rail teel without introducing a rough urface finih or other urface defect in the head of the rail, which could reult in defect initiation ite on their own. A noted, thi proce begin at the individual grinding particle, or abraive grain (alo referred to a grit) level a it cut into the rail head. Thi individual grain proce i repeated thouand of time for each grinding wheel a it cut into the rail head. Thu, it i important to undertand the performance of each individual cutting grain, and in particular the baic grinding mechanim ued in the rail grinding proce, baed on the cutting behavior of thee abraive grain. One of the critical parameter for undertanding and then applying thee theorie of cutting and grinding i the cutting depth achieved by for individual grain. Thi individual grain cutting performance contain the clue to analyzing the grinding capability for the entire grinding tone and then a multi-tone (motor) grinding train. Thu, the grinding of the urface of the rail can be conidered to be the ummation or integration of a large number of cutting grain. The key to determining the cutting depth achieved by each abraive grain i the analyi of the cutting proce and the reulting metal liver or chip that i removed by that grain or grit. According to baic machining theory [, 4], the cutting progre that occur during grinding can be illutrated a hown in Figure. A can be een in Figure, for each individual cutting grain, a chip i removed, the ize of which i dependent on the geometry of the chip and the work piece (the rail). Thi geometry i defined by a erie of three plane; the rake face (with rake angle γ), the flank face (with the flank angle α) and hear plane (with the hear angle φ). At a given cutting peed, the removed chip move away from the rake face with a correponding peed referred to a the chip velocity. The removed chip will have a chip thickne h c, while the remaining portion will have the undeformed chip thickne h, which repreent the cutting depth of the individual grain or grit.

3 grain can be kept at and that cover half the complementary angle of which mean, then it can be determined that () Figure. Schematic View of Grain and Chip Geometry The force involved in the cutting proce have been defined by Merchant [5] baed on the theory of force equilibrium. A een in Figure, the removed chip i ubected to two oppoing force: and. Thee two force can be defined a the reultant force at the hear plane and rake face a illutrated in Figure. The force, which the tool exert on the chip, i reolved into the tool face-chip friction force and normal force. The angle between and i thu the friction angle. The force which the workpiece exert on the chip i reolved along the hear plane into the hearing force,which i reponible for the work expended in hearing the metal, and into the normal force,,which exert compreive tre on the hear plane. Force i alo reolved along the direction of tool motion into, termed a the cutting force, and into, the thrut force [5]. The correponding conumed cutting power can be expreed a: Where i the cutting peed. Thu, a can be een the angle between the different component force can be determined baed on the approximate grain angle and aumed cutting depth. However, the relationhip between the force and the velocitie are till not clear. Noting that the grinding train ( and thu the grinding tone) i moving forward along the rail while the grinding tone are alo rotating acro the rail, the grain on the urface of the grinding tone will have a combined intantaneou peed which i a combination or reultant of the forward peed and the rotating peed. It i thi reultant peed direction that will determine the chip-flow direction and alo it thickne. A hown in Figure, the intantaneou peed of the ingle cutting grain will be formed by combing the forward peed and the rotating peed. In the plane of the reultant peed, the chip will be formed with the grit thruting into the rail. Becaue of the rotating effect, the intantaneou reultant peed will be changing a the grinding wheel rotate and the individual grain change location (and angle of movement) with repect to the rail urface, even though the direction of the forward peed i unchanged. () (4) Figure. Force Equilibrium for Chip The relationhip between thee force can be obtained a following: () The following analyi ue thee relationhip together with exiting reearch in the area of rake cutting angle for grinding grain baed on experimental tudie and theoretical modeling [6~8]. Auming that the rake angle of mot of the cutting Figure. Chip Cutting at Combined Speed Auming the rotational peed of the grinding tone and the

4 forward peed of the grinding train are kept contant, once the poition of the grain (with radiu ditance r to the tone center) ha been determined, the intantaneou line peed can be obtained from. P = Fc vcom = Sumgrti Fc v (5) com TotalGrainNo. The Power-Force-Speed model etablihed can combine key element in the grinding proce to obtain the relationhip between thoe factor. Thu, once the input parameter uch a the grinding peed and power etting are defined, the overall grinding reult, and in particular the cutting depth of the grinding, can be determined. Thu, at the individual grinding particle level, the cutting depth for individual grain can be obtained, uing the relationhip between cutting force and the conumed power at the combined cutting peed v com : Pvcom Fc = (6) Sum Noting that for the hear plane A, the hear tre τ and normal tre σ are found to be: τ = F A, τ 0.45 σ (7) Then the hear plane area A can be defined a (ee Figure 4) F Fc A = τ.4τ (8) hc hc A φ 5 hc/in(φ) Figure 4. Geometry for Cutting Depth and Shear Plane Area Auming that the cutting grain ha a cutting width of h c a hown in Figure 4, and etimating the length of the hear plane to be hc in( ϕ ), then the area of the hear plane in Figure 4 can be computed a A ( + ) hc, where h c h (Figure ). The cutting depth for each individual grit h can then be determined from: 60 grti A Fc.4τ h = = (9) + + Fc τ Pvcom h (0).07 Sum.07τ It hould be noted that the cutting depth and correponding chip thickne will vary a a function of rail material trength and grinding tone compoition (grit ize and type, wheel grade, etc. []) grti Metal removal at the Grinding Wheel Level Once the cutting depth for the individual grain i determined, it i then poible to determine the cutting depth of a ection of the urface of the rail, the grinding zone, after the paing of an individual grinding wheel ( a wheel pa). It i clear the grinding proce for the whole grinding wheel i more complex than imply combining a large number of grain. Given the fact that there are thouand of individual grain, moving acro the urface of the rail, at a reultant peed which i related to both the rotation of the grinding tone and the forward movement of the grinding train ( or in grinding term, the movement of the workpiece- the rail), there will be many overlap and/or untouched area on the urface of rail for the unpredicted grain location and ize. A chematic diagram for the ditribution of grain on the urface of the grinding wheel i hown in Figure 5. Becaue the grain are fixed on the grinding wheel, they will change poition following the rotation of the wheel. The aociated cutting track for thee individual grain can be calculated baed on the correponding motion of the wheel and the rail (the work piece). Defining the location of each individual grit uing the radial ditance to the center r i and the angle θ give.. rx ri = Ι [, ]( r ) Router Rinner x Ni = length( ri) Router R inner θx θ = Ι[ 0, ]( θx)+ ω t ( ) π N = length θ π 0 () In addition to the rotation of the wheel, the paing peed along the rail urface will generate a diplacement of the wheel center. Taking the forward direction along the rail a axi x and the tranver direction a y give the forward peed a: xc = v t () yc = 0 Thu the location for each grain peak ( x i,, y i, ) can be determined (ee Figure 5) with repect to the coordinate for the wheel center at any time t: xi, = xc+ ri co( θ ) i (,,, Ni) () yi, = yc+ ri in( θ ) (,,, N ) 4

5 peak. The ground urface will be calculated a: i, i, i grain rail z, = min( z, z ) (5) Which mean that the valley on the urface lower than the cutting peak cannot be touched by the cutting grain. The grinding depth for each area will then be calculated from: Figure 5. Schematic Diagram for Grit Ditribution A the cutting grain penetrate into the rail urface, the z direction, there will be interaction between the grain cutting peak and the rail urface. Thi, in turn generate a threedimenional et of reult by combining the grain location, the cutting depth h and the cutting width h w. Baed on the grinding mechanim above, the grain hape at the cutting plane ha been aumed to be a triangle which peak into the rail urface a illutrated in Figure 6 and 7. z zgrain_peak x V area z Area D Area Area i, i, = = (6) Equation (6) i then ued to calculate the average grinding depth for a defined area with an appropriate number of cutting point. Thu for example, a mm mm quare zone i defined with point. Thu for each point, Area i, =0.00mm 0.00mm. Uing the z value for each cutting point (Figure 7), baed on the location of each paing grinding grain (cutting point), the change in urface volume can be calculating uing zi, Areai, which repreent the volume of metal removal for the zone (auming z=0 for all point before grinding). The average depth D can then be calculated a noted above. z zgrain_peak (a) Before grinding x (b) After Grinding Figure 6. Comparion of z value with Grain_peak and Surface to be Ground z x x' hw (xi,, zi,) Figure 7. Coordinate Value for Point Around Cutting Peak A hown in Figure 7, location (coordinate) for point at and around the cutting peak can be then be etimated a: i, zgrain _ peak = h i, x x (4) i, zgrain _ around = h+ h hw Where x repreent the point at the cutting edge around COMPARISON WITH TEST DATA Comparion with Grinding Wheel Data In order to illutrate thi behavior, data from proprietary grinding wheel tet have been ued to compare the theoretical analyi of grinding with the actual tet data, repreenting a ingle grinding wheel moving along a lowly rotating work piece repreenting the rail. Thee ingle wheel tet have been implemented uing the ame type of grinding wheel ued in production rail grinding ( and a uch will alo be compared with the full train grinding reult dicued later in thi paper). Furthermore, the work piece ued in the grinding tet ha imilar material propertie a rail. The tet parameter for the ingle grinding wheel tet are preented in Table. Note, the forward travelling motion of the grinding train ha been imulated by the circular motion of the work piece. Permiion ha been given to how only limited average reult, which are preented here-in. 5

6 Table. Parameter for Tet Parameter Value Grinding Wheel Outer Diameter (mm) 50 Grinding Wheel Inner Diameter (mm) 50 Grinding Wheel Rotation Speed (rpm) 69 Workpiece Outer Diameter (mm) Workpiece Inner Diameter 9 Workpiece Rotation Speed (rpm) 8 Workpiece Surface Speed ( m ).75 Table Infeed Rate (mm/rev) 0. Uing thee parameter in the theoretical model, the average cutting depth for individual grain i calculated. Uing the theory of the individual grinding grain cut, and the additional theory of the wheel behavior, a preented here, the ground urface for the each pecific topography zone (rail urface area) can be computed baed on the motion of each effective grain. Becaue of the proprietary nature of the grinding tone, actual data on the grain ize, grade, number of grain, etc. wa not available and wa etimated baed on indutry data []. Likewie, the data on the workpiece wa etimated baed on the propertie of tandard carbon railroad rail. Thee etimated propertie are preented in Table. In order to ave computing time, only a mall zone, the topography zone, ha been ued in the calculation to repreent the effect of a ingle grinding wheel pa. Table. Parameter for Calculation Parameter Value Grinding Wheel Outer Diameter (mm) 50 Grinding Wheel Inner Diameter (mm) 50 Grit Size (um) 500 Etimated Intantaneou Grain No. Sum grit 0 Tenile Strength σ ( N mm ) 780 Shear Strength τ 0.45 σ ( N mm ) 5 Grinding Wheel Rotation (rpm) 69 Cutting Speed vcom = ω R+ v ( m ) 8 Paing Speed ( m ).75 Equivalent Feed Rate on Wheel(mm/rev) Topography Zone ( mm mm ) It hould again be noted that in a ingle grinding pa of the workpiece (the rail), multiple cut are obtained for each grinding particle and the reulting metal removal on the work piece ( the rail) i illutrated by the topographical repreentation hown in Figure 8. Figure 8. Topography Graph on Choen Zone 6

7 The overall cutting depth for thi zone can be then calculated and compared with the average meaured depth of cut from the tet. Thi i hown in Table baed on the equation for cutting depth of individual grit Pvcom h Sum.07τ grti Table. Comparion with Tet & Simulation Grinding Power P (KW) Meaured Cut Depth (mm) Cutting Depth Of Grain (um) Cal d Cut Depth (mm) A can be een in Table, the meaured depth of cut, from the tet, and the calculated depth of cut, from the grinding theory how good agreement for the higher horepower level and moderate agreement with the lower horepower level. Note there i a clear relationhip between depth of cut and horepower. A poible explanation for the hallower depth of cut for the lower horepower i that at lower power etting, the grinding wheel i cutting at a le than optimum efficiency for the tone configuration ( e.g. grade, grit type and ize, etc.). Thi i upported by the grinding literature which ugget that the metal removal- power relationhip varie a a function of wheel grade []. It hould be alo noted that baed on the cutting depth of each grain and the total cutting depth, approximately 8.5 cut are made per ingle grinding pa ( on the rail). Metal Removal at the Grinding Train Level In order to move from the grinding wheel level to the grinding train level, it i neceary to combine multiple wheel, with each wheel operating at a different motor angle ( and a a reult a different poition on the top of the rail, with a different urface radiu) and poibly different power etting. Thi combination of grinding motor and power etting i referred to a a pattern, with correponding different metal removal behavior aociated with each pattern. example, the tet dicued in Table had a Q of approximately 500 cubic mm per econd at approximately KW ( 5.57 cubic inche per minute at 0 HP). By auming contant volume per motor (and at a contant grinding peed, contant cro-ectional area of metal removal per motor ), and auming a contact geometry directly related to the local radiu on the rail head, the correponding metal removal per pattern can be calculated [8]. Thi i illutrated in Figure 5 through 7. Figure 9 how the individual grinding wheel poition acro the rail head a a function of motor angle. A can be een, grinding wheel with different angle will have different contact point with the rail head and correponding different rail head radii at the point of wheel contact.. Thi directly relate to the wheel contact length (and aociated width of the grinding facet) and thu to the cutting depth, which will vary accordingly Figure 9. Tranveral Angle Ditribution of Grinding Wheel [] The relationhip between grinding angle and cutting depth can be obtained baed on the actual rail profile ( uch a from a digital profile meaurement ytem [0, ]), the contact width of the tone and the rail head, and the contant area of metal removal ( contant for a given grinding or forward peed). Given the fact that the width of the cut will vary a a function of the depth of penetration, a een in Figure 0, mot model calculate the cutting proce in a tep by tep manner until the area of metal removal i obtained [9]. Thi in turn yield the depth of cut per motor. The traditional approach to analyi of metal removal a a function of grinding pattern ( ize of grinding train, number of motor, horepower, peed, etc.) i to aume a contant volume of metal removal per unit time Q, uually defined in cubic inche per minute or cubic mm per minute. Thi value can be obtained from grinding tet uch a dicued previouly or from calculation of the total volume of metal removal per grinding pa of a train ( taking into account peed of the train and number of working motor). Thu for 7

8 diplacement of the contact point in Figure. Figure 0. Cutting into Rail head Step-by-Step Thi i repeated for each of the grinding motor in the pattern, with a correponding motor angle and rail head poition for each motor. Furthermore, the cutting equence ha a ignificant effect on the metal removal and on the ground rail profile. Thi i becaue the firt grinding wheel will make it initial cut, changing the rail profile that the econd motor ee, and thu the econd motor mut addre the cut profile. Thi i illutrated in Figure, which how how the contact point of the econd motor will differ if it follow the firt motor or if it i on the rail where no previou cut ha occurred. Note the Figure. Cutting Sequence Effect When thi i applied to a full grinding pattern, uch a with a 96 motor train with 48 motor per rail, the reulting calculation mut take thi equence effect into account, uually a part of the programming proce which include the full et of grinding wheel with different etting angle and power [8]. Table 4 and 5 illutrate two uch et of grinding pattern. Table4. Setting Angle and Power of Pattern0 Angle Motor No Hp Table5. Setting Angle and Power of Pattern0 Angle Motor No Hp Detailed metal removal field data wa available from a erie of field tet conducted by Harco Rail on a US Cla railroad a reported in reference 9 and 0. Reult from 0 different meaurement ite (5 each for two different et of grinding pattern) are preented repectively in Table 6 and Table 7 and compared to both the individual grinding wheel tet reult and the grinding theory which i built up from the individual cutting grain level. While there i ome uncertainty a to the actual power etting of the grinding train, preliminary comparion of the grinding train per tone metal removal rate and the grinding wheel tet how good agreement. Each ite correpond to a detailed before and after grinding et of meaurement at the exact ame location a dicued in Reference 9 and 0. 8

9 Grinding Train Meaurement Table 6. Removal Rate Comparion for Grinding Train Pattern 0, Tet and Theory Area_perStone Q_field/Stone Q_Tet 4 Curve Speed Area Removal Pattern (mph) ( 0 in ) in min in min in Q_Cal d in min Average Grinding Train Meauremen t Table 7. Removal Rate Comparion for Grinding Train Pattern 0, Wheel and Theory Spee Area_perSton Q_field/Ston Q_TetError Area Curv d Patter e ( 0 in ) e! Bookmark Removal e (mph n in min not defined. ( in ) ) in min Q_Cal d in min Average In the cae of Table 6 ( pattern 0), the average Q for the five field meaurement wa 4.89 cubic inche per minute a compared to a Q of 5.57 cubic inche per minute for the wheel tet. The average calculated Q (from cutting grain theory) wa 4.6 cubic inche per minute. In the cae of Table 7 ( pattern 0), the average Q for the five field meaurement wa.5 cubic inche per minute a compared to a Q of 5.57 cubic inche per minute for the wheel tet. The average calculated Q (from cutting grain theory) wa 4. cubic inche per minute. While the variation between the three different analye/tet wa greater in Table 7 ( pattern 0) than in Table 6 (pattern ), the reult are till reaonable. Figure a and b preent thi data graphically. Again it i noted that the actual power etting for the full train metal removal data, which how the greatet variation from meaurement to meaurement, are not know and were aumed to be at the normal grinding etting for the pattern. The power etting for the wheel tet and the grinding theory are better defined ( Table ) Metal Removal Rate(in /min) Wheel Tet Grinding Train Cald by Theory Sequence No. of Grinding Run for Pattern 0.5 Wheel Tet Grinding Train Cald by Theory Sequence No. of Grinding Run (a) (b) Figure. Removal Rate Comparion Between field tet, Wheel Tet and Theory Metal Removal Rate(in /min) Track Curvature in degree of curvature D ( D = 570/R, where R = radiu of curvature in feet) 4 Average of multiple grinding tet 9

10 Specifically, Figure preent the data from Table 6 and 7 graphically for each of the five grinding meaurement (run) in each pattern. The black tar-line repreent the average metal removal rate from the ingle grinding wheel tet. The red quare-line repreent the metal removal rate obtained from meaurement of the grinding train run. The blue circle-line repreent the metal removal rate from the cutting grain theory, uing the ame rail profile a ued with the repective run of grinding train. A noted previouly, the metal removal rate are contant for the wheel tet ( baed on an average of three tet with only modet variation in the reult between tet) and are quite imilar for the grinding theory (with the variation due primarily to the difference in profile of the rail head which differed from run to run). However, the variation in metal removal rate i ignificantly greater for the five grinding run, which ugget that there are difference in the individual grinding run which may include variation in the actual power level that were ued, difference in rail hardne and profile, curvature effect, and other operating condition not noted in the pecific grinding report ( note peed and pattern were contant for each et and curvature wa reaonable imilar). In addition, dynamic in the grinding proce itelf, perhap at the grinding wheel/rail interface, may have ignificant effect on the variability of the grinding reult. In pite of thee variation, a noted previouly, the agreement between the three method in the cae of pattern 0 wa quite good and even for pattern 0 the reult are till reaonable. Furthermore, noting the general agreement of the analyi with the data, it i believed that with improved detailed grinding information and correponding etimation of the pecific parameter in the grinding proce, the theoretical calculation will be cloer to the field data. Thi in turn will provide a more powerful tool to evaluate future grinding pattern. SUMMARY Thi paper preent a bottom up approach to rail grinding theory, uing baic cutting theory, in the form of individual abraive particle or grain and then combining them at the wheel level to look at metal removal (and depth of cut) per wheel. Thi i in turn further combined at the grinding train level to look at how the baic grinding theory compare with actual field reult from a full cale large production grinding train. The paper how that it i poible to model the rail grinding proce itelf, at the grinding grain level, and then build up the proce to look at a ingle grinding motor on the head of the rail, and finally in the more complex configuration of multiple grinding motor in a range of pattern. The fundamental theory addree how grinding i performed by individual abraive particle or grain, and how they generate a metal chip (and the aociated depth of cut). Combining everal thouand of thee grain into a tandard indutry 50 mm (0 ) grinding wheel require undertanding of the relative motion of the rotating wheel and the forward peed for the train ince for each pa of the wheel on the rail, multiple cut are made by each particle. Further combining thee into the grinding train level require incorporation of the individual motor angle and power etting deigned into a full grinding pattern. By undertanding the grinding proce from the bottom up, i.e. through initial undertanding of the cutting proce of individual abraive grinding particle or grain, it i poible to better define the more global grinding proce that i achieved through the application of dozen of grinding wheel, each coniting of thouand of grinding grain. In particular, it i poible to look at the key metal removal rate, that i achieved by a grinding train, from the point of view of metal removal at the individual abraive grain level and the individual grinding wheel level ( with each wheel containing thouand of individual grain). Thi i hown in the reult which indicate reaonably good agreement between the theory and the ingle wheel tet a well a in the full cale grinding data which how modet agreement ( with ignificant variation in the field grinding data itelf). By better undertanding how thee mechanim interact, and in particular how the application of thouand of grinding grain reult in the development of a ground rail profile, better model can be developed to allow for the accurate analyi of exiting and new grinding pattern in a full grinding train application, a a function of pattern and peed. Thi in turn will allow for improved optimization of the actual grinding proce in the field and the developed of optimized grinding trategie. 0

11 ACKNOWLEDGEMENT The author would like to acknowledge Harco Rail for contributing to the funding of thi reearch. REFERENCES. Zarembki, A.M., The Art and Science of Rail Grinding, Simmon-Boardman Book, Inc., Omaha, NE, Augut 005. Zarembki, A.M., Management of Total Rail Grinding Maintenance Proce, Railway Track & Structure, June 0. Marinecu, I. D., Rowe, W. B., Dimitrov, B and Inaaki, I, Tribology of Abraive Machining Procee, William Andrew Publihing, Norwich, NY DeVrie, W. R., Analyi of Material Removal Procee, Springer-Verlag, NY Merchant,Mechanic of the Metal Cutting Proce, ii: Platicity Condition in Orthogonal Cutting, Journal of Applied Phyic, 945,6: Huang, Y.; Liang, S. Y., Force modeling in hallow cut with large negative rake angle and large noe radiu tool application to hard turning, International Journal of Advanced Manufacturing Technology, 00, (): Vinogradov, A. A., On Chip Formation in Cutting Metallic Material Uing Tool with a Large Negative Rake, Journal of Superhard Material, 0, 4(): Ohbuchi, Y.; Obikawa, T., Finite Element Modeling of Chip Formation in the Domain of Rake Angle Cutting, Tranaction of the ASME, 00, 5: 4-9. Zarembki, A. M. and Zhi, S.D., Analyzing Rail Grinding Pattern, Railway Track & Structure, June Zarembki, A.M., High Speed Rail Grinding for High Speed Rail, 7th World Congre on High Speed Rail, Beiing, China, December 00.. Zarembki, A.M., Hagan, B., Effectivene of High Speed Rail Grinding on Metal Removal and Grinding Productivity, 0 AREMA Annual Conference, Minneapoli, MN September 0.