Abstract:
A method for balancing a rotor of an alternator in a diesel-electric locomotive in which the rotor is drivingly coupled to a power output shaft of a diesel engine. A speed sensor and a vibration sensor are coupled to the rotor for providing output signals representative of instantaneous rotational velocity and instantaneous amplitude of vibrational motion of the rotor, respectively. In the inventive method, the rotor is accelerated to a first preselected rotational velocity and a first rotor unbalance is determined from the velocity and vibration signals. The rotor is then accelerated to a second preselected rotational velocity and a second rotor unbalance is determined. The first and the second rotor unbalance determinations are combined to identify a first correction weight and position thereof for minimizing the first and the second rotor unbalance. The identified weight is installed and the process repeated until the unbalance is corrected such that vibration is less than a preselected maximum value.

Description:
This application includes a microfiche appendix of one sheet containing fifty-nine frames. 
     BACKGROUND OF THE INVENTION 
     The present invention relates to balancing of rotors of large dynamoelectric machines and, more particularly, to in situ balancing of a rotor of an alternator operatively coupled to a shaft of an internal combustion engine and assembled in a locomotive. 
     Balancing of rotating apparatus, from automobile tires to aircraft gas turbine engines, is a generally known process. Typically, the apparatus is placed on some form of fixture and rotated at preselected speeds. The fixture has built-in electronics for detecting out of balance conditions and indicating to an operator a mass of weight and the location for adding the mass so as to correct the unbalance condition. Some of these balancing machines may provide for gross corrections, such as with tire balancing, while others may provide for very fine balancing, such as is required for gas turbine engines. The first may sense the forces induced in the machine by the rotating apparatus while the latter may use highly expensive, non-contacting vibration sensing equipment, such as dynamic trim balancing analyzers of the type described in U.S. Pat. No. 3,751,987. These latter type machines, while very accurate, are not generally adapted for use in detecting unbalance in large dynamoelectric machines mounted in an operating system. Initial balancing of rotors of large dynamoelectric machines is generally performed in the same manner as with other rotating apparatus, i.e., before installation in an operating system. However, such initial balancing is often not sufficient to meet the requirements for vibration when the rotor is installed in the dynamoelectric machine and further installed in an operating environment. In particular, when the rotor is operatively coupled to a shaft of an internal combustion engine, the additional vibration induced by the engine may be sufficient to excite undesirable vibrations in the dynamoelectric machine and in the equipment in which the machine is installed. Accordingly, it would be advantageous to provide a method and apparatus which can be used in a manufacturing environment to detect and correct unbalance in a large dynamoelectric machine when the machine is installed in an operating locomotive or similar electric traction vehicle. 
     SUMMARY OF THE INVENTION 
     The above and other disadvantages of the prior art are overcome in a system for balancing a large dynamoelectric machine, herein exemplified as an alternator, while the alternator is installed in an operating condition in a traction vehicle such as a locomotive. The alternator is driven by an internal combustion engine, typically a diesel engine, which can be set to run at a plurality of preselected speeds. Trim balancing is accomplished by use of a speed sensor and an accelerometer coupled to the rotor of the alternator. The signals from the speed sensor and the accelerometer are connected to a commercial spectrum analyzer. A computer, such as a personal computer (PC), is coupled to the spectrum analyzer for reading the vibration amplitude and phase angle determined by the spectrum analyzer. The PC computes the location and mass of any needed weights to correct the unbalance to within acceptable limits. 
     In an illustrative embodiment, the alternator rotor yoke is manufactured with a plurality of equally spaced, drilled and tapped holes specially adapted for receiving and attaching balance weights. Prior to operating the alternator, a marker is attached to the rotor yoke in line with one of the holes. The speed sensor is an optical sensing device positioned on a stationary mount adjacent the marker such that the speed sensor can detect the instantaneous rotational velocity of the rotor by detecting the passage of the marker. The speed sensor signal also provides information to the spectrum analyzer for determining the phase angle of the vibration relative to the marker. An accelerometer is attached to the stationary frame of the alternator at a preselected position. The accelerometer output signal is used by the spectrum analyzer to detect vibration amplitude. 
     In the inventive method, vibration amplitude and phase angle are measured without any balance weights at a first preselected speed and in a first preselected direction, e.g., in a lateral direction. The process is then repeated for a second preselected speed and in a second preselected direction, e.g., in a vertical direction. The computer calculates the estimated location and magnitude of a weight to correct any measured unbalance. The initial weights are bolted to the alternator yoke and the above process repeated. If the vibration amplitude with the initial weights is outside acceptable limits, trim balancing is repeated until the unbalance is acceptable. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a better understanding of the present invention, reference may be had to the following detailed description taken in conjunction with the accompanying drawings in which: 
     FIG. 1 is a simplified illustration of an alternator showing an implementation of the present invention for measuring imbalance of the alternator rotor; 
     FIG. 2 is a schematic representation of the alternator of FIG. 1 illustrating the forces and angles affecting balance of the rotor; 
     FIG. 3 illustrates a sensitivity circle for a particular weight applied to effect balancing; 
     FIG. 4 illustrates sensitivity circles at two different speeds and weights for the alternator of FIG. 1; 
     FIG. 5 illustrates how the sensitivity circles are used to identify a preferred weight for balancing; and 
     FIG. 6 illustrates sensitivity circles obtained with different weights during repetitive balancing checks. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Single plane trim balancing is applicable where vibration is caused by a force unbalance and where there is negligible couple unbalance. This has been found to be the case for the single bearing alternators used on locomotives. If an unbalanced couple is present, trim balancing will have to be done using two planes for attaching balance weights. The present invention deals with single plane balancing only. 
     In the method of the present invention, FIG. 1 shows an accelerometer 10 connected to a spectrum analyzer 12 used to measure the amplitude of vibration (at the frequency of rotation) at a particular position on the alternator 14. In this case, the 3 o&#39;clock position near the middle of alternator 14 has been selected. The phase angle of the vibration signal with respect to a reference position on the alternator rotor yoke 16 is obtained from an optical sensor 18 which also inputs its signal into the spectrum analyzer 12. 
     The optical sensor 18 is mounted, for purposes of this test, to a bracket 20 which is bolted to casing of alternator 14. Bracket 20 supports sensor 18 adjacent rotor yoke 16. The radially outer surface of rotor yoke 16 is preferably darkened, such as by painting black, and a reflective marker 22 attached to the outer surface. The marker 22 may comprise a small piece of reflective tape allowing light reflected from the marker to be detected by sensor 18. The rotor yoke 16 includes a plurality of circumferentially spaced, threaded apertures 23 which can be used to attach small weights to the rotor to correct any unbalance condition. 
     The spectrum analyzer 12 is a commercially available analyzer such as the ONO SOKKI Co., Ltd. type CF-250 which can be controlled by external commands from a personal computer (PC) 26. The computer 26 is connected to analyzer 12 for obtaining vibration amplitude and phase angle. Computer 26 computes the balance weight and location necessary to reduce vibration in a manner described below. 
     FIG. 2 is a schematic representation of the alternator rotor 16 illustrating the forces, weights, and angles used in determining an unbalance condition. The vibration amplitude and phase angle measured, without any balance weights, i.e., baseline data, are denoted by V 0  and φ 0 . The angles are measured in the direction opposite to the direction of rotation of rotor 16. If the direction of rotation is counterclockwise, then positive angles are measured in the clockwise direction from the reference position, which is the position of the reflecting tape or marker 22 adjacent optical sensor 18 in FIG. 1. 
     A linear relationship is assumed between the unbalanced weight W 0  (in gm-inches) and the vibration amplitude it produces, V 0 . This can be represented by the equation: 
     
         W.sub.0 =V.sub.0 xα                                  (1) 
    
     where α is a constant. 
     There is also a difference between the location of the unbalanced force W 0  and phase angle of the measured vibration V 0 . If the position of the unbalanced force is denoted by Γ 0 , this relationship can be represented by the equation: 
     
         Γ.sub.0 =φ.sub.0 -βxRPM                     (2) 
    
     where β is a constant and RPM is the rotational speed of the rotor in RPM. 
     If a known trial weight W 1  is attached to rotor 16 at position θ 1  (W 1  is the weight in gm-inches corresponding to the attached trial weight), the unbalanced force now acting on the rotor is the vector sum of the forces due to W 0  and W 1  and is represented by F 1  at a position Γ 1 . The vibration measured with the trial weight attached is denoted by V 1  and the phase angle of the measured vibration is denoted by φ 1 . 
     The following equations can be written: 
     
         F.sub.1 =V.sub.1 xα                                  (3) 
    
     
         Γ.sub.1 =φ.sub.1 -βxRPM                     (4) 
    
     Taking components of the forces, the following equations can be written: 
     
         F.sub.1 xcos (Γ.sub.1)=W.sub.0 xcos (Γ.sub.0)+W.sub.1 xcos (θ.sub.1)                                           (5) 
    
     
         F.sub.1 xsin (Γ.sub.1)=W.sub.0 xsin (Γ.sub.0)+W.sub.1 xsin (θ.sub.1)                                           (6) 
    
     Substituting for W 0 , Γ 0 , F 1 , and Γ 1  in equations (5) and (6) gives: 
     
         V.sub.1 xαcos (φ.sub.1 -βxRPM)=V.sub.0 xαxcos (φ.sub.0 -βxRPM)+W.sub.1 xcos (θ.sub.1)    (7) 
    
     
         V.sub.1 xαsin (φ.sub.1 -βxRPM)=V.sub.0 xαxsin (φ.sub.0 -βxRPM)+W.sub.1 xsin (θ.sub.1)    (8) 
    
     Equations (7) and (8) are solved for α and β in terms of the known variables. W 0  and Γ 0  are now calculated from equations (1) and (2). The balance weight is equal to W 0  and its position is at Γ 0  +180°. 
     In practice, the first trial weights are determined by using estimated values of the coefficients α and β based on data from several alternators that have been balanced. This would give a trial weight that would be close in magnitude and position to the final balance weight used. 
     On the locomotive, there are controls that cause the engine and alternator 14 to operate at one of several preset speeds (RPM) and a corresponding power setting. At notch 8, alternator 14 is operating at a speed of 1050 RPM and maximum horsepower. Notch 1 is the lowest power setting. It has been observed that on the locomotives currently being trim balanced, the highest vibrations on alternator 14 initially are at notch 8 in the vertical direction. It has also been observed that balancing alternator 14 at notch 8 can adversely affect the lateral vibration at notch 2 (speed about 580 RPM). In general, an initial survey would have to be done at all operating speeds before and after trim balancing to ensure all sensitive vibration modes are monitored and controlled during the balancing procedure. For this reason, in practice, both the notch 8 vertical and notch 2 lateral vibrations are measured and an optimum balance weight is attached to the rotor in order to reduce the notch 8 vertical vibration without substantially increasing the notch 2 lateral vibration. This is done using the sensitivity circle method as described below. 
     The balance weights are plotted with respect to a coordinate system such that the distance of the point from the origin corresponds to the magnitude of the balance weight and the angular position of the balance weight is the angle of the line made by joining the point to the origin to the upper part of the vertical axis. In FIG. 3, the balance weight needed to balance rotor 16 at notch 8 (1050 RPM) is indicated by the point marked W 8 . With the balance weight plotted, circles of equal vibration can be drawn which have their centers at the point representing the balance weight. These circles are called sensitivity circles. The radius of these circles depends on the value of the constant α. FIG. 3 shows one such circle 28 which corresponds to the baseline data. Points on circle 28 give the magnitude and position of weights that would produce the same amplitude of vibration. Since circle 28 passes through the origin, it is the circle for the vibration amplitude with no balance weight. 
     FIG. 4 shows two circles 30, 32. Circle 30 has a center at W 8  which represents the notch 8 balance weight. Circle 32 has a center at W 2  which represents the notch 2 balance weight. The circles 30, 32 correspond to the same level of vibration. The optimum balance weight is the weight corresponding to the point of contact of circles 30, 32 for equal notch 8 and notch 2 vibration. This is shown in FIG. 5. The weight corresponding to this point of contact of the circles can be calculated as follows: 
     If W B  represents the optimum balance weight, θ B  the angular position of this weight, and θ 8  and θ 2  the angular position of weight W 8  and W 2 , respectively, the following equations can be written: 
     
         {W.sub.8 xcos (θ.sub.8)-W.sub.B xcos (θ.sub.B)}x{α.sub.2 +α.sub.8 }={W.sub.8 xcos (θ.sub.8)-W.sub.2 xcos (θ.sub.2)}xα.sub.8                            (9) 
    
     
         {W.sub.8 xsin (θ.sub.8)-W.sub.B xsin (θ.sub.B)}x{α.sub.2 +α.sub.8 }={W.sub.8 xsin (θ.sub.8)-W.sub.2 xsin (θ.sub.2)}xα.sub.8                            (10) 
    
     where α 2  is the value of α for notch 2 and α 8  is the value of α for notch 8. 
     Equations (9) and (10) can be solved for W B  and θ B . 
     In practice, if the second trial weight does not give satisfactory results, the next trial weight can be calculated using data from the previous two trials and the baseline data. In this formulation, only the amplitudes of vibration are used. The phase angle is not used. This formulation is useful if the phase data is inaccurate. 
     FIG. 6 shows two sensitivity circles 34, 36. W B  represents the balance weight needed to balance the alternator (at notch 2 or notch 8) and is the center for the two circles. For the first trial weight, W 1  is placed at position θ 1 , resulting in a vibration of V 1 , represented by the smaller circle 36 in FIG. 6. W 1  will lie on this circle. For the second trial, weight W 2  is placed at position θ 2 , giving a vibration of V 2 . This vibration is represented by the larger circle 34 in FIG. 6. W 2  lies on this circle. The following equations can be written and solved for W B  and θ 0 . 
     
         α.sup.2 x(V.sub.0.sup.2 -V.sub.1.sup.2)-2xW.sub.1 xV.sub.0 xαx{cos (θ.sub.1 -θ.sub.0)}+W.sub.1.sup.2 =0(11) 
    
     
         α.sup.2 x(V.sub.0.sup.2 -V.sub.2.sup.2)-2xW.sub.2 xV.sub.0 xαx{cos (θ.sub.2 -θ.sub.0)}+W.sub.2.sup.2 =0(12) 
    
     The optimum balance weight for notch 2 and notch 8 can be obtained as described above in FIG. 3. 
     Once the necessary balance weight has been calculated, it must be attached to the alternator rotor yoke 16. The rotor yoke 16 has a set of twenty-four 0.5 inch tapped holes 23 that are used for bolting the selected balance weights to rotor yoke 16. Each balance weight is held in place by two 0.5 inch bolts and spacers (not shown). In order to obtain the full range of weights needed (from 1000 gm-inch to 20000 gm-inch) with increments of about 100 gm-inches with a minimum number of parts, the required weight is obtained as an effective weight from the vector combination of two weights selected from a set of eleven weights. Table 1 shows the weight of the eleven weight assemblies (each consisting of one weight, two bolts, and two spacers) in gram-inches. Table 2 shows all the possible combinations of the weight assemblies listed in Table 1, and the relative angle between the weights in each case. 
     A computer program selects the weight combination that gives the closest effective weight to the weight calculated and selects the holes so that the angular position is the closest possible to the calculated position. The computer program is written to interface with spectrum analyzer 12 and control the operation of the spectrum analyzer 12. It also does all of the calculations for determining the balance weights and their locations using the data collected with the help of spectrum analyzer 12. The vibration and phase data measured by the spectrum analyzer are automatically transferred to files in the computer and used by the program for the necessary calculations. The program is menu driven and requires minimum operator training in the use of spectrum analyzer 12. The operator is not required to do any calculations or analysis manually. 
     To more fully explain the method of the present invention, the following is a detail procedure for trim balancing of an alternator installed in a locomotive, which locomotive is in a condition to run at notch 2 and notch 8 in selfload in order to effect a trim balance. For purposes of description, the locomotive is assumed to be a Dash-8 locomotive manufactured by General Electric Company. Although the locomotive is not shown, various known elements will be referred to in the following description. With the locomotive in a load cell and with its diesel engine shut down, a safety panel on a B-side of a blower cab is removed to allow access to the alternator 14. A panel on the alternator covering the access opening 38 (FIG. 1) (held in place by bolts) is then removed. The panel is set aside and a test panel having an opening for passing sensor cables 40 is used during trim balancing. A light coat of black paint is applied over the outer two inches from an edge of the rotor yoke 16. The rotor is turned slowly over using a baring-over tool while the paint is being sprayed. A piece of reflecting tape (marker 22) is applied in line with one of the holes. 
     Tightly mounted by a mounting bracket 20 and bolt is the speed sensor 18. Light from the sensor 18 shines on the reflecting tape 22 when the alternator rotates. The test panel is bolted in place and the cable 40 from the sensor 18 is passed through a hole in the test panel and is pulled so that there is no slack. The end of the cable 40 is then connected to the spectrum analyzer 12. 
     The accelerometer 10 is placed on a block 42 at the middle of the alternator at the 3 o&#39;clock position for measuring vibration in the lateral direction. The end of the accelerometer lead 44 is connected to the spectrum analyzer 12. The spectrum analyzer 12 and the computer 26 are turned on and the name of the customer and locomotive road number may then be entered. The computer 26 should indicate the engine speed and the amplitude of vibration (1/rev) at the alternator 14 in the lateral direction after the engine has been started and the locomotive is in selfload to check whether the instrumentation is working. If the instrumentation is working properly, the throttle should be moved to notch 8 and the engine should be run for ten minutes. 
     The throttle is moved to notch 2 for baseline data. After the engine has been running at notch 2 for two to three minutes, the operator may read notch 2 lateral vibration. The program will first read amplitude and then take an average of four phase angle readings. After the notch 2 readings have been taken, the accelerometer is moved to a vertical position and the throttle is moved to notch 8. 
     After the engine has been running at notch 8 for two to three minutes, the operator may read notch 8 vertical vibration. The program will first read amplitude and then an average of four phase angle readings to obtain baseline data. 
     The operator may then determine from the baseline data whether balancing is needed. One of the following criteria must be met for the alternator to be balanced: (1) notch 2 and notch 8 vibrations must be 4.00 mils maximum; or (2) if the vibration exceeds 4.00 mils but does not exceed 6.00 mils--the difference between notch 2 and notch 8 vibrations must be 1.00 mil or less. Vibrations must not exceed 6.00 mils. 
     Next, the balance weight is calculated. The computer 26 will ask for the hole number at the reflecting tape 22 and will then give the following information: (1) parts to be used; (2) hole locations at which the weights are to be bolted; (3) actual weight in gm-inch; and (4) actual weight location in degrees. The engine is shut down, the panel removed from the alternator, and the engine barred over until the selected holes are at the access opening. Weights are bolted to the alternator rotor yoke using bolts and spacers and the bolts are then torqued to 55 to 60 ft-pounds. With the test panel bolted in place, the speed sensor cable is pulled through until all of the slack is taken up. 
     To determine trial weight data, the accelerometer 10 is placed on the block 42 at the horizontal position for lateral vibration measurement. The engine is started and the throttle is moved to notch 2. Trial weight data is selected from the program and then the operator enters the trial number, weight in gm-inches that has been added, and the actual location of the weight. After the engine has been running at notch 2 for two to three minutes, notch 2 lateral vibration may be read. The program will first read amplitude and then take an average of four phase angle readings. Once notch 2 readings have been taken, the accelerometer is moved to vertical position and the throttle moved to notch 8. After the engine has been running at notch 8 for two to three minutes, notch 8 vertical vibration may be read. The program will first read amplitude and then an average of four phase angle readings. To check whether balancing is complete, the operator should press 6 at the main menu of the program and enter the trial number. If balancing is to be repeated, go to the repeat trial weight step discussed below. If balancing is complete, go to the finish step discussed below. 
     To repeat trial weight step, the engine must again be shut down and the test panel removed from the alternator. The engine is then barred over until the first weight and then the second weight can be reached through the access opening and both weights are removed. With the baseline and trial data saved on computer, the balance weight is calculated by entering the trial number. The program will ask for the hole number at the reflecting tape 22 and will give the following information: (1) parts to be used; (2) hole locations at which the weights are to be bolted; (3) actual weight in gm-inch; and (4) actual weight location in degrees. The engine is then barred over until the selected holes are at the access opening 38. The required weights, bolts, and spacers are collected. The first weight is bolted to the alternator rotor yoke 16 at the first set of holes. The second weight is then bolted at the second set of holes. The test panel is again bolted in place and the speed sensor cable 40 pulled through until all of the slack is taken up. The trial Weight data st®p described above is then repeated to collect data with the new trial weight. 
     To print data, the operator selects print baseline data or print trial data from the main menu on computer 26 and enters the trial number. If more than one trial weight was used, the print trial data step is repeated. 
     Upon completion of the procedure of the present invention, the operator exits the program and removes the test panel from the alternator 14. The speed sensor 18 and bracket 20 are then removed. If any varnish or paint under the weights exist, such varnish and paint is removed and bolts are torqued to 55 to 60 ft-pounds. A production panel is bolted to the alternator 14 over access 38. The accelerometer 10 is removed from the locomotive and the safety panel is replaced. The baseline, final notch 2 lateral and notch 8 vertical vibration amplitudes, and final balance weight are recorded for future reference. The computer 26 and spectrum analyzer 12 may then be turned off. 
     The first time the ONO SOKKI CF-250 spectrum analyzer 12 is used for trim balancing or if the setup of the analyzer 12 is changed, the spectrum analyzer must be initialized. To do so, the baud rate is set to 1200 with the spectrum analyzer 12 turned on before starting the balance program. Once the baud rate has been set, the computer 26 will complete the rest of the initialization. 
     The calibration is set for an accelerometer 10 with a sensitivity of 100 mV/G. If it is necessary to change the calibration, the calibration constant for the accelerometer being used must be determined beforehand and input to computer 26. The accelerometer 10 current may be set to 2.0 mA or 0.56 mA as needed. The spectrum analyzer 12 display shows the present setting. When initialization is complete, the program in computer 26 returns control to the main menu. 
     While the principles of the invention have now been made clear in an illustrative embodiment, it will become apparent to those skilled in the art that many modifications of the structures, arrangements, and components presented in the above illustrations may be made in the practice of the invention in order to develop alternate embodiments suitable to specific operating requirements without departing from the spirit and scope of the invention as set forth in the claims which follow. 
     
                       TABLE 1______________________________________TRIM BALANCE WEIGHTS        WEIGHT  PART  (gm-inch)______________________________________  1     16355  2     16793  3     17231  4     18021  5     18809  6     19566  7     20375  8     21260  9     22049  10    22792  11    23447______________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________    ANGLE BETWEEN WEIGHTSW.sub.1W.sub.2    180 165 150 135 120 105 90__________________________________________________________________________1635516355      0 4270             8466                12518                    16355                        19913                            231291723116355     876        4469             8734                12878                    16810                        20458                            237571802116355    1666        4781             9042                13245                    17248                        20968                            243361802117231     790        4667             9156                13510                    17639                        21469                            249331880916355    2454        5195             9405                13646                    17710                        21495                            249251880917231    1578        4958             9452                13869                    18072                        21975                            255091880918021     788        4870            9563                14113                    18428                        22429                            260491956616355    3211        5667             9801                14063                    18175                        22015                            255011956617231    2335        5332             9787                14246                    18509                        22477                            260721956618021    1545        5140             9842                14455                    18841                        22914                            266001956618809     757        5065             9959                14702                    19199                        23369                            271412037516355    4020        6235            10269                14538                    18692                        22586                            261272037517231    3144        5815            10196                14681                    18999                        23029                            266842037518021    2354        5528            10194                14854                    19306                        23448                            272012037518809    1566        5345            10254                15065                    19639                        23886                            277292037519566     809        5275            10367                15303                    19983                        24323                            282482126016355    4905        6910            10827                15091                    19281                        23227                            268232126017231    4029        6419            10695                15193                    19559                        23649                            273662126018021    3239        6050            10637                15327                    19840                        24050                            278702126018809    2451        5767            10637                15500                    20147                        24470                            283862126019566    1694        5587            10692                15702                    20466                        24890                            288932126020375     885        5505            10810                15954                    20832                        25356                            294472204916355    5694        7550            11360                15610                    19825                        23811                            274532204917231    4818        7007            11181                15677                    20078                        24216                            279832204918021    4028        6581            11077                15779                    20336                        24602                            284772204918809    3240        6226            11028                15920                    20621                        25005                            289822204919566    2483        5964            11035                16090                    20918                        25410                            294792204920375    1674        5781            11099                16308                    21261                        25860                            300222204921260     789        5707            11235                16590                    21665                        26372                            306292279216355    6437        8175            11888                16118                    20352                        24372                            280532279217231    5561        7595            11669                16155                    20583                        24761                            285722279218021    4771        7124            11525                16229                    20821                        25132                            290562279218809    3983        6714            11434                16340                    21085                        25521                            295512279219566    3226        6387            11397                16481                    21362                        25913                            300382279220375    2417        6123            11414                16670                    21685                        26348                            305712279221260    1532        5947            11497                16917                    22066                        26845                            311682279222049     743        5899            11628                17174                    22430                        27304                            317122344716355    7092        8742            12371                16581                    20827                        24875                            285882344717231    6216        8135            12120                16592                    21039                        25249                            290982344718021    5426        7631            11944                16642                    21260                        25609                            295722344718809    4638        7181            11819                16729                    21506                        25986                            300592344719566    3881        6806            11747                16846                    21768                        26365                            305382344720375    3072        6480            11724                17008                    22072                        26788                            310632344721260    2187        6225            11762                17228                    22434                        27271                            316502344722049    1398        6098            11852                17458                    22780                        22718                            321862344722792     655        6070            11984                17705                    23126                        28153                            326991679316355     438        4348             8590                12692                    16578                        20182                            234411723116793     438        4462             8816                13027                    17016                        20715                            240611802116793    1228        4704             9088                13371                    17439                        21216                            246331880916793    2016        5059             9418                13751                    17886                        21732                            252151956616793    2773        5485             9784                14148                    18337                        22243                            257842037516793    3582        6012            10223                14603                    18841                        22804                            264042126016793    4467        6655            10753                15136                    19416                        23435                            270922204916793    5256        7270            11262                15637                    19947                        24010                            277162279216793    5999        7879            11770                16131                    20463                        24563                            283102344716793    6654        8433            12238                16581                    20929                        25059                            28840__________________________________________________________________________