BALANCEPOINT - WHY IT WORKS

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0 height="100%"><tr> <td valign="top" width=100 BGCOLOR="#444444" TEXT="#080000"> <div> <A HREF="id4.htm" TARGET="_top" TITLE="ROTOR BALANCING by OPTIMIZED BLADE PLACE"><U><B><IMG SRC="b7c643a0.png" border=0 width="100" height="314" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </td> <td valign="top" BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B><IMG SRC="c6c77320.png" border=0 width="631" height="50" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="index.htm" TARGET="_top" TITLE="T u r b i n e M e t r o l"><U><B><IMG SRC="bfe321e0.png" border=0 width="50" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id23.htm" TARGET="_top" TITLE="PRODUCTS"><U><B><IMG SRC="b48511e0.png" border=0 width="81" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id55.htm" TARGET="_top" TITLE="SERVICES"><U><B><IMG SRC="b4a4c1e0.png" border=0 width="76" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id66.htm" TARGET="_top" TITLE="PUBLICATIONS"><U><B><IMG SRC="b4c681e0.png" border=0 width="104" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id68.htm" TARGET="_top" TITLE="NEWS"><U><B><IMG SRC="cb13c1e0.png" border=0 width="60" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><A HREF="id2.htm" TARGET="_top" TITLE="COMPANY"><U><B><IMG SRC="b20441e0.png" border=0 width="68" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><IMG SRC="b2b4f1e0.png" border=0 width="79" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id14.htm" TARGET="_top" TITLE="CONTACT US"><U><B><IMG SRC="b2d461e0.png" border=0 width="70" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><A HREF="id17.htm" TARGET="_top" TITLE="ASSOCIATES"><U><B><IMG SRC="b30601e0.png" border=0 width="96" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B><IMG SRC="bfd141e0.png" border=0 width="20" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <FONT SIZE="4" COLOR="#CC6600" FACE="Arial Black" ><IMG SRC="ba312c80.jpg" border=0 width="274" height="200" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT> <IMG SRC="ba912c80.jpg" border=0 width="274" height="200" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <IMG SRC="ba713c80.jpg" border=0 width="275" height="200" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> An Improvement in Existing Techniques for Turbine Rotor Balancing By Optimized Blade Placement</div> <bR> <div> <B>By Neill Fleeman and Russell Jurgensen</B></div> <bR> <div> <B>INTRODUCTION</B></div> <div> <B>In gas turbine and jet engine applications using non-integral compressor, turbine, and thrust fan blades, variance in individual blade weights due to manufacturing tolerances can significantly affect the balance of the assembled rotor. Even if the weight variances are small, if, by random assembly, more of the heavier blades are placed on one side of the rotor, the resulting unbalance condition may be more than can be corrected by additional balance weights or corrective machining processes. This means time-consuming and expensive disassembly and reassembly of the rotor.</B></div> <bR> <div> <B>It must be understood that very little can be inferred about the balance properties of any given blade set based solely on the number of blades in that set. The individual blades are subject to many variables of materials, processes, and construction which cannot be predicted with any degree of certainty within a universe of blades, a family of blades, a batch of blades, or even one set of blades. For example, since the performance of any blade in the engine is due primarily to its shape, blades which have been produced by machining a solid billet of homogeneous material may be mixed within a set with blades which have been produced from near-net forgings and finish ground. In the engine the performance of the two types of blades will be indistinguishable but in terms of balance the two types may present very different weights or weight distributions due to materials and material densities. For this reason, conventional wisdom says that each blade must be dealt with individually in order to optimize its position in the assembly to minimize forces of unbalance.</B></div> <bR> <div> <B>EXISTING METHODS</B></div> <div> <B>To minimize the unbalance effects of random assembly, a number of numerical techniques have been employed by Turbine Metrology, Schenck, and others. Based on the pan weights or moment weights of the blades, these optimized arrangement techniques fall into two general categories:</B></div> <bR> <div> <B>1.    Fixed Pattern Opposition Techniques </B></div> <div> <B>The most common quasi-numerical solution for determining blade placement is the simple Fixed Pattern Opposition scheme. This method determines the rank of each blade's weight and places blades of adjacent ranks in opposition or in a predetermined pattern of position to attempt to achieve overall rotor balance. </B></div> <bR> <div> <B>Example: In an example of a simple 12 blade rotor, a typical Fixed Pattern Opposition method installs the heaviest blade in the Slot 1 position. The second heaviest blade is put into Slot 7 (directly opposite Slot 1 in the 180 degree position). The third heaviest blade is placed in Slot 4 (the 90 degree position) and the fourth heaviest blade is put into Slot 10 (the 270 degree position. The next four weight-ranked blades repeat the pattern with the Slot Number incremented by one, e.g. The fifth heaviest blade is placed in Slot 2, the sixth heaviest in Slot 8, seventh heaviest in Slot 5 eight heaviest in Slot 11. This pattern is repeated until the rotor is completely populated. </B></div> <bR> <div> <B>This type of arrangement is called a “4-pole” or “90 Degree” pattern. Other common Fixed Opposition programs use a 2-pole (180) degree or 3-pole (120 degree) placements. Some programs use more than one type and select the pattern that yields the lowest unbalance. Obviously these types of programs run into difficulty with an odd number of blades or a number that is not divisible by the number of poles. In these cases the remaining blades are used to fill in the remaining slots as best they can.</B></div> <bR> <div> <B>There are a number of variations of this method but if the blade set consists of more than a few blades none of these schemes can provide anything like optimum balancing, particularly as the variance of weights within the blade set increases. Neither can they factor in initial rotor imbalance, if available, or work with special blade types - blades that must be installed in one particular slot to achieve a particular design function. These methods are entirely repeatable, however, and are easy to understand with results that are easy to visualize. Since they can be worked out by hand, a computer may not be required, making them convenient for field repair. </B></div> <bR> <div> <B>2.   Heuristic Methods</B></div> <div> <B>Heuristic Methods have become more common as computing speed has increased. These methods are often used in conjunction with a pre-positioning step based on Fixed Pattern Opposition methods but from that point onward they work in a very different way. Utilizing a variation on the solution of the classic “Traveling Salesman” problem, the Heuristic method starts by calculating the unbalance for the blade set as initially presented, then randomly exchanging the position of two blades on the rotor and recalculating the unbalance.</B><FONT SIZE="2" COLOR="#0000FF" FACE="Verdana" ><B> </B></FONT><B> If the calculated unbalance of the second pattern is smaller than the first, the resultant blade positions are recorded and used for the basis of another exchange iteration. If the result is not better, it is discarded and another random exchange is made and tested. This process is repeated until the rotor unbalance has been reduced to within assembly tolerance or is stopped by time or other constraints. </B></div> <bR> <div> <B>Due to the large number of blade combinations, it is rarely possible to test all potential combinations (“complete solution”) unless the blade set is very small. Therefore the absolute minimum unbalance for the assembly is rarely achieved; practical considerations do not allow it the computational time required.</B></div> <bR> <div> <B>Using the example 12 blade set, conventional statistical methods indicate that there are 479,000,000 (written in exponential notation as 4.79 x 10^8) possible blade combinations. This number of possible combinations can be checked in a reasonable amount of time with a modern computer - from several minutes to an hour or better. A 34 blade set for the thrust fan of a Pratt & Whitney JT 8/9 jet engine, however, has 2.95 x 10^38 possible combinations and would take years to calculate.  And the 75-blade set for a Rolls-Royce Trent 500 High Pressure Compressor section would take centuries of calculating time at present speeds. </B></div> <bR> <div> <B>As the term implies, unless the blade set is small enough to allow a complete solution, Heuristic techniques do not calculate the </B><B>best</B><B> possible placement of blades; they can only </B><B>improve</B><B> placement and that improvement is based, in effect, on the allowed calculation time. The trick with a Heuristic method then is to find a way of directing the algorithm to achieve the best possible results in the shortest possible amount of time.</B></div> <bR> <bR> <div> <B>IMPROVEMENT TO EXISTING METHODS</B></div> <div> <B>1.     Statistical Methods</B></div> <div> <B>As Fleeman and Jurgensen investigated improvements to the basic BalancePoint 6.10 Heuristic techniques, it was quickly realized that numbers at the level of incomprehensibility required to test every possible combination of blades were very similar to - but dozens of orders of magnitude higher than -- those considered by quantum physics in predicting molecular combinations. </B></div> <bR> <div> <B>Application of quantum techniques to the BalancePoint Heuristic algorithm reduced the number of iterations to completely test all possible blade set combinations in our twelve blade example from 479,000,000 to approximately 3,600,000, a 99.2% reduction. On a reasonably fast computer this greatly reduced number of combinations may be tested in no more than a few minutes, yielding a complete solution. When the size of the blade set is so large that a complete solution is still beyond calculational capability, the improved efficiency of the Heuristic means that many more possible arrangements may be considered within the time constraint.</B></div> <bR> <div> <B>2.    Algorithm Stagnation</B></div> <div> <B>In any Heuristic method, as the solution approaches optimum, the algorithm may “stagnate” and fail to make any headway toward an improved solution for thousands or millions of exchanges, even if a large number of improved solutions are still available. In some cases the algorithm may become stagnated to a point from which no improvement to the solution can be made before time or other constraints terminate the process. In cases such as these, rather than continuing to grind away at calculations which yield no benefit, it is desirable to introduce an element into the process which has the effect of redirecting the algorithm. </B></div> <bR> <div> <B>Determination of the Stagnation Threshold must be a dynamic parameter as it cannot be predicted. Likewise, the redirection of the blade set must be carried out in a manner that does not cause the Heuristic to revisit previously tested combinations. Development of Stagnation Threshold detection and upsetting techniques has been key to the ability demonstrated by BalancePoint 6.10 to quickly arrive at extremely well balanced blade arrangements in a very short period of time.</B></div> <bR> <bR> <div> <B>SUMMARY</B></div> <div> <B>The statistical simplification and stagnation correction improvements to the existing Heuristic methods by Fleeman and Jurgensen increase the power of the algorithm by reducing the number of calculations required to produce a complete solution or, if the size of the blade set and/or calculational capability do not allow a complete solution, the improvements mean that vastly more possibilities may be considered per unit of time. This improved Heuristic technique has been termed “Dimensional Tunneling Technology.” Testing of benchmark blade sets indicates that for large blade sets for which a complete solution is not possible, the residual unbalance of the set when using these techniques in BalancePoint 6.10 is reduced by a factor of 2 to 20 as compared with the already low residuals yielded by the Heuristic used in BalancePoint 6.0.</B></div> <bR> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>DOWNLOAD</B><FONT SIZE="2" COLOR="#000000" FACE="Verdana" ><B> a PDF of this article in:  </B></FONT><B> </B><FONT SIZE="2" COLOR="#CC6600" FACE="Arial" ><B>      </B><A HREF="http://www.turbinemetrology.com/BP-TECHNIQUE.pdf" TARGET="_top" TITLE="http://www.turbinemetrology.com/BP-TECHN"><U><B><IMG SRC="cbe27140.png" border=0 width="39" height="20" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></FONT></div> <bR> <bR> <div> <A HREF="id4.htm" TARGET="_top" TITLE="ROTOR BALANCING by OPTIMIZED BLADE PLACE"><U><IMG SRC="c69621e0.png" border=0 width="98" height="30" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> </td> </tr></table></body>