Tom Bishop, PE
EASA Senior Technical Support Specialist
One of the most frequent member requests to our technical support group is for conversion of a 3 phase winding from concentric to lap. An excellent alternative to requesting the conversion is to use the EASA AC Motor Verification and Redesign (ACR) program to calculate the changes. In fact, many members have purchased the redesign program and have called us to confirm their conversions as they develop their proficiency and “comfort level” with the program. However, our emphasis here is not to convince you to purchase the ACR program but to cover the important details for a proper concentric to lap winding conversion.
“Rule of Thumb” Method
Many of us, including me, seek out “rules of thumb” to make our work easier. A rule of thumb for concentric to lap conversions that is all too frequently applied, with undesirable results, is to select the middle or average pitch of the concentric group and use it along with half the turns of the full slot concentric coils, or the same turns if the coils are half slot.
An example that illustrates the hazard of using the average pitch is a 36 slot, 4 pole winding with pitches of 1-5-7-9 and 12 turns per half slot coil. Selecting the middle pitch of 1-7 and using 12 turns results in a lap winding that has the equivalent magnetic flux level to the concentric winding. However, the chord factor is only 0.866, well below the recommended minimum of 0.900. In this case, the 1-7 pitch would result in a 5th harmonic of nearly 5%, whereas a more common 1-8 pitch would have less than 1% content of the 5th harmonic. Harmonics increase winding losses, increase heating and often reduce torque output.
Common Conversion Methods
The example above depicts some of the pitfalls of trying to oversimplify concentric to lap conversions. There are three common methods of converting concentric windings to lap that provide correct results. The first is to use the tables of concentric to lap conversions found in Section 2.13 of the EASA Technical Manual. The second method is to use the EASA ACR computer program, and the third method is to hand calculate the conversion using the formulas in the EASA AC Motor Redesign manual.
The first method is the quickest, if the winding turns ratios and spans (pitches) exactly match a combination found in the tables (see Figure 1). Even though there are over 250 concentric combinations listed, manufacturers continually create new combinations. If the concentric turns and spans (pitches) combination you are dealing with is not in the tables, one of the other methods must be used. A potential drawback to this method is that the winding magnetic flux and current densities are not known. Thus, even though the concentric to lap conversion may be correct, if the as-found data is incorrect, the new data will likewise be incorrect. Therefore, using this method is discouraged unless the data is factory data.
The second method, using the ACR program, not only calculates the conversion from concentric to lap, the program (see Figures 2 and 3) also calculates the magnetic flux and current densities and identifies any values that are not within typically acceptable ranges. The advantage of checking densities is that an error in the data may be detected before rewinding. A variant of the second method is to use a spreadsheet for data entry and concentric to lap conversions. Some members have created spreadsheets that simply convert concentric windings to lap, and others have expanded spreadsheets that also calculate magnetic flux and current densities. As mentioned above, determining the magnetic flux and current densities is a much more reliable method than just converting winding data from concentric to lap.
The third method, hand calculating using the formulas in the EASA AC Motor Redesign manual, can be tedious, and with many inter-related hand calculations, the probability of an error is relatively high. For these reasons, I suggest avoiding use of the hand calculation method.
How to Convert Concentric to Lap
Let’s assume that we have factory concentric winding data to be converted to lap. The conversion consists of multiplying the turns of each coil by the chord factor for that coil's pitch, summing the results and dividing by the chord factor selected for the lap winding. The following exa mple illustrates the process:
Data: 36 slots, 18 coils, 4 pole, 1-8- 10-12 pitch, 32 turns in each coil.
For simplicity and to focus on the conversion, we will not elaborate on the equation to calculate chord factors but will use the values for 9 slots per pole (36/4) given in Coil Pitch/Chord Factor, Table 2-50 in the EASA Technical Manual.
Chord factors: 1-8 = 0.940, 1-10 = 1.000, and 1-12 = 0.940.
Effective turns per group are the sum of the turns of each pitch multiplied by the chord factors.
Effective turns/group = (32 x 0.940) + (32 x 1.000) + (32 x0 .940) = 92.2
Turns for the lap winding must consider that there will be twice as many coils (half-slot) as with the concentric (full-slot) winding. The effective turns per group are halved and then divided by the lap chord factor multiplied by the number of coils per lap group (3) and the lap distribution factor. Distribution factors are given in Distribution Factor For Three Phase Windings, Table 2-49 in the EASA Technical Manual. The distribution factor for 3 coils per group lap standard (alternating pole) is 0.960. For the example, we have selected a pitch of 1-9 with a chord factor of 0.985.
Lap turns = (92.2/2)/(0.985 x 3 x 0.960) = 46.1/2.84 = 16.2 turns. The nearest whole number is 16, which will increase magnetic flux by 16.2/16, or slightly more than 1%. A change in flux of less than 2% is acceptable, and 16 turns would be used for the 1-9 pitch lap winding.
As can be seen from the above, converting from concentric to lap, though usually straightforward, requires multiple calculations and table references (or more calculations). In this case, simply selecting the middle pitch of 1-10 and halving the turns would result in the correct number of lap turns. However, 1-10 is full pitch and increases harmonics, which increase electrical noise and reduce torque. Less desirable from a design perspective would be a full-slot lap winding, frequently requiring full-pitch for insertion. Heat displacement can be affected because some coils are “buried” between others, increasing temperature rise of the buried coils, compounding the above-mentioned negative aspects of the full-pitch winding.
Dealing With Fractional Turn Results
Another issue is that conversion to a lap winding may result in fractional turns. If the calculated turns for example are 11.5 for a lap coil, selecting either 11 or 12 turns will result in a flux change of over 4%, which is more than double the suggested limit of 2%. One solution is to double the circuits and turns and use half of the original wire area. If the original connection associated with the 11.5 turn lap winding was a 1&2 delta, 4 pole and had 2 #17 wires, it could be converted to 23 turns with a 2&4 delta and 1 #17 wire. Caution: Make certain that such a conversion can be used before making new coils. If the winding in this example was 6 poles, a 2&4 circuit connection would not be possible; 4 circuits cannot be used for 6 poles.
Another alternative to doubling the circuits is to use unequal turn coils. In the example above, the turns could be alternated 11-12, if there is an even number of coils per group. The example 36 slot, 4 pole winding would have 12 groups of 3, making the unequal turn alternative probably not viable.
Having an even number of coils per group, or equal turns per circuit, is not assurance that unequal coils will have the same number of turns per slot. If the pitch is 1 to an even number such as 1-12, and the turns count alternates, there will be equal turns per slot. In general, a pitch of 1 to an odd number will result in unequal turns per slot. For example, consider a 48 slot, 4 pole winding that has 12 groups of 4. If there are 11-12-11-12 turns and the pitch is 1-12, all slots will have 23 turns total. If the pitch is changed to 1-11 with the 11-12-11-12 alternating sequence, the total turns per slot will alternate 22-24 all through the winding. In this case there is a solution, which is to use the sequence of 11-11-12-12. That will result in 23 total turns in every slot. To determine if an unequal turn sequence can be used with a pitch of 1 to an odd number, the winding turns layout should be checked either manually or preferably with a spreadsheet.
Check Total Turns Per Slot
Some concentric to lap conversions result in an increase in total turns per slot compared to the original winding. In the 36 slot, 4 pole example above, the lap turns with a 1-8 pitch would be 17. The turns per slot for these half-slot coils would be 2 x 17, or 34. That is greater than the 32 turns per full-slot concentric coil of the original winding. If the 1-8 pitch and 17 turns are selected, it is important that the wire area of the turns not be reduced more than 2%. Doing so would increase heating and have a negative effect on efficiency. A better alternative in this case if slot space cannot accommodate the increased turns, is to use 1-9 pitch and 16 turns. The wire area per slot will be the same if the original wire combination is used. Note though that with half-slot coils there is additional insulation due to the separator between top and bottom coil halves.
Conclusion
In summary, when converting from concentric to lap do not use a rule of thumb approach such as selecting the middle pitch and halving the turns. As noted above, this can lead to a significant change in the magnetic strength of a motor. The method of converting that has the highest probability of accuracy and success is to use a computer program, either a proven spreadsheet or the EASA ACR program. And, if you need assistance with a concentric to lap conversion, you can contact us, preferably by using the Online Verification & Redesign Request available at go.easa.com/support. Note that you must be logged in as a member to access the request form.
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