Type a line (1 min 250 MOhm 10 min 900 MOhm 25 °C; 30 s 120 MOhm 60 s 180 MOhm; PI 1.4) or fill in the fields: the line and the fields stay in step.
Enter the insulation tester readings with their times (at 15 and 30 seconds, at 1 and 10 minutes) and the winding temperature, and the calculator gives the polarization index, the DAR and the absorption ratio, corrects the 1-minute reading to 40 °C and shows the IEEE 43 reference figures. A single ratio from a test report works too. The working is shown with your numbers, the readings are drawn against time, and the result comes as a line you can copy or add to a request.
The IEEE 43 figures are reference figures: the machine maker’s data, the class society rules and the ship’s own records govern. The calculator gives no limit for the DAR, the absorption ratio or a cable, and the correction to 40 °C is an approximation.
The polarization index is the reading at 10 minutes over the reading at 1 minute; the DAR is the reading at 60 seconds over the reading at 30 seconds; the absorption ratio of the Russian norms is the reading at 60 seconds over the reading at 15 seconds. 250 MOhm at 1 min and 900 MOhm at 10 min give a PI of 3.6.
R40 = Kt x Rt. For thermoplastic insulation the resistance halves for every 10 °C: at 25 °C, Kt = 0.3536. For thermosetting insulation IEEE 43-2013 gives fits with the constants 1245 and 4230: at 25 °C, Kt = 0.8186. Both are approximations; readings taken at one temperature compare best.
The minimum 1-minute reading at 40 °C: kV + 1 MOhm, 100 MOhm or 5 MOhm by the type of winding; the minimum PI: 1.5 for class A and 2.0 for class B and above. The machine maker’s data, the class society rules and the ship’s records govern.
| Item | Equals | Note |
|---|---|---|
| Polarization index (PI) | R(10 min) / R(1 min) | 900 / 250 = 3.6 |
| DAR | R(60 s) / R(30 s) | 180 / 120 = 1.5 |
| Absorption ratio | R(60 s) / R(15 s) | used in the Russian norms |
| Kt, thermoplastic insulation | 0.5^((40 - t) / 10) | halving for every 10 °C; 0.3536 at 25 °C, 4.0000 at 60 °C |
| Kt, thermosetting insulation, 10 to below 40 °C | exp(-1245 x (1/(t + 273) - 1/313)) | IEEE 43-2013 fit; 0.7622 at 20 °C, 0.8186 at 25 °C |
| Kt, thermosetting insulation, 40 to below 85 °C | exp(-4230 x (1/(t + 273) - 1/313)) | IEEE 43-2013 fit; 1.5195 at 50 °C, 2.2517 at 60 °C |
| R40 | Kt x Rt | the reading Rt at t °C, corrected to 40 °C |
| 1 GOhm | 1000 MOhm | 1 MOhm = 1000 kOhm; 1 TOhm = 1000 GOhm |
The factors Kt are approximations: when comparing with earlier readings, readings taken at the same temperature, voltage and duration compare best.
The polarization index (10 min over 1 min), the DAR (60 s over 30 s) and the absorption ratio (60 s over 15 s) were each checked against at least two independent sources: insulation tester makers’ guides, accounts of IEEE 43 and the Russian test norms. The correction to 40 °C follows IEEE 43: halving for every 10 °C for thermoplastic insulation and the IEEE 43-2013 fits for thermosetting insulation; the constants, the temperature ranges and the sign of the fits were checked against two independent accounts of the standard: the reading is multiplied by Kt, so a reading taken below 40 °C is corrected down. Two accounts call the fits approximations, with large errors possible outside 10 to 60 °C; the worked example (160 MOhm at 20 °C gives 122 MOhm at 40 °C) is published in one of them and agrees with the fit. The reference figures for the minimum resistance (kV + 1, 100 and 5 MOhm), the minimum PI (1.5 and 2.0) and the caveat above 5000 MOhm are each stated in at least two sources. Figures on which the sources differ, such as DAR limits, are left out.
The polarization index (PI) is the reading at 10 minutes divided by the reading at 1 minute; the dielectric absorption ratio (DAR) is the reading at 60 seconds divided by the reading at 30 seconds. Both readings come from one test at one voltage, and the ratio has no unit. For 250 MOhm at 1 min and 900 MOhm at 10 min the PI is 900 / 250 = 3.6; for 120 MOhm at 30 s and 180 MOhm at 60 s the DAR is 180 / 120 = 1.5. Some norms, the Russian ones among them, use the absorption ratio of the readings at 60 and 15 seconds instead; the calculator gives it when both readings are typed.
R40 = Kt x Rt, with Rt the reading at the winding temperature t. For thermoplastic insulation (older asphalt-based windings) the resistance halves for every 10 °C rise: Kt = 0.5^((40 - t) / 10), 0.3536 at 25 °C. For thermosetting insulation (epoxy and polyester windings), IEEE 43-2013 gives two fits: Kt = exp(-1245 x (1/(t + 273) - 1/313)) from 10 to below 40 °C and exp(-4230 x (1/(t + 273) - 1/313)) from 40 to below 85 °C, 0.8186 at 25 °C. Both are approximations, and outside 10 to 60 °C the error can be large; readings taken at the same temperature compare best. 160 MOhm at 20 °C is 122.0 MOhm at 40 °C by the thermosetting fit and 40 MOhm by the halving.
For the reading at 1 minute on the whole winding, corrected to 40 °C, IEEE 43 gives these reference figures: kV + 1 MOhm, kV being the rated voltage of the machine, for most windings made before about 1970, all field windings and others not described; 100 MOhm for most AC windings built after about 1970 (form-wound coils); 5 MOhm for most machines with random-wound stator coils and form-wound coils rated below 1 kV. They are reference figures from the standard: the machine maker’s data, the class society rules and the ship’s own records govern.
As reference figures, a minimum PI of 1.5 for thermal class A (105) and 2.0 for class B (130) and above. When the 1-minute reading corrected to 40 °C is above 5000 MOhm, IEEE 43 says the PI may not give a reliable view. For the DAR and the absorption ratio the figures in circulation differ, so the calculator gives none: compare with the maker’s figure and with the machine’s earlier readings.
Resistances in kOhm, MOhm, GOhm or TOhm (also written with the ohm sign or as megohm), each with its time: 15 s, 30 s, 1 min, 10 min, or as R15, R30, R60, IR1 and IR10. The winding temperature goes in °C. A PI or a DAR on its own, such as PI 1.4, is compared with the reference figures, where there are any. Russian unit names and decimal commas are read as well, and a voltage is set aside: the test voltage belongs in the line to copy.
The ratios are worked out in the same way for a cable as for a winding. The IEEE 43 figures and its temperature correction are for the windings of motors and generators, so for a cable the calculator shows the ratios only, and the cable maker’s data and the class society rules govern.
The calculator works out the ratios from the figures you enter. When bearings, a brush gear part, a terminal box, a cable or a whole machine is needed, send the line from the calculator with a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
