Week-11 Challenge: Braking
- For a defined driving cycle, calculate the energy required for braking.
The energy required for braking:
Whenever a force is applied to a vehicle's brakes, there is work done due to the friction between the brakes and the wheel. This reduces the vehicle's kinetic energy, slowing it down and causing the temperature of the brakes to increase.Decelerating from very high speeds too quickly can cause several problems:
- The brakes could overheat and the material they are made from could shatter. This will lead to the driver losing control.
- Very high temperatures near the tires could cause the tires to explode. This will lead to the driver losing control.
- A high deceleration needs a high force (Newton's second law), and these high forces can seriously injure the driver.
The energy required for braking can be calculated using Newton's second law. Let’s assume a drive cycle, FTP 75 with a total gross weight of 1000 Kg
The acceleration/ deceleration of the car is given by:
Deceleration =change in velocity/time
= (Final velocity – Initial Velocity)/ Time
The kinetic energy is given by,
K.E = 1/2* (m*V2) Joules.
UDDS Drive Cycle Time Velocity Braking Energy (J) Inst. Energy Consumed (kWh) 0 0 0 0 Assume, 1 0 0 0 GVM = 1000Kg 2 0 0 0 Braking Energy = 1/2*m*V^2 3 0 0 0 4 0 0 0 Total Energy Consumed (kWh) is 114 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 0 10 0 0 0 11 0 0 0 12 0 0 0 13 0 0 0 14 0 0 0 15 0 0 0 16 0 0 0 17 0 0 0 18 0 0 0 19 0 0 0 20 0 0 0 21 3 4500 0.0013 22 5.9 17405 0.0048 23 8.6 36980 0.0103 24 11.5 66125 0.0184 25 14.3 102245 0.0284 26 16.9 142805 0.0397 27 17.3 149645 0.0416 28 18.1 163805 0.0455 29 20.7 214245 0.0595 30 21.7 235445 0.0654 31 22.4 250880 0.0697 32 22.5 253125 0.0703 33 22.1 244205 0.0678 34 21.5 231125 0.0642 35 20.9 218405 0.0607 36 20.4 208080 0.0578 37 19.8 196020 0.0545 38 17 144500 0.0401 39 14.9 111005 0.0308 40 14.9 111005 0.0308 41 15.2 115520 0.0321 42 15.5 120125 0.0334 43 16 128000 0.0356 44 17.1 146205 0.0406 45 19.1 182405 0.0507 46 21.1 222605 0.0618 47 22.7 257645 0.0716 48 22.9 262205 0.0728 49 22.7 257645 0.0716 50 22.6 255380 0.0709 51 21.3 226845 0.063 52 19 180500 0.0501 53 17.1 146205 0.0406 54 15.8 124820 0.0347 55 15.8 124820 0.0347 56 17.7 156645 0.0435 57 19.8 196020 0.0545 58 21.6 233280 0.0648 59 23.2 269120 0.0748 60 24.2 292820 0.0813 61 24.6 302580 0.0841 62 24.9 310005 0.0861 63 25 312500 0.0868 64 24.6 302580 0.0841 65 24.5 300125 0.0834 66 24.7 305045 0.0847 67 24.8 307520 0.0854 68 24.7 305045 0.0847 69 24.6 302580 0.0841 70 24.6 302580 0.0841 71 25.1 315005 0.0875 72 25.6 327680 0.091 73 25.7 330245 0.0917 74 25.4 322580 0.0896 75 24.9 310005 0.0861 76 25 312500 0.0868 77 25.4 322580 0.0896 78 26 338000 0.0939 79 26 338000 0.0939 80 25.7 330245 0.0917 81 26.1 340605 0.0946 82 26.7 356445 0.099 83 27.5 378125 0.105 84 28.6 408980 0.1136 85 29.3 429245 0.1192 86 29.8 444020 0.1233 87 30.1 453005 0.1258 88 30.4 462080 0.1284 89 30.7 471245 0.1309 90 30.7 471245 0.1309 91 30.5 465125 0.1292 92 30.4 462080 0.1284 93 30.3 459045 0.1275 94 30.4 462080 0.1284 95 30.8 474320 0.1318 96 30.4 462080 0.1284 97 29.9 447005 0.1242 98 29.5 435125 0.1209 99 29.8 444020 0.1233 100 30.3 459045 0.1275 101 30.7 471245 0.1309 102 30.9 477405 0.1326 103 31 480500 0.1335 104 30.9 477405 0.1326 105 30.4 462080 0.1284 106 29.8 444020 0.1233 107 29.9 447005 0.1242 108 30.2 456020 0.1267 109 30.7 471245 0.1309 110 31.2 486720 0.1352 111 31.8 505620 0.1405 112 32.2 518420 0.144 113 32.4 524880 0.1458 114 32.2 518420 0.144 115 31.7 502445 0.1396 116 28.6 408980 0.1136 117 25.3 320045 0.0889 118 22 242000 0.0672 119 18.7 174845 0.0486 120 15.4 118580 0.0329 121 12.1 73205 0.0203 122 8.8 38720 0.0108 123 5.5 15125 0.0042 124 2.2 2420 0.0007 125 0 0 0 126 0 0 0 127 0 0 0 128 0 0 0 129 0 0 0 130 0 0 0 131 0 0 0 132 0 0 0 133 0 0 0 134 0 0 0 135 0 0 0 136 0 0 0 137 0 0 0 138 0 0 0 139 0 0 0 140 0 0 0 141 0 0 0 142 0 0 0 143 0 0 0 144 0 0 0 145 0 0 0 146 0 0 0 147 0 0 0 148 0 0 0 149 0 0 0 150 0 0 0 151 0 0 0 152 0 0 0 153 0 0 0 154 0 0 0 155 0 0 0 156 0 0 0 157 0 0 0 158 0 0 0 159 0 0 0 160 0 0 0 161 0 0 0 162 0 0 0 163 0 0 0 164 3.3 5445 0.0015 165 6.6 21780 0.0061 166 9.9 49005 0.0136 167 13.2 87120 0.0242 168 16.5 136125 0.0378 169 19.8 196020 0.0545 170 22.2 246420 0.0685 171 24.3 295245 0.082 172 25.8 332820 0.0925 173 26.4 348480 0.0968 174 25.7 330245 0.0917 175 25.1 315005 0.0875 176 24.7 305045 0.0847 177 25 312500 0.0868 178 25.2 317520 0.0882 179 25.4 322580 0.0896 180 25.8 332820 0.0925 181 27.2 369920 0.1028 182 26.5 351125 0.0975 183 24 288000 0.08 184 22.7 257645 0.0716 185 19.4 188180 0.0523 186 17.7 156645 0.0435 187 17.2 147920 0.0411 188 18.1 163805 0.0455 189 18.6 172980 0.0481 190 20 200000 0.0556 191 22.2 246420 0.0685 192 24.5 300125 0.0834 193 27.3 372645 0.1035 194 30.5 465125 0.1292 195 33.5 561125 0.1559 196 36.2 655220 0.182 197 37.3 695645 0.1932 198 39.3 772245 0.2145 199 40.5 820125 0.2278 200 42.1 886205 0.2462 201 43.5 946125 0.2628 202 45.1 1017005 0.2825 203 46 1058000 0.2939 204 46.8 1095120 0.3042 205 47.5 1128125 0.3134 206 47.5 1128125 0.3134 207 47.3 1118645 0.3107 208 47.2 1113920 0.3094 209 47 1104500 0.3068 210 47 1104500 0.3068 211 47 1104500 0.3068 212 47 1104500 0.3068 213 47 1104500 0.3068 214 47.2 1113920 0.3094 215 47.4 1123380 0.3121 216 47.9 1147205 0.3187 217 48.5 1176125 0.3267 218 49.1 1205405 0.3348 219 49.5 1225125 0.3403 220 50 1250000 0.3472 221 50.6 1280180 0.3556 222 51 1300500 0.3613 223 51.5 1326125 0.3684 224 52.2 1362420 0.3785 225 53.2 1415120 0.3931 226 54.1 1463405 0.4065 227 54.6 1490580 0.4141 228 54.9 1507005 0.4186 229 55 1512500 0.4201 230 54.9 1507005 0.4186 231 54.6 1490580 0.4141 232 54.6 1490580 0.4141 233 54.8 1501520 0.4171 234 55.1 1518005 0.4217 235 55.5 1540125 0.4278 236 55.7 1551245 0.4309 237 56.1 1573605 0.4371 238 56.3 1584845 0.4402 239 56.6 1601780 0.4449 240 56.7 1607445 0.4465 241 56.7 1607445 0.4465 242 56.5 1596125 0.4434 243 56.5 1596125 0.4434 244 56.5 1596125 0.4434 245 56.5 1596125 0.4434 246 56.5 1596125 0.4434 247 56.5 1596125 0.4434 248 56.4 1590480 0.4418 249 56.1 1573605 0.4371 250 55.8 1556820 0.4325 251 55.1 1518005 0.4217 252 54.6 1490580 0.4141 253 54.2 1468820 0.408 254 54 1458000 0.405 255 53.7 1441845 0.4005 256 53.6 1436480 0.399 257 53.9 1452605 0.4035 258 54 1458000 0.405 259 54.1 1463405 0.4065 260 54.1 1463405 0.4065 261 53.8 1447220 0.402 262 53.4 1425780 0.3961 263 53 1404500 0.3901 264 52.6 1383380 0.3843 265 52.1 1357205 0.377 266 52.4 1372880 0.3814 267 52 1352000 0.3756 268 51.9 1346805 0.3741 269 51.7 1336445 0.3712 270 51.5 1326125 0.3684 271 51.6 1331280 0.3698 272 51.8 1341620 0.3727 273 52.1 1357205 0.377 274 52.5 1378125 0.3828 275 53 1404500 0.3901 276 53.5 1431125 0.3975 277 54 1458000 0.405 278 54.9 1507005 0.4186 279 55.4 1534580 0.4263 280 55.6 1545680 0.4294 281 56 1568000 0.4356 282 56 1568000 0.4356 283 55.8 1556820 0.4325 284 55.2 1523520 0.4232 285 54.5 1485125 0.4125 286 53.6 1436480 0.399 287 52.5 1378125 0.3828 288 51.5 1326125 0.3684 289 51.5 1326125 0.3684 290 51.5 1326125 0.3684 291 51.1 1305605 0.3627 292 50.1 1255005 0.3486 293 50 1250000 0.3472 294 50.1 1255005 0.3486 295 50 1250000 0.3472 296 49.6 1230080 0.3417 297 49.5 1225125 0.3403 298 49.5 1225125 0.3403 299 49.5 1225125 0.3403 300 49.1 1205405 0.3348 301 48.6 1180980 0.3281 302 48.1 1156805 0.3213 303 47.2 1113920 0.3094 304 46.1 1062605 0.2952 305 45 1012500 0.2813 306 43.8 959220 0.2665 307 42.6 907380 0.2521 308 41.5 861125 0.2392 309 40.3 812045 0.2256 310 38.5 741125 0.2059 311 37 684500 0.1901 312 35.2 619520 0.1721 313 33.8 571220 0.1587 314 32.5 528125 0.1467 315 31.5 496125 0.1378 316 30.6 468180 0.1301 317 30.5 465125 0.1292 318 30 450000 0.125 319 29 420500 0.1168 320 27.5 378125 0.105 321 24.8 307520 0.0854 322 21.5 231125 0.0642 323 20.1 202005 0.0561 324 19.1 182405 0.0507 325 18.5 171125 0.0475 326 17 144500 0.0401 327 15.5 120125 0.0334 328 12.5 78125 0.0217 329 10.8 58320 0.0162 330 8 32000 0.0089 331 4.7 11045 0.0031 332 1.4 980 0.0003 333 0 0 0 334 0 0 0 335 0 0 0 336 0 0 0 337 0 0 0 338 0 0 0 339 0 0 0 340 0 0 0 341 0 0 0 342 0 0 0 343 0 0 0 344 0 0 0 345 0 0 0 346 0 0 0 347 1 500 0.0001 348 4.3 9245 0.0026 349 7.6 28880 0.008 350 10.9 59405 0.0165 351 14.2 100820 0.028 352 17.3 149645 0.0416 353 20 200000 0.0556 354 22.5 253125 0.0703 355 23.7 280845 0.078 356 25.2 317520 0.0882 357 26.6 353780 0.0983 358 28.1 394805 0.1097 359 30 450000 0.125 360 30.8 474320 0.1318 361 31.6 499280 0.1387 362 32.1 515205 0.1431 363 32.8 537920 0.1494 364 33.6 564480 0.1568 365 34.5 595125 0.1653 366 34.6 598580 0.1663 367 34.9 609005 0.1692 368 34.8 605520 0.1682 369 34.5 595125 0.1653 370 34.7 602045 0.1672 371 35.5 630125 0.175 372 36 648000 0.18 373 36 648000 0.18 374 36 648000 0.18 375 36 648000 0.18 376 36 648000 0.18 377 36 648000 0.18 378 36.1 651605 0.181 379 36.4 662480 0.184 380 36.5 666125 0.185 381 36.4 662480 0.184 382 36 648000 0.18 383 35.1 616005 0.1711 384 34.1 581405 0.1615 385 33.5 561125 0.1559 386 31.4 492980 0.1369 387 29 420500 0.1168 388 25.7 330245 0.0917 389 23 264500 0.0735 390 20.3 206045 0.0572 391 17.5 153125 0.0425 392 14.5 105125 0.0292 393 12 72000 0.02 394 8.7 37845 0.0105 395 5.4 14580 0.0041 396 2.1 2205 0.0006 397 0 0 0 398 0 0 0 399 0 0 0 400 0 0 0 401 0 0 0 402 0 0 0 403 2.6 3380 0.0009 404 5.9 17405 0.0048 405 9.2 42320 0.0118 406 12.5 78125 0.0217 407 15.8 124820 0.0347 408 19.1 182405 0.0507 409 22.4 250880 0.0697 410 25 312500 0.0868 411 25.6 327680 0.091 412 27.5 378125 0.105 413 29 420500 0.1168 414 30 450000 0.125 415 30.1 453005 0.1258 416 30 450000 0.125 417 29.7 441045 0.1225 418 29.3 429245 0.1192 419 28.8 414720 0.1152 420 28 392000 0.1089 421 25 312500 0.0868 422 21.7 235445 0.0654 423 18.4 169280 0.047 424 15.1 114005 0.0317 425 11.8 69620 0.0193 426 8.5 36125 0.01 427 5.2 13520 0.0038 428 1.9 1805 0.0005 429 0 0 0 430 0 0 0 431 0 0 0 432 0 0 0 433 0 0 0 434 0 0 0 435 0 0 0 436 0 0 0 437 0 0 0 438 0 0 0 439 0 0 0 440 0 0 0 441 0 0 0 442 0 0 0 443 0 0 0 444 0 0 0 445 0 0 0 446 0 0 0 447 0 0 0 448 3.3 5445 0.0015 449 6.6 21780 0.0061 450 9.9 49005 0.0136 451 13.2 87120 0.0242 452 16.5 136125 0.0378 453 19.8 196020 0.0545 454 23.1 266805 0.0741 455 26.4 348480 0.0968 456 27.8 386420 0.1073 457 29.1 423405 0.1176 458 31.5 496125 0.1378 459 33 544500 0.1513 460 33.6 564480 0.1568 461 34.8 605520 0.1682 462 35.1 616005 0.1711 463 35.6 633680 0.176 464 36.1 651605 0.181 465 36 648000 0.18 466 36.1 651605 0.181 467 36.2 655220 0.182 468 36 648000 0.18 469 35.7 637245 0.177 470 36 648000 0.18 471 36 648000 0.18 472 35.6 633680 0.176 473 35.5 630125 0.175 474 35.4 626580 0.1741 475 35.2 619520 0.1721 476 35.2 619520 0.1721 477 35.2 619520 0.1721 478 35.2 619520 0.1721 479 35.2 619520 0.1721 480 35.2 619520 0.1721 481 35 612500 0.1701 482 35.1 616005 0.1711 483 35.2 619520 0.1721 484 35.5 630125 0.175 485 35.2 619520 0.1721 486 35 612500 0.1701 487 35 612500 0.1701 488 35 612500 0.1701 489 34.8 605520 0.1682 490 34.6 598580 0.1663 491 34.5 595125 0.1653 492 33.5 561125 0.1559 493 32 512000 0.1422 494 30.1 453005 0.1258 495 28 392000 0.1089 496 25.5 325125 0.0903 497 22.5 253125 0.0703 498 19.8 196020 0.0545 499 16.5 136125 0.0378 500 13.2 87120 0.0242 501 10.3 53045 0.0147 502 7.2 25920 0.0072 503 4 8000 0.0022 504 1 500 0.0001 505 0 0 0 506 0 0 0 507 0 0 0 508 0 0 0 509 0 0 0 510 0 0 0 511 1.2 720 0.0002 512 3.5 6125 0.0017 513 5.5 15125 0.0042 514 6.5 21125 0.0059 515 8.5 36125 0.01 516 9.6 46080 0.0128 517 10.5 55125 0.0153 518 11.9 70805 0.0197 519 14 98000 0.0272 520 16 128000 0.0356 521 17.7 156645 0.0435 522 19 180500 0.0501 523 20.1 202005 0.0561 524 21 220500 0.0613 525 22 242000 0.0672 526 23 264500 0.0735 527 23.8 283220 0.0787 528 24.5 300125 0.0834 529 24.9 310005 0.0861 530 25 312500 0.0868 531 25 312500 0.0868 532 25 312500 0.0868 533 25 312500 0.0868 534 25 312500 0.0868 535 25 312500 0.0868 536 25.6 327680 0.091 537 25.8 332820 0.0925 538 26 338000 0.0939 539 25.6 327680 0.091 540 25.2 317520 0.0882 541 25 312500 0.0868 542 25 312500 0.0868 543 25 312500 0.0868 544 24.4 297680 0.0827 545 23.1 266805 0.0741 546 19.8 196020 0.0545 547 16.5 136125 0.0378 548 13.2 87120 0.0242 549 9.9 49005 0.0136 550 6.6 21780 0.0061 551 3.3 5445 0.0015 552 0 0 0 553 0 0 0 554 0 0 0 555 0 0 0 556 0 0 0 557 0 0 0 558 0 0 0 559 0 0 0 560 0 0 0 561 0 0 0 562 0 0 0 563 0 0 0 564 0 0 0 565 0 0 0 566 0 0 0 567 0 0 0 568 0 0 0 569 3.3 5445 0.0015 570 6.6 21780 0.0061 571 9.9 49005 0.0136 572 13 84500 0.0235 573 14.6 106580 0.0296 574 16 128000 0.0356 575 17 144500 0.0401 576 17 144500 0.0401 577 17 144500 0.0401 578 17.5 153125 0.0425 579 17.7 156645 0.0435 580 17.7 156645 0.0435 581 17.5 153125 0.0425 582 17 144500 0.0401 583 16.9 142805 0.0397 584 16.6 137780 0.0383 585 17 144500 0.0401 586 17.1 146205 0.0406 587 17 144500 0.0401 588 16.6 137780 0.0383 589 16.5 136125 0.0378 590 16.5 136125 0.0378 591 16.6 137780 0.0383 592 17 144500 0.0401 593 17.6 154880 0.043 594 18.5 171125 0.0475 595 19.2 184320 0.0512 596 20.2 204020 0.0567 597 21 220500 0.0613 598 21.1 222605 0.0618 599 21.2 224720 0.0624 600 21.6 233280 0.0648 601 22 242000 0.0672 602 22.4 250880 0.0697 603 22.5 253125 0.0703 604 22.5 253125 0.0703 605 22.5 253125 0.0703 606 22.7 257645 0.0716 607 23.7 280845 0.078 608 25.1 315005 0.0875 609 26 338000 0.0939 610 26.5 351125 0.0975 611 27 364500 0.1013 612 26.1 340605 0.0946 613 22.8 259920 0.0722 614 19.5 190125 0.0528 615 16.2 131220 0.0365 616 12.9 83205 0.0231 617 9.6 46080 0.0128 618 6.3 19845 0.0055 619 3 4500 0.0013 620 0 0 0 621 0 0 0 622 0 0 0 623 0 0 0 624 0 0 0 625 0 0 0 626 0 0 0 627 0 0 0 628 0 0 0 629 0 0 0 630 0 0 0 631 0 0 0 632 0 0 0 633 0 0 0 634 0 0 0 635 0 0 0 636 0 0 0 637 0 0 0 638 0 0 0 639 0 0 0 640 0 0 0 641 0 0 0 642 0 0 0 643 0 0 0 644 0 0 0 645 0 0 0 646 2 2000 0.0006 647 4.5 10125 0.0028 648 7.8 30420 0.0085 649 10.2 52020 0.0145 650 12.5 78125 0.0217 651 14 98000 0.0272 652 15.3 117045 0.0325 653 17.5 153125 0.0425 654 19.6 192080 0.0534 655 21 220500 0.0613 656 22.2 246420 0.0685 657 23.3 271445 0.0754 658 24.5 300125 0.0834 659 25.3 320045 0.0889 660 25.6 327680 0.091 661 26 338000 0.0939 662 26.1 340605 0.0946 663 26.2 343220 0.0953 664 26.2 343220 0.0953 665 26.4 348480 0.0968 666 26.5 351125 0.0975 667 26.5 351125 0.0975 668 26 338000 0.0939 669 25.5 325125 0.0903 670 23.6 278480 0.0774 671 21.4 228980 0.0636 672 18.5 171125 0.0475 673 16.4 134480 0.0374 674 14.5 105125 0.0292 675 11.6 67280 0.0187 676 8.7 37845 0.0105 677 5.8 16820 0.0047 678 3.5 6125 0.0017 679 2 2000 0.0006 680 0 0 0 681 0 0 0 682 0 0 0 683 0 0 0 684 0 0 0 685 0 0 0 686 0 0 0 687 0 0 0 688 0 0 0 689 0 0 0 690 0 0 0 691 0 0 0 692 0 0 0 693 0 0 0 694 1.4 980 0.0003 695 3.3 5445 0.0015 696 4.4 9680 0.0027 697 6.5 21125 0.0059 698 9.2 42320 0.0118 699 11.3 63845 0.0177 700 13.5 91125 0.0253 701 14.6 106580 0.0296 702 16.4 134480 0.0374 703 16.7 139445 0.0387 704 16.5 136125 0.0378 705 16.5 136125 0.0378 706 18.2 165620 0.046 707 19.2 184320 0.0512 708 20.1 202005 0.0561 709 21.5 231125 0.0642 710 22.5 253125 0.0703 711 22.5 253125 0.0703 712 22.1 244205 0.0678 713 22.7 257645 0.0716 714 23.3 271445 0.0754 715 23.5 276125 0.0767 716 22.5 253125 0.0703 717 21.6 233280 0.0648 718 20.5 210125 0.0584 719 18 162000 0.045 720 15 112500 0.0313 721 12 72000 0.02 722 9 40500 0.0113 723 6.2 19220 0.0053 724 4.5 10125 0.0028 725 3 4500 0.0013 726 2.1 2205 0.0006 727 0.5 125 0 728 0.5 125 0 729 3.2 5120 0.0014 730 6.5 21125 0.0059 731 9.6 46080 0.0128 732 12.5 78125 0.0217 733 14 98000 0.0272 734 16 128000 0.0356 735 18 162000 0.045 736 19.6 192080 0.0534 737 21.5 231125 0.0642 738 23.1 266805 0.0741 739 24.5 300125 0.0834 740 25.5 325125 0.0903 741 26.5 351125 0.0975 742 27.1 367205 0.102 743 27.6 380880 0.1058 744 27.9 389205 0.1081 745 28.3 400445 0.1112 746 28.6 408980 0.1136 747 28.6 408980 0.1136 748 28.3 400445 0.1112 749 28.2 397620 0.1105 750 28 392000 0.1089 751 27.5 378125 0.105 752 26.8 359120 0.0998 753 25.5 325125 0.0903 754 23.5 276125 0.0767 755 21.5 231125 0.0642 756 19 180500 0.0501 757 16.5 136125 0.0378 758 14.9 111005 0.0308 759 12.5 78125 0.0217 760 9.4 44180 0.0123 761 6.2 19220 0.0053 762 3 4500 0.0013 763 1.5 1125 0.0003 764 1.5 1125 0.0003 765 0.5 125 0 766 0 0 0 767 3 4500 0.0013 768 6.3 19845 0.0055 769 9.6 46080 0.0128 770 12.9 83205 0.0231 771 15.8 124820 0.0347 772 17.5 153125 0.0425 773 18.4 169280 0.047 774 19.5 190125 0.0528 775 20.7 214245 0.0595 776 22 242000 0.0672 777 23.2 269120 0.0748 778 25 312500 0.0868 779 26.5 351125 0.0975 780 27.5 378125 0.105 781 28 392000 0.1089 782 28.3 400445 0.1112 783 28.9 417605 0.116 784 28.9 417605 0.116 785 28.9 417605 0.116 786 28.8 414720 0.1152 787 28.5 406125 0.1128 788 28.3 400445 0.1112 789 28.3 400445 0.1112 790 28.3 400445 0.1112 791 28.2 397620 0.1105 792 27.6 380880 0.1058 793 27.5 378125 0.105 794 27.5 378125 0.105 795 27.5 378125 0.105 796 27.5 378125 0.105 797 27.5 378125 0.105 798 27.5 378125 0.105 799 27.6 380880 0.1058 800 28 392000 0.1089 801 28.5 406125 0.1128 802 30 450000 0.125 803 31 480500 0.1335 804 32 512000 0.1422 805 33 544500 0.1513 806 33 544500 0.1513 807 33.6 564480 0.1568 808 34 578000 0.1606 809 34.3 588245 0.1634 810 34.2 584820 0.1625 811 34 578000 0.1606 812 34 578000 0.1606 813 33.9 574605 0.1596 814 33.6 564480 0.1568 815 33.1 547805 0.1522 816 33 544500 0.1513 817 32.5 528125 0.1467 818 32 512000 0.1422 819 31.9 508805 0.1413 820 31.6 499280 0.1387 821 31.5 496125 0.1378 822 30.6 468180 0.1301 823 30 450000 0.125 824 29.9 447005 0.1242 825 29.9 447005 0.1242 826 29.9 447005 0.1242 827 29.9 447005 0.1242 828 29.6 438080 0.1217 829 29.5 435125 0.1209 830 29.5 435125 0.1209 831 29.3 429245 0.1192 832 28.9 417605 0.116 833 28.2 397620 0.1105 834 27.7 383645 0.1066 835 27 364500 0.1013 836 25.5 325125 0.0903 837 23.7 280845 0.078 838 22 242000 0.0672 839 20.5 210125 0.0584 840 19.2 184320 0.0512 841 19.2 184320 0.0512 842 20.1 202005 0.0561 843 20.9 218405 0.0607 844 21.4 228980 0.0636 845 22 242000 0.0672 846 22.6 255380 0.0709 847 23.2 269120 0.0748 848 24 288000 0.08 849 25 312500 0.0868 850 26 338000 0.0939 851 26.6 353780 0.0983 852 26.6 353780 0.0983 853 26.8 359120 0.0998 854 27 364500 0.1013 855 27.2 369920 0.1028 856 27.8 386420 0.1073 857 28.1 394805 0.1097 858 28.8 414720 0.1152 859 28.9 417605 0.116 860 29 420500 0.1168 861 29.1 423405 0.1176 862 29 420500 0.1168 863 28.1 394805 0.1097 864 27.5 378125 0.105 865 27 364500 0.1013 866 25.8 332820 0.0925 867 25 312500 0.0868 868 24.5 300125 0.0834 869 24.8 307520 0.0854 870 25.1 315005 0.0875 871 25.5 325125 0.0903 872 25.7 330245 0.0917 873 26.2 343220 0.0953 874 26.9 361805 0.1005 875 27.5 378125 0.105 876 27.8 386420 0.1073 877 28.4 403280 0.112 878 29 420500 0.1168 879 29.2 426320 0.1184 880 29.1 423405 0.1176 881 29 420500 0.1168 882 28.9 417605 0.116 883 28.5 406125 0.1128 884 28.1 394805 0.1097 885 28 392000 0.1089 886 28 392000 0.1089 887 27.6 380880 0.1058 888 27.2 369920 0.1028 889 26.6 353780 0.0983 890 27 364500 0.1013 891 27.5 378125 0.105 892 27.8 386420 0.1073 893 28 392000 0.1089 894 27.8 386420 0.1073 895 28 392000 0.1089 896 28 392000 0.1089 897 28 392000 0.1089 898 27.7 383645 0.1066 899 27.4 375380 0.1043 900 26.9 361805 0.1005 901 26.6 353780 0.0983 902 26.5 351125 0.0975 903 26.5 351125 0.0975 904 26.5 351125 0.0975 905 26.3 345845 0.0961 906 26.2 343220 0.0953 907 26.2 343220 0.0953 908 25.9 335405 0.0932 909 25.6 327680 0.091 910 25.6 327680 0.091 911 25.9 335405 0.0932 912 25.8 332820 0.0925 913 25.5 325125 0.0903 914 24.6 302580 0.0841 915 23.5 276125 0.0767 916 22.2 246420 0.0685 917 21.6 233280 0.0648 918 21.6 233280 0.0648 919 21.7 235445 0.0654 920 22.6 255380 0.0709 921 23.4 273780 0.0761 922 24 288000 0.08 923 24.2 292820 0.0813 924 24.4 297680 0.0827 925 24.9 310005 0.0861 926 25.1 315005 0.0875 927 25.2 317520 0.0882 928 25.3 320045 0.0889 929 25.5 325125 0.0903 930 25.2 317520 0.0882 931 25 312500 0.0868 932 25 312500 0.0868 933 25 312500 0.0868 934 24.7 305045 0.0847 935 24.5 300125 0.0834 936 24.3 295245 0.082 937 24.3 295245 0.082 938 24.5 300125 0.0834 939 25 312500 0.0868 940 25 312500 0.0868 941 24.6 302580 0.0841 942 24.6 302580 0.0841 943 24.1 290405 0.0807 944 24.5 300125 0.0834 945 25.1 315005 0.0875 946 25.6 327680 0.091 947 25.1 315005 0.0875 948 24 288000 0.08 949 22 242000 0.0672 950 20.1 202005 0.0561 951 16.9 142805 0.0397 952 13.6 92480 0.0257 953 10.3 53045 0.0147 954 7 24500 0.0068 955 3.7 6845 0.0019 956 0.4 80 0 957 0 0 0 958 0 0 0 959 0 0 0 960 2 2000 0.0006 961 5.3 14045 0.0039 962 8.6 36980 0.0103 963 11.9 70805 0.0197 964 15.2 115520 0.0321 965 17.5 153125 0.0425 966 18.6 172980 0.0481 967 20 200000 0.0556 968 21.1 222605 0.0618 969 22 242000 0.0672 970 23 264500 0.0735 971 24.5 300125 0.0834 972 26.3 345845 0.0961 973 27.5 378125 0.105 974 28.1 394805 0.1097 975 28.4 403280 0.112 976 28.5 406125 0.1128 977 28.5 406125 0.1128 978 28.5 406125 0.1128 979 27.7 383645 0.1066 980 27.5 378125 0.105 981 27.2 369920 0.1028 982 26.8 359120 0.0998 983 26.5 351125 0.0975 984 26 338000 0.0939 985 25.7 330245 0.0917 986 25.2 317520 0.0882 987 24 288000 0.08 988 22 242000 0.0672 989 21.5 231125 0.0642 990 21.5 231125 0.0642 991 21.8 237620 0.066 992 22.5 253125 0.0703 993 23 264500 0.0735 994 22.8 259920 0.0722 995 22.8 259920 0.0722 996 23 264500 0.0735 997 22.7 257645 0.0716 998 22.7 257645 0.0716 999 22.7 257645 0.0716 1000 23.5 276125 0.0767 1001 24 288000 0.08 1002 24.6 302580 0.0841 1003 24.8 307520 0.0854 1004 25.1 315005 0.0875 1005 25.5 325125 0.0903 1006 25.6 327680 0.091 1007 25.5 325125 0.0903 1008 25 312500 0.0868 1009 24.1 290405 0.0807 1010 23.7 280845 0.078 1011 23.2 269120 0.0748 1012 22.9 262205 0.0728 1013 22.5 253125 0.0703 1014 22 242000 0.0672 1015 21.6 233280 0.0648 1016 20.5 210125 0.0584 1017 17.5 153125 0.0425 1018 14.2 100820 0.028 1019 10.9 59405 0.0165 1020 7.6 28880 0.008 1021 4.3 9245 0.0026 1022 1 500 0.0001 1023 0 0 0 1024 0 0 0 1025 0 0 0 1026 0 0 0 1027 0 0 0 1028 0 0 0 1029 0 0 0 1030 0 0 0 1031 0 0 0 1032 0 0 0 1033 0 0 0 1034 0 0 0 1035 0 0 0 1036 0 0 0 1037 0 0 0 1038 0 0 0 1039 0 0 0 1040 0 0 0 1041 0 0 0 1042 0 0 0 1043 0 0 0 1044 0 0 0 1045 0 0 0 1046 0 0 0 1047 0 0 0 1048 0 0 0 1049 0 0 0 1050 0 0 0 1051 0 0 0 1052 0 0 0 1053 1.2 720 0.0002 1054 4 8000 0.0022 1055 7.3 26645 0.0074 1056 10.6 56180 0.0156 1057 13.9 96605 0.0268 1058 17 144500 0.0401 1059 18.5 171125 0.0475 1060 20 200000 0.0556 1061 21.8 237620 0.066 1062 23 264500 0.0735 1063 24 288000 0.08 1064 24.8 307520 0.0854 1065 25.6 327680 0.091 1066 26.5 351125 0.0975 1067 26.8 359120 0.0998 1068 27.4 375380 0.1043 1069 27.9 389205 0.1081 1070 28.3 400445 0.1112 1071 28 392000 0.1089 1072 27.5 378125 0.105 1073 27 364500 0.1013 1074 27 364500 0.1013 1075 26.3 345845 0.0961 1076 24.5 300125 0.0834 1077 22.5 253125 0.0703 1078 21.5 231125 0.0642 1079 20.6 212180 0.0589 1080 18 162000 0.045 1081 15 112500 0.0313 1082 12.3 75645 0.021 1083 11.1 61605 0.0171 1084 10.6 56180 0.0156 1085 10 50000 0.0139 1086 9.5 45125 0.0125 1087 9.1 41405 0.0115 1088 8.7 37845 0.0105 1089 8.6 36980 0.0103 1090 8.8 38720 0.0108 1091 9 40500 0.0113 1092 8.7 37845 0.0105 1093 8.6 36980 0.0103 1094 8 32000 0.0089 1095 7 24500 0.0068 1096 5 12500 0.0035 1097 4.2 8820 0.0025 1098 2.6 3380 0.0009 1099 1 500 0.0001 1100 0 0 0 1101 0.1 5 0 1102 0.6 180 0.0001 1103 1.6 1280 0.0004 1104 3.6 6480 0.0018 1105 6.9 23805 0.0066 1106 10 50000 0.0139 1107 12.8 81920 0.0228 1108 14 98000 0.0272 1109 14.5 105125 0.0292 1110 16 128000 0.0356 1111 18.1 163805 0.0455 1112 20 200000 0.0556 1113 21 220500 0.0613 1114 21.2 224720 0.0624 1115 21.3 226845 0.063 1116 21.4 228980 0.0636 1117 21.7 235445 0.0654 1118 22.5 253125 0.0703 1119 23 264500 0.0735 1120 23.8 283220 0.0787 1121 24.5 300125 0.0834 1122 25 312500 0.0868 1123 24.9 310005 0.0861 1124 24.8 307520 0.0854 1125 25 312500 0.0868 1126 25.4 322580 0.0896 1127 25.8 332820 0.0925 1128 26 338000 0.0939 1129 26.4 348480 0.0968 1130 26.6 353780 0.0983 1131 26.9 361805 0.1005 1132 27 364500 0.1013 1133 27 364500 0.1013 1134 27 364500 0.1013 1135 26.9 361805 0.1005 1136 26.8 359120 0.0998 1137 26.8 359120 0.0998 1138 26.5 351125 0.0975 1139 26.4 348480 0.0968 1140 26 338000 0.0939 1141 25.5 325125 0.0903 1142 24.6 302580 0.0841 1143 23.5 276125 0.0767 1144 21.5 231125 0.0642 1145 20 200000 0.0556 1146 17.5 153125 0.0425 1147 16 128000 0.0356 1148 14 98000 0.0272 1149 10.7 57245 0.0159 1150 7.4 27380 0.0076 1151 4.1 8405 0.0023 1152 0.8 320 0.0001 1153 0 0 0 1154 0 0 0 1155 0 0 0 1156 0 0 0 1157 0 0 0 1158 0 0 0 1159 0 0 0 1160 0 0 0 1161 0 0 0 1162 0 0 0 1163 0 0 0 1164 0 0 0 1165 0 0 0 1166 0 0 0 1167 0 0 0 1168 0 0 0 1169 2.1 2205 0.0006 1170 5.4 14580 0.0041 1171 8.7 37845 0.0105 1172 12 72000 0.02 1173 15.3 117045 0.0325 1174 18.6 172980 0.0481 1175 21.1 222605 0.0618 1176 23 264500 0.0735 1177 23.5 276125 0.0767 1178 23 264500 0.0735 1179 22.5 253125 0.0703 1180 20 200000 0.0556 1181 16.7 139445 0.0387 1182 13.4 89780 0.0249 1183 10.1 51005 0.0142 1184 6.8 23120 0.0064 1185 3.5 6125 0.0017 1186 0.2 20 0 1187 0 0 0 1188 0 0 0 1189 0 0 0 1190 0 0 0 1191 0 0 0 1192 0 0 0 1193 0 0 0 1194 0 0 0 1195 0 0 0 1196 0 0 0 1197 0.2 20 0 1198 1.5 1125 0.0003 1199 3.5 6125 0.0017 1200 6.5 21125 0.0059 1201 9.8 48020 0.0133 1202 12 72000 0.02 1203 12.9 83205 0.0231 1204 13 84500 0.0235 1205 12.6 79380 0.0221 1206 12.8 81920 0.0228 1207 13.1 85805 0.0238 1208 13.1 85805 0.0238 1209 14 98000 0.0272 1210 15.5 120125 0.0334 1211 17 144500 0.0401 1212 18.6 172980 0.0481 1213 19.7 194045 0.0539 1214 21 220500 0.0613 1215 21.5 231125 0.0642 1216 21.8 237620 0.066 1217 21.8 237620 0.066 1218 21.5 231125 0.0642 1219 21.2 224720 0.0624 1220 21.5 231125 0.0642 1221 21.8 237620 0.066 1222 22 242000 0.0672 1223 21.9 239805 0.0666 1224 21.7 235445 0.0654 1225 21.5 231125 0.0642 1226 21.5 231125 0.0642 1227 21.4 228980 0.0636 1228 20.1 202005 0.0561 1229 19.5 190125 0.0528 1230 19.2 184320 0.0512 1231 19.6 192080 0.0534 1232 19.8 196020 0.0545 1233 20 200000 0.0556 1234 19.5 190125 0.0528 1235 17.5 153125 0.0425 1236 15.5 120125 0.0334 1237 13 84500 0.0235 1238 10 50000 0.0139 1239 8 32000 0.0089 1240 6 18000 0.005 1241 4 8000 0.0022 1242 2.5 3125 0.0009 1243 0.7 245 0.0001 1244 0 0 0 1245 0 0 0 1246 0 0 0 1247 0 0 0 1248 0 0 0 1249 0 0 0 1250 0 0 0 1251 0 0 0 1252 1 500 0.0001 1253 1 500 0.0001 1254 1 500 0.0001 1255 1 500 0.0001 1256 1 500 0.0001 1257 1.6 1280 0.0004 1258 3 4500 0.0013 1259 4 8000 0.0022 1260 5 12500 0.0035 1261 6.3 19845 0.0055 1262 8 32000 0.0089 1263 10 50000 0.0139 1264 10.5 55125 0.0153 1265 9.5 45125 0.0125 1266 8.5 36125 0.01 1267 7.6 28880 0.008 1268 8.8 38720 0.0108 1269 11 60500 0.0168 1270 14 98000 0.0272 1271 17 144500 0.0401 1272 19.5 190125 0.0528 1273 21 220500 0.0613 1274 21.8 237620 0.066 1275 22.2 246420 0.0685 1276 23 264500 0.0735 1277 23.6 278480 0.0774 1278 24.1 290405 0.0807 1279 24.5 300125 0.0834 1280 24.5 300125 0.0834 1281 24 288000 0.08 1282 23.5 276125 0.0767 1283 23.5 276125 0.0767 1284 23.5 276125 0.0767 1285 23.5 276125 0.0767 1286 23.5 276125 0.0767 1287 23.5 276125 0.0767 1288 24 288000 0.08 1289 24.1 290405 0.0807 1290 24.5 300125 0.0834 1291 24.7 305045 0.0847 1292 25 312500 0.0868 1293 25.4 322580 0.0896 1294 25.6 327680 0.091 1295 25.7 330245 0.0917 1296 26 338000 0.0939 1297 26.2 343220 0.0953 1298 27 364500 0.1013 1299 27.8 386420 0.1073 1300 28.3 400445 0.1112 1301 29 420500 0.1168 1302 29.1 423405 0.1176 1303 29 420500 0.1168 1304 28 392000 0.1089 1305 24.7 305045 0.0847 1306 21.4 228980 0.0636 1307 18.1 163805 0.0455 1308 14.8 109520 0.0304 1309 11.5 66125 0.0184 1310 8.2 33620 0.0093 1311 4.9 12005 0.0033 1312 1.6 1280 0.0004 1313 0 0 0 1314 0 0 0 1315 0 0 0 1316 0 0 0 1317 0 0 0 1318 0 0 0 1319 0 0 0 1320 0 0 0 1321 0 0 0 1322 0 0 0 1323 0 0 0 1324 0 0 0 1325 0 0 0 1326 0 0 0 1327 0 0 0 1328 0 0 0 1329 0 0 0 1330 0 0 0 1331 0 0 0 1332 0 0 0 1333 0 0 0 1334 0 0 0 1335 0 0 0 1336 0 0 0 1337 0 0 0 1338 1.5 1125 0.0003 1339 4.8 11520 0.0032 1340 8.1 32805 0.0091 1341 11.4 64980 0.0181 1342 13.2 87120 0.0242 1343 15.1 114005 0.0317 1344 16.8 141120 0.0392 1345 18.3 167445 0.0465 1346 19.5 190125 0.0528 1347 20.3 206045 0.0572 1348 21.3 226845 0.063 1349 21.9 239805 0.0666 1350 22.1 244205 0.0678 1351 22.4 250880 0.0697 1352 22 242000 0.0672 1353 21.6 233280 0.0648 1354 21.1 222605 0.0618 1355 20.5 210125 0.0584 1356 20 200000 0.0556 1357 19.6 192080 0.0534 1358 18.5 171125 0.0475 1359 17.5 153125 0.0425 1360 16.5 136125 0.0378 1361 15.5 120125 0.0334 1362 14 98000 0.0272 1363 11 60500 0.0168 1364 8 32000 0.0089 1365 5.2 13520 0.0038 1366 2.5 3125 0.0009 1367 0 0 0 1368 0 0 0 1369 0 0 0
This energy can be converted to kWh when multiplied with a factor of 2.7778e-7Thus, The total energy consumed for Braking is 140 kWh
- Why electric motors can’t develop braking torque at high speeds like starting? How electric and mechanical brakes are coordinated?
The process of applying brakes can be termed braking. There are two types of braking;- Mechanical Braking
- Electrical Braking
Mechanical braking:- All act by generating frictional forces as two surfaces rub against each other.
- The stopping power or capacity of a brake depends largely on the surface area of frictional surfaces as well as on the actuation force applied.
- The friction and wear encountered by the working surfaces are severe.
- Thus, the durability of a brake or service life between maintenance depends heavily on the type of material used to line the shoe or pad.
Mechanical brakes are assemblies consisting of mechanical elements for the slowing or stopping of shafts in equipment drives. They use levers or linkages to transmit force from one point to another. Braking slows or stops the movement of the coupled shafts.
There are several types of mechanical brakes like,
- Drum brakes: Commonly used on automobile rear wheels, work when shoes press against a spinning surface called a drum
- Disc brakes: Constructed of brake pads, a caliper, and a rotor. During operation, the brake pads are squeezed against the rotor. Cone brakes are made with a cup and a cone, which are lined with heat and wear-resistant material. During actuation, the cone is pressed against the mating cup surface.
- Engine Braking: A compression engine brake is a device that can convert a diesel engine into an air compressor, a power absorbing device. These devices are used in trucking applications to provide a means for retarding the vehicle, supplementing the normal vehicle braking system. The retarding operation is under full control of the vehicle operator and can be used simultaneously with the normal service brakes. Engine brakes can be installed at any time on a new or used vehicle for most applications.
- Electrical braking:
Electrical Brakes are used to reduce or cease the speed of motors. We know that there are various types of motors available (DC motors, induction motors, synchronous motors, single-phase motors, etc.) and the specialty and properties of these motors are different from each other, hence this braking method also differs from each other. But we can divide braking into three parts mainly, which are applicable for almost every type of motor.- Regenerative Braking
- Plugging type braking
- Dynamic braking
- Regenerative Braking:
Regenerative braking takes place whenever the speed of the motor exceeds the synchronous speed. This baking method is called regenerative braking because here the motor works as a generator and the supply itself is given power from the load, i.e., motors. The main criterion for regenerative braking is that the rotor must rotate at a speed higher than synchronous speed, only then the motor will act as a generator and the direction of current flow through the circuit and direction of the torque reverses and braking takes place. The only disadvantage of this type of braking is that the motor must run at a super synchronous speed which may damage the motor mechanically and electrically, but regenerative braking can be done at sub-synchronous speed if the variable frequency source is available. - Plugging Type Braking:
Another type of braking is Plugging type braking. In this method the terminals of supply are reversed, as a result of the generator torque also reverses which resists the normal rotation of the motor, and as a result, the speed decreases. During plugging external resistance is also introduced into the circuit to limit the flowing current. The main disadvantage of this method is that here power is wasted. - Dynamic Braking:
Another method of reversing the direction of torque and braking of the motor is dynamic braking. In this method of braking of the motor which is at a running condition is disconnected from the source and connected across a resistance. When the motor is disconnected from the source, the rotor keeps rotating due to inertia and it works as a self-excited generator. When the motor works as a generator the flow of the current and torque reverses. During braking to maintain the steady torque sectional resistances are cut out one by one.
- Regenerative Braking:
the electric motor can’t develop braking torque at high speed like starting due to varying limitations and performance characteristics.
- For an ideal Four – Quadrant or Two – Quadrant motor, its performance characteristics may look similar especially in its Forward Motoring and Braking operation.
- In the practical case of the braking period, the motor must function as a generator. So, it must have suitable braking characteristics.
- e., Even though, if a motor produces a peak torque value of 100N.m at Forward motoring mode, the same value can’t be achieved by the motor during its Forward braking operation.
- The peak value of acceleration achieved by the motor can’t be achieved during the deceleration
- To run at the peak value of forward braking, the power converter must also be modified with complex bi-directional circuits, helping to charge batteries.
- The battery also be able to accept a high charge/discharge rate
electric and mechanical brakes can be coordinated in mostly two ways,- Series
- Parallel
- In a series braking system,
- The regenerative braking system could restore kinetic energy and potential energy to a battery or any other form of power during braking, is a special system for electric and hybrid electric vehicles.
- However, the large current produced by the generator during braking would affect battery performance and shorten battery life.
- A hybrid-power system is an excellent energy storage system, in which an ultra-capacitor bank and a battery pack are connected through a DC/DC power converter.
- The ultra-capacitor in this system can store instantaneous large currents quickly, which can protect the battery from large currents, suggesting that the ultra-capacitor can restore the regenerative energy very quickly, which will improve starting and acceleration performance, extend driving range, and increase fuel economy
- In a parallel braking system,
- The regenerative braking system is the own system of Electric and Hybrid Electric vehicles.
- The system can restore the kinetic energy and potential energy, used during start and accelerating, into the battery through the electrical machine.
- The total brake force is composed of friction brake force on the front axle, friction brake force on the rear axle, and regenerative brake force when a vehicle is equipped with regenerative braking system brakes.
- The parallel brake strategy is not only safe enough but also can restore the largest amount of the brake energy.
- In a series braking system,
An example of Parallel Braking system is Nissan’s EDIB technology in Leaf
The model’s features are;
- Safe braking
- EVs and hybrid vehicles use regenerative braking, which utilizes the motor to convert the kinetic energy during deceleration into electrical energy.
- With energy regeneration, an EV can run on less electricity and a hybrid vehicle on less fuel.
- The EDIB (Electric Driven Intelligent Brake) allows and controls optimization of the regenerative brake and regular friction brake (hydraulic brake).
- Technology Functionality
- After stepping on the brake pedal, the system produces a natural and adequate braking force that corresponds to the operation.
- The amount of energy regeneration also needs to be increased as much as possible.
- EDIB (Electric Driven Intelligent Brake) controls the regenerative brake and friction brake to support both requirements.
- Further, it also controls the reactive force from the pedal to unify the feeling when stepping down on the pedal and the sense of deceleration.
- Technology Configuration
- When the driver steps on the brake pedal, the stroke sensor detects the operation of the brake.
- That information is communicated to the ECU and controls the motor.
- The motor engages the piston and amplifies the friction brake's pressure (hydraulic pressure).
- Through optimum control of the friction brake's hydraulic pressure, the energy regeneration outcome is maximized.
3. Make a MATLAB program which plots the contour of given motor speed, torque, and efficiency values. Attach the code as a .m file attach a screenshot of all the plots.
close
clear
clc
% x - axis corresponds to Motor Speed, w in rad/s
% y - axis corresponds to Torque, T in N.m
x = linspace(1,1000); % Speed of Motor in rad/s
y = linspace(1,250); % Torque produced by Motor in N.m
%Allocate motor Core and Copper loss constants
kc = 0.2; %Copper loss constant
ki = 0.008; %Iron loss constant
kw = 0.0001; %Windage loss constant
conL = 20; %Constant motor loss
%To make an array of mesh
[X, Y] = meshgrid(x,y);
%To calculate Output Power,
Pout = (X.* Y); %Power = Torque * Speed
%To find losses
B = (Y.^2)*kc; %Equation to find Copper loss
C = X.*ki; %Equation to find Iron loss
D = (X.^3)*kw; %Equation to find Windage loss
%Relation between Input Power and Output Power
%Input Power = Output Power + Losses
Pin = Pout + B + C + D + conL;
Z = Pout./ Pin; %To calculate efficiency
%Set the efficiencies for which Contour to be plotted
V = [0.7:0.05:0.95];
box off
grid off
contour(X, Y, Z, V)
xlabel('Speed of Motor (rad/s)');
ylabel('Developed Torque (N.m)');
hold on
%Plot contour for Output Power
%The array for Output Power is already calculated, to draw contour @3-5kW
V = [4000:2000:10000];
contour(X, Y, Pout, V);
hold off
title('Plot for efficiency Contour, Speed vs Torque')
Output Contour:
Observation:
- The most efficient region in the contour is the innermost elliptical shape with an efficiency of over 90%
- It is evident from the contour that, the efficiency decreases as values are away from the innermost shape
- As the contour lines move away from the center, the efficiency falls even to 70%
- It is optimal for the Motor to operate between the innermost ellipse and its adjacent one for maximum efficiency and performance