1122:
787:
42:
In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a system determine how many times the belt or rope must be wrapped around a curved surface to prevent it
1149:
Conditions under which the belt and pulleys are operating – The friction between the belt and pulley may decrease substantially if the belt happens to be muddy or wet, as it may act as a lubricant between the surfaces. This also applies to extremely dry or warm conditions which will evaporate any
34:
to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted to the other end of the belt or rope. Belt friction can be
1162:
An understanding of belt friction is essential for sailing crews and mountain climbers. Their professions require being able to understand the amount of weight a rope with a certain tension capacity can hold versus the amount of wraps around a pulley. Too many revolutions around a pulley make it
910:
627:
620:
1117:{\displaystyle T_{0}e^{-\mu _{\tau }ks\,{\sqrt {\cos ^{2}\alpha -{\frac {\sin ^{2}\alpha }{\mu _{g}^{2}}}}}}\leq T\leq T_{0}e^{\mu _{\tau }ks\,{\sqrt {\cos ^{2}\alpha -{\frac {\sin ^{2}\alpha }{\mu _{g}^{2}}}}}}}
1163:
inefficient to retract or release rope, and too few may cause the rope to slip. Misjudging the ability of a rope and capstan system to maintain the proper frictional forces may lead to failure and injury.
465:
127:
1153:
Overall design of the setup – The setup involves the initial conditions of the construction, such as the angle which the belt is wrapped around and geometry of the belt and pulley system.
1146:
Construction of the drive-pulley system – This involves strength and stability of the material used, like the pulley, and how greatly it will oppose the motion of the belt or rope.
328:
905:
864:
782:{\displaystyle \omega =\mu _{\tau }{\sqrt {k_{n}^{2}-{\frac {k_{g}^{2}}{\mu _{g}^{2}}}}}=\mu _{\tau }k{\sqrt {\cos ^{2}\alpha -{\frac {\sin ^{2}\alpha }{\mu _{g}^{2}}}}}}
385:
211:
1143:
Belting material used – The age of the material also plays a part, where worn out and older material may become more rough or smoother, changing the sliding friction.
405:
235:
817:
517:
355:
184:
157:
837:
490:
281:
43:
from slipping. Mountain climbers and sailing crews demonstrate a working knowledge of belt friction when accomplishing tasks with ropes, pulleys, bollards and
524:
1231:
412:
1177:
1342:
71:
1328:
241:, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.
248:
if the magnitude of the belt angle increases (e.g. it is wrapped around the pulley segment numerous times).
1291:
1136:
257:
288:
872:
1203:
842:
1369:
245:
44:
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23:
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36:
795:
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333:
162:
135:
214:
1295:
822:
475:
266:
1363:
244:
The tension on the pulling side of the belt and pulley has the ability to increase
615:{\displaystyle T_{0}e^{-\int _{s}\omega ds}\leq T\leq T_{0}e^{\int _{s}\omega ds}}
1257:
1235:
1313:
1304:
1279:
1329:"Introduction to Computational Contact Mechanics: A Geometrical Approach"
27:
256:
If a rope is laying in equilibrium under tangential forces on a rough
61:
The equation used to model belt friction is, assuming the belt has no
1150:
water naturally found in the belt, nominally making friction greater.
238:
252:
Generalization for a rope lying on an arbitrary orthotropic surface
407:
are satisfying the following criteria for all points of the curve
62:
1135:
There are certain factors that help determine the value of the
260:
then three following conditions (all of them) are satisfied:
866:
is a coefficient of friction in the tangential direction.
1127:
This generalization has been obtained by
Konyukhov A.,
460:{\displaystyle -\mu _{g}<\tan \alpha <+\mu _{g}}
913:
875:
845:
825:
798:
630:
527:
498:
478:
415:
393:
366:
336:
291:
269:
223:
192:
165:
138:
74:
1345:. CKIT – The Bulk Materials Handling Knowledge Base
22:is a term describing the friction forces between a
1116:
899:
858:
831:
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614:
511:
484:
459:
399:
379:
349:
322:
275:
229:
205:
178:
151:
121:
1280:"Contact of ropes and orthotropic rough surfaces"
1260:. Missouri University of Science and Technology
122:{\displaystyle T_{2}=T_{1}e^{\mu _{s}\beta }\,}
26:and a surface, such as a belt wrapped around a
283:is positive for all points of the rope curve:
8:
1284:Journal of Applied Mathematics and Mechanics
16:Friction forces between a belt and a surface
819:is a geodesic curvature of the rope curve,
1211:. International Technical Rescue Symposium
469:3. Limit values of the tangential forces:
1303:
1197:
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1193:
1102:
1097:
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918:
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803:
797:
769:
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747:
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719:
710:
693:
688:
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673:
667:
658:
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629:
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550:
542:
532:
526:
503:
497:
477:
451:
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371:
365:
357:is a normal curvature of the rope curve.
341:
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290:
268:
222:
197:
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143:
137:
118:
107:
102:
92:
79:
73:
65:and its material is a fixed composition:
1205:The Mechanics of Friction in Rope Rescue
519:are satisfying the following inequality
1189:
186:is the tension of the resisting side,
217:coefficient, which has no units, and
7:
472:The forces at both ends of the rope
360:2. Dragging coefficient of friction
159:is the tension of the pulling side,
1278:Konyukhov, Alexander (2015-04-01).
263:1. No separation – normal reaction
1234:. Ruhr-Universität. Archived from
14:
1139:. These determining factors are:
839:is a curvature of a rope curve,
323:{\displaystyle N=-k_{n}T>0}
1:
900:{\displaystyle \omega =const}
1230:Mann, Herman (May 5, 2005).
1202:Attaway, Stephen W. (1999).
1178:Frictional contact mechanics
859:{\displaystyle \mu _{\tau }}
1386:
54:
30:. When a force applies a
380:{\displaystyle \mu _{g}}
206:{\displaystyle \mu _{s}}
1258:"Coulomb Belt Friction"
400:{\displaystyle \alpha }
1305:10.1002/zamm.201300129
1118:
901:
860:
833:
813:
783:
616:
513:
486:
461:
401:
381:
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277:
231:
230:{\displaystyle \beta }
207:
180:
153:
123:
37:Belt friction equation
1343:"Belt Tension Theory"
1327:Konyukhov A., Izi R.
1119:
902:
861:
834:
814:
812:{\displaystyle k_{g}}
784:
617:
514:
512:{\displaystyle T_{0}}
487:
462:
402:
382:
352:
350:{\displaystyle k_{n}}
325:
278:
232:
208:
181:
179:{\displaystyle T_{1}}
154:
152:{\displaystyle T_{2}}
124:
1137:friction coefficient
1131:Friction coefficient
911:
873:
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823:
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72:
1296:2015ZaMM...95..406K
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1004:
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258:orthotropic surface
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149:
119:
1238:on March 25, 2018
1110:
1108:
1007:
1005:
832:{\displaystyle k}
777:
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699:
485:{\displaystyle T}
276:{\displaystyle N}
237:is the angle, in
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1243:
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1210:
1199:
1173:Capstan equation
1123:
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1120:
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128:
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96:
84:
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57:Capstan equation
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1384:
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1255:
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1241:
1239:
1232:"Belt Friction"
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1191:
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1160:
1133:
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1020:
973:
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909:
908:
871:
870:
846:
841:
840:
821:
820:
799:
794:
793:
743:
742:
721:
706:
637:
626:
625:
591:
586:
576:
546:
538:
528:
523:
522:
499:
494:
493:
474:
473:
447:
419:
411:
410:
389:
388:
367:
362:
361:
337:
332:
331:
301:
287:
286:
265:
264:
254:
219:
218:
215:static friction
193:
188:
187:
166:
161:
160:
139:
134:
133:
103:
98:
88:
75:
70:
69:
59:
53:
35:modeled by the
17:
12:
11:
5:
1383:
1381:
1373:
1372:
1362:
1361:
1356:
1355:
1334:
1319:
1290:(4): 406–423.
1270:
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1222:
1188:
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1168:
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1083:
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1047:
1042:
1038:
1033:
1027:
1023:
1019:
1016:
1013:
1002:
997:
993:
988:
985:
980:
976:
969:
966:
963:
958:
954:
947:
944:
939:
935:
931:
927:
921:
917:
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893:
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853:
849:
828:
806:
802:
772:
767:
763:
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750:
746:
739:
736:
733:
728:
724:
718:
713:
709:
705:
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672:
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661:
656:
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609:
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583:
579:
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572:
569:
564:
561:
558:
553:
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541:
535:
531:
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502:
481:
454:
450:
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437:
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431:
426:
422:
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396:
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344:
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146:
142:
130:
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115:
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95:
91:
87:
82:
78:
55:Main article:
52:
49:
15:
13:
10:
9:
6:
4:
3:
2:
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1371:
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1128:
1125:
1103:
1098:
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1077:
1070:
1067:
1064:
1059:
1055:
1048:
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1031:
1025:
1021:
1017:
1014:
1011:
1000:
995:
991:
986:
983:
978:
974:
967:
964:
961:
956:
952:
945:
942:
937:
933:
929:
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919:
915:
894:
891:
888:
885:
882:
879:
876:
867:
851:
847:
826:
804:
800:
790:
770:
765:
761:
756:
753:
748:
744:
737:
734:
731:
726:
722:
716:
711:
707:
703:
694:
689:
685:
679:
674:
670:
664:
659:
654:
650:
642:
638:
634:
631:
622:
607:
604:
601:
596:
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587:
581:
577:
573:
570:
567:
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559:
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533:
529:
520:
504:
500:
479:
470:
467:
452:
448:
444:
441:
438:
435:
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429:
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368:
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317:
314:
311:
306:
302:
298:
295:
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270:
261:
259:
251:
249:
247:
246:exponentially
242:
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198:
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171:
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144:
140:
113:
108:
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93:
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68:
67:
66:
64:
58:
50:
48:
46:
40:
38:
33:
29:
25:
21:
20:Belt friction
1347:. Retrieved
1337:
1322:
1287:
1283:
1273:
1262:. Retrieved
1251:
1240:. Retrieved
1236:the original
1225:
1213:. Retrieved
1204:
1161:
1158:Applications
1134:
1126:
868:
791:
623:
521:
471:
468:
409:
359:
285:
262:
255:
243:
131:
60:
41:
19:
18:
1349:2010-02-01
1264:2010-02-01
1242:2010-02-01
1184:References
387:and angle
1370:Mechanics
1314:1521-4001
1256:Chandoo.
1095:μ
1090:α
1087:
1071:−
1068:α
1065:
1041:τ
1037:μ
1018:≤
1012:≤
992:μ
987:α
984:
968:−
965:α
962:
938:τ
934:μ
930:−
877:ω
852:τ
848:μ
762:μ
757:α
754:
738:−
735:α
732:
712:τ
708:μ
686:μ
665:−
643:τ
639:μ
632:ω
602:ω
593:∫
574:≤
568:≤
557:ω
548:∫
544:−
449:μ
439:α
436:
421:μ
417:−
395:α
369:μ
299:−
225:β
195:μ
114:β
105:μ
1364:Category
1331:. Wiley.
1167:See also
330:, where
51:Equation
45:capstans
1292:Bibcode
1215:May 29,
239:radians
213:is the
32:tension
28:bollard
1312:
792:where
132:where
1209:(PDF)
907:then
624:with
1310:ISSN
1217:2020
492:and
442:<
430:<
315:>
63:mass
24:belt
1300:doi
1078:sin
1056:cos
975:sin
953:cos
869:If
745:sin
723:cos
433:tan
1366::
1308:.
1298:.
1288:95
1286:.
1282:.
1192:^
1124:.
789:,
47:.
39:.
1352:.
1316:.
1302::
1294::
1267:.
1245:.
1219:.
1104:2
1099:g
1082:2
1060:2
1049:s
1046:k
1032:e
1026:0
1022:T
1015:T
1001:2
996:g
979:2
957:2
946:s
943:k
926:e
920:0
916:T
895:t
892:s
889:n
886:o
883:c
880:=
827:k
805:g
801:k
771:2
766:g
749:2
727:2
717:k
704:=
695:2
690:g
680:2
675:g
671:k
660:2
655:n
651:k
635:=
608:s
605:d
597:s
588:e
582:0
578:T
571:T
563:s
560:d
552:s
540:e
534:0
530:T
505:0
501:T
480:T
453:g
445:+
425:g
373:g
343:n
339:k
318:0
312:T
307:n
303:k
296:=
293:N
271:N
199:s
172:1
168:T
145:2
141:T
109:s
100:e
94:1
90:T
86:=
81:2
77:T
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