مقاومة التدحرج
مراجع

1 2 3 4  "SAE MOBILUS". saemobilus.sae.org. DOI:10.4271/06-11-02-0014. مؤرشف من الأصل في 2021-10-29. اطلع عليه بتاريخ 2021-04-19.
↑  Peck، William Guy (1859). Elements of Mechanics: For the Use of Colleges, Academies, and High Schools. A.S. Barnes & Burr: New York. ص. 135. اطلع عليه بتاريخ 2007-10-09. rolling friction less than sliding friction.
1 2 3  "User guide for CONTACT, Rolling and sliding contact with friction. Technical report TR09-03 version v16.1. VORtech, 2016" (PDF). مؤرشف من الأصل (PDF) في 2018-11-19. اطلع عليه بتاريخ 2017-07-11.
1 2 3  Hibbeler، R.C. (2007). Engineering Mechanics: Statics & Dynamics (ط. Eleventh). Pearson, Prentice Hall. ص. 441–442. ISBN:9780132038096.
↑  A handbook for the rolling resistance of pneumatic tires Clark, Samuel Kelly; Dodge, Richard N. 1979 نسخة محفوظة 2021-10-26 على موقع واي باك مشين.
1 2 3  "Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance -- Special Report 286. National Academy of Sciences, Transportation Research Board, 2006" (PDF). مؤرشف من الأصل (PDF) في 2021-10-21. اطلع عليه بتاريخ 2007-08-11.
↑  Tyres-Online: The Benefits of Silica in Tyre Design نسخة محفوظة 2013-02-04 على موقع واي باك مشين.
↑  Астахов, p.85
↑  An example of such usage for railroads is here.
↑  Деев, p. 79. Hay, p. 68
↑  Астахов, Chapt. IV, p. 73+; Деев, Sect. 5.2 p. 78+; Hay, Chapt. 6 "Train Resistance" p. 67+
↑  Астахов, Fig. 4.14, p. 107
↑  Andersen Lasse G.؛ Larsen Jesper K.؛ Fraser Elsje S.؛ Schmidt Bjarne؛ Dyre Jeppe C. (2015). "Rolling Resistance Measurement and Model Development". Journal of Transportation Engineering. ج. 141 ع. 2: 04014075. DOI:10.1061/(ASCE)TE.1943-5436.0000673.
↑  "Rolling Resistance and Fuel Saving" (PDF). مؤرشف من الأصل (PDF) في 2016-04-08.
↑  If one were to assume that the resistance coefficients (Crr) for motor vehicles were the same as for trains, then for trains the neglected resistances taken together have a Crr of about 0.0004 (see Астахов, Fig. 4.14, p.107 at 20km/hr and assume a total Crr =0.0010 based on Fig. 3.8, p.50 (plain bearings) and adjust for roller bearings based on a delta Crr of 0.00035 as read from Figs. 4.2 and 4.4 on pp. 74, 76). Compare this Crr of 0.0004 to motor vehicle tire Crr's of at least 10 times higher per "Rolling resistance coefficient examples" in this article
↑  kgf/tonne is used by Астахов throughout his book
↑  Деев uses N/T notation. See pp. 78-84.
↑  Willett, Kraig. "Roller Data". www.biketechreview.com (بالإنجليزية البريطانية). Archived from the original on 2010-02-20. Retrieved 2017-08-05.
↑  "Rolling Resistance Coefficient - slow rigid wheel on a perfectly elastic surface - calculator". fxSolver. مؤرشف من الأصل في 2023-03-19. اطلع عليه بتاريخ 2022-02-18.
↑  Hersey, equation (2), p. 83
↑  Астахов, p. 81. "نسخة مؤرشفة". مؤرشف من الأصل في 2020-09-01. اطلع عليه بتاريخ 2021-11-20.{{استشهاد ويب}}:  صيانة الاستشهاد: BOT: original URL status unknown (link)
↑  "Coefficients of Friction in Bearing". Coefficients of Friction. مؤرشف من الأصل في 2020-11-12. اطلع عليه بتاريخ 2012-02-07.
↑  Hay, Fig. 6-2 p.72(worst case shown of 0.0036 not used since it is likely erroneous)
↑  Астахов, Figs. 3.8, 3.9, 3.11, pp. 50-55; Figs. 2.3, 2.4 pp. 35-36. (Worst case is 0.0024 for an axle load of 5.95 tonnes with obsolete plain (friction --not roller) bearings
↑  Астахов, Fig. 2.1, p.22
↑  Hersey, Table 6, p.267
↑  "Roller Data" (PDF). مؤرشف من الأصل (PDF) في 2012-03-13.
1 2  Roche, Schinkel, Storey, Humphris & Guelden, "Speed of Light." (ردمك 0-7334-1527-X)
↑  "Rolling Resistance". www.engineeringtoolbox.com. مؤرشف من الأصل في 2022-02-01. اطلع عليه بتاريخ 2022-02-18.
↑  Crr for large truck tires per Michelin نسخة محفوظة 2013-05-07 على موقع واي باك مشين.
↑  Green Seal 2003 Report
1 2 3 4  Gillespie (ردمك 1-56091-199-9) p117
1 2  Baker, Ira O., "Treatise on roads and pavements". New York, John Wiley, 1914. Stagecoach: Table 7, p. 28. Diameter: pp. 22-23. This book reports a few hundred values of rolling resistance for various animal-powered vehicles under various condition, mostly from 19th century data.
↑  Hersey, subsection: "Static rolling friction", p.266.
1 2  Williams, 1994, Ch. "Rolling contacts", eq. 11.1, p. 409.
↑  Hersey, subsection: "Coulomb on wooden cylinders", p. 260
↑  U.S. National Bureau of Standards, Fig. 1.13
↑  Some think that smaller tire wheels, all else being equal, tend to have higher rolling resistance than larger wheels. In some laboratory tests, however, such as Greenspeed test results (accessdate = 2007-10-27), smaller wheels appeared to have similar or lower losses than large wheels, but these tests were done rolling the wheels against a small-diameter drum, which would theoretically remove the advantage of large-diameter wheels, thus making the tests irrelevant for resolving this issue. Another counter example to the claim of smaller wheels having higher rolling resistance can be found in the area of ultimate speed  ‏ soap box derby racing. In this race, the speeds have increased as wheel diameters have decreased by up to 50%. This might suggest that rolling resistance may not be increasing significantly with smaller diameter within a practical range, if any other of the many variables involved have been controlled for. See talk page. نسخة محفوظة 2021-03-06 على موقع واي باك مشين.
↑  Zéhil، Gérard-Philippe؛ Gavin، Henri P. (2013). "Three-dimensional boundary element formulation of an incompressible viscoelastic layer of finite thickness applied to the rolling resistance of a rigid sphere". International Journal of Solids and Structures. ج. 50 ع. 6: 833–842. DOI:10.1016/j.ijsolstr.2012.11.020.
↑  Zéhil، Gérard-Philippe؛ Gavin، Henri P. (2013). "Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions". International Journal of Solids and Structures. ج. 50 ع. 6: 843–852. DOI:10.1016/j.ijsolstr.2012.11.021.
↑  Zéhil، Gérard-Philippe؛ Gavin، Henri P. (2013). "Simplified approaches to viscoelastic rolling resistance". International Journal of Solids and Structures. ج. 50 ع. 6: 853–862. DOI:10.1016/j.ijsolstr.2012.09.025.
↑  Sina, Naser; Hairi Yazdi, Mohammad Reza; Esfahanian, Vahid (1 Mar 2020). "A novel method to improve vehicle energy efficiency: Minimization of tire power loss". Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering (بالإنجليزية). 234 (4): 1153–1166. DOI:10.1177/0954407019861241. ISSN:0954-4070. S2CID:199099736. Archived from the original on 2021-11-21.
↑  Sina, Naser; Nasiri, Sayyad; Karkhaneh, Vahid (1 Nov 2015). "Effects of resistive loads and tire inflation pressure on tire power losses and CO2 emissions in real-world conditions". Applied Energy (بالإنجليزية). 157: 974–983. DOI:10.1016/j.apenergy.2015.04.010. ISSN:0306-2619. Archived from the original on 2021-04-21.
1 2  Roberts, Fig. 17: "Effect of torque transmission on rolling resistance", p. 71
↑  Деев, p.30 including eq. (2.7) and Fig. 2.3
↑  Астахов, Figs. 3.8, 3.9, 3.11, pp. 50-55. Hay, Fig. 60-2, p. 72 shows the same phenomena but has higher values for Crr and not reported here since the railroads in 2011 . were claiming about the same value as Астахов
↑  Hersey, Table 6., p. 267
↑  Per this assumption,  F=kN^{0.5} where  F is the rolling resistance force and  N is the normal load force on the wheel due to vehicle weight, and  k is a constant. It can be readily shown by differentiation of  F with respect to  N using قواعد الاشتقاق that  {\operatorname {d} N \over N}=2{\operatorname {d} F \over F}
↑  Roberts, pp. 60-61.
↑   A Relationship between Tyre Pressure and Rolling Resistance Force under Different Vehicle Speed | Apiwat Suyabodha |Department of Automotive Engineering, Rangsit University, Lak-hok, Pathumthani, Thailand | 2017 نسخة محفوظة 2021-07-19 على موقع واي باك مشين.
↑   C. Michael Hogan, Analysis of Highway Noise, Journal of Soil, Air and Water Pollution, Springer Verlag Publishers, Netherlands, Volume 2, Number 3 / September, 1973 نسخة محفوظة 2023-03-07 على موقع واي باك مشين.
↑  Gwidon W. Stachowiak, Andrew William Batchelor, Engineering Tribology, Elsevier Publisher, 750 pages (2000) (ردمك 0-7506-7304-4)
↑  http://144.206.159.178/ft/200/607426/12614863.pdf%5Bوصلة+مكسورة%5D
↑  http://www.rubberchemtechnol.org/resource/1/rctea4/v3/i1/p19_s1?isAuthorized=no%5Bوصلة+مكسورة%5D
1 2 3 4  "Schwalbe Tires: Rolling Resistance". مؤرشف من الأصل في 2021-04-16.
↑  The Recumbent Bicycle and Human Powered Vehicle Information Center نسخة محفوظة 18 أكتوبر 2021 على موقع واي باك مشين.
↑  U.S National Bureau of Standards p.? and Williams p.?
↑  Roberts, "Effect of temperature", p.59
↑  Астахов, p. 74, Although Астахов list these components, he doesn't give the sum a name.
↑  Шадур. Л. А. (editor). Вагоны باللغة الروسية(Railway cars). Москва, Транспорт, 1980. pp. 122 and figs. VI.1 p. 123 VI.2 p. 125
↑  Association of American Railroads, Mechanical Division "Car and Locomotive Encyclopedia", New York, Simmons-Boardman, 1974. Section 14: "Axle journals and bearings". Almost all of the ads in this section are for the tapered type of bearing.
↑  Астахов, Fig 4.2, p. 76
↑  Statistics of railroads of class I in the United States, Years 1965 to 1975: Statistical summary. Washington DC, Association of American Railroads, Economics and Finance Dept. See table for Amtrak, p.16. To get the tons per passenger divide ton-miles (including locomotives) by passenger-miles. To get tons-gross/tons-net, divide gross ton-mi (including locomotives) (in the "operating statistics" table by the revenue ton-miles (from the "Freight traffic" table)
Астахов П.Н. باللغة الروسية "Сопротивление движению железнодорожного подвижного состава" (Resistance to motion of railway rolling stock) Труды ЦНИИ МПС (ISSN 0372-3305). Выпуск 311 (Vol. 311). - Москва: Транспорт, 1966. – 178 pp. perm. record at UC Berkeley (In 2012, full text was on the Internet but the U.S. was blocked)
Деев В.В., Ильин Г.А., Афонин Г.С. باللغة الروسية "Тяга поездов" (Traction of trains) Учебное пособие. - М.: Транспорт, 1987. - 264 pp.
Hay, William W. "Railroad Engineering" New York, Wiley 1953
Hersey, Mayo D., "Rolling Friction" Transactions of the ASME, April 1969 pp. 260–275 and Journal of Lubrication Technology, January 1970, pp. 83–88 (one article split between two journals) Except for the "Historical Introduction" and a survey of the literature, it is mainly about laboratory testing of mine railroad cast iron wheels of diameters 8″ to 24 done in the 1920s (almost a half century delay between experiment and publication).
Hoerner, Sighard F., "Fluid dynamic drag", published by the author, 1965. (Chapt. 12 is "Land-Borne Vehicles" and includes rolling resistance (trains, autos, trucks).)
Roberts, G. B., "Power wastage in tires", International Rubber Conference, Washington, D.C. 1959.
U.S National Bureau of Standards, "Mechanics of Pneumatic Tires", Monograph #132, 1969–1970.
Williams, J. A. Engineering tribology'. Oxford University Press, 1994.
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