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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

ʹǤ͹Ǥʹ ‘ŽŽ‹‰ ‡•‹•–ƒ ‡

‘ŽŽ‹‰ ”‡•‹•–ƒ ‡ ‹• ˜‡”› •ƒŽŽ ‘’ƒ”‡† –‘ •Ž‹†‹‰ ”‡•‹•–ƒ ‡Ǥ – •–‡• ˆ”‘ –Š‡ ˆƒ – –Šƒ–ǡ ‡‹–Š‡”
–Š‡ ”‘ŽŽ‹‰ •—”ˆƒ ‡ ‘” –Š‡ ”‘ŽŽ‹‰ ‡Ž‡‡– ƒ”‡ ƒ„•‘Ž—–‡Ž› ”‹‰‹†Ǥ Š‡”‡ˆ‘”‡ǡ ™Š‡ –Š‡ ”‘ŽŽ‡” ‹•
†‡ˆ‘”‡† ™Š‹Ž‡ ”‘ŽŽ‹‰ ȋ‡˜‡ –‘ ƒ •ƒŽŽ ‡š–‡–Ȍǡ –Š‡ ”‡ƒ –‹‘ ˆ”‘ –Š‡ ‰”‘—† †‘‡• ‘– ‘‹ ‹†‡
™‹–Š –Š‡ ™‡‹‰Š– ‘ˆ –Š‡ ”‘ŽŽ‡”Ǥ Š‹• „”‹‰• ƒ„‘—– ƒ –‘”“—‡ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤ͸ͲȐǡ ™Š‹ Š Šƒ• –‘ „‡
‘˜‡” ‘‡ –‘ ”‘ŽŽ ˆ—”–Š‡”Ǥ

[Fig 2.60: rolling of deformable body]
The torque produced is given by:

[T = (W x d)] Resisting torque

Unlike rigid bodies, for deformable bodies, the reaction force from the ground and the CG do not
coincide, producing a torque.

It should be noted that, the ground may be flexible, and a small pit could form due to the weight (W)
of the rolling element. A torque is needed to pull the rolling element out of the pit.

Therefore, it is more appropriate to call this effect rolling resistance rather than rolling friction.

ʹǤ͹Ǥ͵ ‘ŽŽ‹‰ ‘ ƒ ‹ Ž‹‡† ’Žƒ‡
 ƒ•‡ ‘ˆ ’—”‡ ”‘ŽŽ‹‰ ‘ ƒ Š‘”‹œ‘–ƒŽ •—”ˆƒ ‡ǡ –Š‡ •–ƒ–‹ ˆ”‹ –‹‘ ‹• œ‡”‘Ǥ ‘™‡˜‡”ǡ ™Š‡ ”‘ŽŽ‹‰ —’
‘” †‘™ ƒ ‹ Ž‹ƒ–‹‘ǡ •–ƒ–‹ ˆ”‹ –‹‘ ‹• –Š‡ ‘Ž› ƒ‰‡ › –Šƒ– ’”‘˜‹†‡• –‘”“—‡ ˆ‘” ”‘ŽŽ‹‰ǡ ƒ† ˆ‘”
„‘–Š ƒ•‡• ‘ˆ ”‘ŽŽ‹‰ —’ ‘” †‘™ ƒ ‹ Ž‹ƒ–‹‘ǡ –Š‡ ˆ”‹ –‹‘ ˆ‘” ‡ ƒŽ™ƒ›• ƒ –• —’™ƒ”†•Ǥ
‡”‡ǡ ™‡ ‘•‹†‡” –Š‡ ‹•–ƒ–ƒ‡‘—• ‡“—‹Ž‹„”‹— ‘ˆ –Š‡ •›•–‡Ǥ Š‹• ‘–ƒ‹• –Š‡ ‹‡”–‹ƒŽȀ’•‡—†‘
ˆ‘” ‡• ƒ• ™‡ –”‡ƒ– –Š‡ •‹–—ƒ–‹‘ ƒ• ’•‡—†‘ •–ƒ–‹ ˆ‘” „‡––‡” ‘’”‡Š‡•‹‘Ǥ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 69 age 69
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