Name: flat belt forces and pulley moment
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 28 s
Channel: JoVE

Płaski pas owija się wokół dwóch kół pasowych, A i B, o promieniach odpowiednio 30 cm i 10 cm.
Kąt między paskiem a poziomem wynosi 20 stopni na kołach pasowych.
Koło pasowe B obraca się zgodnie z ruchem wskazówek zegara i napędza koło pasowe A, powodując naprężenie T2 na jednym końcu paska i napięcie T1 na drugim.
Biorąc pod uwagę, że maksymalne dopuszczalne napięcie T2 wynosi 1000 N, a współczynnik tarcia statycznego między paskiem a kołami pasowymi wynosi 0,4, jaki jest maksymalny moment na kole pasowym A?
Kąt zwilżania pasa z powierzchnią, obliczony na podstawie geometrii systemu, wynosi 140 stopni.
Kąt zwilżania pasa do powierzchni w radianach i współczynnik tarcia statycznego są podstawiane do wyrażenia dla naprężeń pasa w celu uzyskania T1.
Gdy koło pasowe B obraca się zgodnie z ruchem wskazówek zegara, różnica naprężeń utworzona na kole pasowym B generuje moment na kole pasowym A.
Rysowany jest wykres swobodnego ciała dla koła pasowego A i stosowany jest warunek równowagi momentu.
Wartości promienia i rozciągania są podstawiane w celu uzyskania momentu maksymalnego.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. Strony 439 \u2012 441.</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley. Strony 372.</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strony 469-470.</li>
</ol>

płaskie pasy: rozwiązywanie problemów

Flat Belts: Problem Solving

Płaskie pasy są niezbędne w wielu zastosowaniach przemysłowych, ponieważ pomagają przekazywać moc z jednego koła pasowego na drugie. Pojęcie sił i momentów jest używane do wyznaczenia maksymalnego momentu na kołowrocie. Na przykład, rozważmy pas płaski, który owija się wokół dwóch kół pasowych, A i B, o promieniach odpowiednio 30 cm i 10 cm. Kąt między pasem a poziomem wynosi 20 stopni na kołowrotach. Kiedy kołowrotek B obraca się zgodnie z ruchem wskazówek zegara i napędza kołowrotek A, na jednym końcu pasa powstaje napięcie T2, podczas gdy na drugim powstaje napięcie T1.

<img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;" />

Kąt kontaktu pas-powierzchnia, β, , musi zostać obliczony, aby ustalić maksymalny moment. Kąt ten jest uzyskiwany na podstawie geometrii układu i okazuje się wynosić 140 stopni. Następnie ten kąt w radianach oraz wartość współczynnika tarcia statycznego, równą 0,4, są podstawiane do wyrażenia dla naprężeń w pasie.

<img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;" />

Biorąc pod uwagę, że maksymalne dozwolone napięcie T2 wynosi 1000 N, obliczona wartość T1 wynosi 376,93 N. Kiedy kołowrotek B obraca się zgodnie z ruchem wskazówek zegara na kołowrocie B powstaje różnica napięć, generująca moment na kołowrocie A. Rozważając diagram swobodnego ciała dla kołowrotu A, , można zastosować warunek równowagi momentu.

<img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

Następnie wartości promienia i napięcia są podstawiane w celu obliczenia maksymalnego momentu wynoszącego 186,921 Nm.

Płaskie pasy: Rozwiązywanie problemów

Pasy płaskie mają kluczowe znaczenie w wielu zastosowaniach przemysłowych, ponieważ pomagają przenosić moc z jednego koła pasowego na drugie. Pojęcie sił i momentów jest używane ...

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JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Friction

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KEY TERMS AND CONCEPTS

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flat belt forces and pulley moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system.

As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β, is needed to find the maximum moment, so it is first found from the geometry of the setup. The angle is 140 degrees.

Next, the contact angle in radians and the coefficient of static friction, 0.4, are used in the belt tension equation. With the maximum allowable tension T2 set to 1000 N, the value of T1 is calculated as 376.93 N. A free-body diagram for pulley A then helps apply moment equilibrium. Using the pulley radius and the belt tensions, the maximum moment is found to be 186.921 N.m.

Flat Belt Forces and Pulley Moment

dry friction

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flat belts: problem solving

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key terms and concepts

Learn how belt tension, friction, and pulley radius are used to calculate the maximum moment in a flat belt drive system with two pulleys.

Flat Belt Forces and Pulley Moment | JoVE K12

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mechanical engineering

Flat Belt Forces and Pulley Moment

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