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

Uma correia plana envolve duas polias, A e B, com raios de 30 cm e 10 cm, respectivamente.
O ângulo entre a correia e a horizontal é de 20 graus nas polias.
A polia B gira no sentido horário e aciona a polia A, causando tensão T2 em uma extremidade da correia e tensão T1 na outra.
Dado que a tensão máxima permitida T2 é 1000 N e o coeficiente de atrito estático entre a correia e as polias é 0,4, qual é o momento máximo na polia A?
O ângulo de contato da correia à superfície, calculado a partir da geometria do sistema, é de 140 graus.
O ângulo de contato da correia com a superfície em radianos e os valores do coeficiente de atrito estático são substituídos na expressão das tensões da correia para obter T1.
À medida que a polia B gira no sentido horário, uma diferença de tensão criada na polia B gera um momento na polia A.
Um diagrama de corpo livre para a polia A é desenhado e a condição de equilíbrio de momento é aplicada.
Os valores de raio e tensão são substituídos para obter o momento máximo.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. Pág. 439 \u2012 441.</li>
	<li>Oliveira, J.L.; Kraige, L.G. e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. Pág. 372.</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. Pág. 469-470.</li>
</ol>

correias planas: resolução de problemas

Flat Belts: Problem Solving

As correias planas são cruciais em muitas aplicações industriais, pois ajudam a transmitir energia de uma polia para outra. O conceito de forças e momentos é utilizado para determinar o momento máximo em uma polia. Por exemplo, considere uma correia plana que envolve duas polias, A e B, com raios de 30 cm e 10 cm, respectivamente. O ângulo entre a correia e o horizontal é de 20 graus nas polias. À medida que a polia B gira no sentido horário e impulsiona a polia A, a tensão T2 é causada em uma extremidade da correia, enquanto a tensão T1 é criada na outra.

<img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;" />

O ângulo de contato da correia com a superfície, β, deve ser calculado para determinar o momento máximo. Este ângulo é obtido a partir da geometria do sistema e encontrado como sendo 140 graus. Como resultado, o ângulo de contato da correia com a superfície em radianos, juntamente com o valor do coeficiente de atrito estático, 0.4, é substituído na expressão para as tensões da correia.

<img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;" />

Considerando que a tensão máxima permitida T2 é de 1000 N, o valor calculado de T1 é de 376.93 N. À medida que a polia B gira no sentido horário, é criada uma diferença de tensão na polia B, gerando um momento na polia A. Considerando um diagrama de corpo livre para a polia A, a condição de equilíbrio de momentos pode ser aplicada.

<img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

Os valores do raio e da tensão são então substituídos para obter o momento máximo de 186.921 N.m.áximo de 186.921 N.m.

Correias planas: Resolução de problemas

As correias planas são cruciais em muitas aplicações industriais, pois ajudam a transmitir energia de uma polia para outra. O conceito de forças e momentos é usado ...

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JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

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Friction

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KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

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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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Flat Belt Forces and Pulley Moment

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