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

يلتف حزام مسطح حول بكرتين ، A و B ، بنصف قطر 30 سم و 10 سم على التوالي.
الزاوية بين الحزام والأفقي هي 20 درجة عند البكرات.
تدور البكرة B في اتجاه عقارب الساعة وتدفع البكرة A ، مما يتسبب في التوتر T2 في أحد طرفي الحزام والتوتر T1 في الطرف الآخر.
بالنظر إلى أن الحد الأقصى المسموح به للشد T2 هو 1000 نيوتن ومعامل الاحتكاك الساكن بين الحزام والبكرات يساوي 0.4 ، فما هو الحد الأقصى للعزم على البكرة A؟
زاوية التلامس من الحزام إلى السطح ، محسوبة من هندسة النظام ، هي 140 درجة.
يتم استبدال زاوية التلامس من الحزام إلى السطح بالراديان ومعامل قيم الاحتكاك الساكن في التعبير عن توترات الحزام للحصول على T1.
عندما تدور البكرة B في اتجاه عقارب الساعة ، فإن فرق التوتر الناتج في البكرة B يولد لحظة في البكرة A.
يتم رسم مخطط الجسم الحر للبكرة A ، ويتم تطبيق شرط التوازن اللحظة.
يتم استبدال قيم نصف القطر والتوتر للحصول على الحد الأقصى للفتة.

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	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 439 - 441.</li>
	<li>مريم ، جي إل. كريج ، إل جي وبولتون ، ج. (2020). الميكانيكا الهندسية - الإحصاء. هوبوكين ، نيو جيرسي: جون وايلي. ص 372.</li>
	<li>بير ، إف بي ؛ جونستون ، إي آر ؛ مازوريك ، د. إف. كرومويل ، بي جيه وسيلف ، ب. (2019). ميكانيكا المتجهات للمهندسين - الإحصاء والديناميكيات. نيويورك: ماكجرو هيل. ص 469-470.</li>
</ol>

الأحزمة المسطحة: حل المشكلات

Flat Belts: Problem Solving

<div style="direction:rtl">تُعدُّ الأحزمة المسطحة عنصرًا أساسيًا في العديد من التطبيقات الصناعية، حيث تساهم في نقل القدرة من بكرة إلى أخرى. يُستخدم تحليل القوى والعزوم لتحديد العزم الأقصى المؤثر على البكرة. على سبيل المثال، لنأخذ في الاعتبار حزامًا مسطحًا يلتف حول بكرتين، أ وب، بأقطار 30 سم و10 سم على التوالي. تكون الزاوية بين الحزام والمستوى الأفقي 20 درجة عند موضع كل من البكرتين. بينما تدور البكرة ب في اتجاه دوران عقارب الساعة، مما يؤدي إلى دفع البكرة أ، ينشأ التوتر T2 عند نهاية الحزام، بينما يتولد التوتر T1 عند الطرف الآخر. <img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;"> يجب حساب زاوية التماس بين الحزام وسطح البكرة، β، لتحديد العزم الأقصى. يتم استنتاج هذه الزاوية من تحليل الهندسة الميكانيكية للنظام، وتبيّن أنها تساوي 140 درجة. بالتالي، يتم تحويل زاوية التماس إلى الراديان، ومن ثم تُستخدم مع معامل الاحتكاك الساكن الذي تبلغ قيمته 0.4، في المعادلة الخاصة بتوتر الأحزمة. <img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;"> بافتراض أن الحد الأقصى المسموح به لقيمة التوتر هو 1000 نيوتن، فإن القيمة المحسوبة لـ T1 تكون 376.93 نيوتن. عندما تدور البكرة ب باتجاه دوران عقارب الساعة، ينشأ فرق في التوتر عند البكرة ب، مما يؤدي إلى توليد عزم دوران على البكرة أ. من خلال رسم مخطط الجسم الحر للبكرة أ، يمكن تطبيق شرط اتزان العزوم لحساب العزم الناتج. <img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> بعد تعويض قيم نصف القطر والتوتر، يتم الحصول على العزم الأقصى، والذي يساوي 186.921 نيوتن.م.</div>

تعتبر الأحزمة المسطحة ضرورية في العديد من التطبيقات الصناعية لأنها تساعد في نقل الطاقة من بكرة إلى أخرى. يتم استخدام مفهوم القوى واللحظات ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Friction

احتكاك

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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,...

pivot bearings

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collar bearings

Friction Torque in Collar Bearings

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Journal bearings support rotating shafts and axles while helping keep them stable. They are used in machines such as engines, turbines, and pumps. Their job is to reduce friction, wear, and vibration. A journal bearing works by keeping a thin film of lubricant between the bearing surface and the rotating shaft. This film limits direct contact and lowers frictional force. The video uses a rope winch with dry or only partly lubricated journal bearings to show the idea. As the spool turns...

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rolling resistance

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rolling resistance: 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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Flat Belt Forces and Pulley Moment

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