Name: flat belt tension and friction
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 28 s
Channel: JoVE

ضع في اعتبارك حزاما مسطحا ملفوفا حول مجموعة من البكرات ، ويعاني من توترات الحزام في نهايات بكرة القيادة.
بالنسبة لحركة البكرة عكس اتجاه عقارب الساعة ، يكون حجم T2 أكبر من T1 بسبب الاحتكاك بين الحزام وسطح البكرة.
تتيح معرفة الزاوية الإجمالية للتلامس بين الحزام والسطح ومعامل الاحتكاك تقدير التوترات.
يتم رسم مخطط الجسم الحر لعنصر تفاضلي AB للحزام.
بافتراض الحركة الوشيكة ، فإن قوة الاحتكاك تعارض الحركة المنزلقة للحزام ، مما يتسبب في زيادة حجم شد الحزام الذي يعمل عند النقطة B بمقدار dT.
بتطبيق توازن القوة الأفقي والرأسي وباستخدام تقريبي جيب التمام والجيب ، يتم الحصول على معادلتين لتوازن القوة.
يتم إهمال ناتج تفاضلين مقارنة بالفروق من الدرجة الأولى في معادلات التوازن الرأسي ، بينما يتم تبسيط معادلة التوازن الأفقي بشكل أكبر.
يؤدي الجمع بين معادلات التوازن والتكامل بين الحدود المقابلة إلى التعبير الذي يربط توترات الحزام.
تنطبق هذه المعادلة على الأحزمة المسطحة التي تمر فوق أي سطح ملامس منحني.

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	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 439 - 440.</li>
	<li>مريم ، جي إل. كريج ، إل جي وبولتون ، ج. (2020). الميكانيكا الهندسية - الإحصاء. هوبوكين ، نيو جيرسي: جون وايلي. ص 373.</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 463</li>
</ol>

قوى الاحتكاك على الأحزمة المسطحة

Frictional Forces on Flat Belts

<div style="direction:rtl">

 تُستخدم الأحزمة المسطحة عادةً في التطبيقات الصناعية المختلفة لنقل القدرة من بكرة إلى أخرى. عندما يتم لف الحزام المسطح حول مجموعة من البكرات، فإنه يتعرض لاختلاف في الشد عند نقاط التلامس مع بكرة القيادة نتيجة الاحتكاك بين سطح الحزام وسطح البكرة. عندما تتحرك البكرة في اتجاه عكس عقارب الساعة، يكون الشد T2 في الجانب الذي يتحرك فيه الحزام بعيدًا عن البكرة أعلى من الشد T1 في الجانب الذي يتحرك فيه الحزام نحو البكرة.

 لتقدير قوى الشد في الحزام المسطح، يجب معرفة الزاوية الكلية للالتفاف بين الحزام وسطح البكرة، بالإضافة إلى معامل الاحتكاك بين السطحين. يمكن تحليل قوى الشد من خلال رسم مخطط الجسم الحر لعنصر تفاضلي صغير AB من الحزام، بافتراض اقتراب الحركة من حالة الانزلاق.

 <img alt="Figure 1" src="/files/ftp_upload/14322/14322_PT_Fig_1v2.svg" style="text-align: center; height: 350px;">

 تقاوم القوة الاحتكاكية الحركة الانزلاقية للحزام، مما يؤدي إلى زيادة الشد عند النقطة B بمقدار تفاضلي dT. يمكن استخدام هذا التغير التفاضلي في الشد لربط قيم الشد عند نقاط مختلفة على طول الحزام.

 لتحديد العلاقة بين قوى الشد في الحزام، يتم تطبيق معادلات التوازن للقوى الأفقية والرأسية، مع استخدام تقريب جيب التمام وجيب الزاوية الصغيرة.

 <img alt="Equation 1" src="/files/ftp_upload/14322/14322_PT_Equation_1v2.svg" style="text-align: center; height: 30px;">

 <img alt="Equation 2" src="/files/ftp_upload/14322/14322_PT_Equation_2v2.svg" style="text-align: center; height: 30px;">

 تأخذ هذه المعادلات في الاعتبار القوى المؤثرة على العنصر التفاضلي AB في الاتجاهين الأفقي والرأسي. يتم إهمال الحدود الصغيرة من الدرجة الثانية في معادلات التوازن الرأسي، بينما يتم تبسيط معادلة التوازن الأفقي بشكل أكبر. بعد ذلك، يتم دمج معادلات التوازن ضمن الحدود المناسبة للحصول على العلاقة النهائية بين توترات الحزام.

 <img alt="Equation 3" src="/files/ftp_upload/14322/14322_PT_Equation_3v2.svg" style="text-align: center; height: 45px;">

 تؤدي هذه العملية إلى استنتاج تعبير يربط بين توترات الحزام.

 <img alt="Equation 4" src="/files/ftp_upload/14322/14322_PT_Equation_4v2.svg" style="text-align: center; height: 15px;">

 تنطبق هذه المعادلة على الأحزمة المسطحة التي تمر فوق أي سطح منحني.

 تلعب قوى الاحتكاك على الأحزمة المسطحة دورًا أساسيًا في تحديد أداء وكفاءة الأنظمة التي تعتمد على نقل القدرة بواسطة الأحزمة. يمكن أن يؤدي التوتر الزائد في الحزام إلى تآكل مبكر وانخفاض في الكفاءة، في حين أن التوتر غير الكافي قد يؤدي إلى الانزلاق وفقدان القدرة المنقولة. يتم ضبط التوتر المناسب في الحزام من خلال تعديل المسافة بين البكرات أو باستخدام أنظمة شد متخصصة.

</div>

تستخدم الأحزمة المسطحة بشكل شائع في العديد من التطبيقات الصناعية لنقل الطاقة من بكرة إلى أخرى. عندما يتم لف حزام مسطح حول ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Friction

احتكاك

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

flat belt tension and friction

Flat belt tension and friction control how power moves from one pulley to another. Flat belts are used in many industrial systems to transmit power between pulleys. As the belt wraps around the pulleys, the tension changes because of friction between the belt and the pulley surface.

When a pulley turns counterclockwise, the belt side moving away from the pulley has the higher tension, called T2. The side moving toward the pulley has the lower tension, called T1. To estimate these tensions, the total angle of contact and the coefficient of friction between the surfaces must be known.

The belt can be analyzed with a free-body diagram of a small belt element, AB. This analysis assumes impending motion, which means the belt is close to slipping. Friction acts against the sliding motion, so the tension at point B increases by a small amount, dT.

The tension relationship is found using horizontal and vertical force equilibrium. Cosine and sine approximations help simplify the force equations for the small belt element. In the vertical equation, the product of two differentials is neglected, and the horizontal equation is simplified further. The equations are then combined and integrated between the proper limits to obtain the belt-tension expression.

This result applies to flat belts that pass over curved contacting surfaces. Frictional forces are important because they affect the performance and efficiency of the belt-driven system. If the belt is too tight, it can wear out early and reduce efficiency. If it is too loose, it can slip and reduce power transmission. Proper tension is usually set by changing the distance between the pulleys or by using a tensioning device.

Flat Belt Tension and Friction

dry friction

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frictional forces on flat belts

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key terms and concepts

Learn how friction changes tension in a flat belt, why angle of contact matters, and how proper belt tension helps prevent wear and slippage.

Flat Belt Tension and Friction | 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 Tension and Friction

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