Name: tire deformation and rolling resistance
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Rolling Resistance

ضع في اعتبارك إطارا يتدحرج بسرعة ثابتة. القوى المؤثرة عليه هي وزنه وقوته الطبيعية.
تتشوه أسطح التلامس ، مما يخلق منطقة تلامس محدودة. ينتج عن هذا توزيع القوى العادية في كل نقطة اتصال.
يتعرض الجزء الأمامي من هذه المنطقة للتشوه ، مما يؤخر حركة التدحرج.
في المقابل ، يخضع القسم الخلفي لعملية ترميم أصغر نسبيا تدفع الإطار إلى الأمام.
القوة العادية الناتجة المؤثرة عند A هي مجموع هذه القوى.
للحفاظ على تدحرج الإطار بسرعة ثابتة وموازنة لحظة الوزن حول A ، يجب تطبيق قوة دافعة أفقية على مركز الإطار. هنا يجب أن تكون جميع القوى متزامنة.
يعطي حالة توازن اللحظة عند النقطة A القوة الدافعة من حيث معامل مقاومة التدحرج.
عادة ما يكون الوزن مضروبا في معامل مقاومة التدحرج على نصف القطر أصغر من معامل الاحتكاك الحركي مضروبا في الوزن.
لذا ، فإن قوة الاحتكاك المتدحرجة أصغر من قوة الانزلاق.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 452 - 439.</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.</li>
</ol>

مقاومة التدحرج

<div style="direction:rtl">

عندما تتدحرج أسطوانة صلبة بثبات على سطح صلب، فإن القوة العمودية التي يطبقها السطح على الأسطوانة تكون متعامدة مع الخط المماس عند نقطة التلامس. ومع ذلك، نظرًا لعدم الصلابة المطلقة للمواد، فإن رد فعل السطح على الأسطوانة يتوزع على شكل ضغوط عمودية عبر منطقة التلامس.

على سبيل المثال، تخيل أسطوانة صلبة تتدحرج على سطح ناعم نسبيًا. يؤدي وزن الأسطوانة إلى الضغط على السطح أسفلها، ومع استمرار التدحرج، تتعرض المادة أمامها للتشوه مما يؤدي إلى إبطاء حركتها، في حين أن المادة الموجودة خلفها تستعيد حالتها الأصلية المشوهة جزئيًا، مما يولد قوة تدفع الأسطوانة إلى الأمام. يتم تمثيل الضغوط العمودية المؤثرة على الأسطوانة بالقوتين الناتجتين Nd و Nr . تكون قوة التشوه Nd ومكونها الأفقي عادةً أكبر من قوة الاستعادة Nr ، مما يستلزم تطبيق قوة دفع أفقية على الأسطوانة للحفاظ على حركتها المستمرة.


تحدث مقاومة التدحرج بشكل رئيسي بسبب هذا التأثير، لكنها تتأثر أيضًا، وإن كان بدرجة أقل، بالالتصاق السطحي والانزلاق الجزئي بين الأسطوانة والسطح الملامس.

لتوضيح هذا المفهوم، لنأخذ إطار مركبة يتدحرج بسرعة ثابتة. القوى الرئيسية المؤثرة عليه هي وزنه المؤثر عموديًا إلى الأسفل، والقوة العمودية التي يطبقها السطح الداعم باتجاه الأعلى. أثناء تدحرج الإطار، يعاني الجزء الأمامي من منطقة التلامس من التشوه مما يعيق حركته، في حين يكون تأثير الاستعادة في الجزء الخلفي أقل نسبيًا، مما ينتج عنه قوة تدفع الإطار إلى الأمام. النتيجة الصافية لهذه التأثيرات هي أن القوة العمودية الناتجة، والتي تكون متعامدة عند النقطة A (مركز منطقة التلامس)، تمثل محصلة هذه القوى المتضادة.

<img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;">

للحفاظ على تدحرج الإطار بسرعة ثابتة وتحقيق التوازن حول النقطة A، يجب تطبيق قوة دفع أفقية F عند مركز الإطار. ولتحقيق الاتزان، يجب أن تكون جميع القوى المؤثرة على الإطار متزنة. باستخدام شرط توازن العزوم حول النقطة A، يمكننا تحديد القوة الدافعة المطلوبة للحفاظ على سرعة ثابتة بدلالة معامل مقاومة التدحرج α:

<img alt="Equation 1" src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;">

عادةً ما تكون هذه القوة الدافعة أقل من ناتج معامل الاحتكاك الحركي في وزن الإطار:

<img alt="Equation 2" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;">

تشير هذه العلاقة إلى أن قوة الاحتكاك أثناء التدحرج تكون عادةً أصغر من قوة الاحتكاك الانزلاقي التي تنشأ عند انزلاق الإطار على السطح. ونتيجةً لذلك، فإن مقاومة التدحرج تكون أقل تأثيرًا على أداء المركبة مقارنةً بالاحتكاك الانزلاقي.

</div>

عندما تتدحرج الأسطوانة الصلبة بثبات على سطح صلب ، تكون القوة العادية التي يطبقها السطح على الأسطوانة متعامدة مع الظل عند ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Friction

احتكاك

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

tire deformation and rolling resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force.

A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact area slows because it is being deformed. The material behind the cylinder begins to recover, and that recovery pushes the cylinder forward.

These effects are often shown as two resultants, N d for the deformation force and N r for the restoration force. The deformation force and its horizontal component are larger than the restoration force. Because of that imbalance, a horizontal driving force must be applied to keep the cylinder moving.

The same idea applies to a tire rolling at constant speed. Its weight acts downward, and the ground provides an upward normal force. The front of the contact patch deforms and slows the tire, while the rear part restores more weakly and pushes it forward. The resultant normal force at point A is the sum of these opposing effects.

To keep the tire in equilibrium and maintain constant speed, a horizontal driving force F must act at the center of the tire. Using moment equilibrium about point A, the needed driving force can be written in terms of the rolling resistance coefficient a. This force is usually smaller than the force from kinetic friction, so rolling resistance is less harmful than sliding when a tire skids.

Rolling resistance is mainly caused by surface deformation, but adhesion and small-scale sliding between surfaces can also play a smaller role. These effects help explain why rolling wheels still lose some energy even when they do not appear to slip.

Tire Deformation and Rolling Resistance

dry friction

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kinetic friction

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self-locking screw

Screw Jack Self-Locking Behavior

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frictional forces on flat belts

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Friction Torque in Collar Bearings

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journal bearings

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rolling resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

rolling resistance: problem solving

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Learn how tire deformation creates rolling resistance, why a driving force is needed, and how it compares with sliding friction in moving wheels.

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Tire Deformation and Rolling Resistance

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