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

חגורה שטוחה עוטפת שתי גלגלות, A ו- B, עם רדיוסים של 30 ס"מ ו -10 ס"מ , בהתאמה.
הזווית בין החגורה לאופקית היא 20 מעלות בגלגלות.
גלגלת B מסתובבת בכיוון השעון ומניעה את גלגלת A, מה שגורם למתח T2 בקצה אחד של החגורה ולמתח T1 בקצה השני.
בהתחשב בכך שהמתח המרבי המותר T2 הוא 1000 N ומקדם החיכוך הסטטי בין החגורה לגלגלות הוא 0.4, מהו המומנט המרבי בגלגלת A?
זווית המגע בין החגורה למשטח, המחושבת על פי הגיאומטריה של המערכת, היא 140 מעלות.
זווית המגע בין החגורה למשטח ברדיאנים והמקדם של ערכי החיכוך הסטטי מוחלפים בביטוי עבור מתחי חגורה לקבלת T1.
כאשר גלגלת B מסתובבת בכיוון השעון, הפרש מתח שנוצר בגלגלת B יוצר רגע בגלגלת A.
משורטט תרשים גוף חופשי עבור גלגלת A, ומוחל מצב שיווי המשקל.
ערכי הרדיוס והמתח מוחלפים כדי לקבל את המומנט המרבי.

<ol>
	<li>היבלר, R.C. (2016). מכניקה הנדסית - סטטיקה ודינמיקה. הובוקן, ניו ג'רזי: אולם פירסון פרנטיס. עמ' 439 \u2012 441.</li>
	<li>מרים, י"ל; Kraige, L.G. ובולטון, J.N. (2020). מכניקה הנדסית - סטטיקה. הובוקן, ניו ג'רזי: ג'ון ווילי. עמ' 372.</li>
	<li>באר, פ"פ; ג'ונסטון, א.ר.; מזורק, ד"ו; קרומוול, פי ג'יי ועצמי, ב. (2019). מכניקה וקטורית למהנדסים - סטטיקה ודינמיקה. ניו יורק: מקגרו-היל. עמ' 469-470.</li>
</ol>

חגורות שטוחות: פתרון בעיות

Flat Belts: Problem Solving

<div style="direction:rtl">

חגורות שטוחות הן חיוניות ביישומים תעשייתיים רבים מכיוון שהן עוזרות להעביר כוח מגלגלת אחת לאחרת. מושג הכוחות והמומנטים משמש לקביעת המומנט המרבי על גלגלת. לדוגמה, חשבו על חגורה שטוחה העוטפת שתי גלגלות, A ו-B, עם רדיוסים של 30 ס"מ ו-10 ס"מ, בהתאמה. הזווית בין החגורה לאופקי היא 20 מעלות בגלגלות. כאשר הגלגלת B מסתובבת עם כיוון השעון ומניעה את הגלגלת A, מתח T2 נגרם בקצה אחד של הרצועה, בעוד מתח T1 נוצר באחר.

<img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;"> 

זווית המגע בין חגורה למשטח, β,  חייב להיות מחושב כדי לקבוע את המומנט המקסימלי. זווית זו מתקבלת מהגיאומטריה של המערכת ונמצאת כ-140 מעלות. כתוצאה מכך, זווית המגע בין חגורה למשטח ברדיאנים, יחד עם ערך מקדם החיכוך הסטטי, 0.4, מוחלפת בביטוי למתחי החגורה. 
<img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;"> 

בהתחשב בכך שהמתח המרבי המותר T2 הוא 1000 N, הערך המחושב של T1 הוא 376.93 N. כאשר הגלגלת B מסתובבת עם כיוון השעון, נוצר הפרש מתח בגלגלתB, ויוצר רגע בגלגלת A. בהתחשב בתרשים גוף חופשי עבור גלגלת A, ה ניתן להחיל את המצב של מומנט שיווי משקל. <img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> 

ערכי הרדיוס והמתח מוחלפים כדי לקבל את המומנט המקסימלי של 186.921 ננומטר.</div>

חגורות שטוחות חיוניות ביישומים תעשייתיים רבים מכיוון שהן עוזרות להעביר כוח מגלגלת אחת לאחרת. נעשה שימוש במושג הכוחות והרגעים ...

Education

JoVE Core

Mechanical Engineering

הנדסת מכונות

Unit 1

יחידה 1

Friction

חיכוך

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

Dry Friction in Crates and Everyday Motion

Dry friction appears when two solid surfaces touch and try to move past each other. Students can see it when they walk, slide a box across a table, or rub their hands together. Even though it is common, the forces behind it are not easy to see. A simple crate on a rough horizontal floor helps explain the idea. When an external force pushes the crate sideways, two main forces act on it. The normal force acts perpendicular to the surface and helps balance the crate’s weight, while the frictional...

static friction

Static Friction at the Point of Slip

Static friction is the force that keeps two surfaces from starting to slide past each other. It acts when there is a tendency for motion, but not yet actual slipping. This force helps explain everyday actions like walking on the ground and driving a car. A towing example shows how static friction changes as force is applied. A truck pulls a car with a rope, and the car stays still at first. The car is in static equilibrium, which means the forces on it are balanced. Gravity and the normal...

kinetic friction

Sliding Friction Between Moving Surfaces

Kinetic friction is the sliding friction that acts when two surfaces move against each other. It opposes relative motion and acts parallel to the contact surface, in the opposite direction of travel. In the truck and car example, the car first stays still because static friction holds it in place. When the truck’s force becomes greater than the limiting static frictional force, the friction at the contact surface drops to a lower value. The car then begins to slide, and its speed increases. At...

characteristics of dry friction

Static and Kinetic Dry Friction

Dry friction is the resistance between two solid surfaces that move against each other without lubrication or any fluid. A common example is a gardener pushing a wheelbarrow across the ground. The wheel and the ground create dry friction that slows the motion. Before the wheelbarrow starts to move, static friction acts at the contact surface. Static friction is the force that opposes motion before slipping begins, and it helps keep the wheelbarrow stable. It is present only when there is no...

types of friction problems

Dry Friction in Crate, Ladder, and Frame Problems

Dry friction problems often focus on crates, ladders, and frames that are close to slipping. Dry friction is the force that resists relative motion, or the tendency for motion, between two surfaces in contact. In many physics and engineering problems, this force helps keep an object still or defines the point where motion is about to begin. One common case has no clear impending motion. A force may be applied to a crate, but the crate stays at rest. The friction force between the floor and the...

friction: problem solving

Friction on a Banked Road

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upward impending motion

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self-locking screw

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A square-threaded screw jack can hold a heavy load because of its self-locking behavior. This feature makes the device more reliable when it is used to lift large weights or apply a strong force. If the screw keeps its position after the turning moment is removed, the jack is self-locking. Self-locking happens because friction changes the way the forces act on the thread. The friction force reverses direction, and the reaction force moves to the other side of the thread’s normal. In this case,...

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frictional forces on flat belts

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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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Pivot bearings support axial loads on a rotating shaft. A bearing helps two parts move relative to each other while reducing friction and wear. In this design, the pivot is placed at the end of the shaft to carry the axial thrust. The pivot surface can be flat, conical, or truncated, depending on the application. In a flat pivot bearing, the axial load is spread over the bearing area. The pressure is uniform and can be found by dividing the load by the area. To study the forces more closely,...

collar bearings

Friction Torque in Collar Bearings

Collar bearings support axial loads on rotating shafts, and their friction helps determine the torque needed to start motion. They are used in many machines and may have a single collar or multiple collars, depending on the application and load needs. For a single collar bearing under an axial load, the contact area is the ring-shaped region between the external radius and the internal radius of the collar. If the bearing is assumed to support the load evenly, the uniform normal pressure is...

journal 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

Lawn Roller Force Calculation

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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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