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

일정한 속도로 굴러가는 타이어를 생각해 보십시오. 그것에 작용하는 힘은 무게와 수직력입니다.
접촉 표면이 변형되어 유한한 접촉 영역이 만들어집니다. 그 결과 각 접점에서 수직력이 분산됩니다.
이 영역의 앞부분은 변형을 겪어 롤링 동작을 지연시킵니다.
대조적으로, 뒷부분은 타이어를 앞으로 밀어내는 상대적으로 작은 복원을 거칩니다.
결과적으로 A에 작용하는 수직력은 이러한 힘의 합입니다.
타이어가 일정한 속도로 굴러가도록 하고 A에 대한 무게의 균형을 맞추기 위해서는 타이어 중앙에 수평 구동력을 가해야 합니다. 여기서 모든 힘은 동시적이어야 합니다.
점 A에서의 모멘트 평형 조건은 구름 저항 계수 측면에서 추진력을 제공합니다.
반경에 대한 구름 저항 계수를 곱한 무게는 일반적으로 운동 마찰 계수에 무게를 곱한 값보다 작습니다.
따라서 롤링 마찰력은 슬라이딩 힘보다 작습니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 452 \u2012 439쪽.</li>
	<li>메리암, J.L.; Kraige, L.G. 및 Bolton, J.N. (2020). 엔지니어링 역학 \u2012 정역학. 뉴저지 호보켄: 존 와일리. 372쪽.</li>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 469쪽.</li>
</ol>

굴림 저항

단단한 원통이 단단한 표면 위를 안정적으로 굴러갈 때, 원통의 표면이 가하는 수직력은 접점에서 접선과 수직입니다. 그러나 어떤 물질도 완전히 단단하지 않기 때문에, 원통에 대한 표면의 반응은 다양한 수직압을 포함합니다.

예를 들어, 비교적 부드러운 표면 위에서 굴러가는 단단한 실린더를 상상해 보세요. 실린더의 무게는 그 아래의 표면을 압축합니다. 실린더가 움직일 때, 앞쪽의 물질은 변형으로 인해 느려지고 뒤쪽의 물질은 변형된 상태에서 회복되어 실린더를 앞쪽으로 밀어냅니다. 이러한 방식으로 실린더에 작용하는 정상적인 압력은 실린더의 결과적인 힘인 Nd에 의해 묘사됩니다. 변형력(N)과 그 수평 성분은 일관되게 복원력(N)보다 크므로 실린더의 움직임을 유지하기 위해서는 수평 구동력이 실린더에 가해져야 합니다.

굴림 저항은 주로 이 효과로 인해 발생하지만, 접촉면 사이의 표면 접착력 및 상대적인 마이크로 슬라이딩에 의해 덜 영향을 받습니다.

이 개념을 더 설명하기 위해서 일정한 속도로 굴러가는 타이어를 생각해 보세요. 타이어에 작용하는 주요 힘은 타이어의 무게와 수직으로 아래로 작용하는 지면이 수직으로 위로 작용하는 수직력입니다. 타이어가 구르면서 접촉 영역의 앞부분이 변형을 경험하고, 이것은 타이어의 구르는 운동을 지연시킵니다. 이에 반해 뒷부분은 타이어를 앞으로 밀어내는 상대적으로 작은 복원력을 겪습니다. 최종 효과는 접촉 영역의 중심인 지점 A에서 작용하는 수직력이 이러한 반대력의 합이라는 것입니다.

<img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;">

타이어가 일정한 속도로 굴러가도록 유지하고 지점 A에 대한 무게의 모멘트의 균형을 맞추려면 타이어의 중심에 수평 구동력(F)이 가해져야 합니다. 평형을 이루기 위해서는 타이어에 작용하는 모든 힘이 동시에 가해져야 합니다.

단단한 실린더가 단단한 표면에서 꾸준히 굴러갈 때, 실린더의 표면에 의해 가해지는 수직력은 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Friction

마찰

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

wedges

Wedges and Self-Locking Stability

A wedge is a simple machine that can lift, support, and split heavy objects. It can also change the height of structural or mechanical parts. Because it amplifies force, a wedge makes it easier to move or hold large loads with less effort. One example is lifting a heavy slab. In that case, the wedge turns the applied force into a much larger force that acts almost perpendicular to the original push. That force change helps raise the load without requiring a large input force. To analyze wedge...

frictional forces on screws

Square-Thread Screw Mechanics and Friction

Square-threaded screws use a helical thread to turn force into lifting motion. They are common fasteners, but they are also useful for transmitting power and motion in machines. A jack with a square-threaded screw lifts heavy loads when force is applied at the handle and the screw turns. A screw can be viewed as a cylindrical shaft with an inclined square ridge wrapped around it. The distance between two neighboring threads is called the pitch. The lead is the distance the screw advances in...

upward impending motion

Screw Jack Force and Friction Analysis

A square-threaded screw jack lifts heavy loads by turning handle force into a twisting moment. Its upward motion depends on overcoming static friction between the screw threads and the jack. To study this motion, the thread can be treated as if it were a block on the groove of the jack after the thread is completely unraveled. A free-body diagram helps show the forces acting on this simplified system. The force at the handle creates a horizontal force that pushes the movable thread up the...

self-locking screw

Screw Jack Self-Locking Behavior

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,...

screw: problem solving

Screw Torque and Self-Locking

Screw torque and self-locking are analyzed by looking at a threaded screw shaft and a plate gear. The shaft has a mean radius and a lead. The plate gear also has a mean radius. The coefficient of static friction between the screw and the gear is part of the setup. The first step is to find the static friction angle, φ. This angle is defined by the coefficient of static friction. Next, the lead angle is calculated from the lead and the mean radius of the shaft. It gives the screw geometry...

frictional forces on flat belts

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...

flat belts: problem solving

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,...

pivot bearings

Axial Load Support in Pivot Bearings

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

Friction Moment in Journal Bearings

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...

bearings: problem solving

Double-Collar Bearing Torque Calculations

Double-collar bearing torque calculations show how friction and axial force affect bearing performance. Engineers use these calculations to test whether the bearing can handle the forces and moments it experiences during operation. This helps them choose and design bearings for specific applications and setups. For a double-collar bearing with set dimensions and an axial force applied, the maximum frictional moment can be found with a standard expression. The equation is rearranged, and the...

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

Lawn Roller Force Calculation

Rolling resistance is the force that makes a rolling object harder to move across a surface. It is also called rolling friction. It comes from deformation in the object and the surface that touch each other. Internal friction, hysteresis, and other energy losses in the materials also play a role. Because of this force, extra energy is needed to keep a wheel, tire, or ball moving. The video applies this idea to a lawn roller. The roller has a mass of 100 kg, a radius of 25 cm, and a coefficient...

key terms and concepts

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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