Name: friction’s role in machine efficiency
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 14 s
Channel: JoVE

機械の機械効率は、入力作業に対する出力の比率です。
理想的な機械の場合、比率は 1 であり、入力作業と出力作業が等しいことを意味します。
たとえば、木材を圧縮する理想的なトグルバイスでは、反力による出力仕事と、加えられた力による入力仕事と等しくなります。
それに対して、実際の機械は摩擦力を受けます。
摩擦力は、垂直反力から求めることができます。
寄与する力による仮想仕事の合計は、仮想仕事の原理で適用すると、入力仕事と摩擦力による仕事との差として出力仕事を与えます。
出力作業を入力作業で分割することで、機械効率が得られます。摩擦がない場合の効率は1つです。ただし、摩擦係数が 0 でない場合、効率は、トグル角度が摩擦角度と等しい場合は 0 になり、トグル角度が摩擦角度より小さい場合は負になります。
これは、ビスは摩擦角度よりも大きいトグル角度にのみ使用する必要があることを意味します。

<ol>
	<li>ビール、FP、ジョンストン、ER、マズレック、DF、コーンウェル、PJおよびセルフ、BP(2016)。エンジニアのためのベクトル力学。第11版、ニューヨーク:マグロウヒル教育。580-581ページ。</li>
</ol>

実機の機械効率について

機械の機械効率は、入力を出力にどれだけ効果的に変換できるかを表す基本的な概念です。この概念によれば、機械の効率は出力と入力の比率と等しいです。エネルギー損失のない理想的な機械は効率が1です。つまり、入力と出力は等しいということです。

しかし、現実には、どの機械も完全に理想的ではなく、すべてがある形式のエネルギー損失を経験します。機械のエネルギー損失の主な原因の1つは摩擦です。例えば、木製ブロックを圧縮するために使用される切替式バイスを考えてみましょう。摩擦がない場合、バイスの出力仕事は加わる力の入力仕事と等しいため、これは理想的な機械です。

しかし、現実には、バイスのスライディングブロックは水平面に対して摩擦力を受けます。実際のバイスの機械効率を求めるためには、まず、垂直反力と対応する摩擦力を計算します。次に、仮想変位中のすべての力の合計仮想仕事を評価します。仮想仕事の原理を適用すると、バイスの出力は入力と摩擦力の仕事の差となります。

その結果、ネット反力を計算することができます。バイスの角度が摩擦角と等しい場合、ネット反力はゼロになり、摩擦角より小さい場合は負になります。つまり、バイスは角度が摩擦角を超えた場合にのみ使用すべきです。

摩擦がない場合のバイスの機械効率は1です。しかし、摩擦が存在する場合、効率は摩擦係数によってゼロまたは1未満になることがあります。摩擦係数が小さいほど、効率は1に近づきます。逆に、摩擦係数が大きいほど、効率は低くなります。

機械の機械効率は、入力を出力にどれだけ効果的に変換できるかを説明する重要な概念です。現実には、どの機械も完全に理想的ではなく、摩擦によるエネルギー損失があるため、効率を分析する際には摩擦とその係数の影響を考慮することが重要です。理想的な機械は完璧な効率を達成できますが、実機は摩擦などのエネルギー損失により、常に理想的な効率以下となります。

機械の機械効率は、機械が入力作業を出力作業にどれだけ効果的に変換できるかを説明する基本的な概念です。...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Virtual Work

仮想仕事

KEY TERMS AND CONCEPTS

主要用語と概念

Mechanical Efficiency of Real Machines

friction’s role in machine efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work.

Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction.

To find the efficiency of a real vise, first calculate the normal reaction and the frictional force. Then use the principle of virtual work to evaluate the total virtual work of all the forces during a virtual displacement. With friction present, the output work equals the input work minus the work done by friction.

This analysis also gives the net reaction force. It is zero when the angle of the vise equals the angle of friction. It becomes negative when the angle is smaller than the angle of friction, so the vise should be used only when its angle is greater than the friction angle.

A vise with no friction has an efficiency of one. When friction is present, the efficiency can be less than one or even zero, depending on the coefficient of friction. A lower coefficient of friction gives an efficiency closer to one, while a higher coefficient lowers the efficiency.

Friction’s Role in Machine Efficiency

work

Work in Force and Motion

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Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

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Finding Forces with Virtual Work in Linked Bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

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Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

mechanical efficiency of real machines

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

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Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

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Types of Equilibrium in Mechanical Systems

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Spring-Mass Motion and Energy Stability

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stability of equilibrium configuration: problem solving

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Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Learn how friction lowers mechanical efficiency in real machines, using a toggle vise example, virtual work, and the angle of friction.

Friction’s Role in Machine Efficiency | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Friction’s Role in Machine Efficiency

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