Name: screw jack force and friction analysis
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 21 s
Channel: JoVE

角ネジのスクリュージャッキを考えてみましょう。ハンドルに力を加えると、ねじりモーメントが発生し、ねじが上向きに差し迫った動きを引き起こします。これは、ネジのねじ山とジャッキの間の静摩擦を克服することによって達成されます。
完全にほどけた糸をジャッキの溝に接触しているブロックと見なし、その自由体図を描きます。
ねじりモーメントは、可動ねじをジャッキねじの固定傾斜に押し上げる水平力を生成し、荷重はねじ山に軸方向の力を加えます。
溝はねじ山に反力を加えます。この反応には、垂直成分と摩擦成分の両方があり、摩擦係数を介して関連しています。
差し迫った運動の静摩擦の角度は、摩擦係数のタンの逆数に等しくなります。
次に、水平軸と垂直軸に沿った力の平衡方程式を適用します。
反力の観点から方程式を並べ替え、それらを等式化することで、上向きの差し迫った運動のモーメント平衡方程式が決まります。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。432-433ページ。</li>
	<li>メリアム、JL、クレイジ、LGおよびボルテン、JN(2016)。エンジニアリングメカニクス:静力学とダイナミクス。第8版、シンガポール:John Wiley & Sons。355-356ページ。</li>
	<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。451ページ。</li>
</ol>

上向きのスクリュー運動

四角いスクリュージャックは、重い荷物を持ち上げるためや相当な力をかけるために広く使用される機械装置です。その操作は、ハンドルにかけられた力を捩じれモーメントに変換し、スクリューの上向き運動を引き起こすことに基づいています。この運動は、スクリューの螺旋とジャックとの間の静止摩擦を克服することによって達成されます。

スクリュージャックがどのように機能するかをより理解するためには、完全に展開された螺旋をジャックの溝と接触するブロックと考えてください。この状況の自由物体図を描くことで、システムに作用する力を分析することができます。

<img alt="Figure 1" src="/files/ftp_upload/14319/14319_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" />

ハンドルでかかる力によって生成される捩じれモーメントは、可動スレッドをジャックスレッドの固定された斜面に押し上げる水平力を生み出します。同時に、持ち上げられている荷物はスレッドに軸方向の力をかけます。

ジャックの溝はスクリュースレッドに反力を及ぼします。この反力は、摩擦係数を介して関連する正規成分と摩擦成分からなります。迫りくる運動の静止摩擦の角度は、摩擦係数の逆正接を求めることによって決定することができます。

<img alt="Equation 1" src="/files/ftp_upload/14319/14319_PT_Equation_1.png" style="text-align: center; height: 18px;" />

この情報を用いて、水平軸と垂直軸にわたる力の平衡方程式を適用します。

<img alt="Equation 2" src="/files/ftp_upload/14319/14319_PT_Equation_2v2.svg" style="text-align: center; height: 28px;" />

<img alt="Equation 3" src="/files/ftp_upload/14319/14319_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

 これらの方程式によって、かかる力、反力、およびスクリュージャックの結果的な運動の関係を分析することができます。

反力を含んだ方程式を並べ替え、それらを等しくすることで上向きの迫りくる運動のモーメント平衡方程式を得ることができます。

<img alt="Equation 4" src="/files/ftp_upload/14319/14319_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

このモーメント平衡方程式を解くことにより、スクリュージャックの上向き運動を開始するために必要な最小の力をハンドルにかけることができます。この計算によって、さまざまな応用において効果的に重い荷物を持ち上げるか大きな力をかけるために、スクリュージャックの設計と操作を最適化することができます。

角ねじねじジャッキは、重い荷物を持ち上げたり、かなりの力を加えたりするために広く使用されている機械装置です。その動作は...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Friction

摩擦

KEY TERMS AND CONCEPTS

主要用語と概念

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 fixed incline of the jack thread. At the same time, the load acts downward as an axial force on the thread.

The groove of the jack also pushes back on the screw thread with a reaction force. That reaction force has both normal and frictional parts, and they are linked by the coefficient of friction. The angle of static friction for impending motion is found by taking the inverse tangent of the coefficient of friction.

With these force relationships, equilibrium equations can be written for the horizontal and vertical directions. These equations describe how the applied force, the reaction forces, and the motion of the screw jack are connected. Rearranging the equations in terms of the reaction force and setting them equal leads to the moment equilibrium equation for upward impending motion.

Solving that moment equilibrium equation gives the minimum force needed at the handle to start the screw jack moving upward. This result is useful for understanding how the jack is designed and operated. It also helps the jack lift heavy loads or apply large forces when needed.

Screw Jack Force and Friction Analysis

dry friction

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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

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self-locking screw

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key terms and concepts

Explore how a square-threaded screw jack uses force, friction, and equilibrium equations to lift loads and find the minimum handle force needed.

Screw Jack Force and Friction Analysis | JoVE K12

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mechanical engineering

Screw Jack Force and Friction Analysis

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