Name: screw torque and self-locking
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 21 s
Channel: JoVE

平均半径が20ミリメートル、リード線が10ミリメートルの角ねじのシャフトが、平均半径35ミリメートルのプレートギアと接触しているとします。ネジとギアの間の静摩擦係数は0.3です。
シャフトに8ニュートンメートルのねじりモーメントが加えられたときに圧倒される可能性のあるプレートギアの抵抗トルクを評価します。
最初に、静摩擦係数を使用して静摩擦角度を計算し、リードと平均半径の値を代入してリード角を決定します。
上向きの差し迫った動きの場合、シャフトに発生する軸力は、対応する値を代入することによって決定できます。
プレートギアの抵抗トルクは、シャフトの軸力とギアの平均半径の積に等しくなります。
値を代入することにより、加えられたねじりモーメントを圧倒できる抵抗トルクを決定できます。
ここでは、静摩擦角がリード角よりも大きくなっています。そのため、モーメントが取り除かれてもシャフトはセルフロックされます。

<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。434-437ページ。</li>
</ol>

ねじ：問題解決

機械工学では、ねじ軸とプレートギアの相互作用は、特定のねじ軸に対して適用される、ねじりモーメントによって打ち勝つことができるプレートギアの抵抗トルクを分析します。この概念をより理解するために、与えられた平均半径とリードを持つねじ軸と指定された平均半径を持つプレートギアを用いた一般的な状況を考えてみましょう。ねじとギアの静止摩擦係数も提供されます。

ねじ軸に適用される特定の捩じりモーメントによって打ち勝たれることができるプレートギアの抵抗トルクを評価するために、まずは静止摩擦係数を使用して静止摩擦角を計算する必要があります。静止摩擦角は、接触角の正接が静止摩擦係数と等しい角度のことを示します。

次に、リードと平均半径の値を代入してリード角を求めます。これは、リードを軸の円周に対する比率として定義されます。

軸方向の力、F、は、プレートギアを回転させる軸に沿った力を示します。特定の方向に対する運動の際、軸に発生する軸方向の力は、捩じりモーメント、静止摩擦角、リード角、および平均半径を使用して計算されます。

<img alt="Equation 1" src="/files/ftp_upload/14321/14321_PT_Equation_1v2.svg" style="text-align: center; height: 30px;" />

プレートギアに対する抵抗トルクは、軸の軸方向の力とギアの平均半径の積に等しいです。値を代入することで、適用された捩じりモーメントに打ち勝つことができる抵抗トルクが求められます。

また、静止摩擦角がリード角よりも大きい場合、モーメントが除去されても軸は自己ロックされます。

最後に、静止摩擦角、リード角、軸方向の力、および抵抗トルクを含む一連の計算を使用して軸が自己ロックされているかどうかを判断することができます。この分析は、様々な機械工学の応用における軸やギアの機械的な振る舞いを理解する上で重要です。

機械工学では、ねじ山シャフトとプレートギアの間の相互作用には、プレートギアの抵抗トルクの分析が含まれます...

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

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 needed for the torque analysis.

The axial force, F, acts along the axis of the shaft and drives the plate gear to rotate. For impending motion in a chosen direction, this force is found from a formula that uses the torsional moment, static friction angle, lead angle, and mean radius. The resisting torque on the plate gear is then the axial force multiplied by the gear’s mean radius.

By substituting the given values, the resisting torque can be determined and compared with the applied torsional moment. The same calculations also show whether the shaft is self-locking. If the static friction angle is greater than the lead angle, the shaft stays locked even after the moment is removed.

Screw Torque and Self-Locking

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 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

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 to calculate axial force, resisting torque, and self-locking for a threaded screw shaft and plate gear using friction and lead angle.

Screw Torque and Self-Locking | JoVE K12

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mechanical engineering

Screw Torque and Self-Locking

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