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

Rozważmy wał z gwintem kwadratowym o średnim promieniu 20 milimetrów i skoku 10 milimetrów stykającym się z kołem zębatym płytkowym o średnim promieniu 35 milimetrów. Współczynnik tarcia statycznego między śrubą a kołem zębatym wynosi 0,3.
Oceń moment oporu na kole zębatym płytkowym, który może zostać przeciążony, gdy na wał zostanie przyłożony moment skręcający wynoszący osiem niutonometrów.
Początkowo oblicz kąt tarcia statycznego za pomocą współczynnika tarcia statycznego i określ kąt wyprzedzenia, podstawiając wartości ołowiu i średniego promienia.
W przypadku ruchu zbliżającego się do góry, siłę osiową powstającą w wale można określić, podstawiając odpowiednie wartości.
Moment oporu na płycie koła zębatego jest równy iloczynowi siły osiowej wału i średniego promienia koła zębatego.
Podstawiając wartości, można określić wyporny moment obrotowy, który może obezwładnić przyłożony moment skręcający.
W tym przypadku kąt tarcia statycznego jest większy niż kąt wyprzedzenia. Tak więc wał jest samoblokujący, nawet jeśli moment zostanie usunięty.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska: Statyka. Czternasta edycja, New Jersey: Pearson. Strony 434-437.</li>
</ol>

wkręty: rozwiązywanie problemów

W dziedzinie inżynierii mechanicznej analizuje się oddziaływanie pomiędzy gwintowanym wałem a kołem płytowym, analizując moment skręcający działający na koło, który może zostać przekroczony, gdy do wału zostanie zastosowany określony moment. Aby lepiej zrozumieć ten koncept, rozważamy sytuację ogólną z gwintowanym wałem o określonym promieniu średnim i kroku oraz kołem płytowym o określonym promieniu średnim. Podany jest również współczynnik tarcia statycznego pomiędzy wkrętem a kołem.

Aby ocenić moment skręcający działający na koło, który może zostać przekroczony, gdy do wału zostanie zastosowany określony moment skręcający, pierwszym krokiem jest obliczenie kąta tarcia statycznego przy użyciu współczynnika tarcia statycznego. Kąt tarcia statycznego, oznaczony jako φ, to kąt, którego tangens jest równy współczynnikowi tarcia statycznego.

Następnie, kąt wiodący jest określany poprzez podstawienie wartości kroku i promienia średniego. Jest równy stosunkowi kroku do obwodu wału.

Siła osiowa, oznaczona jako F, to siła działająca wzdłuż osi wału, która powoduje obrót koła. Dla ruchu zbieżnego w określonym kierunku siła osiowa wytworzona w wałku może zostać określona za pomocą wzoru, zawierającego moment skręcający, kąt tarcia statycznego, kąt wiodący i promień średni.

<img alt="Equation 1" src="/files/ftp_upload/14321/14321_PT_Equation_1v2.svg" style="text-align: center; height: 30px;" />

Moment przeciwdziałający na koło równa się iloczynowi siły osiowej wału i promienia średniego koła. Podstawiając wartości, można określić moment przeciwdziałający, który może przekroczyć zastosowany moment skręcający.

Także, jeśli kąt tarcia statycznego jest większy od kąta wiodącego, wał jest samoblokujący nawet po usunięciu momentu.

W końcu, można określić, czy wał jest samoblokujący za pomocą serii obliczeń dotyczących kąta tarcia statycznego, kąta wiodącego, siły osiowej i momentu przeciwdziałającego. Ta analiza jest kluczowa dla zrozumienia zachowania się mechanicznego wałów i kół w różnych zastosowaniach inżynieryjnych.

Wkręty: Rozwiązywanie problemów

W inżynierii mechanicznej interakcja między gwintowanym wałem śrubowym a kołem zębatym płytkowym polega na analizie momentu oporu działającego na koło zębate płytowe, które ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Friction

Tarcie

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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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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wedges

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frictional forces on screws

Square-Thread Screw Mechanics and Friction

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upward impending motion

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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

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flat belts: problem solving

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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

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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 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

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

Screw Torque and Self-Locking

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