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

Rozważ podnośnik śrubowy z gwintem kwadratowym. Przyłożenie siły do jego uchwytu powoduje powstanie momentu skręcającego, który powoduje zbliżający się ruch w górę. Osiąga się to poprzez pokonanie tarcia statycznego między gwintami a podnośnikiem.
Rozważ całkowicie rozplątany gwint jako blok stykający się z rowkiem podnośnika i narysuj jego schemat swobodnego korpusu.
Moment skręcający wytwarza siłę poziomą, która popycha ruchomy gwint w górę po ustalonym nachyleniu gwintu podnośnika, a obciążenie wywiera siłę osiową na gwint.
Rowek wywiera siłę reakcji na gwint. Reakcja ta ma zarówno normalne, jak i cierne składniki, które są powiązane współczynnikiem tarcia.
Kąt tarcia statycznego dla zbliżającego się ruchu jest równy brązowej odwrotności współczynnika tarcia.
Teraz zastosuj równania równowagi dla sił wzdłuż osi poziomej i pionowej.
Przegrupowanie równań pod względem siły reakcji i ich zrównanie określa równanie równowagi momentów dla zbliżającego się ruchu w górę.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska: Statyka. Czternasta edycja, New Jersey: Pearson. Strony 432-433.</li>
	<li>Meriam, J.L., Kraige, L.G. i Bolten, J.N. (2016). Mechanika inżynierska: statyka i dynamika. Ósma edycja, Singapur: John Wiley & Sons. Strony 355-356.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. i Self, B.P. (2016). Mechanika wektorowa dla inżynierów. Jedenasta edycja, Nowy Jork: McGraw-Hill Education. Strony 451.</li>
</ol>

ruch wznoszący

Śruba podnosząca o wielu gwintach to mechaniczne urządzenie szeroko stosowane do podnoszenia ciężkich ładunków lub wywierania znacznej siły. Jej działanie polega na przekształceniu siły przyłożonej do uchwytu w moment obrotowy, powodujący ruch ku górze śruby. Ten ruch jest osiągany przez pokonanie tarcia statycznego między wątkami śruby a mechanizmem podnośnika.

Aby lepiej zrozumieć, jak działa śruba podnosząca, rozwinięty wątek można rozpatrzyć jako blok w kontakcie z występem podnośnika. Rysując diagram ciała swobodnego dla tego scenariusza, można analizować działające na system siły.

<img alt="Figure 1" src="/files/ftp_upload/14319/14319_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" />

Wytworzony moment obrotowy przez siłę przyłożoną do uchwytu generuje siłę poziomą, która unoszący się wątek popycha w górę nieruchomy wklęsły wątek podnośnika. Jednocześnie podnoszony ładunek wywiera siłę osiową na wątek.

Wklęsły wątek podnośnika wywiera siłę reakcji na wątek śruby. Siła reakcji składa się zarówno z elementów normalnych, jak i tarcia, które są ze sobą powiązane przez współczynnik tarcia. Kąt tarcia statycznego dla ruchu ku górze można określić, obliczając odwrotną tangens współczynnika tarcia.

<img alt="Equation 1" src="/files/ftp_upload/14319/14319_PT_Equation_1.png" style="text-align: center; height: 18px;" />

Na podstawie tych informacji można zastosować równania równowagi dla sił wzdłuż osi poziomej i pionowej.

<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;" />

Te równania umożliwiają analizę związku między siłą działającą, siłami reakcji ruchu śruby podnoszącej.

Przeorganizowanie równań pod względem siły reakcji i ich równoważenie dostarcza równania momentu równowagi dla ruchu ku górze.

<img alt="Equation 4" src="/files/ftp_upload/14319/14319_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

Rozwiązanie tego równania momentu równowagi pozwala określić minimalną siłę wymaganą przy uchwycie, aby rozpocząć ruch ku górze śruby podnoszącej. Obliczenie to umożliwia optymalizację projektu i działania śruby podnoszącej do różnych zastosowań, zapewniając jej skuteczne podnoszenie ciężkich ładunków lub wywieranie dużych sił, gdy jest to potrzebne.

Ruch wznoszący

Podnośnik śrubowy z gwintem kwadratowym jest urządzeniem mechanicznym szeroko stosowanym do podnoszenia ciężkich ładunków lub przykładania znacznej siły. Jego działanie opiera się na ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Friction

Tarcie

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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

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wedges

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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

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

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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

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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

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

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 Jack Force and Friction Analysis

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