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

Stellen Sie sich eine Welle aus einer Vierkantgewindeschraube mit einem mittleren Radius von 20 Millimetern und einer Steigung von 10 Millimetern vor, die mit einem Plattengetriebe mit einem mittleren Radius von 35 Millimetern in Kontakt kommt. Der Haftreibungskoeffizient zwischen Schraube und Zahnrad beträgt 0,3.
Bewerten Sie das Widerstandsmoment am Plattengetriebe, das überlastet werden kann, wenn ein Torsionsmoment von acht Newtonmetern auf die Welle aufgebracht wird.
Berechnen Sie zunächst den Haftreibungswinkel anhand des Haftreibungskoeffizienten und bestimmen Sie den Steigungswinkel, indem Sie die Werte für Steigung und mittleren Radius ersetzen.
Für eine bevorstehende Aufwärtsbewegung kann die in der Welle entwickelte Normalkraft durch Einsetzen der entsprechenden Werte bestimmt werden.
Das Widerstandsmoment am Plattenrad entspricht dem Produkt aus der Axialkraft der Welle und dem mittleren Radius des Zahnrads.
Durch Ersetzen der Werte kann das Widerstandsmoment bestimmt werden, das das aufgebrachte Torsionsmoment überwältigen kann.
Dabei ist der Haftreibungswinkel größer als der Steigungswinkel. So ist die Welle selbsthemmend, auch wenn das Moment entfernt wird.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. S. 434-437.</li>
</ol>

schraube: problemlösung

In der Maschinenbautechnik besteht die Wechselwirkung zwischen einer Gewindeschraubenwelle und einem Zahnrad darin, das Widerstandsmoment am Zahnrad zu analysieren, das durch ein bestimmtes Torsionsmoment auf der Welle überwunden werden kann. Um dieses Konzept besser zu verstehen, betrachten wir eine generische Situation mit einer Gewindeschraubenwelle mit vorgegebenem mittleren Radius und Steigung und einem Zahnrad mit spezifiziertem mittleren Radius. Der Koeffizient der Haftreibung zwischen der Schraube und dem Zahnrad wird ebenfalls angegeben. Um das Widerstandsmoment am Zahnrad zu bewerten, das durch ein bestimmtes Torsionsmoment auf der Welle überwunden werden kann, ist der erste Schritt die Berechnung des statischen Reibungswinkels mithilfe des Koeffizienten der Haftreibung. Der statische Reibungswinkel, als φ bezeichnet, ist der Winkel, dessen Tangens gleich dem Koeffizienten der Haftreibung ist. Als nächstes wird der Steigungswinkel durch das Einsetzen der Werte der Steigung und des mittleren Radius bestimmt. Er entspricht dem Verhältnis von Steigung zur Umfangslänge der Welle. Die axial wirkende Kraft, als F bezeichnet, ist die Kraft entlang der Achse der Welle, die das Zahnrad zur Drehung veranlasst. Für eine bevorstehende Bewegung in eine bestimmte Richtung kann die in der Welle entwickelte axiale Kraft mithilfe einer Formel, die das Torsionsmoment, den statischen Reibungswinkel, den Steigungswinkel und den mittleren Radius enthält, bestimmt werden. <img alt="Equation 1" src="/files/ftp_upload/14321/14321_PT_Equation_1v2.svg" style="text-align: center; height: 30px;"> Das Widerstandsmoment am Zahnrad entspricht dem Produkt aus der axialen Kraft der Welle und dem mittleren Radius des Zahnrads. Durch Einsetzen der Werte kann das Widerstandsmoment bestimmt werden, das das aufgebrachte Torsionsmoment überwinden kann. Außerdem, wenn der statische Reibungswinkel größer ist als der Steigungswinkel, ist die Welle selbsthemmend, selbst wenn das Moment entfernt wird. Schließlich kann man durch eine Reihe von Berechnungen, die den statischen Reibungswinkel, den Steigungswinkel, die axiale Kraft und das Widerstandsmoment einschließen, feststellen, ob die Welle selbsthemmend ist. Diese Analyse ist entscheidend, um das mechanische Verhalten von Wellen und Zahnrädern in verschiedenen ingenieurwissenschaftlichen Anwendungen zu verstehen.

Schraube: Problemlösung

Im Maschinenbau geht es bei der Wechselwirkung zwischen einer Gewindespindelwelle und einem Plattenrad um die Analyse des Widerstandsmomentes am Plattenrad, das ...

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Mechanical Engineering

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Unit 1

Einheit 1

Friction

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KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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

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static friction

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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

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types of friction problems

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friction: problem solving

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wedges

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frictional forces on screws

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upward impending motion

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self-locking screw

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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

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flat belts: problem solving

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pivot bearings

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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...

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rolling resistance

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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

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mechanical engineering

Screw Torque and Self-Locking

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