Name: sizing a solid power transmission shaft
Uploaded: 2024-05-23T12:59:58.000Z
Duration: 1 min 9 s
Channel: JoVE

Un arbre plein tourne, transmettant la puissance du moteur à une machine-outil reliée à l’engrenage. Étant donné la contrainte de cisaillement admissible, calculez le plus petit diamètre possible de l’arbre plein.
Tout d’abord, calculez le couple exercé sur l’engrenage à l’aide de la révolution de l’arbre et des valeurs de transmission de puissance.
Les forces tangentielles correspondantes agissant sur les engrenages sont calculées à l’aide du couple.
Les diagrammes de moment de flexion déterminent les valeurs de moment de flexion des forces agissant sur les plans horizontal et vertical.
Pour toutes les sections transversales potentiellement critiques, calculez la racine carrée de la somme des carrés des moments de flexion et de torsion.
Obtenir le rapport du moment polaire en substituant les valeurs connues et calculées dans la relation qui assimile la contrainte de cisaillement au rapport du moment polaire et à la valeur maximale dérivée de la racine carrée de la somme des carrés des moments de flexion et de torsion.
Enfin, déterminez le rayon de l'arbre et le plus petit diamètre admissible à l'aide de la valeur du rapport de moment polaire.

arbres de transmission : résolution de problèmes

La conception d'un arbre plein qui transmet la puissance d'un moteur à une machine-outil implique une série de calculs pour garantir que l'arbre peut résister aux contraintes appliquées par les moments et les couples de flexion. Calculez d’abord le couple exercé sur l’engrenage, en tenant compte de la puissance transmise par l’arbre et de sa vitesse de rotation. Ensuite, calculez les forces tangentielles agissant sur les engrenages, qui sont directement liées au couple et au rayon de l'engrenage.

Ensuite, utilisez les diagrammes de moment de flexion de l'arbre pour identifier les valeurs de moment de flexion dues aux forces agissant dans les plans horizontaux et verticaux. Au niveau des sections transversales potentiellement critiques de l'arbre, déterminez les contraintes combinées de ces moments de flexion et de torsion en calculant la racine carrée de la somme des carrés de ces valeurs. Cette analyse permet d'évaluer si l'arbre peut supporter la contrainte sans défaillance. Ensuite, calculez le moment d'inertie polaire, qui est essentiel pour relier la contrainte de cisaillement aux moments de torsion et de flexion.

<img alt="Equation 1" src="/files/ftp_upload/15664/15664_Equation_1.svg" style="text-align: center; height: 58px;">

Ce calcul vérifie la capacité de l’arbre à supporter les forces appliquées. Enfin, calculez le diamètre minimum requis de l’arbre en fonction du moment d’inertie polaire, en vous assurant qu’il peut résister aux contraintes calculées avec une utilisation minimale de matériau tout en respectant les normes de sécurité et de performance.

Arbres de transmission : résolution de problèmes

Un arbre plein tourne, transmettant la puissance du moteur à une machine-outil reliée à l’engrenage. Étant donné la contrainte de cisaillement admissible, calculez le ...

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Transmission Shafts: Problem Solving

sizing a solid power transmission shaft

A solid power transmission shaft must be sized so it can carry both torque and bending loads. In this problem, the shaft connects a motor to a machine tool through a gear, so the design must resist the stress created by rotation and force transfer.

The first step is to calculate the torque on the gear. This uses the power carried by the shaft and its rotational speed. The tangential force on the gear is then found from the torque and the gear radius.

Next, bending moment diagrams are used for the shaft. These diagrams show the bending moments produced by forces in the horizontal and vertical planes. At critical transverse sections of the shaft, the bending and torsional stresses are combined by taking the square root of the sum of the squares of these values.

That combined-stress check helps show whether the shaft can resist failure under the applied loading. The polar moment of inertia is then calculated. This value links shear stress with torsion and bending moments and is used to verify the shaft’s strength.

The final step is to find the minimum required shaft diameter from the polar moment of inertia. This gives a solid shaft size that can handle the calculated stresses while using as little material as possible. The design must still meet safety and performance standards.

Sizing a Solid Power Transmission Shaft

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design of transmission shafts - stress analysis

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transmission shafts: problem solving

A solid power transmission shaft must be sized so it can carry both torque and bending loads. In this problem, the shaft connects a motor to a machine tool through a gear, so the design must resist the stress created by rotation and force transfer. The first step is to calculate the torque on the gear. This uses the power carried by the shaft and its rotational speed. The tangential force on the gear is then found from the torque and the gear radius. Next, bending moment diagrams are used for...

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key terms and concepts

Learn how a solid transmission shaft is sized by calculating torque, tangential force, bending moments, combined stress, and minimum diameter for safe design.

Sizing a Solid Power Transmission Shaft | 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.

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Sizing a Solid Power Transmission Shaft

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