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

Considérons un arbre de vis à filetage carré d’un rayon moyen de 20 millimètres et d’un fil de 10 millimètres en contact avec un engrenage à plaque de rayon moyen de 35 millimètres. Le coefficient de frottement statique entre la vis et l’engrenage est de 0,3.
Évaluez le couple de résistance sur l’engrenage à plaque qui peut être surpuissant lorsqu’un moment de torsion de huit newton-mètre est appliqué à l’arbre.
Initialement, calculez l’angle de frottement statique à l’aide du coefficient de frottement statique et déterminez l’angle d’attaque en substituant les valeurs de l’avance et du rayon moyen.
Pour un mouvement imminent vers le haut, la force axiale développée dans l’arbre peut être déterminée en substituant les valeurs correspondantes.
Le couple de résistance sur l'engrenage à plaque est égal au produit de la force axiale de l'arbre et du rayon moyen de l'engrenage.
En substituant les valeurs, il est possible de déterminer le couple de résistance qui peut dominer le moment de torsion appliqué.
Ici, l’angle de frottement statique est supérieur à l’angle d’attaque. Ainsi, l’arbre est autobloquant même si le moment est supprimé.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. P. 434 à 437.</li>
</ol>

vis : résolution de problèmes de vis

En génie mécanique, l'interaction entre un arbre fileté et un engrenage plat implique l'analyse du couple de résistance sur l'engrenage plat pouvant être surmonté lorsqu'un moment de torsion spécifique est appliqué à l'arbre. Pour mieux comprendre ce concept, considérons une situation générique avec un arbre fileté doté d'un rayon moyen et d'un pas donnés, ainsi qu'un engrenage plat doté d'un rayon moyen spécifié. Le coefficient de frottement statique entre la vis et l'engrenage est également fourni. Pour évaluer le couple de résistance sur l'engrenage plat pouvant être surmonté lorsque qu'un certain moment de torsion est appliqué à l'arbre, la première étape consiste à calculer l'angle de frottement statique en utilisant le coefficient de frottement statique. L'angle de frottement statique, noté φ, est l'angle dont la tangente est égale au coefficient de frottement statique. Ensuite, l'angle de pas est déterminé en substituant les valeurs du pas et du rayon moyen. Il est égal au rapport entre le pas et la circonférence de l'arbre. La force axiale, notée F, est la force agissant le long de l'axe de l'arbre qui fait tourner l'engrenage plat. Pour un mouvement imminent dans une direction spécifique, la force axiale développée dans l'arbre peut être déterminée en utilisant une formule impliquant le moment de torsion, l'angle de frottement statique, l'angle de pas et le rayon moyen. <img alt="Equation 1" src="/files/ftp_upload/14321/14321_PT_Equation_1v2.svg" style="text-align: center; height: 30px;"> Le couple de résistance sur l'engrenage plat est égal au produit de la force axiale de l'arbre et du rayon moyen de l'engrenage. En substituant les valeurs, le couple de résistance qui peut surmonter le moment de torsion appliqué peut être déterminé. De plus, si l'angle de frottement statique est supérieur à l'angle de pas, l'arbre est auto–bloquant même si le moment est supprimé. Enfin, on peut déterminer si l'arbre est auto–bloquant grâce à une série de calculs impliquant l'angle de frottement statique, l'angle de pas, la force axiale et le couple de résistance. Cette analyse est cruciale pour comprendre le comportement mécanique des arbres et des engrenages dans différentes applications d'ingénierie.

Vis : Résolution de problèmes de vis

En génie mécanique, l’interaction entre un arbre de vis fileté et un engrenage à plaque implique l’analyse du couple de résistance sur l’engrenage ...

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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

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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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