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

考虑一个方牙螺纹千斤顶。在手柄处施加力会产生扭转力矩，从而使螺杆产生向上的即将发生的运动。这一过程通过克服螺杆螺纹与千斤顶之间的静摩擦力来实现。
将完全展开的螺纹视为与千斤顶沟槽接触的一个整体，并绘制其受力分析图。
扭转力矩产生一个水平力，推动可动螺纹沿千斤顶螺纹的固定斜面上升，而载荷则对螺纹施加轴向力。
沟槽对螺纹施加一个反作用力。该反作用力包含法向分量和摩擦分量，二者通过摩擦系数相关联。
即将发生运动时的静摩擦角等于摩擦系数的反正切值。
现在，应用沿水平轴和垂直轴的力的平衡方程。
将方程重新整理为反应力的表达式并令其相等，可确定向上即将运动时的力矩平衡方程。

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	<li>希伯勒，RC（2016 年）。工程力学:静力学。第十四版，新泽西州:皮尔逊。第 432-433 页。</li>
	<li>Meriam， JL， Kraige， LG 和 Bolten， JN（2016 年）。工程力学:静力学和动力学。第八版，新加坡:John Wiley & Sons。第 355-356 页。</li>
	<li>比尔，FP，约翰斯顿，ER，Mazurek，DF，康威尔，PJ 和塞尔夫，BP（2016 年）。工程师的矢量力学。第十一版，纽约:麦格劳-希尔教育。第 451 页。</li>
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螺旋上升运动

方螺纹蜗轮千斤顶是一种被广泛用于提升重物或施加巨大力量的机械装置。它的运作原理是将施加在手柄上的力转化为扭矩力矩，从而导致螺杆产生向上的运动。这种运动是通过克服螺杆与千斤顶之间的静摩擦力来实现的。

为了能够更好地理解方螺纹蜗轮千斤顶的功能，可以将完全展开的螺纹视为与千斤顶凹槽进行接触的块。通过绘制该场景中的受力分析图，我们可以分析作用在该系统中的力。

<img alt="Figure 1" src="/files/ftp_upload/14319/14319_PT_Figure_1v2.svg" style="text-align: center; height: 300px;">

通过手柄施加的力所产生的扭矩力矩来产生一个水平力，将可移动的螺纹推向固定的斜坡上来。同时，被提升的负载能够对螺纹施加轴向的力。

千斤顶的凹槽对螺纹施加一个反作用力。这个反作用力是由法向力和摩擦力这两个部分组成，它们通过摩擦系数来相互关联。通过计算摩擦系数的反正切可以得出即将发生运动的静摩擦角。

<img alt="Equation 1" src="/files/ftp_upload/14319/14319_PT_Equation_1.png" style="text-align: center; height: 18px;">

With this information, apply the equilibrium equations for the forces along the horizontal and vertical axes.

<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;">

有根据此信息，可以使用平衡方程来计算出位于水平和垂直轴上的力。

这些方程允许对其中所施加的力、反作用力和螺纹千斤顶运动之间的关系来进行分析。

通过将方程置换为反作用力并使它们相等，那么则可以得到向上运动的力矩平衡方程。

<img alt="Equation 4" src="/files/ftp_upload/14319/14319_PT_Equation_4v2.svg" style="text-align: center; height: 13px;">

通过解决这个力矩的平衡方程，可以确定启动螺纹千斤顶向上运动所需的最小力。这个计算可以使得针对各种应用对螺纹千斤顶的设计和操作进行优化，以确保它能够有效地提升重物或其所施加较大的力。

方牙螺纹千斤顶是一种广泛用于提升重物或施加较大力的机械装置。其工作原理基于……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Friction

摩擦

KEY TERMS AND CONCEPTS

关键术语与概念

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

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upward impending motion

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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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