Dimensioning Screw Jacks

1. Introduction

Proper dimensioning of a Screw Jack is essential for safe and efficient operation. This learning article explains the necessary calculations – from determining the required drive power to checking for buckling and critical speeds.

2. Motor power

Motor power is crucial to ensure that the lifting element can lift or move the required load. The motor's power should be sufficient to achieve the desired torque and speed, depending on the size and weight of the load to be moved.

2.1 Determining motor power

1. Dynamic lifting force Fdyn = m * g in kN (g = 9.81 m/s² where 10 m/s² is assumed)
2. Required drive speed

1. Drive torque of the system

1. From the drive torque and the required drive speed, the formula for determining the motor power PM is derived.

3. What is efficiency (%) and how is it calculated?

Imagine you want to lift a load using a screw. You turn the screw with force – that’s the input energy. The screw moves the load – that’s the useful (output) energy.

The efficiency tells you how much of your input energy is actually used to move the load – in other words, how efficient the system is.

Simply put:

1. 100% efficiency = no energy is lost
2. 50% efficiency = half of the energy is lost, e.g., due to friction
3. 10% efficiency = only a small part of the energy actually moves the load

So, efficiency helps you understand how “well” a drive system works.

3.1 Calculation

Efficiency is measured by comparing how much energy you put in and how much of it actually reaches the output. In other words:

Specifically for a Screw Drive

1. Measure the input power:

You measure the torque (how strongly you turn) and the rotational speed (how fast you turn), like this:

2. Measure the useful (output) power:

You measure how much force actually acts on the load and how fast it moves:

3. Then compare the two values:

Example:

1. You input 100 W (e.g., motor power)
2. At the end, 85 W actually move the load

→ The efficiency is 85%

Important to know: Some energy is always lost – for example, through friction, heat, or deformation. A high efficiency means that only a small amount of energy is lost.

4. Speed

The speed of a Screw Jack refers to the rate at which the linear motion of the Screw Jack occurs. It's important to understand how the speed works in your Screw Jack, as it has a significant impact on the performance and application.

The allowable spindle speed is then determined by:

The allowable speed is typically calculated without the nut. As a result, the unsupported spindle length changes permanently, and a higher speed may be permitted under certain circumstances.

5. Buckling

Buckling refers to the deformation or bending of lifting system components under the influence of compressive forces or loads. Buckling can occur when an elongated component, such as a spindle or a push rod, is subjected to a compressive load that exceeds a critical threshold.

Buckling can be avoided by selecting components with sufficient stiffness and limiting the load to values below the buckling load.

For a rough preliminary dimensioning, the following formula is sufficient:

5.1 Euler 1

5.2 Euler 2

5.3 Euler 3

To ensure that the components of your Screw Jack withstand the loads, buckling can be analyzed through more detailed calculations, which are shown below:

The limiting slenderness ratio indicates how slender or relatively thin a spindle is in relation to its length. A lower value means the spindle is relatively thick compared to its length, while a higher value indicates that the spindle is more slender in relation to its length.

A too high limiting slenderness ratio can lead to instability, causing vibrations or oscillations in the spindle. Conversely, a low limiting slenderness ratio may mean that the spindle is unnecessarily large and heavy.

If the slenderness ratio λ of the spindle is < λ0, the buckling calculation is performed according to Tetmajer (inelastic).

The slenderness ratio can be calculated using the following formula:

5.4 Determination of buckling stress according to Tetmajer

5.5 Determination of buckling stress according to Euler

6. Bending critical speed

Long, rapidly rotating spindles can begin to oscillate under both compressive and tensile loads. This calculation is considered in the critical speed. The critical speed must be taken into account only for the traveling nut version, as spindle rotation occurs only in this case. Factors to consider include the diameter and length of the spindle, as well as its bearing.

7. Lead angle

The lead angle is an important parameter in the dimensioning of Screw Jacks. It refers to the angle at which the threaded spindle or worm shaft of your Screw Jack is inclined. The lead angle affects how your Screw Jack converts linear motion into rotational movement and vice versa.

A larger lead angle results in more linear movement per revolution of the spindle or worm. A smaller lead angle leads to higher speed but lower force transmission, whereas a larger lead angle results in lower speed but higher force transmission.

Here is how to calculate the lead angle:

When dimensioning lifting platforms with threaded spindles as the drive mechanism, the following rules apply for the lead angle of the screw as well as any potential self-locking of the thread: