Power Screws

In this tutorial, you will learn the basics of power screws, the basic terminology associated with them, requirements for their usage, and the derivation of some basic relations. You will understand what a power screw is and its usage in different applications depending on its design properties.

Contents:

1. What is a Power Screw?
2. Terminologies Associated with Screws
3. Types of Threads Used in Power Screws
4. Why Do We Use Multiple Thread Screws?
5. Torque Required to Lift Loads
6. Torque Required to Lower Loads
7. Self-Locking in Screws
8. Calculating Efficiency in Power Screws

What is a Power Screw?

A Power Screw is any mechanical device used to convert rotary motion into linear motion, usually to transmit power. As such, they often form major components in machines requiring precise movement and control of components.

• There are three major components of any power screw assembly, the screw, the nut, and the component which moves linearly and thus holds the screw and nut together. Depending on the application, either the screw rotates in a bearing and the nut moves linearly, or the nut is held stationary, and the screw moves axially.
• Power screws have a large mechanical advantage and significant load-bearing capacity. They are relatively easy to design and can be manufactured without any complicated machinery requirements. They are simple and quiet in operation and relatively easy to maintain.
• A major disadvantage of power screws is their poor efficiency, sometimes as low as 40%. Hence, they are not preferred for continuous power transmission and are often used for intermediate stepping motion. Also, friction tends to cause significant wear if not maintained properly.
• Power screws find application in Screw Jacks, Vices, various Clamps, CNC Machines, Universally Testing Machines, 3D printers, and much more.

Terminologies Associated with Screws

The diagram below depicts the various terms associated with any screw.

• Pitch: It is measured along the axis of the screw. It is the distance between one point on the thread and the corresponding point on the adjacent thread. It is denoted by the letter p.
• Lead: It is the distance along the screw axis by which the nut advances in one revolution of the screw.
  For a single-threaded screw, the lead equals the pitch; for a double-threaded screw, the lead is twice the pitch, and so on.
  It is denoted by letter l.
• Nominal Diameter: It is the largest diameter of the screw, and as such is often termed the major diameter.
  It is denoted by the letter d.
• Core Diameter: It is the smallest diameter of the screw, usually the diameter of the base shaft on which the threads are wound.
  It is denoted by the letter d_c.
  d_c = d – p.
• Helix Angle: It is the angle made by the inclined surface of the screw with a plane perpendicular to the axis of the screw. It is often called the lead angle. It is denoted by the symbol α.
• Mean Diameter: Mean diameter is derived using the below equation:
  d_m = d – 0.5 p.

Types of Threads Used in Power Screws

The form of thread used plays an important role when it comes to power transmission by power screws. These threads must be capable of transmitting loads with minimal friction and must not fail during use.

The diagram below shows the different types of cross section of threads.

As such, four major types of threads are used in power screws, which are compared in the table below:

Why Do We Use Multiple Thread Screws?

Multiple threaded power screws are used in applications where higher traveling speeds are required. They are often called multiple start screws. Usually, they have two or more threads cut side-by-side, spread evenly around the rod.

• It provides large axial motion per revolution of the screw. This significantly increases the traveling speed of the sliding member. For a double start screw, the traveling speed is twice that of the standard screw.
• The helix angle increases, significantly improving the efficiency of the screw.
• However, the mechanical advantage obtained from them is lower than that of a standard screw. Often, they lose the self-locking property and can be dangerous in a certain application.
• They are usually used in high-speed actuators and sluice valves.

Torque Required to Lift Loads

The diagram below shows the various forces acting on one screw thread when lifting the load

The various forces acting here are:

• Load W – acting vertically downward
• Normal Reaction N – Acts perpendicular to the inclined plane
• Frictional Force μN – Acts in the direction opposing the motion. Here μ = tan φ, where φ is friction angle
• Effort P – acts horizontally in the direction of motion

We can use these forces to analyze the problem

• Calculation of Effort
  Consider Equilibrium of Horizontal Forces
  P = μ N cos α + N sin α
  Consider Equilibrium of Vertical Forces
  W = N cos α – μ N sin α
  Divide the two
  \(\frac{P}{W} = \frac{μ cos α + sin α}{cos α – μ sin α}\)
  P = W \(\frac{μ + tan α}{1 – μ tan α}\)
  P= W \(\frac{tan φ + tan⁡α}{1- tanφtan⁡α}\)
  P = W tan (ϕ + α)
• Calculation of Torque
  M_t = P d_m/2
  M_t = \(\frac{W d_m}{2}\) tan(ϕ + α)

Torque Required to Lower Loads

The diagram below shows the various forces acting on one screw thread when lowering the load

The various forces acting here are:

• Load W – acting vertically downward
• Normal Reaction N – Acts perpendicular to the inclined plane
• Frictional Force μN – Acts in the direction opposing the motion. Here μ = tan φ, where φ is friction angle
• Effort P – acts horizontally in the direction of motion

We can use these forces to analyze the problem

Calculation of Effort
Consider Equilibrium of Horizontal Forces
P = μ N cos α – N sin α
Consider Equilibrium of Vertical Forces
W = N cos α + μ N sin α
Divide the two
\(\frac{P}{W} = \frac{μ cos α – sin α}{cos α + μ sin α}\)
P = W \(\frac{μ – tan α}{1 + μ tan α}\)
P= W \(\frac{tan φ – tan⁡α}{1 + tanφtan⁡α}\)
P = W tan(ϕ – α)

Calculation of Torque
M_t = P d_m/2
M_t = \(\frac{W d_m}{2}\) tan(ϕ – α)

Self-Locking in Screws

A screw is said to be self-locking if it will hold the load in place without any external effort. We know the torque to lower the load is given by M_t = \(\frac{W d_m}{2}\) tan(ϕ – α)

• When φ < α, the torque required is negative and no force is required to lower the load.
• In a condition when the load itself begins to move down, the screw is said to be over-hauling or back driving. This property is usually not useful except in certain applications like the Yankee Screwdriver.
• When φ ≥ α, positive torque is required to lower the load and the load will not turn the screw by itself. This is called the self-locking of the screw.
• Self-Locking is not possible for screws with a low coefficient of friction. The coefficient of friction decreases due to wear or excessive lubrication.
• Self-Locking is also lost when the lead of the screw is large. Therefore, multi-thread screws lack self-locking properties. A single-threaded screw is better for self-locking properties.

Calculating Efficiency in Power Screws

Here, we refer to the force diagram in a screw when lifting a load.
Work Output = Force x Distance Travelled in direction of force = W x l.
Work Input = Force x Distance Travelled in direction of force = P x πd_m
Hence, Efficiency η = \(\frac{Work\,Output}{Work\, Input} =
\frac{W l}{P \pi d_m} = \frac{W}{P} \left(\frac{l}{\pi d_m}\right)
\)

We know,
tan α = l/π d_m and P = W/tan (ϕ + α)

Thus,
η = \(\frac{tan α}{tan(ϕ + α)}\)

From the derived equation, we see that the efficiency of a screw is a function of friction angle and helix angle. As such, we can conclude that the efficiency of a screw depends on

• Mean Diameter of screw d_m
• Lead of Screw
• Coefficient of friction