How to select and calculate the ball screw

             A ball screw is a mechanical component that transfers rotational motion to linear motion or the other way around. It is frequently used in machine tools, industrial machinery, and precision equipment that requires exact linear motion.

A ball screw is made up of a screw shaft and a ball nut. A helical groove is carved into the surface of the screw shaft, and the ball nut has a corresponding pair of ball bearings that roll down the groove as the shaft turns. This rolling motion turns the shaft's rotating motion into the nut's linear motion.

Ball screws have been selected over other types of screws because they are more accurate, have less friction, and are more efficient. They can also withstand larger weights and speeds than other screw kinds. They are also less prone to wear and require less maintenance.

Ball screws are used in many kinds of applications such as CNC machines, robotic arms, medical equipment, and aerospace components. They are frequently used in applications requiring precise positioning, such as machine tools and manufacturing lines.

 

Type Of Ball Screw

There are various types of ball screws, each designed to satisfy the specific needs of various applications. The following are some of the most frequent types of ball screws:

1. Ground ball screws: These are precision ball screws with tight tolerances for maximum accuracy and repeatability. They are commonly employed in applications requiring high precision and smooth operation, such as CNC machines and medical equipment.

2. Rolled ball screws: These ball screws are less expensive than ground ball screws because the thread form is rolled onto the surface of the screw shaft rather than ground. They may not, however, provide the same level of precision as ground ball screws.

3. Miniature ball screws: These are little ball screws that are commonly employed in applications with restricted space, such as microscopes and other small precision devices. They have good precision and little friction, although their load capacity may be lower than that of bigger ball screws.

4. Large diameter ball screws: These ball screws are intended for use in heavy-duty applications requiring high load capacity and rigidity, such as heavy machinery and construction equipment.

5. High-lead ball screws: These ball screws have a bigger lead angle than regular ball screws, allowing them to move further every revolution. They are frequently employed in applications requiring high speed and quick travel, such as automation equipment and machine tools.

 

How To Choose A Ball Screw

To calculate a ball screw, you must first determine its important parameters, such as lead, pitch, diameter, and torque capacity, to guarantee that it can execute the intended application accurately and efficiently. In this tutorial, we will go through how to calculate ball screws in depth.

1.  Determine the Ball Screw's Lead The lead is the distance travelled by the nut in one screw revolution. Divide the screw pitch by the number of starts to get it. The pitch of the screw is the distance between consecutive threads, while the number of starts is the number of independent threads on the screw shaft.

If the screw pitch is 5mm and the number of starts is 4, the lead is computed as follows:

Lead = Screw Pitch / Number of Starts

Lead = 5mm lead / 4mm

lead = 1.25mm

2. Determine the Screw Shaft Diameter The maximum load and maximum bending moment experienced by the ball screw dictate the diameter of the screw shaft. The diameter is computed as follows:

d = ((16 * M) / (π * ut))^1/3

Where

d is the screw shaft diameter,

M is the critical bending moment,

ut is the screw shaft material's ultimate tensile strength.

To determine M, you must first know the maximum load that the ball screw will be subjected to as well as the distance between the supports. The following formula can be used to calculate the critical bending moment:

M = (W * L^2) / 4

Where

W represents the maximum load

L represents the distance between the supports.

If the maximum load is 1000N and the distance between the supports is 200mm, the critical bending moment is computed as

M = (W * L2) / 4

M = (1000N * (0.2m)2) / 4

M = 10Nm

To calculate the diameter of the screw shaft, we must first determine the screw shaft material's ultimate tensile strength. Consider the ultimate tensile strength to be 500 MPa. The diameter of the screw shaft can be calculated using the formula above.

d = ((16 * M) / (π * ut))^1/3

d = ((16 * 10Nm) / (π * 500MPa))^1/3

d = 12.05mm

3. Calculate the Torque Capacity The torque capacity of a ball screw is determined as follows:

T = (π/16) * d^3 * sy

Where

T is the torque capacity,

d is the screw shaft diameter, and

sy is the screw shaft material's yield strength.

To calculate torque capacity, we must first determine the yield strength of the screw shaft material. Let us suppose the yield strength is 450 MPa. Using the preceding formula, the torque capacity of the ball screw is:

T = (π/16) * d^3 * sy

T = (π/16) * (12.05mm)^3 * 450MPa

T = 580.8 Nm

4. Determine the Critical Speed The critical speed is the maximum rotational speed of the ball screw without creating resonance or vibration. It is calculated using the following formula:

Nc = (30 * π * D) / √(L^2 - D^2)

Where

Nc denotes the critical speed,

D the screw shaft diameter,

L the length of the unsupported screw.

We need to know the length of the unsupported screw to determine the critical speed.

Assume that the length