how can we calculate the torque required for the expansion of tube having following specifications

outside dia. = 9.525mm

tube thickness = 1.245mm

yield of tube material = 25000

% elongation = 8%

expansion length = 12.700mm.

To calculate the torque required for the expansion of a tube, we need to consider several factors, including the material properties, dimensions, and the mechanics of how the tube will be expanded. Let's break this down step by step.

Understanding the Tube Specifications

We have the following specifications for the tube:

• Outside Diameter (OD): 9.525 mm
• Tube Thickness: 1.245 mm
• Yield Strength of Material: 25,000 psi
• Percentage Elongation: 8%
• Expansion Length: 12.700 mm

Step 1: Calculate the Inside Diameter

The inside diameter (ID) of the tube can be calculated using the outside diameter and the thickness:

ID = OD - 2 × Thickness

Substituting the values:

ID = 9.525 mm - 2 × 1.245 mm = 7.035 mm

Step 2: Determine the Cross-Sectional Area

The cross-sectional area (A) of the tube can be calculated using the formula for the area of a circle:

A = π/4 × (OD² - ID²)

Calculating the areas:

OD² = (9.525 mm)² = 90.675625 mm²

ID² = (7.035 mm)² = 49.490225 mm²

Now, substituting these values into the area formula:

A = π/4 × (90.675625 mm² - 49.490225 mm²) = π/4 × 41.1854 mm² ≈ 32.387 mm²

Step 3: Calculate the Required Force for Expansion

The force (F) required to expand the tube can be calculated using the yield strength and the cross-sectional area:

F = Yield Strength × A

Converting yield strength from psi to N/mm² (1 psi ≈ 0.00689476 N/mm²):

Yield Strength = 25,000 psi × 0.00689476 N/mm²/psi ≈ 172.37 N/mm²

Now, substituting the values:

F = 172.37 N/mm² × 32.387 mm² ≈ 5,573.48 N

Step 4: Calculate the Torque

The torque (T) required for expansion can be calculated using the formula:

T = F × r

Where r is the radius of the tube. The radius can be calculated as:

r = OD/2 = 9.525 mm / 2 = 4.7625 mm

Now, substituting the values into the torque formula:

T = 5,573.48 N × 4.7625 mm = 26,558.58 N·mm

Final Considerations

When performing these calculations, it’s important to consider safety factors and the specific application of the tube expansion. The calculated torque is a theoretical value, and real-world applications may require adjustments based on friction, material imperfections, and other factors.

In summary, by following these steps, you can effectively calculate the torque required for the expansion of a tube given its specifications. This method combines material science with mechanical engineering principles to ensure accurate results.