Question

In the resistance spot welding process, the surface roughness at the contact between the copper electrode and the steel sheet is same as the roughness at the contact between the two steel sheets being welded (the average roughness is equal to 0.125 mm). Calculate the amount of heat generated at the electrode-sheet contact and at the steel sheet to steel sheet contact. The following data:

The resistivity of steel-7.5 x 10⁻⁷ ohm-metre;
The resistivity of copper = 1.77 × 10⁻⁸ ohm- metre;
The ratio of nominal area to true area = 10,000; current= 15 kilo-ampere during weld time of 300 milliseconds, the diameter of electrode is 25 mm.

Answer 1

The amount of heat generated at the electrode-sheet contact is approximately 6,075 Joules, and the amount of heat generated at the steel sheet to steel sheet contact is approximately 6,375 Joules.

To calculate the amount of heat generated at the electrode-sheet contact and at the steel sheet to steel sheet contact, we need to use Joule's law:

Heat (Q) = I²Rt

where:

I is the current (15 kA = 15,000 A)

R is the electrical resistance

t is the time (300 ms = 0.3 s)

Calculating the resistance at the electrode-sheet contact:

The resistance at the contact between the copper electrode and the steel sheet can be calculated using the following formula:

R_electrode = (ρ_steel * A_contact) / (A_nominal)

where:

ρ_steel is the resistivity of steel (7.5 × 10⁻⁷ ohm-meter)

A_contact is the true contact area between the electrode and the steel sheet

A_nominal is the nominal area of the electrode

We know that the ratio of nominal area to true area is 10,000, so we can calculate the true contact area:

A_contact = A_nominal / (ratio of nominal area to true area) = (π * (d/2)²) / 10,000

Plugging in the values:

A_contact = (π * (25 mm/2)²) / 10,000 ≈ 3.927 × 10⁻⁴ m²

Now we can calculate the resistance:

R_electrode = (7.5 × 10⁻⁷ ohm-meter * 3.927 × 10⁻⁴ m²) / (π * (25 mm/2)²) ≈ 1.45 × 10⁻⁵ ohm

Calculating the resistance at the steel sheet to steel sheet contact:

The resistance at the contact between the two steel sheets can be calculated using the same formula:

R_steel = (ρ_steel * A_contact) / (A_nominal)

In this case, the true contact area is the same as the nominal area, so we can simplify the formula:

R_steel = ρ_steel * t / (d * d)

Plugging in the values:

R_steel = (7.5 × 10⁻⁷ ohm-meter * 0.125 mm * 0.125 mm) / (25 mm * 25 mm) ≈ 1.5 × 10⁻⁵ ohm

Calculating the heat generated at each contact:

Now that we know the resistance at each contact, we can calculate the heat generated using Joule's law:

Heat_electrode = I²R_electrode * t = (15,000 A)² * (1.45 × 10⁻⁵ ohm) * 0.3 s ≈ 6.075 × 10³ Joules

Heat_steel = I²R_steel * t = (15,000 A)² * (1.5 × 10⁻⁵ ohm) * 0.3 s ≈ 6.375 × 10³ Joules