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When two metal conductors are in contact, an additional resistance known as contact resistance appears at the junction. This resistance is composed of two main components: the constriction resistance and the surface film resistance. The formula for contact resistance is:

Rj = Rs + Rb (1)

Where:

  • Rs: Constriction resistance
  • Rb: Surface film resistance

The total resistance of a conductor is given by:

R = Rl + Rj (2)

Where:

  • Rl: Inherent resistance of the conductor
  • Rj: Contact resistance

The inherent resistance Rl can be calculated using the formula:

R1 = ρ * l / s

Where:

  • ρ: Resistivity of the material
  • l: Length of the conductor
  • s: Cross-sectional area

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Additionally, the contact resistance is influenced by factors such as mechanical pressure, material hardness, and the number of contact points. For example:

F: Mechanical pressure applied to the two conductors (in Newtons)

HB: Brinell hardness of the materials

Digital camera: A coefficient related to material deformation, typically ranging from 0.3 to 1. When the contact surface is flat and elastic deformation dominates, this value is smaller. If plastic deformation occurs, the value is closer to 1.

N: Number of contact points

The surface film resistance Rb depends on the properties of the surface layer. As shown in the equations, when designing a product, R1 remains relatively constant, but changes in Rj affect the total resistance R. Since Rj is influenced by both Rs and Rb, it's crucial to control these factors during manufacturing.

For instance, poor riveting quality can increase contact resistance, leading to higher temperatures. In our factory, we've observed that replacing substandard rivets with qualified ones reduced average temperature rise by over 50 degrees. Similarly, welding issues—such as weak or incomplete welds—can reduce the effective cross-section of the conductor, increasing shrinkage resistance and causing significant temperature rise.

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Figure 1

In one test, a poorly welded phase showed a temperature rise exceeding the allowable range by 10–50°C. After replacing the contacts, the average temperature drop was more than 40°C. These problems often occur in critical areas like static/dynamic contacts, thermal components, and soft joints.

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Figure 2

Another important factor is contact pressure. The empirical formula for contact resistance and pressure is:

Rj = kj / (0.102F)^m

Where:

  • F: Contact pressure (in Newtons)
  • m: Coefficient depending on contact type
  • kj: Dependent on material, surface condition, and contact method

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Increasing the contact pressure F enhances the effective contact area and reduces the influence of surface films. This lowers both the constriction and film resistance. When the pressure is sufficient, the gas adsorption layer is minimized, and the surface film is crushed, leading to better conductivity and lower temperature rise.

Surface coatings also play a role. Many manufacturers now use tin or thin silver plating to reduce costs. However, tin has a much higher resistivity than silver, which increases Rb significantly. If the silver coating is too thin, the contact becomes similar to bare metal, making it prone to oxidation and further increasing resistance. Therefore, controlling the quality of surface coatings is essential for maintaining low contact resistance and ensuring safe operation of electrical devices.

As demonstrated, contact resistance has a major impact on the temperature rise of electrical appliances. To meet safety standards, it’s crucial to keep contact resistance as low as possible through proper design, material selection, and manufacturing processes.

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