Calculating the solder wave pressure and penetration in gaps relationship.

For soldering SMDs mounted on the solder side of a PCB, the wave pressure to the board generally must be higher than for soldering components with protruding leads on the solder side. With higher wave pressures, the risk of solder flooding via gaps in the board increases. Here, the relation between solder pressure, gap dimensions and wetting power is explained using a calculation model. We make the assumption that solder pressure works only vertically.


where

Δh1 = relative wave height measured from the topside of the board

Δh2 = relative wave height measured from the underside of the board

b = board thickness
r = solder radius in gap
R = solder radius at SMD component
x = solder shadow zone
y = height of non-wettable component body.    

From Young and Laplace, we know the relation between liquid pressure, surface tension and capillary. This relation can be expressed as


where

Δh = liquid rise or depression (R can be positive or negative)
γ = the surface tension of the liquid
R = capillary radius (for small holes R1 = R2, for parallel gaps R2 = ∞)
d = liquid density
g = specific gravity.

If the known values for the surface tension, density and specific gravity are substituted, we find


If we assume that the board in Figure 1 contains a routed slot, we can substitute it as a parallel gap. In that case, we have the following relationship:


From Eq. 2, we can calculate the theoretical allowed wave height pressure Δh2 = Δh1 + b. For a specific gap “r,” we can calculate Dh1 for the case that the solder is just not penetrating to the top side of the board.

Note: In Eq. 2, however, r must be equal to or smaller than the board thickness “b”, so [r ≤ b] and not (r ≤ d). So the corrected Eq. 2 is Dh1 = 5 / r.

Example 1. When the board thickness is 1.6 mm and the board contains a routed gap of 4 mm, we find r = 2 mm. Since rmax = b, we calculate with r = 1.6 mm. This gives Δh1 = 3.1 mm and Δh2 = Δh1 + b = 4.7 mm. The maximum allowable wave height pressure in this case is 4.7 mm. Smaller gaps may permit higher pressures.

Keep in mind, however, that only the vertical solder pressure is taken into account in these examples. A horizontal pressure component enlarges the risk of solder flooding considerably. Note: This wave height pressure can be used only if the board is fitted in a pallet of sufficient thickness; otherwise solder will flood the board as it enters the solder wave. The board must be kept flat during soldering.

Wetting capacity on SMDs. When the maximum allowable wave height pressure is known, that figure can be used to calculate the theoretical wetting possibilities for SMDs. Using the figure for Δh2 from the previous calculation, it is possible to calculate the smallest radius R in which the solder is able to penetrate, using Eq. 1.

For this case we can transform Eq. 1 to:

for parallel gaps or R = 5 / Δh
for narrow gaps R = 10 / Δh

In most cases we have to calculate for dense circuits, and in such cases, it is realistic to calculate with the formula for narrow spaces:


Solder pads for SMDs. The relation between x, y and R in Figure 1 can be expressed using Pythagoras equation, as:


Now it is possible to calculate the relation between the SMD body height (y) and the shadow zone (x), where the solder is unable to penetrate, in case the SMD body surfaces are not wettable with solder. This allows calculation of the necessary solder pad dimensions for specific SMDs, in the event the wave height pressure must be limited for whatever reason. The solder pad dimension should at least extend the shadow zone (x in Figure 1) to enable solder to flow to the joint area.

Gerjan Diepstraten is a senior process engineer with Vitronics Soltec BV (vitronics-soltec.com); gdiepstraten@nl.vitronics-soltec.com. This column appears monthly.