Electrodeposition Coating Tank Blending: Replacement Rate Calculation and Renewal Time Control Case Study
Project Background
An automotive body cathodic electrodeposition (CED) line needed to switch to a coating from a different supplier because of tightening quality requirements and cost pressure. Instead of draining and refilling the tank, the plant chose tank blending — a method widely adopted in production for both environmental protection and economic efficiency. Because fresh coating can only be added after a portion of the bath has been consumed, the customer needed a theoretical basis linking renewal time, applied quantity and replacement ratio before approving the switch.
Challenge
- Predict at which point the replacement rate would be high enough to deliver stable film appearance and performance.
- Avoid overdosing fresh coating, which locks up capital and extends blending risk on a line running every day.
- Build a laboratory tank-blending simulation test that reproduces real production conditions.
Consumption and Renewal Model
After initial filling, a large quantity of coating sits in the tank. During production, aged coating is consumed daily and fresh coating is replenished to keep solids content and other bath parameters stable, so the bath is under continuous dynamic renewal. A consumption-and-renewal model was established on three assumptions:
- The tank volume remains constant, so the total mass of electrodeposition coating in the tank Mn is fixed and denoted M.
- After replenishment the bath solids content stays stable; daily consumption mass equals daily replenishment mass m, with a constant rate V = m/M.
- Continuous circulation and agitation achieve homogeneous mixing, and aged and fresh coating are consumed proportionally as film formation proceeds.
Calculation Method
By definition of the renewal period, T.O (d) = M/m, hence V = m/M = 1/T.O. On day n, the mass fraction of the aged component a is Pa,n = (1 − m/M)n = (1 − V)n = (1 − 1/T.O)n (Equation 1), and the fresh component b is Pb,n = 1 − Pa,n (Equation 2). The cumulative mass of fresh coating added is ΣMb = n·m (Equation 3). Rearranging Equation 1 logarithmically gives n = log(1−m/M) Pa,n (Equation 4).
For a differentiated, continuous model — consumption and feeding treated as dropwise addition with m approaching infinitesimal and n approaching infinity — the aged fraction becomes Pa,x = e−x (Equation 5) and the fresh fraction Pb,x = 1 − e−x (Equation 6), where x = nM/M is the number of renewal times. The same equations can be applied at x T.O once the renewal cycles are known.
Line Data Used for the Calculation
| Parameter | Value |
|---|---|
| Tank volume | Approx. 200 m³ |
| Typical bath solids content | 20% |
| Total mass of coating in bath, M | 100 t |
| Daily consumption / replenishment mass, m | 2 t |
| Renewal period, T.O = M/m | 50 d |
Results: Replacement Rate Against Feeding Time
Applying Equation 6 with T.O = 50 d to the line data gives the following calculated progression:
| Feeding days (n) | Renewal times (x = n/T.O) | Fresh coating fraction Pb,x |
|---|---|---|
| 10 | 0.2 | 18% |
| 25 | 0.5 | 39% |
| 50 | 1.0 | 63% |
| 100 | 2.0 | 86% |
The replacement rate rises rapidly at the early stage of switching. As production continues, the fresh fraction keeps increasing while the incremental rate of replacement gradually slows down — the practical reason why blending programmes should be planned around a target window rather than chasing complete replacement.
Two Working Scenarios Delivered to the Plant
- Scenario 1: calculate the fresh coating fraction (renewal replacement rate) from the total fresh coating charged so far by first working out the renewal times.
- Scenario 2: specify a target fresh coating fraction, then calculate the required renewal times and the total fresh coating dosage.
Representative key data sets were tabulated for both scenarios so that operators can read off dosage and timing directly on the shop floor.
Outcome
The model gave the customer a quantitative switching plan: renewal period fixed at 50 days, dosage and replacement rate linked by a single equation, and a simulation test design for laboratory verification. Quality control and risk assessment could then be implemented both theoretically and on the production floor, protecting film performance while avoiding unnecessary paint consumption.
