Dry-electrode calendering is a process that compresses a dry active-material sheet to a target thickness using a pair of rolling rolls.
Problem Definition
There were reports that a domestic equipment maker had begun performance verification of dry-electrode process equipment on an all-solid-state battery maker’s mass-production line. The verification items can be summarized as process stability, electrode uniformity, and suitability for continuous operation. This is where a mechanical contradiction arises. Increasing the rolling load improves target-thickness uniformity, but it also increases the roll’s own deflection, which in turn produces width-direction thickness deviation. The question is this: to what level, relative to the electrode thickness tolerance, is the rolling-roll deflection allowable?
Kinematic Analysis
The calendering unit has a pair of rolling rolls arranged opposite each other to compress the sheet. The rolling load acts as a width-direction line load (N/mm), and the roll can be approximated as a simple beam supported by bearings at both ends. When roll self-weight and rolling reaction force overlap, center-span deflection occurs, which causes over-compression only at the sheet’s center. Correcting the deflection requires crown (convexity) machining or a preload structure on the opposing roll shaft.
Calculation and Formula Verification
The following is a design example condition (assumed values, confirm after field measurement). Roll bearing support span $L=750$mm, roll diameter $d=300$mm, steel material $E=210{,}000$N/mm², rolling line load $w=40$N/mm.
The second moment of area is as follows.
$$I=\frac{\pi d^4}{64}=\frac{\pi \times 300^4}{64}\approx 3.976\times10^{8}\text{mm}^4$$
The maximum deflection for a simply supported beam under uniformly distributed load is as follows.
$$\delta_{max}=\frac{5wL^4}{384EI}\approx 1.97\times10^{-3}\text{mm}=1.97\mu m$$
This deflection value already consumes most of the ±2μm electrode thickness-uniformity tolerance. That is, roll deflection alone leaves almost no tolerance margin.
The maximum bending stress is as follows.
$$M=\frac{wL^2}{8}\approx 2{,}812{,}500\text{N·mm},\quad \sigma_{max}=\frac{Mc}{I}\approx 1.06\text{N/mm}^2$$
Against the alloy steel’s yield strength of approximately 350N/mm², the strength-based safety factor exceeds 300×, effectively an over-designed region. The results of the dual safety-factor verification are as follows: the strength-based SF is 10 or higher, an excessive margin. The deflection-based SF, obtained by dividing the 2μm tolerance by the calculated 1.97μm, is approximately 1.02 — effectively no margin. The deflection-based criterion governs the real safety factor for this process.
Shop-notes
A deflection-based SF of 1.02 is at a dangerous level from a field tolerance-management standpoint. Roll crown machining (center-convex machining) to offset deflection is adopted as the primary alternative. A hydraulic bending-roll alternative (adding a separate bending cylinder on the opposing shaft) was also reviewed but not adopted. The reasons are as follows: compared with crown machining, it increases part count and therefore failure points, and it requires constant bending-force re-adjustment as temperature changes, raising the risk of an engineering change order (ECO). Machinability note: crown amount is typically machined in the 10–30μm range per 1m of roll length, and actual verification with a profile gauge after precision grinding is required. If grinding tolerance is not separately specified on the drawing, deviation will occur from the supplier’s arbitrary machining. Roll diameter, material, and actual line-load values should be confirmed after field measurement.
Design-Reflection Checklist
- Roll crown amount specified on drawing
- Deflection-based safety factor calculated
- Actual field-measured line-load value reflected
- Profile measurement verification performed after crown machining
One-line summary: For dry-electrode calendering rolls, deflection (rigidity) — not strength — governs the design, and without crown machining the tolerance margin is effectively exhausted.