Ceramics Formulas

How to Calculate Sintering Shrinkage, Press Yield, and Grinding Time in Technical Ceramics

Worked formulas for sintering shrinkage allowance, press yield, fired dimensional yield, diamond grinding time, and thermal shock stress, with real units and numbers.

Every dimension on a technical ceramic drawing is the output of a calculation chain that starts at the powder hopper. A 96 percent alumina part shrinks 14 to 18 percent linearly during sintering, so the pressing die is cut oversize by that exact factor. Yields at pressing, firing, and grinding multiply, so a shop running 96, 94, and 97 percent at those three steps ships only about 88 parts per 100 pressed. This guide works through the five calculations that control those numbers, with real units and worked examples: shrinkage allowance, press yield, fired dimensional yield, diamond grinding time, and thermal shock stress.

Start with linear shrinkage. Green dimension equals fired dimension divided by (1 minus shrinkage), so a 25.00 mm fired length at 15.5 percent shrinkage needs a green dimension of 25.00 / 0.845 = 29.59 mm. Shrinkage itself comes from densities: S = 1 minus (green density / fired density)^(1/3). With a pressed green density of 2.35 g/cm3 and a fired density of 3.90 g/cm3, that cube root is 0.845, giving 15.5 percent. Measure green density on five pressed blanks by mass over dimensioned volume, not on one. The Sintering Shrinkage Allowance calculator runs both forms and flags when your die allowance and your density data disagree by more than 0.3 percent.

Press yield is good green parts divided by press cycles. Run 10,000 cycles, scrap 380 blanks for laminations, end capping, and cracked edges, and press yield is 96.2 percent. Track it with the Powder Press Yield calculator per die set, because a worn punch can drop yield 2 points before anyone notices it visually. Green body scrap rate is the mirror number, rejects over total, but count it in mass as well as pieces: 380 blanks at 22 g each is 8.4 kg of powder per shift, and unlike fired scrap it is usually recyclable. The Green Body Scrap Rate calculator splits rejects by defect type so you can Pareto laminations against density variation.

Fired dimensional yield is parts within tolerance after sintering divided by parts loaded, and it is governed by shrinkage variation, not the mean. If shrinkage varies plus or minus 0.3 percent around 15.5 percent, a 29.59 mm green part fires to 25.00 mm plus or minus 0.09 mm, so an as-fired tolerance of plus or minus 0.1 mm is barely capable and plus or minus 0.05 mm is not, which is why tight features go to grinding. Feed measured shrinkage spread and the drawing tolerance into the Fired Dimensional Yield calculator to predict yield before committing a kiln load. A predicted 90 percent yield on a 2,000 piece load means planning for 200 fired rejects.

Diamond grinding time is stock volume divided by removal rate, or in shop practice, passes times pass time. To face grind 0.25 mm of stock at 0.015 mm infeed per pass, you need 17 passes; at 10 seconds per pass plus 20 seconds of spark out and 30 seconds of handling, cycle time is 220 seconds, or 3.7 minutes per part. Removal rates for 96 percent alumina with resin bond diamond run 2 to 6 mm3 per second; fully dense zirconia grinds 30 to 50 percent slower. The Diamond Grinding Time calculator takes stock, infeed, feed rate, and part count and returns hours per lot, the number your grinding schedule hangs on.

Thermal shock capability sets test loads for burner nozzles, igniters, and weld fixtures. The first Hasselman parameter is R = strength times (1 minus Poisson ratio) divided by (elastic modulus times thermal expansion coefficient). For 96 percent alumina, R = 350 MPa x 0.78 / (300 GPa x 7.4e-6 per K) = 123 K, which matches the 120 to 150 C quench delta at which alumina test bars start cracking. Silicon nitride, with lower modulus and expansion, survives 500 to 750 C deltas. The Thermal Shock Test Load calculator converts a specified quench delta into peak thermal stress so you can set a water quench screen that catches flaws without breaking good parts.

Finally, chain the yields to size the pressing order. Rolled throughput yield is the product of step yields: 0.962 at pressing x 0.94 fired dimensional x 0.97 at grinding = 0.877. To ship 10,000 parts, press 10,000 / 0.877 = 11,403 blanks, and buy powder for that quantity plus 2 to 3 percent spillage and purge loss: 11,403 x 22 g x 1.025 = 257 kg. Every input in this chain is measurable on the floor within one week: five density blanks, one shift of press counts, one kiln load of dimensional data. Run the numbers before tooling is cut, because a 0.5 percent shrinkage error on a hard die is a 100 percent scrap rate.

Published 2026-07-02.