Magnet Math

How to Calculate Powder Yield, Sintering Shrinkage, and Grinding Loss in NdFeB Magnet Production

Worked formulas for the five calculations that govern sintered NdFeB production: powder yield, sintering shrinkage, grinding loss, coating yield, and magnetization throughput.

Sintered NdFeB production runs alloy through five math checkpoints: powder yield after milling, dimensional shrinkage after sintering, mass loss after grinding, coating acceptance, and magnetization throughput. Each is a ratio with its own units, and each compounds into the next. A shop that holds 97 percent powder yield but only 70 percent machining yield still consumes about 1.5 kg of strip cast alloy for every kilogram shipped. This guide works each formula with real numbers so you can build the same stack for your own line. Inputs come from three places: floor scales at every transfer point, furnace and press logs, and final CMM or micrometer data. If you cannot weigh it, you cannot compute it.

Powder yield is usable jet milled powder divided by alloy charged, times 100. Charge 500 kg of strip cast flake into hydrogen decrepitation, then jet mill to a 3 to 5 micron D50. Ultrafines pulled off by the cyclone, oversize returns, and material held up in the mill typically cost 2 to 4 percent, so 500 kg in yields 485 kg of pressable powder, a 97.0 percent yield. Weigh the alloy on a calibrated scale before hydrogen decrepitation and weigh sealed powder containers after milling under nitrogen. The Powder Yield calculator accepts both weights plus a reclaim fraction, since oversize reworked through the mill should not be counted as loss twice.

Linear sintering shrinkage is S = (green length minus sintered length) divided by green length. Compacts press to about 4.4 g/cm3 and sinter to 7.55 g/cm3, so volume shrinks roughly 42 percent, but linear shrinkage is anisotropic: expect 15 to 20 percent along the alignment direction and 13 to 15 percent transverse. Worked example: a 60.0 mm green length that sinters to 49.8 mm gives S = 10.2 / 60.0 = 17.0 percent. To size tooling, divide the target dimension by (1 minus S): a 50.0 mm finished block at 17 percent shrinkage needs a 60.2 mm cavity. The Sintering Shrinkage calculator solves both directions from your green and sintered density measurements.

Grinding loss is mass removed divided by sintered block mass. A 5.2 kg sintered block sliced into 48 segments weighing 3.90 kg finished carries a 25.0 percent grinding loss. Budget the inputs directly: wire or blade kerf takes about 0.3 mm per cut, and each ground face carries 0.2 to 0.4 mm of stock allowance to clean the sintered skin and hold plus or minus 0.05 mm. Simple rectangles land near 15 to 20 percent loss, while thin arcs for rotor segments run 30 to 40 percent. Enter kerf count, stock per face, and part geometry into the Grinding Loss calculator to predict the number before you commit a block to the saw.

Coating yield is accepted coated parts divided by parts loaded, and it hides a mass calculation too. Standard NiCuNi plating builds 15 to 25 microns total; at nickel density 8.9 g/cm3, a 20 micron coat on a part with 25 cm2 of surface area adds about 0.45 g, which matters on a 20 g magnet with a tight weight spec. Typical plating reject rates run 2 to 6 percent from blisters, edge burn, and thin spots at racking contact points. Track loads in and accepted parts out per barrel or rack lot, then run the Coating Yield calculator to check whether your plater's losses match the invoice.

Magnetization capacity converts electrical numbers into parts per hour. Full saturation needs an applied field of at least 2 to 2.5 times intrinsic coercivity, so a grade with Hcj of 20 kOe wants 40 to 50 kOe, roughly 3200 to 4000 kA/m, inside the fixture bore. Capacitor discharge energy is E = 0.5 C V squared: a 3000 microfarad bank charged to 3000 V stores 13.5 kJ per pulse. With a 6 second charge and handling cycle and 4 parts per fixture, capacity is 2400 parts per hour. The Magnetization Capacity calculator ties bank energy, cycle time, and fixture count into one throughput figure you can schedule against.

Finally, multiply the stages to get the number that runs the business: compound yield. Take 0.97 powder, 0.98 press and sinter, 0.75 machining, and 0.96 coating: 0.97 x 0.98 x 0.75 x 0.96 = 0.684, so 68.4 percent of alloy mass ships as product and every finished kilogram consumes 1.46 kg of alloy. Recompute the stack monthly from weighed transfer data, not estimates, because a 3 point slip in machining yield moves alloy demand by roughly 65 kg per finished tonne. When one stage moves, rerun only that calculator and let the chain update; that is faster and less error prone than rebuilding the whole spreadsheet.

Published 2026-07-02.