Designing a shaft, step by step

Shaft design is iterative by nature: you cannot know the notch factors until you know the diameters, and you cannot know the diameters until you know the notch factors. Here is a sequence that converges quickly.

1 — Layout first, numbers second

Decide where the bearings and the mounted components go before you decide any diameter. The axial layout fixes the bending moments, and the bending moments dominate everything else. Keep overhangs short and the bearing span only as long as it needs to be.

2 — Get the loads

Torque from P and n, then the gear and belt forces from chapter 2, each with its own angular position. Apply a service factor for shock now, not later.

3 — Reactions and moment diagrams in two planes

Then combine into the resultant M(x). Note the two or three candidate sections: the maximum moment, and any section with a nasty notch and a moment that is merely large.

4 — First diameter estimate

Use the DE-Goodman design form with the estimates from Table 7-1 (K_t = 1.7 for a decent fillet, 2.14 for a keyway, 5 for a ring groove), guess k_b ≈ 0.9, and take K_f = K_t as a conservative first pass. Round up to a standard size and a bearing bore.

5 — Build the real geometry

Now the steps, the shoulders, the actual fillet radii, the keyway positions and lengths. Standard proportions: D/d ≈ 1.2 at a bearing shoulder, r = d/10 where nothing is in the way, r ≈ 0.02d only where a bearing corner forces it.

6 — Check every section

This is what ShaftLab does automatically: the safety factor at each notch with the real K_t, the real q and the local k_b. Look at the n(x) curve and fix the minimum.

7 — Then the stiffness checks

Deflection at the gears, slope at the bearings, twist, critical speed. If one fails, scale all the diameters by the fourth-root ratio from chapter 7 rather than guessing.

8 — And the details

Key lengths, retaining-ring positions, the yield check with the stall torque, and — always — a look at where the fatigue crack would start if you had got it wrong.