Parallel Key Stress Design Simulator — Shear & Bearing Stress

Parameters

Transmitted power P

Rotational speed N

rpm

Shaft diameter d

Key width b

Key height h

Key effective length L

Key material

Sets the yield strength σ_y

Target safety factor S

Design is NG below this value

Results

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Torque T (N·m)

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Shear stress τ (MPa)

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Bearing stress σ_c (MPa)

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Shear safety factor

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Bearing safety factor

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Required key length (mm)

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Shaft–key–hub cross-section

Torque flows from the shaft (centre) through the key to the hub (outer ring). The cyan line is the shear plane; the key sides are the bearing faces. Colour shows the safety factor (green = margin / red = short).

Stress vs key length L

Safety factor comparison (shear, bearing, target)

Theory & Key Formulas

$$T = \frac{9549\,P}{N}, \qquad F = \frac{2T}{d}$$

Transmitted torque T [N·m] (P: power kW, N: speed rpm) and the tangential force F [N] at the shaft surface (d: shaft diameter).

$$\tau = \frac{F}{b\,L} = \frac{2T}{d\,b\,L}, \qquad \sigma_c = \frac{F}{(h/2)\,L} = \frac{4T}{d\,h\,L}$$

Shear stress τ and bearing stress σ_c. b: key width, h: key height, L: effective length. Bearing assumes half the key height carries the load.

$$n_{\text{shear}} = \frac{0.577\,\sigma_y}{\tau}, \qquad n_{\text{bearing}} = \frac{\sigma_y}{\sigma_c}$$

Shear and bearing safety factors. σ_y: yield strength. Shear yield is 0.577σ_y by the von Mises criterion. The design is OK when both factors meet the target S.

What is the Parallel Key Stress Design Simulator?

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A "parallel key" is that small steel bar you drop into a slot cut along a shaft, right?

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That's the one. When you fix a gear, pulley or coupling onto a motor shaft, you cut a slot in both the shaft and the hub (the mating bore) and slide a rectangular key into them. As the shaft turns, the key catches the hub and torque is transmitted. It is more positive than a screw and still allows disassembly, so it is one of the most common joining elements in machine design.

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Can such a small part really be enough? Do keys ever break?

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They do — and the key point is that a key has two failure modes. One is shear: the key is cut clean in two. The other is bearing (crushing): the key side or the keyway is pressed and plastically deformed. Try raising "Transmitted power P" on the left. Both τ (shear stress) and σ_c (bearing stress) rise, and you will see the safety factors drop.

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Two modes... which one fails first?

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With standard key sizes, bearing usually comes first. Compare σ_c = 4T/(d·h·L) with shear τ = 2T/(d·b·L) — the bearing coefficient is larger, so the bearing safety factor tends to be the smaller one. This tool detects the governing mode automatically and tells you in the verdict. In the field, "the key deformed a little but did not actually break" is a common complaint, and that is exactly the signature of bearing overload.

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When the strength is short, do I just make the key bigger?

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The first lever is to lengthen the key, L. Both τ and σ_c are inversely proportional to L, so the "Stress vs key length" chart below shows both dropping smoothly as L grows. But the key length is capped by the hub (boss) width. If that is still not enough, the order of options is: use two keys (180° apart), move to a stronger material such as SCM440, or switch to a splined shaft. The width b and height h are fixed by the shaft diameter through standard sizes — never quietly shrink them.

Frequently Asked Questions

First find the tangential force at the shaft surface from the torque T: F = 2T/d, where d is the shaft diameter. The shear stress is τ = F/(b·L), where b is the key width and L is the effective key length. The bearing (crushing) stress assumes half the key height h/2 carries the load: σ_c = F/((h/2)·L) = 4T/(d·h·L). This tool compares τ and σ_c with the material limits and shows a separate safety factor for each.

For standard parallel keys (width:height roughly 4:3 to 1:1), bearing (crushing and plastic deformation of the keyway) usually becomes critical first. The bearing stress σ_c tends to be numerically larger than the shear stress τ, and the allowable bearing stress is taken conservatively against yield. For thin or narrow keys, however, shear can govern instead. This tool detects and displays the governing mode automatically.

The required length is the larger of the shear-limited length L_s = 2T·S/(d·b·τ_y) and the bearing-limited length L_b = 4T·S/(d·h·σ_y), where S is the target safety factor and τ_y ≈ 0.577σ_y. As a rule of thumb the key length stays within about 1.5 times the hub (boss) width; if that is not enough, use two keys, switch to a spline, or take other measures.

The key width b and height h are selected from the standard sizes (JIS B 1301 / DIN 6885) according to the shaft diameter d. For example, a 22-30 mm shaft uses 8×7, a 30-38 mm shaft uses 10×8 and a 38-44 mm shaft uses 12×8. Choose the standard key from the shaft diameter first, check the stresses and safety factors with this tool, then tune the strength with the length L. Using a smaller-than-standard key invites shaft failure from keyway stress concentration.

Real-World Applications

Power transmission drives: Joining a motor shaft to a gear, pulley or sprocket is the most basic use of a parallel key. Gearbox input and output shafts, pump and fan impeller mounting — almost every rotating machine uses keys. The designer selects the standard key from the shaft diameter, then sets the effective length L for the transmitted torque.

Couplings and joints: Flexible flange couplings and gear couplings that connect two shafts use keys to hand torque to and from each shaft. Because couplings see torque fluctuation and start-up shock, the steady torque is multiplied by a service factor before the key strength is checked.

Machine tools and industrial machinery: Machine-tool spindles, conveyor drive rollers, agitator impeller shafts — anywhere positive torque transmission and serviceable disassembly are needed. In repeatedly reversing applications, backlash between key and keyway causes fretting wear, so clearance-fit keys need attention.

Strength verification and troubleshooting: When a rotating machine misbehaves — "the gear slips", "there is an abnormal noise" — bearing-overload deformation of the key is often the cause. A quick calculation like this tool checks the stress level and decides whether the key dimensions, count or material need revision rather than just re-tightening. A full check also covers the shaft stress concentration and reduced torsional strength caused by the keyway.

Common Misconceptions and Pitfalls

A common mistake is to check the key strength but ignore the shaft. A keyway is a notch machined into the shaft, and the stress concentration at its corners reduces the torsional strength of the shaft itself by 20-30%. Even with an adequate key safety factor, the keyed shaft can fail in fatigue first. Always check the key strength together with the torsional strength of the shaft with the keyway accounted for. This tool handles the key alone, so it must be used alongside a shaft torsion calculation.

Next, the assumption that the transmitted torque is just the rated torque. A motor start-up torque is 2-3 times the rating, and fluctuating loads such as reciprocating compressors or crushers peak even higher. Using the catalogue steady torque directly will crush the key in bearing at the instant of start-up. In practice the design torque includes a service factor (roughly 1.2-3.0) chosen for the load type. The power you enter in this tool should already include that margin.

Finally, the idea that a longer key keeps getting stronger without limit. Stress is indeed inversely proportional to L, but in a long key the shaft twist makes the load uneven along the length, concentrating it at the entry side. As a guide the key length is effective up to about 1.5 times the shaft diameter; beyond that the gain levels off. If the required length exceeds the hub width, that is a sign to switch to two keys (120° or 180° apart), an involute spline, or a combined shrink fit.