Machine Design

Sorting out shaft connections

Motors and gearboxes that generate high torque and acceleration may make shaft keys obsolete.

Dan Sheba
Kiril Zumbulev
Applications Engineers
alpha gear drives Inc.
Bartlett, Ill.

Edited by Kenneth Korane

Designers should analyze stresses and backlash when weighing keyed versus keyless shafts.

Stresses in the keyway are critical in evaluating the shaft's torque capacity.

Opposing forces exerted by the shaft and hub attempt to shear the key.

Loads applied by the shaft and hub keyways can compress and permanently deform the key.

Manufacturing tolerances on key and keyway contribute to backlash.

Knowing the advantages and disadvantages of keyless and keyed shaft connections is vital when connecting gearboxes and motors. Today's demands for speed, precision, and compactness have motor and drive manufacturers making smaller devices that generate high torque, rapid acceleration, and accurate rotary positioning. But these advances also mean backlash, stress distribution, and balance must be addressed in smaller shaft-locking devices. In many cases it takes keyless connections to handle the dynamic loads, rendering shaft keys obsolete.

A straightforward way to compare keyed and keyless designs is in terms of torque transmission. Let's look at an example using a 16-mm shaft. Shaft and key are made of 35S20 steel, with key and keyway dimensions sized according to DIN Standard 6885. The following calculations determine the maximum torque that can be transmitted through both keyed and keyless shafts, as well as the maximum transmissible torque for the key.

Assuming the coupling does not slip, torque transmitted through the shaft is:

T =πJ/r.

The polar moment of inertia is: J = πr 4 /2. And π, the yield stress for 35S20 steel, is 380 X 10 6 N/m 2 .

For the example, J = 6 10 -9 m 4 and

This is the maximum torque that can be transmitted through the keyless shaft before plastic deformation begins.

Stress levels on the keyway sides are critical in evaluating keyed applications. Assuming the key will not fail before the shaft, the shaft can hold a maximum torque of:

T = πdlh/2

where l, the effective length of the keyway, = 25 mm; and h, the keyway depth, = 3 mm. For the keyed shaft,

Thus, 228 Nm is the maximum torque that can be transmitted before the 16-mm-diameter keyed shaft plastically deforms.

Industrial applications commonly use flat keys. Flat keys have two modes of likely failure: shear and crushing. For our application, calculations use the maximum yield stress and do not include a safety factor.

Shear failure of flat keys.
The shaft and hub keyways exert equal and opposite forces on the key. These forces attempt to shear the key at the shaft radius and result in shear deformation. To determine shear stresses:

π = F / ωl,
= π ω l, and
= Fr

where F = shear force acting on the key, and ω= 5-mm key width.

From the above equations,

F = 47, 500 N and
= 47,500(0.008) = 380 Nm.

Crushing failure of flat keys.
Shaft and hub keyways can compress and permanently deform the key. Compressive (or crushing) stress equals the applied force divided by the contact area.

π = F/(l(H/2)).

where F = compressive force and H = key height of 5 mm.

F = πH/2, and
T = Fr.

In this case, F = 23,750 N and T = 190 Nm.

The key handles a 190-Nm torque before plastic deformation.

Another factor to consider is the fit when mating the key and keyway. According to ISO JS9 for a parallel key with normal fit, the tolerance for a 5-mm-wide keyway is ±0.015 mm. Key tolerance per DIN 6885 is 0.05/-0.00. Thus, clearance between the shaft keyway and key is up to 0.015 mm. In addition, manufacturing tolerances permit keyways to be 0.015 mm off the shaft centerline.

Key sliding.
If the key slides instead of twists, calculate the backlash angle from:

α= 180b/(rπ).

Because the angle is small, use the 0.015-mm tolerance value for arc length b.

From this calculation, the backlash angle is 0.1074°. In other words, tolerances permit shaft angular movement up to 0.1074°. This equates to = 6.445 arc-min of potential backlash.

Key twisting.
If the key is centered in the keyway and twists, calculate backlash by first determining arc length b.

Backlash, then is:

α==180b / () 0.32 arc - min.

Backlash is the most vital aspect when addressing performance. Completely eliminating backlash is rarely possible. However, precisely fitting the gear-box to motor and accurately machining mating components can minimize it. Backlash increases as keyways wear due to factors such as frequent machine load reversals and high acceleration and deceleration rates.

Repeated impacts between the key and keyway compress and remove material from the keyway, widening it, and increasing the impact velocity with each load change. Over time, backlash will increase at an accelerated rate. Under highly dynamic load conditions, keyways can quickly wear to the point of excessive backlash and even failure. Moreover, keyways can prove problematic when disassembly is necessary. Depending on the environment and duty cycle, oxidation and corrosion can "weld" together key assembly components.

On the other hand, keyless, frictional-type connections between motors and gearboxes eliminate many of the above-stated problems. One type of frictional connection, the shrink disk, has zero clearance and, consequently, adds no backlash to the system.

Also, as the previous calculations demonstrate, keyless connections transmit more torque for a given size. Finally, eliminating keyways lets engineers disregard keyed-shaft notch factors. This permits smaller shaft diameters and bearings, which reduces overall system costs.

alpha gear drives Inc., a Wittenstein AG company, (630) 540 5300,


TAGS: Fasteners
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