Design of Sunken Keys

Design of Sunken Keys

Keys are a common way of fastening items such as sprockets, pulleys and gearboxes on to cylindrical shafts. A key is defined by being a removable element that is capable of transferring torque between a shaft and a hub. In general, keys are either square or rectangular and are usually parallel/flat, although gib head keys for example utilise a taper.

 

Saddle Keys

Saddle keys sit atop the shaft and only require a key slot to be machined into the hub.  A curved face is machined onto the key steel and friction between the key steel and shaft transmit the power to the hub. The transmitted power can be increased by using flat key steel and machining a flat surface onto the shaft where the saddle key is seated.

 

Sunken Keys

Sunken keys require keyway grooves in both the shaft and the hub.  Keys are often square or rectangular in cross section, although the rectangular keys offer greater stability when under loads.  This increased stability is due to their wider and lower profile offering better seating in the grooves and increased resistance to the turning moments and shear forces.

Sunken keys can also be tapered, with the key steel driven into a tapered groove within the hub and a parallel groove on the shaft.  The key steel is inserted until it firmly locks, with gib head key steel facilitating easy removal due to its headed design.

Where taper keys lock the hub to the shaft and prevent the hub moving along the shaft’s length, parallel or woodruff keys require a separate locking mechanism such as clamping collars or grub screws.  The main disadvantage with tapered keys is causing a slight eccentricity as all machining clearances are moved to the keyway side.

Woodruff keys are a deep shaft penetration, semi circular key that is generally only suited to low torque applications.

Standard feather keys are machined part way along a shaft and the key steel is rounded on both ends.  The shaft groove is machined with a tight tolerance to the key steel so that the key remains in place, although the key steel can also be bolted into place.  Tolerance is built into the hub, allowing it to slide over the in-situ feather key steel.

Several other feather key types are available and require a keyway groove machined from the shafts end.  These are the peg feather key and the double headed feather key, where the key steel is located by either a peg through the hub or by heads on either end of the key steel which fit over both ends of the hub.

For higher torque applications, Kennedy (multiple square keys set at 90 or 120 degrees), Round (lower shear concentration) and Barth (tight fitting and bevelled) keys can be used.

 

Types of keys and keyways

Figure 1 – Types of keys and keyways

 

Failure Modes

As previously discussed, keys transmit torque between a shaft and a hub, with forces applied to the keyway groove in the shaft and hub and also to the key steel itself. To transmit this torque, the shaft applies a force through the area of the key steel in contact with the shaft. This force is transmitted through the key steel and reacts with the hub through the area of key steel in contact with it.

Considering how the torque and forces are distributed, the main consideration for failure modes is shear or crushing of the key steel. It should be noted however, that if a shaft also operates in reverse, the negative tolerance used as assembly clearance can cause both impact and fatigue damage to the key steel over time.

For reference, Figure 2 (a) shows the forces acting on the key steel during shear, while Figure 2 (b) illustrates the crushing forces.

 

shear and crushing forces

Figure 2 – Diagram showing shear and crushing forces exerted on key steel

 

As a general rule, the following can be applied when considering the correct key for an application;

Key length <= 1.5 x shaft diameter

Square keys should only be used on shafts up to 22mm. Above 22mm it is recommended to use a rectangular key.

 

 

Example Sunken Key Calculation for Key Length and Width

Source: Analysis and Design Machine Elements

 

τd =Design stress in shearing

σdc=Design stress in crushing

b=Keysteel height

l=Keysteel Length

d=Shaft diameter

General Rule : τd=0.5σdc

 

Example Problem

Find the Length and Width of a sunken key, having a depth of 20mm on a 100mm diameter shaft.

Assume;

The shearing resistance of the key steel is equal to that of the shaft.

 

τd=0.4σdc

 

The twisting moment / torsional capacity of the shaft based upon the shear strength can be calculated from;

 

Mt=(πτd d3)/16=(πτd×(100)3)/16

 

d = Shaft Diameter

For the torsional capacity of key steel considering crushing;

 

Mt keyC= (h/2 l) σdc (d/2)=(20/2 l) σdc (100/2)

 

For a standard design;

 

Mt=Mt keyC

 

So;

 

(πτd(100)3)/16=(20/2 l) σdc (100/2)

Substituting τd=0.4σdc

(1256636σds)/(8000σds)=l=157.1 mm

Rounding up; l=160mm

 

For the torsional capacity of the key steel under shearing;

 

Mt keyS=(bl) τd (d/2)=(160b) τd (100/2)

For Mt keyC=Mt keyS

(160b) τd (100/2)=(20/2 ×160) σdc (100/2)

Substituting τd=0.4σdc

b=(80000σdc)/(3200σdc)=25mm


It is also possible to obtain the height (b) from Mt=Mt keyS and would give a result of around 24.5mm

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