25 September 2001
Designers often overlook a shaft connection's effects on a motion control system's performance. It's important you know both the advantages and drawbacks of various means of connecting a hub to a shaft to transmit torque and rotary motion. What follows are the eight basic connection methods.
The most common shaft connection is the straight bore and keyway. Here the torque force is applied across the key in a shear mode. Key sizes and tolerances have been standardized and can be found in a number of standards (e.g., AGMA/ANSI 9002-A86, DIN 6885, and JIS Js9).
The key's torque handling capacity is directly related to its length, width, and material properties:
as shown in Figure 1.
Additionally, the keyway's depth in the mating parts (hub and shaft) must be such that it isn't crushed:
The safety values for keyway crush and shear stress are typically 13% of the ultimate tensile strength of the material used (e.g., 8,000 pounds per square inch for mild steel).
Other factors to include are the key's fit in its mating keyway. AGMA keyway tolerances for Class I fit (most common in the U.S.), allow for keyways that may be 0.01 inch off the shaft centerline. For example, a 1-inch shaft with a standard 1/4 by 1/8 key has a potential clearance of 0.008 inch across each keyway (0.004 + 0.004) and could twist in the keyway up to 0.548°. This relates to a 0.47° potential backlash on each coupling hub (Figure 2) and a 0.94° backlash across a complete shaft coupling, resulting in a 1:391 positioning error. With couplings for servo drives having only 0.05° of windup and zero backlash, this looseness is unacceptable. This clearance may also allow the key to roll in the keyway (1.9° in our example), causing high edge loading, which can shear the key.
A more positive approach is to transmit torque via friction. The collet clamp is split both radially and axially and deforms the hub to apply contact pressure to the shaft. This eliminates the keyway's looseness. The clamping force can be applied directly, using a two-piece design (Figure 3a), or by bending two moment arms about point D, as shown in the one-piece design (Figure 3b).
In the two-bolt, fully split design, the screws' clamping force Fk1 applies a contact pressure to the shaft. Torque is transmitted through friction, according to these equations:
For the collet clamp, single-split hub, the equation is
Either method's contact pressure must be evaluated to ensure that neither hub nor shaft yields under the clamping force. The contact pressure equation is
The contact pressure must be less than the yield strength of the material used.
Another method of applying contact pressure is the shrink fit. The hub is heated (or shaft is cooled) such that it grows (shrinks) in diameter. Then the parts are assembled and held in location until they return to room temperature. The interference generated creates high contact pressure on the shaft-hub interface. This pressure (force/area), along with the coefficient of friction of the mating materials, is used to calculate the torque transmission. In this case, the equations for contact pressure and torque transmission are
Of course, once the parts have cooled to room temperature, it's nearly impossible to remove them. A better way is to introduce a means of interference that can be removed.
Taper Shaft or Bushing
A common method of introducing an interference is to manufacture a tapered shaft and tapered bore. At installation, axial force is applied (by tightening a nut against a thread on the taper shaft's end) to advance the hub along the tapered shaft (Figure 4).
In this case, the axial force is
Take care that the design accounts for the parts' change in axial position. Furthermore, you'll need a method for removing the part later. You can also use a key and keyway, parallel to either the taper or the shaft centerline, for insurance in case the axial load isn't maintained.
Another method uses an intermediate bushing with a tapered outer diameter (OD) to fit a tapered bore in the hub and a straight bore in the bushing to fit a straight shaft. In this case, the bushing advances axially, but the hub and shaft maintain their original alignment. The tapered shaft connection equations also apply here. Instead of a nut tightened onto a large thread at the shaft's end, a number of smaller screws are positioned near the bushing's OD. The total axial force is now
The clamp ring (Figure 5) provides another method of introducing removable interference. In this case, the assembly contains all of the tapered machining. The tapered rings are split; axial compression spreads one out toward the hub, while the other is forced inward toward the shaft. Here, both a straight bore in the hub and a straight shaft are used. Because all taper machining is within the assembly, there's no axial movement of the part.
The compression bushing is a thin-walled piston filled with an incompressible, malleable material (clay) or fluid (Figure 6). When the material is squeezed, the cylinder walls bulge and apply pressure to the mating components. Both straight bore and shaft are used (as with clamp rings). Torque capacity is calculated as before, using contact pressure to transmit torque.
Noncircular Shaft or Spline
Noncircular shafts (e.g., hexagons, squares, or splines) can also be used for torque transmission. However, normal clearance between the mating parts makes them unsuitable for motion control applications.
The final way to connect parts uses a threaded bore and threaded shaft end. Ensure that the direction of rotation doesn't unscrew the parts. However, because this connection method is unidirectional, it's unsuitable for motion control applications.
It's important that you, the designer, don't overlook these facts. Maximum performance requires you to be aware of the advantages and disadvantages of various means of shaft connections. MC
Howard Schwerdlin is engineering manager of Rimtec Corp. He has 25 years of experience in the power transmission industry and is the author of numerous technical articles concerning couplings and mechanical vibration. Contact him at 211 S. Lombard Road, Addison, Ill. 60101; tel: (877) 4-RIMTEC or (630) 628-0036; fax: (630) 628-0041; firstname.lastname@example.org; www.RimtecCorporation.com.