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July 20, 1998

6 Min Read
The Principles of Design: Fastening Plastic Components on Steel Shafts

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Editor's note: This is the first in a
series of articles describing solid
solutions for plastics design chal-
lenges from Professor Gunter Er-
hard, formerly with BASF AG,
Ludwigshafen, Germany, in ther-
moplastic applications engineering.
Professor Erhard is now an indus-
try consultant, a frequent seminar
instructor, and a lecturer at the
University of Karlsruhe, Germany.

When a plastic part such as a lever, gear, or other element that must transmit torque is fastened on a metal shaft, the method of fastening basically depends on the magnitude of the torque to be transmitted, the temperature, and cost factors. For example, to transmit low torque, simple friction fits will do. At temperatures of about 60 C, however, this method fails, and a more complicated type of fit, a positive connection for example, must be employed.


ArticleImage188.gif

Figure 1. A simple spline and groove fit.

Positive Connection

The type of connection based on a spline and a groove, commonly employed in machinery construction, has limitations in plastic components under maximum load conditions (see Figure 1). If the key is poorly positioned with respect to the action of the force at the circumference, the hub can even separate from the shaft. For this reason, the connection of the plastic to the metal should be based on a multifluted spline. This involves more work, but is more positive, since the force is transmitted more uniformly.

Using the following relationship, it is possible to estimate the torque that can be transmitted from the force applied to the flanks:

ArticleImage788.gif


where,
Md= torque in Nm,
i = number of flutes (it can be assumed that for a plastic component all flutes are subject to the same load),
rm = average radius in mm,
hb = height, width of load-bearing flute in mm.


ArticleImage288.gif

Figure 2. Permissible values of
the surface force on key flanks.

Permissible values of Pm for various materials are shown in Figure 2.
If very high torque is to be transmitted, the plastic component must be fitted with a metal hub. This metal hub is incorporated via insert moulding in an injection mould. This is the most involved, but also the most positive means. When designing such metal hubs, special attention must be paid to the following points:

  • There can be only one axial attachment point, with an unhindered possibility for shrinkage toward it.

  • If possible, the point of axial attachment should be located close to the gate.

  • The force-transmitting flanks of the positive connection should be perpendicular to the circumference and uniformly distributed around it.

  • For the wall thickness of the plastic hub, the following applies: ra/ri is approximately equal to 1.3 to 2.0. See Figure 3.


ArticleImage388.gif

Figure 3. proper and improper metal hub
design for transmissions of high torque.

The use of drawn aluminum profiles as depicted in Figure 4, for example, represents an especially economical and technically well-designed solution. To absorb the axial forces, the hubs that are cut from the rod require only a circumferential groove.

ArticleImage488.gif

Figure 4. Hub made from drawn aluminum profile.






















Knurled Connection

Small gears, levers, cams, and many other components can be fastened to metal shafts reliably, yet without excessive effort, if the metal shaft has a knurled surface at the area of attachment. An optimal connection is achieved when a preload is developed as the result of shrinkage of the injection moulded plastic, that is, when the appropriately knurled metal component is insert moulded in an injection mould.

The tough and elastic thermoplastics are especially well-suited for such connections. The connection can be achieved also simply by mechanically pressing the shaft into the plastic component. The optimum hub diameter dn in a plastic part is given by:

dn is approximately equal to dr - t,
where
dr = outside diameter of knurling in mm,
t = pitch of knurling in mm.

A surprisingly good value of the transmittable torque can be obtained from the simple relationship:

ArticleImage888.gif


where Ty,b is the shear stress at failure. The following is obtained for the shear stress at failure from the failure criterion according to Henkey, Mises, and Huber:

ArticleImage988.gif


where,

sigma1.gif

y,b is the stress at failure at yield or break, which can be taken from stress-strain diagrams. Here's an example.


ArticleImage588.gif

Figure 5. Manual control lever as integrated
plastic component with a knurled connection
for attachment to the control shaft.

A control lever for actuating a hydraulic mechanism in a construction vehicle, previously manufactured from several metal parts and a rubber handle (Figure 5), is to be injection moulded in one piece in PA 6, and attached to the control shaft via a knurled connection. The knurling in the moulded part is already produced slightly undersized in the
injection mould.

The force on the control lever at which the connection is destroyed must now be determined for the following dimensions:

Outside diameter of knurling:12 mm
Width of knurling: 20 mm
Lever arm: 200 mm
Maximum temperature: 40 C


ArticleImage688.gif

Figure 6. Stress-strain diagram for dry PA 6.

Various material databases contains the stress-strain diagram for
PA 6 (dry), Figure 6, and give the yield stress Y = 75 MPa.
The maximum transmittable torque is calculated as:

ArticleImage1088.gif


while the force applied to the 200-mm lever arm is calculated to be:

ArticleImage988.gif


It is impossible to apply a force of such magnitude by hand. As a consequence, it is thus not possible to destroy the connection by hand. This example also illustrates in an impressive manner how costs can be saved through integrated design.

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