Materials For Cooling Fans

• Introduction
• The Model
• The Selection
• Postscript
• Further reading
• Related case studies

Introduction

Automobile engines have a fan which cools the radiator when the forward motion of the car is insufficient to do the job (Figure 7.1). Commonly, the fan is driven by a belt from the main drive-shaft of the engine. The blades of the fan are subjected both to centrifugal forces and to bending moments caused by sudden acceleration of the motor. At least one fatality has been caused by the disintegration of a fan when an engine which had been reluctant to start suddenly sprang to life and was violently raced while a helper leaned over it. The failures were traced to defects (cracks in fan blades) which propagated under the accelerational loads. What criteria should one adopt in selecting materials to avoid this? And which materials satisfy these criteria?

The radius, R, of the fan is determined by other considerations: flow rate of air, and the space into which it must fit. And the material of which it is made must be cheap. Any automaker who has survived to the present day has cut costs relentlessly on every component. But safety comes first. The fan must not fail. The design requirements, then, are those of Table 7.1.

Figure 7.1 A fan. It must not fail catastrophically during an overspeed.

Table 7.1 The design requirements

The Model

A blade (Figure 7.1) has mean section area A and length αR, where α is the fraction of the fan radius ρ which is blade (the rest is hub). Its volume is αRA and the angular acceleration is ω²R, so the centrifugal force at the blade root is

(M7.1)

The force is carried by the section A, so the stress at the root of the blade is

.

(M7.2)

This stress must not exceed the failure stress σ_f divided by a safety factor (typically about 3) which does not affect the analysis and can be ignored. The stress at which fast fracture will occur is:

,

where K_1c is the fracture toughness of the material of the blade and α is the length of the largest defect it contains. Non-destructive testing can ensure that this is less than some detection limit, a*. Thus, for safety:

,

or

.

(M7.3)

The lengths R and a* are fixed, as is α. The safe rotational velocity ω is maximized by selecting materials with large values of

.

(M7.4)

The material cost of the fan is

where C_m is the cost/kg of the material, ρ its density and V the volume of material in the fan. The volume is essentially fixed by the radius R, which is a constraint on the selection. Thus the material cost is minimized by selecting materials with large values of the volume per unit cost:

.

(M7.5)

The Selection

Safety first. Figure 7.2 shows fracture toughness K_1c plotted against density, ρ. The materials above the selection line (slope = 1) have high values of M₁. This selection must be balanced against the cost. Low cost fans can be made by die-casting a metal, or by injection-molding a polymer. Figure 7.3 shows the volume of material per unit cost, M₂, for materials which can be formed in these ways. The box is set to capture materials which are cheap. The materials which pass both stages are listed in Table 7.2.

Figure 7.2 A chart of fracture toughness, K_1c, against density, ρ, showing the index M₁.

Figure 7.3 A chart of volume/unit cost, M₂, against forming method.

The final selection requires judgement. How much is safety worth? In the remote past, very little; today, a great deal. If the fan is viewed as a safety-critical component, we do not choose cast iron, but instead select steel, aluminum, magnesium or filled polymers.

Postscript

To an auto-maker additional cost is anathema; but the risk of a penal law suit is worse. Here (as elsewhere) it is possible to 'design' a way out of the problem. The problem is not really the fan; it is the undisciplined speed-changes of the engine which drives it. The solution (now we put it this way) is obvious: decouple the two. Increasingly, the cooling fans of automobiles are driven, not by the engine, but by an electric motor (cost: about that of a fan-belt) which limits it to speeds which are safe — and gives additional benefits in allowing independent control, and much more freedom in where the fan is placed.

Table 7.2 Candidate materials for cooling fans

Further Reading

Young, WC (1989) 'Roark's Formulas for Stress and Strain', 6th edition, McGraw-Hill, NY, USA

Related Case Studies

1. Materials for Flywheels

2. Materials to Resist Fracture

3. Safe Pressure Vessels