Machinery's Handbook, 31st Edition
582 Thermal Stresses and Stiffness Equation (26) assumes certain geometric relationships and a coefficient of friction of 0.15. If compatible thread lubricants are used during assembly, the torque must be reduced. To ensure safety and reliability, all threaded assemblies must be subjected to long-term testing under operating pressures, temperatures, and stresses caused by installation procedures exceeding those likely to be encountered in service. Thermal Stresses.— When materials with different coefficients of thermal expansion are bolted, riveted, bonded, crimped, pressed, welded, or fastened by any method that prevents relative movement between the parts, there is potential for thermal stress to exist. Typical examples are joining of nonreinforced thermoplastics parts with materials such as metals, glass, or ceramics which usually have much lower coefficients of thermal ex- pansion than plastics. The basic relationship for thermal expansion is (27) where D L = change in length, a = coefficient of thermal expansion (see Table 8, page 372), L = linear dimension under consideration (including hole diameters), and D T = temperature change. If the plastics component is constrained so that it cannot expand or contract, the strain ε T , induced by a temperature change, is calculated by (28) The stress can then be calculated by multiplying the strain ε T by the tensile modulus of the material at the temperature involved. A typical example is of a plastics part to be mounted to a metal part, such as a window in a housing. Both components expand with changes in temperature. The plastics imposes insignificant load to the metal, but considerable stress is generated in the plastics. For such an example, the approximate thermal stress s T in the plastics is given by (29) where a m = coefficient of thermal expansion of the metal, a p = coefficient of thermal expansion of the plastics, and E p = tensile modulus of the plastics at the temperature in- volved. Other equations for thermal expansion in various situations are shown in Fig. 12. Most plastics expand more than metals with temperature increase, and their modulus drops. The result is a compressive load in the plastics that often results in buckling. Con versely, as the temperature drops, the plastics shrinks more than the metal and develops an increased tensile stress. These conditions can cause tensile rupture of the plastics part. Clearances around fasteners, warpage, creep, or failure, or yield of adhesives tend to relieve the thermal stress. Allowances must be made for temperature changes, especially with large parts subjected to wide variations. Provision is often made for relative motion D L rel between two materials, as illustrated in Fig. 12: (30) Designing for Stiffness.— The designer must take full advantage of the ability of plastics to be easily formed into a desired shape, in contrast to woods where every shape must be machined or assembled from planks or blocks. To a lesser degree, the same is often true of metals, although die-castable metals have a considerable shape versatility. Though the modulus of elasticity is much less in plastics than in metals, stiffness is a property not just of the material but also of the structure that can be made from it. When the product must support bending loads, as in a bookshelf, a simple beam of rectangular cross section would be the logical approach if the shelf material were pine or mahogany. If the material is plastic, other cross sections of higher stiffness per unit weight can be considered to take advantage of plastics’ ease of formability and low density. Fig. 13 shows some alterna- tives to the traditional rectangular cross section that achieve greater stiffness with less material. L L T rel p m ∆ = α − α ∆ ^ h L L T ∆ = α ∆ L L T T ε = ∆ =α∆ E T T m p p σ = α −α ∆ ^ h
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