Chapter 10 Threaded Fasteners and Power Screws 10.1 Introduction A layan ight consider threaded fasteners (screws, nuts, and bolts) to be the ost undane and uninteresting of all achine eleents. In fact fasteners are used everywhere. There are ore than illion fasteners on an airplane, cost over a illion dollars. Engineers are concerned with the selection and use of fasteners, and they need to know choices available, governing factors and standards. Power screws are also coonly used achine coponents. Their engineering and design has uch in coon with that of threaded fasteners. 10. Thread Fors, Terinology, and Standards Figure 10.1 (p. 386) Helical threads of pitch p, lead L and lead angle λ. Fig. 10.1 illustrates a helical thread wound around a cylinder, as used on screw-type fasteners, power screws and wors. L lead, p pitch, λ lead angle, and hand of thread. Virtually all bolts and screws have a single thread, power screws and wors have double, triple and even quadruple threads. Unless otherwise noted, all threads are assued to be right-hand. Fig. 10. shows the standard geoetry of screw threads used on fasteners. 1
Standard sizes for the two, Unified and ISO systes are given in Tables 10.1 and 10.. Figure 10. (p. 386) Unified and ISO thread geoetry. The basic profile of the external thread is shown.
Table 10.1a (p. 387) Basic Diensions of Unified Screw Threads (Continued on next two slides.) Table 10.1b (cont.) 3
Unified threads are specified as size-threads per inch and series. For exaple: ½ in.-0unf, 1 in.-8unc. Metric threads are identified by diaeter and pitch as M8 x 1.5. Fig. 10.4 illustrates ost of the standard thread fors used for power screws. Standard sizes are given in Table 10.3. Table 10.3a (p. 390) Standard Sizes of Power Screw Threads (Continued on next slide.) 4
Figure 10.4 (p. 389) Power screw thread fors. [Note: All threads shown are external (i.e., on the screw, not on the nut); d is the ean diaeter of the thread contact and is approxiately equal to (d + d r )/.] 10.3 Power Screws Power screws, soeties called linear actuators or translation screws, are used to convert rotary otion of either the nut or the screw to relatively slow linear otion of the ating eber along the screw axis. The purpose of any power screws is to obtain a great echanical advantage in lifting weights, as in screw type jacks, or to exert large forces, as in presses and tensile testing achines, hoe garbage copactors, and C-claps. The purpose of others, such as icroeter screws or the lead screw of a lathe, is to obtain precise positioning of the axial oveent. 5
Figure 10.5 (p. 391) Weight supported by three screw jacks. In each screw jack, only the shaded eber rotates. Fig. 10.5 shows a siplified drawing of three different screw jacks supporting a weight. They are basically sae, the torque is Fa. Let s take one turn of the screw thread, a triangle would be fored, see Fig. 10.6: Figure 10.6 (p. 391) Screw thread forces. 6
L tan λ πd (10.1) where λ lead angle L lead d ean diaeter of thread contact Take an infinitesially sall segent of the nut in Fig. 10.6, there are load w, noral force n, friction force fn, and tangential force q. Note, torque q x d /. d is the ean diaeter of the thread contact and is approxiately equal to (d + d r )/. Suing tangential/horizontal forces, F t 0: q n(fcosλ + cosα n sinλ) 0 (a) Suing axial/vertical forces, α n is thread shape angle relative to noral direction. F a 0: w + n(fsinλ - cosα n cosλ) 0 or w n cosλ f sin λ (b) Cobining Eqs. a and b, we have f cosλ + sin λ q w cosλ f sin λ (c) Integration over the entire thread surface in contact results in the sae equation except that w and n becoe W and N The equation for torque required to lift load W is d f cosλ + sin λ T Q cosλ f sin λ (10.) Note, T also Fa in Fig. 10.5c. Since L is usually known, according to tanλ L/πd, (10.) changes to: fπd + L T πd (10.3) Most applications of power screws require a bearing surface or thrust collar between stationary and rotating ebers. In Fig. 10.5 this function is served 7
by the ball thrust bearing of diaeter d c. If the coefficient between the is f c, then the total torque to lift W is fπd + L Wfcdc T πd + (10.4) For the special case of the square thread, cos α n 1, and Eq. 10.4, f d L Wfcdc T π + πd + (10.4a) For the Ace thread, cos α n is so nearly equal to unity (α n 14.5 0, cos α n cos(14.5/180)0.9968) that Eq. 10.4a can usually be used. The preceding analysis pertained to raising a load or to turning the rotating eber against the load. The analysis for lowering a load, or turning a rotating eber with the load is exactly the sae except that the directions of q and fn (Fig. 10.6) are reversed. The total torque required to lower the load W is T + fπd L πd cosα + fl For square thread, f d L π πd + fl T + n Wfcd c Wfcd c (10.5) (10.5a) 10.3.1 Values of Friction Coefficients When a ball or roller thrust bearing is used, f c is usually low enough that collar friction can be neglected, thus eliination the second ter fro preceding equations. When a plain thrust collar is used, values of f c vary generally between about 0.08 and 0.0. 10.3. Values of Threaded Angle in the Noral Plane Fig. 10.7 shows the thread angle easured in the noral plane α n and in the axial plane α. Fro Fig. 10.7 it can be seen, tanα n tanα cosλ (10.6) For sall helix angles, cosλ is often taken as unity. 8
Figure 10.7 (p. 394) Coparison of thread angles easured in axial and noral planes (α and α n ). 10.3.3 Overhauling and Self-Locking A self-locking screw is one that requires a positive torque to lower the load; an overhauling screw is one that has low enough friction to enable the load to lower itself. If collar friction can be neglected, Eq. 10.5 shows that a screw is self-locking if L f πd (10.7) For a square thread, this siplifies to L f π, or f tanλ (10.7a) d 10.3.4 Efficiency The work output fro a power screw for one revolution of the rotating ebers is the product of force ties distance, or WL. Corresponding work input is πt. The ratio WL/πT is efficiency. Substituting T in Eq. 10.4, with collar friction neglected, 9
Efficiency, e L πd πd πfd + L (10.8) For the case of square thread L d e π π d πfd + L (10.8a) Considering tan λ L/πd (10.1), the Eq. 10. 8 gives tan λ e f cosα + f cot λ (10.9) n For the square thread, 1 tan e f λ 1+ f cot λ (10.9a) Figure 10.10 (p. 398) Screw jack lifting a nonrotating load. Exaple 1. A screw jack, Fig. 10.10, with a 1-in., double-thread Ace screw is used to raise a load of 1000 lb. A plain thrust collar of 1 ½-in. ean diaeter is used. Coefficients of running friction are estiated as 0.1 and 0.09 for f and f c, respectively. 1) Deterine the screw pitch, lead, thread depth, ean pitch diaeter and helix angle. ) Estiate the starting torque for raising and for lowering the load. 3) Estiate the efficiency of the jack when raising the load. 10
Solution: 1) Fro Table 10.3, there are five threads per inch, hence p 0. in. Because of the double thread, L p 0.4 in. Fro Fig. 10.4a, thread depth p/ 0.1 in. Fro Fig. 10.4a, d d p/ 1 0.1 0.9 in. Fro Eq. 10.1, λ tan -1 (L/π d ) tan -1 (0.4/π0.9) 8.05 0 ) For starting, increase the given coefficients of friction by 1/3, giving f 0.16, and f c 0.1. Fro Eq. 10.6 to find α n α n tan -1 (tanα cosλ) tan -1 (tan14.5 0 cos8.5 0 ) 14.36 0 Substituting in Eq. 10.4, we have fπd + L Wfcdc T πd cosα + 141.3 + 90 0 1000 0.9 0.16π 0.9+ 0.4 cos14.36 1000 0.1 1.5 0 + 0.9π cos14.36 0.16 0.4 n 31.3lb in. For lowering the load using Eq. 10.5: fπd L πd cosα + fl T + n Wfcd 0 1000 0.9 0.16π 0.9 0.4 cos14.36 1000 0.1 1.5 0 + 0.9π cos14.36 + 0.16 0.4 10.4 + 90 100.4lb in. 3) Efficiency is the ratio of friction-free torque to actual torque. In Eq. 10.4 if take f and fc as zero then friction free T 63.7 + 0 63.7 lb in; if take f 0.1 and fc 0.09, then actual torque T 11.5 + 67.5 189 lb in. The efficiency to raise the load is e 63.7/189 33.7% c Hoe work: Fourth edition: 10,4, 10.7, 109, 10.10, 10.11. 11