# POWER SCREWS (ACME THREAD) DESIGN

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3 A screw in some applications carries a load transverse to its axis. Such loads produce bending moments in the screw, which result in the development of bending stresses. To determine the required section modulus, S, for such an application M max S = S u Long power screws loaded in compression can fail by elastic instability as given by the Euler formula F C π E = A b r where F = total load, A = area of section, E = modulus of elasticity, b/r = slenderness ratio, and С is the coefficient of constraint, which depends on end conditions. For round ends, С = 1; for fixed ends, С = 4; and for the end conditions that occur in practice, С can rarely be assumed greater than. For power screws that behave as short columns, it is not possible to calculate with accuracy the maximum stress produced by a nominally concentric load because of the large influence of the indeterminate crookedness and eccentricity. The maximum unit stress that a column will sustain, however, can be expressed by any of a number of formulas, each of which contains one or more terms that is empirically adjusted to secure conformity with test results. Of such formulas, those given below are the best known and provide the basis for most of the design formulas used in American practice. In these equations F denotes the load at failure, A the cross-sectional area, b the length, and r the least radius of gyration of the section; the meaning of other symbols used is explained in the discussion of each formula. Rankine formula P σ = A L 1+ φ r This is a semirational formula. The value of σ -is sometimes taken as the ultimate strength of the material and the value of φ as σ / C π E, thus making the formula agree with the results of tests on short prisms when L/r is very small and with Euler's equation when L/r is very large. More often σ and φ are adjusted empirically to make the equation agree with the results of tests through the L/r range of most importance. Modulus of Elasticity in Tension For the part of the stress-strain diagram that is straight, stress is proportional to strain, and the value of E is the constant of proportionality. That is, stress E = strain This is the slope of the straight-line portion of the diagram. The modulus of elasticity indicates the stiffness of the material, or it s resistance to deformation. To choose a value in this software, simply click on the database icon and find the material for your application. -3- = σ

4 Tensile strength The tensile strength of a material, Su, and S y is determined from test results, supplier specifications, or given data. The most accurate and reliable data available should be used. When there is doubt about the accuracy of the data, larger-than-average design factors should be used. For the repeated, reversed bending in a shaft caused by transverse loads applied to the rotating shaft, the ultimate tensile strength is related to the endurance strength of the shaft material. The actual conditions under which the shaft is manufactured and operated should be considered when specifying the design stress. Shear strength The strength in shear Ss of a material is an important property. Unfortunately, these values are seldom reported and we use the following estimates to determine Ss Sus = S u S ys = 0. 5 S y where S and S are reported as tensile properties. u Design factor y Under typical industrial conditions, the design factor of N = 3 is recommended. If the application is very smooth, a value as low as N = may be justified. Under conditions of shock or impact, N = 4 or higher should be used, and careful testing is advised. Coefficient of friction, f The coefficient of friction for use in analyzing ball screws depends on the materials used and the manner of lubricating the screw. For well-lubricated steel screws acting in steel nuts, f = 0.15 should be conservative. While it has long been the custom to assume a value of f = 0.15 as a reasonable expectation, more recently, Ham and Ryan have conducted a group of experiments and found that if the threads are cut accurately, if the thread surfaces are smooth, and if they are well lubricated, the coefficient of friction may be expected to average as low as Messrs. Ham and Ryan recommend that for an average quality of materials and workmanship, the coefficient of friction in motion be taken as 0.15; while for inferior workmanship and quality of materials, the coefficient of friction may be assumed as Increase these values 30 to 35 per cent for starting friction. Additionally the research indicates that the coefficient of friction is practically independent of the axial load; it undergoes negligible changes due to speed for the speed ranges encountered in practice; it decreases somewhat as the lubricants used become heavier; it shows little variation for different combinations of material, being lowest for soft steel on bronze, and hardened and ground steel on bronze; and it is in close agreement with the results obtained by the theoretical equations. -4-

5 Typical Acme screw-driven system Wormgear drive Chain drive Collar Thrust bearing Support F φ *φ Acme screws h Radial bearing Yoke Hatch, F Motion Fig. 1 Thread surface Screw thread force analysis P λ P = Force required to move the load Ff = Friction force N = Normal force λ = Lead angle Dp = Pitch diameter F = Load to be moved F N Ff πdp Force exerted up the plane L = Lead Fig. Ff λ N P πdp Force exerted down the plane L = Lead -5-

6 Typical stress-strain diagram Yield point, Sy True stress curve Yield strength, Sy True stress curve Sy Stress, σ Tensile strength, Su Elastic limit Proportional limit Sy Stress, σ Tensile strength, Su Elastic limit Proportional limit Strain,? Strain,? Diagram for steel Diagram for aluminium and other metals having no yield point Fig. 3-6-

7 MDESIGN SOFTWARE - Example Power Screw Design Input data: Modulus of elasticity E = 0684 MPa Tensile strength limit Su = MPa Shear strength limit Sus = MPa Design Factor N = 1 Number of screws NS = Load to be moved F = N Action distance S = 381 mm Time to pass the action distance t = 1 s Thread angle φ= 14.5 Coefficient of friction f = 0.15 Results: Nominal major diameter D = mm Pitch P = 6.35 mm Minimum minor diameter Dr = mm Minimum pitch diameter Dp = mm Tensile stress area At = mm Shear stress area per inch of engagement As = mm Minimal required length of engagement h = 7.15 mm Torque required to raise the load Tu = 05.0 Nm Torque required to lower the load Td = Nm Efficiency e = 7.41 % Linear speed V = 0.03 m/s Rotational speed n = 300 rpm Power required to drive each screw P1 = 6440 W Total power P = 188 W -7-

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19. Quad -rings The sealing principle of the Quad ring is nearly the same as the O-ring sealing. The initial sealing is achieved by the diametrical squeeze in a right angled groove. The system pressure

### Fatigue. 3. Final fracture (rough zone) 1. Fatigue origin. 2. Beach marks (velvety zone)

Fatigue Term fatigue introduced by Poncelet (France) 1839 progressive fracture is more descriptive 1. Minute crack at critical area of high local stress (geometric stress raiser, flaws, preexisting cracks)