Modeling and Simulation for Material Selection and Mechanical Design Part 16 ppsx

Table 14 Estimated Preload Level for Different Unified Screw Types Preload level (kN), Unified Screw Thread Tensile strength and yield strength ratio of screw Thread size Nominal As (mm2) 1=4–20 5=16–18 3=8–16 7=16–14 1=2–13 9=16–12 5=8–11 3=4–10 7=8-9 1–8 1 1=4–7 1 1=2–6 1 3=4–5 2–4 1=2 3–4 4–4 5–4 1=4–28 5=16–24 20.5 33.8 50.0 68.6 91.5 117.0 146.0 215.0 298.0 391.0 625.2 906.4 1,226 1,613 3,852 7,148 11,484 23.5 37.4 Rm (MPa) kR (À) 300 0.6 400 0.6 400 0.8 500 0.6 500 0.8 600 0.8 800 0.8 900 0.8 1,000 0.9 1,100 0.9 1,200 0.9 1,400 0.9 2.80 4.62 6.84 9.38 12.5 16.0 20.0 29.4 40.8 53.5 85.5 124.0 167.7 220.6 526.9 978 1,571 3.21 5.12 3.74 6.17 9.12 12.5 16.7 21.3 26.6 39.2 54.4 71.3 114.0 165.3 223.6 294.2 702.5 1,304 2,095 4.29 6.82 4.99 8.22 12.2 16.7 22.3 28.5 35.5 52.3 72.5 95.1 152.0 220.4 298.1 392.3 936.7 1,738 2,793 5.72 9.10 4.67 7.71 11.4 15.6 20.9 26.7 33.3 49.0 67.9 89.1 142.5 206.7 279.5 367.7 878.2 1,630 2,618 5.36 8.53 6.23 10.3 15.2 20.9 27.8 35.6 44.4 65.4 90.6 118.9 190.0 275.6 372.6 490.3 1,171 2,173 3,491 7.14 11.4 7.48 12.3 18.2 25.0 33.4 42.7 53.3 78.4 108.7 142.6 228.1 330.7 447.2 588.4 1,405 2,608 4,189 8.57 13.6 10.0 16.4 24.3 33.4 44.5 56.9 71.0 104.6 144.9 190.2 304.1 440.9 596.2 784.5 1,873 3,477 5,586 11.4 18.2 11.22 18.5 27.4 37.5 50.1 64.0 79.9 117.6 163.1 214.0 342.1 496.0 670.8 882.6 2,108 3,912 6,284 12.86 20.5 14.02 23.1 34.2 46.9 62.6 80.0 99.9 147.1 203.8 267.4 427.6 620.0 838.4 1,103 2,634 4,889 7,855 16.07 25.6 15.42 25.4 37.6 51.6 68.8 88.0 109.9 161.8 224.2 294.2 470.4 682.0 922.3 1,214 2,898 5,378 8,640 17.68 28.1 16.8 27.7 41.0 56.3 75.1 96.0 119.8 176.5 244.6 320.9 513.1 744.0 1,006 1,324 3,161 5,867 9,426 19.3 30.7 19.6 32.4 47.9 65.7 87.6 112.0 139.8 205.9 285.4 374.4 598.7 868.0 1,174 1,545 3,688 6,845 10,997 22.5 35.8 Copyright 2004 by Marcel Dekker, Inc All Rights Reserved 3=8–24 7=16–20 1=2–20 9=16–18 5=8–18 3=4–16 7=8-14 1–12 1 1=4-12 1 1=2–12 1 3=4–12 2–8 3–8 4–6 5–6 56.6 76.6 103.0 131.0 165.0 241.0 328.0 428.0 692.3 1,020 1,413 1,787 4,200 7,465 11,871 7.74 10.5 14.1 17.9 22.6 33.0 44.9 58.6 94.7 139.5 193.3 244 575 1,021 1,624 10.3 14.0 18.8 23.9 30.1 44.0 59.8 78.1 126.3 186.0 257.7 326 766 1,362 2,165 13.8 18.6 25.0 31.9 40.1 58.6 79.8 104.1 168.4 248.1 343.6 435 1,021 1,815 2,887 12.9 17.5 23.5 29.9 37.6 54.9 74.8 97.6 157.8 232.6 322.1 407 958 1,702 2,707 17.2 23.3 31.3 39.8 50.2 73.3 99.7 130.1 210.4 310.1 429.5 543 1,277 2,269 3,609 20.6 27.9 37.6 47.8 60.2 87.9 119.7 156.1 252.5 372.1 515.4 652 1,532 2,723 4,331 27.5 37.3 50.1 63.7 80.3 117.2 159.5 208.2 336.7 496.1 687.2 869 2,043 3,631 5,774 31.0 41.9 56.4 71.7 90.3 131.9 179.5 234.2 378.8 558.1 773.1 978 2,298 4,085 6,496 38.7 52.4 70.5 89.6 112.9 164.8 224.4 292.8 473.5 697.7 966.4 1,222 2,873 5,106 8,120 42.6 57.6 77.5 98.6 124.1 181.3 246.8 322.0 520.9 767.4 1,063 1,345 3,160 5,616 8,932 46.5 62.9 84.5 107.5 135.4 197.8 269.2 351.3 568.2 837.2 1,160 1,467 3,447 6,127 9,744 54.2 73.4 98.6 125.4 158.0 230.8 314.1 409.9 662.9 976.8 1,353 1,711 4,022 7,148 11,368 Boundary conditions: (1) Yield point controlled tightening; (2) Friction tot ¼ 0.16; (3) Proper screw section design, so failure is located at threaded cross-section (As is smallest area of cross-section; no thread stripping, no head stripping) Notes (1) For torque controlled tightening in practice, the preload can be reduced (app  0.7); (2) for utilization of eq ¼ 90% of Rp0.2, multiply relevant preload by 0.9; (3) yield strength ratio kR ¼ Rp0.2=Rm; (4) for angular controlled tightening, multiply relevant preload by [1 þ 0.3(1 À kR)=kR] Copyright 2004 by Marcel Dekker, Inc All Rights Reserved The difference between initial and residual preload is caused by contact plastification (seating) or relaxation (material creeping, especially at high temperatures) 1 Minimum Initial Preload The minimum preload required is responsible for the selection of screw size For a given screw strength and assembly method, the minimum level is generated for maximum friction coefficient Therefore, in Table 13 for metric screw thread geometry, a friction coefficient mtot ¼ 0.16 is assumed (relevant values of mtot see Table 4) The listed preload levels are reached for yield point controlled tightening Using the legend, preloads for other tightening methods can be calculated To achieve a preload level for a friction coefficient mtot ¼ 0.08, multiply relevant value of table by 1.15 From the preload level of Table 13, with formulae of Fig 16, the corresponding torque values can be obtained But for torque controlled tightening one must remember that the smallest torque corresponds to the smallest friction coefficient and this has to be specified for assembly specification If a screw with high friction is tightened with the specified torque of low friction, the generated preload is reduced (see aspect 1 of legend from Table 13) Table 13 refers to screws for existing nut thread If thread rolling screws (Fig 6) are used, the preload level is reduced by some percentage because of the higher thread friction (app À5%) For generating nearly the same preload with thread rolling screws as with same screws for existing nut thread, the tightening torque has to be increased significantly (see also Ref [63] or Fig 67) Table 14 gives the same information as Table 13 for unified screw thread geometry For designations of screw threads, see Fig 5 How does one find the required minimum initial preload Fp0? As a rule, the initial preload should be at least five times the maximum operating load of the screw (nfFax) added by 10% for relaxation loss This rule applies to stable threaded fastening systems without creeping effects The initial preload must prevent any component from separating (guaranteeing sealing function, see also Fig 49; avoiding of increasing load factor f, see also Fig 25), microsliding (fretting, self-loosening) or significant relaxation (continued preload loss with possible failure in consequence) 2 Boundary Conditions in Practice For selection of screw size, handling during operation and field maintenance is an important consideration As an example, a screw of dimension M6 or higher can normally be hand tightened by workers without danger of Copyright 2004 by Marcel Dekker, Inc All Rights Reserved overtightening A screw up to M12 can be tightened=retightened with normal wrenches and moderate manpower Screw dimensions between M6 and M12 can be used by nearly every person without special qualification=training and=or special equipment The design engineer can always decide if a few large screws or more small screws are used to achieve the summarized preload An increased number of small screws has the advantage of better stress homogeneity in the components, better sealing of flanges, reduced local separating of components with low stiffness under operating load But a multi-screw-fastening-system needs a detailed calculation of the loading of each particular screw and a defined tightening sequence during assembly Screws, which need exact preload, should be tightened by yield point control or angular control (see also Fig 51) Finally, the requirements from deproliferation have to be met The number of different parts which have to be purchased, stored, and managed, has to be minimized This means, consolidating similar screws due to screw length, screw diameter, screw head, screw material, and screw surface C Determination of Screw Geometry If the screw thread size is known, several additional geometry details have to be determined These are screw head, length of thread engagement, screw body, thread length, and other design options This chapter shows the fundamental aspects for design decisions 1 Thread Engagement If the design principle from Fig 2 is valid, the thread engagement requires a minimum value temin, and thread stripping of screw or nut cannot happen Figure 33 points out the result from calculations regarding the VDI 2230 guideline [70] for metric thread series (thread standard, see Fig 4) The diagram illustrates the relative minimum thread engagement temin=d over tensile strength of nut thread component Rmn for different property classes of screw Details are printed in the diagram Generally speaking, the required length of thread engagement increases with increasing screw strength Rms and decreasing nut strength Rmn This diagram has two dimensions of interpretation: for thread engagements higher than the relevant temin, no thread stripping will occur and in any case the screw shank will fail (direction of ordinate-axis) If the relevant point for temin on the selected hyperbolic curve is located in the tangential section, the screw thread will strip for engagements smaller than temin If the relevant point for temin is Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 34 Clamping length lc and plastification length lp of threaded fastening system from Ref 18.) threaded cross-section with area As and the unthreaded cross-section with area Ab resp A2 (area of cross-section with flank diameter d2) The length of a threaded shank with rolled thread flanks as shown in (a) is limited by the length of the rolling die for screw production A full shank (b) has a constant outer diameter in the range of the nominal screw diameter d Such a screw possesses good self-centering behavior through holes An exactly defined centering function can be realized with an increased shank (c) A reduced shank (d) often is an optimum between screw-weight, -cost, and -function, because the reduced shank has a diameter in the range of thread flank diameter d2, so the screw production line can be made effective A wasted shank (e) gives a high screw resilience with low additional screw force under loading; here the body diameter dB should be made as long as possible (a guiding diameter is necessary under head and the transition between different diameters has to be designed with large radii for avoiding of stress concentrations) As a guideline, a shank type (a) or (d) should be taken whenever possible The clamping length is the distance between head support and start of thread engagement and the plastification length is the length of free shank under preload with smallest cross-section As or Ab Therefore, lc is the same Copyright 2004 by Marcel Dekker, Inc All Rights Reserved for all screw types (a)–(e) In contrast, the plastification length varies from lp ¼ lc at type (a) to smaller values at types (b)–(e) By reason of the significant area difference between As and Ab resp A2 at the same screw, only the smallest cross-section will plastify under tensile load; this smallest cross-section comes to failure before the other cross-section gets plastified dependent on the materials ratio of Rp0.2s over Rms 3 Screw Head The screw head includes two important aspects: (a) type of screw drive, and (b) type of support area The type of screw drive is responsible for capability of assembly process, the type of head support area is influencing the designed function of the fastening system Figure 35 presents the established and widely used types of screw drive geometries They are distinguished by external and internal types For external and internal geometry four designations are important: hexagon, bihexagon, triple square, and hexalobular If considering internal configurations also, cross-recess drives (e.g [21]) and slotted screw drives are of interest These two geometries are dominant for small screws without high Figure 35 Basics of screw drive selection Copyright 2004 by Marcel Dekker, Inc All Rights Reserved preload because they cannot provide high torque values which can be transmitted reliably between bit and screw The most common screw drive globally is the hexagon geometry This is important for components which have to work and must be repaired in areas without technical experience This drive type is suitable for high torque values if there is only a small clearance between bit=wrench wrench and screw and if the drive has no damage Using an open wrench as a rough estimation, only half of the torque compared with a ring spanner can be applied with reliability The reason is that when using an open wrench, only two flanks are used for torque transmission Since six drive flanks and a small contact angle between bit and screw for the line contact, the hexagon drive may lead to damaging the surface of the screw, especially if the screw is coated for corrosion protection or if worn bits are used In Fig 35, these aspects lead to a sum of 9 assessment-points from the 20 possible A significant improvement of drive torque loading capacity and reliability is achieved with 12 flanks (bihexagon and triple-square drive geometries) A bihexagon drive geometry is created by two hexagon drives, which have the same center point and an angular misfit of 308 A triple square drive geometry is created by three square contours, which have the same center point and an angular misfit of 308 each A hexalobular drive geometry [established by Textron-Camcar under the designation TORX#] consists of one (small) convex and one (large) concave contour radius, which are alternately combined [22] This leads to smooth contact pressure between screw and bit as well as small-sized outer bit diameters for compact design structures There is no significant difference in using this design compared to bihexagon or triple square, except that the same maximum drive diameter, the hexalobular drive geometry has a lower drive section modulus against torsional failure Triple square or bihexagon drives should be used For the internal drive configurations, the same comments are valid Compared to the external configurations with the same head diameter, the drive flanks are smaller and the internal configurations are stressed to a higher level for same torque transmission The bit is much smaller which is very positive for the accessibility In most cases for internal bihexagon, triple square or hexalobular drive, the bit determines the torque limit, not the drive of the screw Internal drive configurations usually have lower weight of the screw head than external drives, but internal drives can lead to head stripping under preload, if their bit-engagement is too deep On the other hand, a minimum bit engagement is necessary for reliable assembly process These two influences determine the height of head for screws with internal drive Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Slotted screws are only relevant for applications with low requirements for screw tightening They have a cam-out-reaction under torque loading and the blade of the screw driver can have a radial misalignment, which leads to damage of screw, screw driver and possibly of component surface Cross-recess drives are an obvious improvement over the slotted screws in low torque applications like screws for fastening wooden constructions or plastic components They provide a radial alignment between screw and driving bit, but the negative cam-out-reaction is significant The life time of cross-recess bits is quite short Of course, there exists many other drive systems for special requirements, such as Square drive, Multispline, Hexapol#, Triwings#, Clutch- Figure 36 Contact conditions of high torque screw drives (From Ref 17.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved type#, Torx-Plus#, or Polydrive#, which often are trademarks of different companies Figure 36 demonstrates the contact conditions of high torque screw drives from Figure 35 in a more detailed manner In any case, the tolerance situation is important for the torque loading limit of the drive The clearance in Fig 36 is oversized in order to emphasize that all screw drives have single contact lines at each drive flank, if they are undeformed (only contact points in drawn cross-sections) The applied torque Ttot leads at each drive flank to a circumferential force Fc, which can be divided into a normal part Fn (torque transmission) and a tangential part Ft (contact sliding and in consequence flank wear) For an ideal drive geometry, this Fc can be calculated as shown in Fig 36 Between Fc and Ft, one can measure the contact angle E This value is 308 for hexagon and bihexagon drive, 458 for triple square (see also Fig 63) and about 608 for hexalobular drive geometry A small contact angle means high contact sliding under torque loading This is the reason for surface damaging of the screw area engaged to the bit as well as the reason for wear of the bit flanks Figure 36 confirms that a bihexagon drive has the same contact conditions as a hexagon geometry, but the increased number of engaged flanks lowers the Fc at each single flank The triple square and hexalobular drive systems have an increased contact angle, so they should be taken as a designed screw drive system today, if no advantages of other drive systems are predominant If the clearance between bit and screw drive contour is too large, the bit life time decreases significantly and the danger of screw drive damaging occurs Often for small-volume-designs, the space for screw head and the accessibility for bit are limited Figure 37 compares the space requirements of three screw head designs with hexalobular drive type for same thread diameter d and same support diameter da Part (a) refers to an external configuration, which is characterized not only by high stiffness of the screw head, but also by large height requirements The bit for driving the screw normally has a largest diameter up to 2.0d as the head support diameter da If using a standard design with internal configuration (b) the height of screw head is reduced to %80% of (a) Also, the size of the screw drive flanks is reduced to only % 60% of (a) This can cause problems if the screw has high material strength and if the screw is tightened to high preload level beyond the screw material yield limit In this case, the cross-section of the driving bit exceeds its fatigue limit, so that the life time of the bits is decreased drastically Another aspect of internal drive configuration is the ratio of screw head height and length of bit engagement This ratio has to Copyright 2004 by Marcel Dekker, Inc All Rights Reserved of head is only 0.7d, no head stripping occurs under preload due to the reason of the conical head-shank-transition The large length of bit engagement guarantees a high assembly process capability The large size of screw drive flanks leads to a long bit life time for any tightening method The internal configuration offers an easier drive accessibility by a small bit diameter compared to the external configuration of (a) Another important design aspect of screw head is the type of support area Figure 38 displays three established types of support area between screw head and clamped part Each type has its own calculation for the effective bearing diameter Deb [72] This diameter Deb represents the virtual diameter, where the circumferential force produced by the contact friction can be concentrated for calculation; it influences the head frictional torque Th directly (see Fig 16) A plain support type is used as a standard; it is easy to manufacture and requires no special geometrical matching of screw and clamped part Large head support diameters da are suitable for low surface contact pressure (see also Figure 39) and for covering large clearance holes Countersunkand ball-section-support types provide a centering function between screw Figure 39 Required relative support diameter for given maximum contact pressure (From Ref 16.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved axis and position of clamped part Therefore, the positioning tolerance of such multi-screw-fastenings has to be precise (e.g wheels of vehicles) Countersunk- or ball-section-support types have to be tightened with different torque values to obtain the same preload depending on the effective support diameter Deb Normally the assembly torque Ttot is increased by %15% compared to the plain support type and similar other boundary conditions However, this approximation cannot replace a detailed calculation By reason of the increased head frictional torque Th, countersunk and ballsection-support types provide an enhanced safety against self-loosening If using countersunk- and ball-section-support types, the tolerances of countersunk angle, the ball diameter of the screw, and the clamped part must fit together In any case, a full bearing area in the support contact is guaranteed [see also ISO 7721 [43]] If using plain support type with clamped parts of high strength in the range of the screw strength or higher, the detailed geometry of the screw support area should be designed in a slightly concave manner, so that the contact diameter is defined clearly If using thin sheet materials, significant angle tolerances between screw axis and support area or rough surfaces The effective bearing diameter Deb in practice can differ from the theoretical calculations regarding Fig 38 A measurement of Deb in experiment is recommended Important for design of screw geometry is the support diameter da Figure 39 illustrates the dependence of required minimum head support diameter for a given permitted maximum surface pressure (plain support type) The three functional curves belong to different property classes of screws (tensile strength values 1200, 800, and 400 MPa; for property classes, see also Table 10) The lowest curve represents a screw made of low-strength material like aluminum For example, a given maximum surface pressure of 100 MPa in the contact zone between head and surface of clamped part means a very large relative head diameter of 3.2  d if using a bolt with a strength of 1200 MPa and a relative diameter of only 2  d if using a bolt of strength 400 MPa (e.g made from aluminum) This diagram makes it clear that only screws with flange head and a low screw strength can reach the demand for low surface pressure with acceptable head diameter This is required for materials of clamped part with limited loadability and significant creep behavior, e.g magnesium components at elevated temperatures The permitted contact pressure pchperm for the particular material clamped should not be exceeded to avoid any excessive plastic deformation in the head contact area, even if the bolted joint is in operation (this would result in a loss of preload) As a rough estimation, the permitted contact pressure pchperm should not exceed the minimum of (Rp0.2 þ Rm)=2, either of the screw material or of the clamped part material This can only be done Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 40 Influence of head support details on tightening behavior if no creep occurs In that case, experiments must determine the contact pressure limit pchperm, which does not lead to significant preload loss Often it is about half of Rp0.2 If a high-strength screw with only low assembly torque to limit the low permitted head contact pressure is used, the danger of misassembly occurs (missing information for the right handling in field service, perhaps by unauthorized workers) Figure 40 finally emphasizes the result of a torque-preload measurement over tightening angle done at RIBE laboratory with two slightly different contact angles for head support (with plain, but concave bearing geometry) Part (a) belongs to a support angle of only 18 between screw head support area and spot face of clamped part Here, the maximum preload reaches about 57 kN and the maximum tightening torque increases up to 107 N m Part (b) contains a screw with support angle of 38, which leads to almost the same maximum preload of 55 kN, but to a very high maximum tightening torque of 168 N m (as a result of metallic adhesion between screw and clamped part caused by severe local stress peaks at support diameter region) This means that very small changes of the head support geometry or surface can lead to significant changes in tightening behavior, especially if overelastic tightening methods are applied (see also Fig 18) Besides this, Fig 18 confirms that in spite of the large difference in friction for both situations (a) and (b), the preload is almost the same—this result can be achieved only with overelastic tightening methods Copyright 2004 by Marcel Dekker, Inc All Rights Reserved D Design Options 1 Established Main Types Besides the rules of basic mechanics for threaded fastening systems, a large number of design options exist The most important options are proposed below The design engineer has to select the correct options important for him Of course, some options are suitable for more than one design target and others are very specialized Figure 41 indicates design options for three optimization targets (a)–(c): improved assembly, improved fatigue limit, and avoiding of self-loosening For all optimization targets, the most important actions are listed Figure 41 is self-explanatory, but some aspects are discussed in a more detailed manner in the following lines Thread ends for finding the best nut thread are most important for short screws which have no significant self-alignment by the through hole of the clamped part (clamping length lc under 1  d, see also Ref [21]) The automated handling of screws is much easier if the screw exhibits a center of gravity location with dominating shank-weight so that the screws tend to fall ‘‘head-up’’ The mathematical condition given in Fig 41 is a rough approximation for guidance For further details, see Ref [21] The fatigue limit of a bolted joint depends on all the parts of the fastening system One action to improve the fatigue behavior is to increase the material limit of the screw (materials selection, etc local residual stresses, etc rpar; or to reduce the additional operating force of the screw during operating by increasing the elastic resilience of the screw Examples are given in Fig 41 Another aspect is the reduction of stress concentrations which appear most at first bearing thread flank (see also Fig 2) Self-loosening can happen under high preload if microsliding in the contact zones of head support and thread contact appears (e.g large dynamic transversal loading, see also Fig 76) A head support with locking teeth is a very effective action to prevent self-loosening without influencing the preload level of the fastening system Washers or similar additional elements with ribs or teeth are usually of no help against self-loosening Thread flank clamping as an alternative is based on ‘zero-clearance’ between nut thread and screw thread flanks, but a clamping torque reduces the acting preload after tightening Adhesives also eliminate flank clearance between nut thread and screw thread without a clamping torque (but with a thread frictional coefficient mt of about 0.20) Adhesives have a limited operating temperature of %2508C depending on the adhesive material Three other design targets can be: improving preload, reducing weight, and avoiding unauthorized disassembly Established design options to meet these requirements are demonstrated in Figure 42 Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 42 Design options for bolted joints due to preload, weight, and disassembly Copyright 2004 by Marcel Dekker, Inc All Rights Reserved For improving the preload acting in the fastening system, the main actions are increased screw diameter (1), increased screw strength (2) and selecting an optimized tightening method (3, see also Fig 18) For components made of low-strength materials, the time dependency of preload is important (relaxation effects, see also Fig 66) In this case often, it is more useful to reduce the preload retention during time of operation than increasing the initial assembly preload which is decreased extremely over time (4 in Fig 42) For reducing weight in part (b) of Fig 42, six actions are mentioned Of course, first the weight of the fastening element can be minimized, e.g., by using an aluminum screw instead of steel screws This is very positive especially if light metal components with low-strength and high thermal expansion coefficient have to be fastened A secondary weight saving effect is that for low-strength nut thread components an aluminum screw offers a reduced minimum thread engagement with chance for a small component size (see also Fig 33 for screw with a strength of 400 MPa and section 4 in Fig 42) For components with high strength and in consequence high load bearing limit, the use of a high-strength screw is suitable The size of this high-strength screw can be reduced compared to a screw made of material of a lower property class (2) The same effect can be realized with a better tightening level of the screw (3) Here also, the design limits of screw and components must be sufficient so that, the tightening method is fundamental for a design analysis (3 in column (a) and Fig 50) Additional actions for reducing weight can be minimizing screw head volume and, if necessary, a hollow screw shank (interesting for large screws, which are not stressed up to their loading limit) The right column in Fig 42 shows actions for avoiding unauthorized disassembly of a threaded fastening system For using a special screw drive (2), the compatibility with maximum torque level during tightening and with available tightening tools in production and field service has to be checked A shear-off-drive is designed, so that the drive is sheared-off if the ultimate tightening torque is generated Then the screw can be disassembled by extensive mechanical work resulting in destroying the screw Applications include locking devices An important aspect is the missing corrosion protection in the broken shear plane of the screw Another way to avoid an unauthorized disassembly is using a combination of thread rolling screw, adhesives, and large thread engagement The screw can be tightened, but the screw drive is not suitable to transmit such a high torque which would be necessary for disassembly This solution is used for components with safety relevance (which may not be opened, e.g., control units for anti-locking-brake-systems) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved From the point of screw mechanics, washers should be avoided because they always lead to more surface contacts in the fastening system with roughness and in consequence with possible preload retention (seating, relaxation) But washers are useful to prevent surface damage of component surface by rotating screw head during tightening (e.g., for fastening of painted components) Another reason for using washers can be providing a high-strength contact surface for the screw head, which transmits the preload to the lowstrength component material (reduction of contact pressure for the component) then, the washer needs a thickness of about 20% of the nominal screw diameter and a hardness, which is in the range of the screw or higher To avoid self-loosening of the screw, any washer design must be checked very critically because only a few washer geometries can guarantee this (see Fig 41) 2 Special Elements for Threaded Fastenings Two groups of fastening elements which have a strong growth for new developments of components are visible in Figs 43 and 44 Staking elements are of great importance for automated generation of a screw thread or nut thread in thin sheet metal components without sufficient material for thread engagement Figure 43 contains self-explanatory details for a staking bolt with additional characteristics for use In contrast to welding bolts or nuts, Figure 43 Principle of staking bolt; system RIMS (From Ref 64.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 45 Example of Rfixx-plus-element (From Ref 61.) and a high total process capability, especially for high preload levels (e.g overelastic tightening) Figure 46 summarizes the most important aspects comparing studs and screws 4 Characteristics of Washers Both washers and flange heads can be designed with the same support diameter for the component (Fig 47) The design engineer has to decide which geometry must be selected for the fastening solution In Fig 47, the most important aspects are summarized In practice, the main reasons for using washers are the prevention of damage of (painted) surfaces, the reduction of contact pressure at clamped parts with low material strength (e.g plastics) or covering large through holes For high-duty threaded fastening systems, always a washer head (flange head) of the screw should be considered by reason of the enhanced assembly process capability Flange heads of screws can be produced economically up to (2.5–3)  nominal screw diameter Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 48 Assembly behavior of screw and washer with similar support diameter; measured data the washer rotates on the component and for higher preloads the screw rotates on the washer But the contact zones under screw head change (different roughness, different materials, and different lubrication), which leads to a significant change of the head frictional torque (recorded in the measuring diagram of Fig 48 over preload in screw shank) For automated assembly procedures, this can cause error signals of the tightening device, especially if the screw is tightened with yield control 5 Characteristics of Sealings If a gas- or liquid-tight threaded fastening system is required, three contacts have to be considered: (1) head contact sealing, (2) component contact sealing, (3) thread contact sealing (Fig 49) Often, number (2) is most important For the design engineer, the task of selecting the right ratio between clamping length lc and screw distance x is an important one This ratio x=lc should be smaller than 10 in order to minimize critical zones for leaking The mean nominal contact pressure for a gasket should be larger than 2 MPa In order to obtain the same tightening behavior with and without sealing, a gasket should be as thin as possible (e.g., spring steel sheet with some mm polymer-coating to fill the roughness of technical surfaces) For further details, see Fig 49 For sealing technology with liquid gaskets and adhesives, see Ref [52] E Loading vs Loading Capacity—Design Analysis 1 General Procedure A design analysis has to guarantee that no failure of the fastening system can happen This is only possible by comparing maximum loading (of screw, Copyright 2004 by Marcel Dekker, Inc All Rights Reserved pressure limits, which are also dependent on the specific geometry (Ttotpermt1, pchpermt1, pchpermt2, Fthreadpermt1, Fthreadpermt2, Fheadpermt1, Fheadpermt2, and Ftranspermt2) For example, the permitted contact pressure under head after tightening at temperature t1 (pcht1) and during operating at temperature t2 (pcht2) must not reach extensive plastification of the bearing surface, which is characterized by pchpermt1 and pchpermt2 Ttotpermt1 is the maximum torque during tightening which can be transmitted by the screw drive without problems Fthreadpermt1 and Fthreadpermt2 are the maximum preloads before thread stripping of the bolted joint occurs (stripping can take place at both, nut thread or screw thread depending on the tolerances and material strengths, see also Fig 33) Fheadpermt1 and Fheadpermt2 are the maximum preloads before head stripping of the screw takes place During operation, acting transversal forces have to be lower than Ftranspermt2 The first loading of the fastening system is done during tightening So, the minimum and maximum assembly preload Fpamin and Fpamax have to be calculated (of course, dependent on the tightening method) If the assembly preload is known, also the tightening torques Ttotamin and Ttotamax for assembly can be determined From these tightening preloads and tightening torques, the loadings with bullets under (2) are applied during operation, e.g., axial static or dynamic force This leads to the results of minimum and maximum operating preload Fpomin and Fpomax One important aspect, especially for tightening methods with screw plastification, is the reduction of torsional stress after taking away the tightening torque (about À10% to À30% of the highest torsional stress under torquing conditions) This increases the axial loading limit of the screw, so also plastified screws can bear significant additional loads in a threaded fastening system Besides this, a chemical stability is assumed in general for this design analysis The design criteria under (3) compare all relevant loading values with the corresponding loading limits (forces, stresses, pressure, and torque) Only if all criteria are valid, the bolted joint is designed safety But sometimes, certain criteria are not important; so the number of relevant criteria can vary (e.g., only low level tightening makes stripping, contact pressure, drive torque limit, and screw overloading uncritical, so most of the design criteria can be neglected) The design criteria are distinguished for axial= transversal force and design section compatibility (see also Fig 2) The selection and assessment of the design criteria are an engineering task If the threaded fastening system only works at room temperature, no temperature influence has to be considered (t1 and t2 are missing) If the fastening system operates at various temperatures, the highest and lowest temperature have to be considered, so then t3 occurs Copyright 2004 by Marcel Dekker, Inc All Rights Reserved well as deviation in screw strength from 1000 to 1200 MPa (10.9) This results in four different linear functions between tightening torque and preload On each curve, there are three markings (rhomb for an equivalent one-dimensional stress seq ¼ 0.9Rp0.2 during tightening, triangle for corresponding seq ¼ Rp0.2 and quadrangle for seq ¼ Rm) Now, if the screw is tightened with torque control in the range of 16– 20 N m (see gray field in Fig 51), the generated preload can vary from 8 to 22 kN (8 kN for case D and minimum torque of 16 N m; 22 kN for case A and maximum torque of 20 N m) Please note this is a ratio of maximum preload over minimum preload of almost 3 In practice, this means that for this fastening system and this tightening specification, only 7 kN are guaranteed at minimum On the other hand, for case A, the yield point of the screw is achieved at about 24 N m (position of triangle), so for this situation, the tightening torque cannot be increased significantly As a result, in general, the disadvantage of torque controlled tightening is that the tightening torque Ttot must be specified for lowest possible torque value (case A in Fig 51) For other combinations of deviations, this gives a poor preload Fp (e.g case D in Fig 51) The difference of overelastic tightening compared to torque control is outlined for yield point controlled tightening in Fig 51 If yield control is used, for every screw the beginning of plastification is detected, so every screw, is tightened to its triangle marking Then the preload is generated in the range from 18 to 27 kN (ratio maximum preload over minimum preload is reduced significantly from 3 for torque control to %1.5!; arrows with dashed lines) In practice, this means a slightly increase of maximum preload and an extensive increase of minimum preload (see also Fig 18) The smaller deviation of preload must lead to higher deviation in torque values (Ttot is in the range of 24–43 N m in Fig 51) One should never worry about changing torque values if overelastic tightening is used; the preload is safe, if the screw strength and the friction are as specified 3 Dynamic Loading Capacity The dynamic loading capacity of threaded fastening systems depends on a lot of details regarding the entire joint-like value of external alternating loading, stiffness and resilience, eccentricity, symmetry, component separating, thread geometry, residual stresses, occurring stress peaks, manufacture of screw, and finally besides others also fatigue strength of screw material Therefore, an exact determination is only possible by experiment resp measurement of the original system in the particular application Testing of the dynamic behavior of a designed structure covers the most often performed tests Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Generally speaking, the maximum stress concentration factor of about 8 (at the first bearing thread flank of screw, see Fig 2) reduces the screw material fatigue limit by a theoretical factor of 8 compared to results obtained with cylindrical samples without notch geometry effects (often listed in engineer’s handbooks For a first approximation of the screw fatigue limit without additional information, take the sample value of the cylindrical screw diameter and divide by 10 This often is necessary for screws made of nonferrous metals) If no data for fatigue-limit are available, as a rough approximation, the sample fatigue limit of steels is about half of the tensile strength and the fatigue limit of aluminum is about one-third of the tensile strength regarding the same sample for axial loading, see Ref [48] Reference [70] gives an empirical relationship between steel screw fatigue limit and screw diameter as reported in Fig 52 The diagram, on the one hand, distinguishes between thread rolling before and after heat treatment, and on the other, considers the preload dependence, correlated by the term Fp=(Rp0.2ÁAs)—a ratio up to 0.7 belongs to screw tightening without plastification, a ratio of 0.8 belongs to yield point controlled tightening and a ratio of 0.9 belongs to angular controlled tightening with significant plastification of screw shank The diagram shows two general aspects: (1) overelastic tightened screws still have a significant fatigue limit, and (2) the fatigue limit of screws Figure 52 Fatigue limit sasperm0 of steel screws depending on screw diameter d (After Ref 70.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved  ... responsible for the selection of screw size For a given screw strength and assembly method, the minimum level is generated for maximum friction coefficient Therefore, in Table 13 for metric screw... flange head and a low screw strength can reach the demand for low surface pressure with acceptable head diameter This is required for materials of clamped part with limited loadability and significant... drive torque limit, and screw overloading uncritical, so most of the design criteria can be neglected) The design criteria are distinguished for axial= transversal force and design section compatibility