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The lubrication cycle is set at the pump. Voltage supply via cable. Lubrication pressure, empty message and signaling of malfunctions can be read at the display.

Multiple parts are bolted together with a through-bolt and washer/nut combination. The bolt may be hex, socket, or pan head style (see fig. 7).

Equations (14) and (16) are used to determine the maximum and minimum expected preloads for various sizes of A-286 alloy and 300 Series CRES fasteners (see tables I and II).

The lubrication cycle is programmed by the machine control system (PLC). The voltage supply and connection to the control system are provided via a cable.

Parts are bolted together with a bolt threaded into the last part (with or without insert). The bolt may be hex, socket, or pan head style (see fig. 9).

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The recommended factor of safety for joint separation, SFsep, is equal to 1.2 for structural applications and 1.4 for pressure system applications.

This page provides details on the analysis of bolted joints. This source of this page is Chambers, Jeffrey A., "Preloaded Joint Analysis Methodology for Space Flight Systems," NASA Technical Memorandum 106943, 1995.

For bolts subjected to the combination of simultaneous tension and shear, the following interaction equation must be satisfied (ref. 7):

The possibility of encountering shear tearout can be greatly reduced if design practices are employed which maintain minimum e/D ratios of 2.0 or more. Occasionally the hardware design does not permit maintaining the 2.0 factor and the ratio must be reduced. In this situation, the e/D ratio may be reduced to as low as 1.5, however, it is never advisable to permit edge conditions resulting in an e/D ratio of less than 1.5 (ref. 9). As the ratio falls below 1.5, shear tearout failure becomes less prominent as the dominating stresses are tensile in nature. The failure mode then becomes a tensile (hoop stress) failure across the minimum section between the bolt and edge of the abutment.

The allowable pull-out strengths have been tabulated in table V for 6061-T6 aluminum alloy parent material. Similar values can easily be calculated for other parent materials.

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Standard MS Class II nuts (including fixed and floating plate nuts) are designed to develop the full tensile strength of a bolt having an ultimate tensile strength of 125 ksi when the tensile area (At) is based on the basic pitch diameter of the bolt. As such, the nut strength may be expressed as

Although it is good design practice to avoid putting bolts into direct bending, occasions do arise where bending is experienced. Bolt bending may result from double shear, misalignment during assembly, use of long spacers, or from flanges that are several orders of magnitude stiffer than the bolt. In the latter case the flange tends to rotate as a rigid body, forcing the head of the bolt to rotate which applies moment loading to the bolt. For bolts subjected to the combination of tension, shear, and bending loads acting simultaneously, the following relation must hold (ref. 1):

The first requirement is explicitly defined by the payload safety verification requirements associated with space flight hardware which mandates that all safety and fracture critical fasteners possess positive (>0.0) margins of safety for all modes of failure. These margins of safety (MS) for bolts under various states of loading can be expressed (but are not limited to) as follows:

Under the initial preloading the bolt carries a tensile load while the flanges carry an equal compressive load. If an external tensile load, Pet, is introduced very near the contact surface between the two flanges (n ≊ 0), then both flanges are further compressed through almost their entire depth. Only a very small portion of the flanges between the induction points is left to undergo relaxation of its compressive preload. In the spring diagram, springs a and d are very long in comparison to springs b and c. As the external load is applied, springs b and c are relieved (unloaded) of some of their compression while springs a and d are further compressed (loaded). The compressive deflection relieved in springs b and c is partly offset by the additional compressive deflection gained in springs a and d. Any additional elongation (and hence loading) in the bolt is equal to the difference in deflections between the unloaded and loaded sections of the flanges. This action with the flanges reacts a large portion of the external loading as shown in fig. 5(a). When the magnitude of Pet reaches that of the initial preload, Po, all remaining compression in springs b and c has been relieved and the flange faces separate. Once the flanges have separated, the bolt is left to carry the entire external load.

The ultimate strength of the insert in the internal thread shear failure mode is dependent on the amount of shear area available to resist axial loading of the bolt. This thread shear area is a function of the thread size and type as well as the length of thread engagement. In much the same manner as the external thread shear strength of the bolt, the insert internal thread shear strength is based on the major diameter of the mating external threads. This thread shear area can be estimated by (ref. 8).

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If the external loading is applied at the free faces of the flanges (n = 1.0), the entire thickness of the flanges are relieved of their compression as loading is applied. All springs a, b, c, and d are relaxed. Since there is no flange material beyond the loading planes to undergo additional compression (such as in the previous case), the bolt elongates at the same rate that the flanges are relieved. In this situation the joint follows the load-deflection curve as shown in fig. 5(b). Again, separation of the flanges is not encountered until all compression in the flanges has been relieved. For equal loading applied in both cases, the latter case (n = 1.0) results in greater load being transferred to the bolt.

These torque tables should be followed in conjunction with the procedures and restrictions set forth in MSFCSTD- 486B. If a particular fastener arrangement or application (e.g., shear) is encountered, but not listed here, the parent document should again be sought for the appropriate torque levels.

Combining all factors for a manually torqued, lubricated fastener with negligible thermal effects, enables equations (12) and (13) to be expressed as

The tensile area, At, is the minimum cross-sectional area of the bolt and is calculated from the following equation (ref. 1):

The Memolub automatic lubrication system consists of a small lubricant dispenser with progressive distributor with several outputs. The automatic lubrication system lubricates the guideway and rack of the equipped axes automatically. The lubricating pinion unit lubricates the rack. The wiper and lubrication unit lubricates the guideway.

The shear area of the insert's externally threaded region is calculated in the same manner as that for the external thread shear area of the bolts given by equation (63) with the exception that the area must be reduced by the amount of area lost for the insert locking keys (if applicable). With external thread shear area, the insert pull-out strength is

In most practical joint applications the behavior of the joint is at some point between these two extremes. For common joint designs the load is carried somewhere near the midplanes of the flanges as shown in fig. 6. With loading introduced near these midplanes (n = 0.5), the flange regions inboard and outboard of the loading planes work together much like the case of n ≊ 0 but to a lesser degree. The loading plane factor is described by reference 1 as

In general, for most modes of failure a margin of safety can be calculated for both ultimate and yield strengths. Both of these margins should be checked to determine which is limiting (critical) since a positive margin may exist for one while a negative margin exists for the other.

Preload relaxation (or embedding) occurs as the contact surfaces of the flanges and joining elements experience local yielding as they conform to one another over a period of time. Surface defects and machine marks that form high points on the contact surfaces experience local yielding under the preload. This eventually works to seat the surfaces together and relieves some portion of the preload as shown in fig. 2. There may also be some localized yielding in the threads of the bolt and nut that results in additional relaxation. Preload relaxation can also be encountered if elastomeric joint materials (e.g., gaskets) are used and experience permanent set over time. Dynamic or cyclic loading can lead to settling in the joint through fretting of the contact surfaces. The amount of preload relaxation can be quite difficult to characterize since it must consider the materials, loading, and physical (e.g., corrosive) environment in which the joint exists. The amount of embedding for typical metal-to-metal joints in a noncorrosive environment is typically between 2 and 10 percent (ref. 4). For design and analysis purposes it is safe to assume the preload loss to be about 5 percent, that is,

The bolt material ultimate shear strength, Fsu, can usually be found for most ductile materials in references such as MIL-HDBK-5F or ASTM material specifications. The shear yield strength, Fsy, may be assumed to be 0.577Fty.

At any load Pet resulting in Psep < Po,min, the system possesses compressive energy and behaves as discussed earlier. When the portion of loading carried by the joint equals the preload (represented by the dashed line), ΔPj = Psep = Po,min, the compressive force held in the joint is totally exhausted and the joint begins to separate. Loading the joint beyond the separation point results in all of the loading being transferred through the bolt.

Guideways, racks, and pinions can be lubricated by an optional automatic lubrication system. Depending on customer needs and integration requirements, the selected system reduces the downtimes of the overall plant. Güdel provides documents for installation, integration, and operation. Orientation aids for lubricants, lubrication interval, cycle, or quantity, help to ensure an adequate lubricating film.

The margin of safety should be calculated for all three modes of failure, for ultimate strength only, to determine the limiting mode of failure.

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The lubrication cycle can be programmed via the automatic control system. For this, a 24V connection line must be led to the control system.

To maintain contact within the joint, the thermal deflection of the bolt must be balanced by the total deflection in the flanges. For purposes of developing the relation, assume a connection with flanges made of aluminum and a bolt made of steel (αj > αb) is subjected to a uniform temperature increase. The flanges attempt to expand more than the bolt will allow which increases the load in the bolt. Therefore the total elongation of the bolt is the result of two components: the unrestricted thermal elongation plus an elongation due to the increased load in the joint. The total deflection in the flanges is the difference between the unrestricted thermal expansion and the additional compression due to the increase in preload. The change in preload can be derived as shown below.

In general, a bolted joint performs best when it is preloaded such that the working loads are reacted primarily by the portion of the joint in compression. If designed properly, the bolt actually carries only a small portion (usually less than 20 percent) of that external loading while the greater portion of loading is offset by the release of the compressive energy introduced to the flanges during torquing. Essentially, a large portion of work is performed by the joint while a small portion of work is performed on the bolt. The joint is initially placed in compression by applying a tensile preload to the bolt. An initial preload is introduced so that the compression in the flanges is never completely relieved and hence the flange faces never separate. In order to obtain this level of preload, the bolt is usually prestressed very near its working limits (usually 65 to 90 percent of its yield strength). This preload is most commonly obtained by torquing of the elements and can be determined by (ref. 1)

Shear tear out is possible when the bolt is positioned near the free edge of one or more of the abutment components and is loaded in shear. The bolt fails the abutment by shearing (or tearing) the material between the hole and the free edge of the abutment. This type of failure is common with lug type fittings and thin sheet abutments. The ultimate shear out load is

Note 2: The equations presented here are for joint systems where the applied shear loads are minimal in comparison to the axially applied loads (preload included). Joints designed principally for shear require special considerations, and hence the reader is cautioned to use extreme care when designing such a joint.

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The stiffness factor, ϕ, determines the proportion in which the load is shared between bolt and joint. Since the extensional deflection, δ, of the bolt under an arbitrary tensile loading, Pet, is equal to the amount of net deflection in the flanges, the force in each component can be determined with the aid of the load-deflection diagram (fig. 6).

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The total axial load in a fastener consists of the preload plus that portion of the external mechanical load not reacted by the joint. The total axial bolt load, Pb, can be given by (ref. 1)

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The basic preload may vary from the intended value, either more or less, by an amount established by the preload uncertainty factor, u. Preload uncertainty is a function of many factors including torquing devices, lubrication, load measurement, etc. It accounts for parameters affecting the degree to which the applied torque actually results in joint preload. These parameters can be the sensitivity of the torque measuring device or inconsistencies in running friction from one bolt to another, among others. In general, it is safe to assume that the preload uncertainty for a hand-operated torque wrench used on a lubricated fastener is ±25 percent (ref. 1). For comparison, if load sensing (instrumented) bolts are used, the preload uncertainty factor may be reduced to ±5 percent.

The shear area, As, is normally equal to the minimum tensile area, for example, As = At, unless the joint is designed such that the shear plane acts on the unthreaded shank of the fastener. If the shear plane acts solely through the unthreaded portion of the bolt, the shear area may be based on the nominal diameter.

Separation of a joint occurs when the external tensile load relieves all of the initial compressive preload applied to the joint. Once the joint separates, the flanges cannot contribute to the load carrying capability of the connection, and the bolt is left to carry all of the external loading. In addition to increasing the total bolt load, this condition also severely hampers the fatigue resistance of the joint under cyclic loading. In fluid or pressure applications joint separation may also lead to leaking. For these reasons and others, separation is an unwanted condition for the joint. Therefore the design criteria states that separation of a preloaded joint must not occur. Figure 12 illustrates this separation condition in terms of the load-deflection diagram.

Unfortunately, this method is quite complex since frictional coefficients between heavily loaded parts are not easily estimated with accuracy. A simpler approach is to assume that the nut factor usually ranges from 0.11 to 0.15 for lubricated fasteners. The lower end of this range provides the most conservative approach with respect to bolt loading since it produces the highest bolt preload. The upper end of the range provides the most conservative estimate for joint separation (to be discussed later) since it yields the lowest bolt preload. For unlubricated fasteners, a nut factor on the order of 0.2 may be used. When selecting a nut factor, the engineer may wish to examine both extremes of a reasonable range in order to assess the impacts on joint design.

Tables VII, VIII, and IX were derived from MSFC-STD-486B (ref. 3) for tensile applications. The torque values given in MSFC-STD-486B have been reduced in proportion to the relative material strengths given in MIL-HDBK- 5F.

The terms n and ϕ represent the effectiveness of the joint in reducing the amount of external loading transferred to the bolt. Both parameters can be examined by considering the joint as a system of springs as shown in figure 4.

The bolt stiffness, Kb, is equal to the axial stiffness of a circular rod with a cross section based on the nominal bolt diameter. The joint stiffness, Kj, is taken as the stiffness of the flange region which experiences the compressive preload. It can be very difficult to determine the exact region of the flange which is placed in compression and equally difficult to determine its stiffness. Several methods exist that estimate (either mathematically or experimentally) the stiffness of this load affected region; however, the method outlined by Shigley (ref. 6) has been used in this report. This method assumes that compressive loading in the flange(s) is distributed through 45° conical sections like those shown in fig. 6. Relations for the various joint parameters are given for several typical joint configurations shown in figures 7 to 10.

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For most joints, it is usually acceptable to assume the loading planes to be located at the midplanes of the flanges or the midplanes outermost members if more than two components are being bolted. The joint configuration should always be examined closely to insure that this assumption is applicable.

where dh is the minimum contact diameter of the bolt head (or washer) and dt is the maximum diameter of the lug through-hole. The margins of safety are again calculated for both yield and ultimate using equation (74).

The lubrication cycle is set at the pump. Voltage supply via a battery. Lubrication pressure, empty message and signaling of malfunctions can be read at the display.

Note 1: Establishing an initial preload of 65 precent of yield is specific to some NASA space flight hardware. Other applications may require more or less initial preload depending on functional requirements. However, when a preload target level is established, additional stresses (e.g., torsional stresses) must be considered that may be additive to the axial preload stress.

The externally applied shear load, V, is again found by resolving all external shear loads into a resultant load acting at the individual fastener. The shear load usually has components determined from translational forces as well as components resulting from resisting moments in the joint. The allowable shear load can be given by

The applied torque, T, and nominal diameter, D, are generally known and measurable parameters, but the nut factor, K, is not. The nut factor is essentially a factor applied to account for the effects of friction in the torquing elements (both in the threads and under the bolt head/nut). From Barrett (ref. 2), the typical nut factor, or torque coefficient, can be approximated as a function of thread geometry and element coefficients of friction and may be expressed as

Note 3: The reader is cautioned that equations (59) and (62) can be unconservative in certain situations. The proper interaction equations should always be checked for critical applications.

If the bolt is loaded in shear, bearing failure may occur as the bolt is pressed against the side of the throughhole or bushing. This loads the surrounding material with high bearing stresses that can locally fail the sheet or lug material. The limiting bearing load is given as

Bolted joints are used in countless mechanical designs as the primary means of fastening. However common though, the behavior of bolted joints is quite complicated. For the typical bolted joint, various factors affect everything from the initial torquing and preloading to the final forces carried in the bolt. The parameters that must be considered to characterize joint behavior literally number in the hundreds making the proper selection, combination, and use of the variables quite confusing, especially to the occasional user. When it is also considered that the failure of a bolted joint will usually adversely affect the function or safety of the system, these factors take on even more importance. Given their role in the system's performance, the accurate characterization of bolted joints is of great interest. This is especially true when dealing with critical systems such as those encountered with space flight systems.

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Pillow block bearings consist of a sealed single-row ball bearing with a spherical outer ring which is mounted in a housing.

The FlexxPump automatic lubrication system is a lubrication system for Güdel components. The FlexxPump feeds the lubricant from the cartridge into the lines. Depending on the design, the lubricant is distributed through splitters, combined through Y-segments, or distributed directly to the lubrication areas. Rack and pinions are lubricated by lubricating pinions; guideways are lubricated by lubricating elements.

Bearing under the head of the bolt (or nut) may need to be examined in situations of high preload, large external loads, or soft abutment materials. The limiting bearing load is the same as that of equation (72) except the bearing area is replaced by the effective projected area over which the load acts. This bearing area is given by

Depending on the joint application, there are other modes of failure that may need to be addressed. These may include shear tear out of the lug material, bearing of the bolt against the lug, and bearing of the bolt head and/or nut against the lug.

The bending allowable is usually based on the modulus of rupture (ref. 7) of the bolt material. The margin of safety relation is (Note 3)

where Pet is the resultant external force directed at the joint. This can be obtained through a free-body diagram of the system, finite element results, or other means. This external force must however include all components (e.g., prying action, moment resistance, etc.) that may increase or decrease the final force acting at the bolt. A factor of safety (SF) is applied to the external loading only (as opposed to Pb as a whole) since inaccuracies of the preloading process have already been accounted for in the development of Po. The factors of safety for general space flight hardware are usually dependent on the method of verification used (ref. 5) and may differ from program to program. For nonpressurized, untested applications the safety factors are normally 1.25 and 2.0 for yield and ultimate strengths, respectively, while 1.1 and 1.4 are typical for nonpressurized, tested applications. Safety factors are strongly dependent on the specific application, method of loading, and overall design requirements, and therefore should be reviewed carefully before using them with the joint equations.

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As an alternative to the typical nut factor method of determining preload, the torque-preload relationships can be determined experimentally. Here, the torque-preload relationships are determined by direct measurements taken from instrumented joint specimens. Statistical data is recorded for the torque required to achieve a desired bolt force. Many relationships have been developed for various sizes, types, lubrications, and bolt materials commonly used in space flight hardware and are well documented in MSFC-STD-486B (ref. 3). For tensile loading applications, if the fastener is torqued in accordance with the guidelines, it may be assumed that the pretensioning develops 65 percent of the tensile yield strength of the bolt material. (Note 1)

For joints using threaded inserts, such as the joint shown in fig. 14, three basic modes of failures may be encountered. The first mode of failure, shear failure of the insert's internal threads, is exhibited as the fastener pulls out of the insert, failing the internal threads of the insert. The second failure mode, shear failure of the insert's external threads, is exhibited as the insert pulls from the parent material, failing the external threads of the insert. The third mode of failure, shear failure of the parent material's internal threads, results as the fastener and insert together pull from the parent material, failing the internal threads of the parent material. Each failure mode may be investigated using the methods described in the following sections.

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A more rigorous method of determining both the shear tear out and bearing failures is developed in Bruhn (ref. 7) and NASA TM X-73305 (ref. 10). This is the recommended method if the preceding equations indicate marginal results (e.g., MS < 0.5) or if the e/D ratio is below 1.5.

If equation (56) is viewed graphically, a curve is defined in the Rt-Rs space such as that shown in figure 11. Any combination of Rt and Rs beneath this curve satisfies the criteria and the bolt possesses some margin against failure. The margin of safety is represented by the shortest distance from the Rt-Rs point to the curve established by equation (56). This distance can be quite difficult to determine however, so an alternate method for estimating a relative numerical margin of safety given by equation (59) may be used.

For NAS and MS standard fasteners of A-286 material with a yield strength of 85,000 psi, lubricated and torqued in accordance with reference 3, equation (3) may be expressed as

A bolted joint is most commonly preloaded, or prestressed, through the initial torquing of the joining elements. When an external torque is applied to the system, the bolt is elongated and the abutments (flanges) are compressed. The elongation of the bolt results in an initial tensile load, Po, in the bolt. Likewise, the compressed abutments deflect and carry a compressive load (Po) in the region surrounding the bolt. For most typical joint designs, the bolt and flange do not deflect at the same rate under preloading as a result of their different stiffnesses. The abutments are often much stiffer than the bolt resulting in less deflection than in the bolt (δj < δb). The preloading mechanism can be described graphically as shown in fig. 1.

Although the actual thread shear area of the parent material is increased slightly over that of the insert's external thread shear area, for conservative purposes the shear area of the parent material internal thread is assumed to be the same as the insert's reduced external thread shear area used for equation (78). The parent material pull-out strength is then

where Le is the engaged length of bolt thread. Usually, only the ultimate thread strength under axial loading is checked with the ultimate load being given as

where t is the thickness of the sheet or lug, e is the perpendicular distance from the hole centerline to the free edge of the sheet, and D is the nominal fastener diameter (as shown in fig. 13). A factor of two is used in the calculation of the shear area since the tear out occurs along two planes; one on each side of the bolt. This area is quite conservative since it considers the shear planes acting along the shortest distance between the edge of the hole and edge of the sheet (across section a-a). More realistically, this shearing action would occur at planes (sections b-b) located at some angle relative to the centerline (ref. 7).

By including the effects of preload uncertainty, thermal effects, and preload relaxation, the maximum and minimum expected preloads in the joint may be described by (ref. 1)

The thread shear area of the bolt is the cylindrical area formed by the minor diameter of the mating internal threads and the length of thread engagement (ref. 8). This shear area can be estimated from the following relation:

This report is a compilation of some of the most basic equations governing simple preloaded joint systems and discusses the more common modes of failure associated with such hardware. It is intended to provide the mechanical designer with the tools necessary for designing a basic bolted joint. Although the information presented is intended to aid in the engineering of space flight structures, the fundamentals are equally applicable to other forms of mechanical design.

The toothed-wheel pump aggregate with container serves to supply lubricant to the central  lubrication at systems. For regular lubricant dispensing, the toothed-wheel pump aggregate has to be controlled by a PLC. To this end, a pulse rhythm needs to be sent for every lubrication cycle, by means of a control signal.

Only the first two requirements will be discussed in this report. The third requirement addresses joints subject to dynamic or cyclic loading and is a matter that needs to be addressed separately. In most applications the bolted connections in space flight hardware are considered to be statically loaded. The dynamic load components present during the launch, orbit, and landing phases are usually short in duration and therefore replaced by equivalent static loads that would be developed by the dynamic events (ref. 5).

Torquing and preload uncertainty, however, are not the only parameters affecting the initial joint preload. Temperature changes and preload relaxation can modify initial preload. Thermal loading on the joint may be experienced if the bolt and flange materials have different coefficients of thermal expansion and the joint is subjected to a temperature change. Under a given temperature change (measured from the assembly state) the bolt and abutments expand or contract at differing rates which introduces a tension or relaxation in the bolt (Pth). Small changes in global operating conditions or large local temperature gradients can result in significant changes in joint loading and therefore must be considered.