Minimum-cost flow problem

2013-12-26T19:46:32Z

88.251.108.210: /* Minimum weight bipartite matching */ reference error fixed

{{Refimprove|date=July 2009}}

The '''ISO metric screw threads''' are the world-wide most commonly used type of general-purpose [[screw thread]].<ref>[http://isotc.iso.org/livelink/livelink/fetch/2000/2122/687806/ISO_TC_001__Screws_.pdf?nodeid=4938938&vernum=0 ISO/TC/ 1 Business Plan], 2007-03-05, Version 1.3. Table 3: The market share of each screw thread, p. 7.</ref> They were one of the first [[international standard]]s agreed when the [[International Organization for Standardization]] was set up in 1947.{{Citation needed|date=July 2009}}

The "M" designation for metric screws indicates the outer diameter of the screw, in millimeters (e.g. an M6 screw has an outer diameter of 6 millimeters).

==Basic profile==
[[Image:ISO and UTS Thread Dimensions.svg|thumb|right|400px|Basic profile of all ISO metric screw threads]]

The design principles of ISO general-purpose metric screw threads ("M" series threads) are defined in international standard ISO 68-1.<ref>
{{cite book
|title=ISO 68-1:1998 ISO general purpose screw threads – Basic profile – Part 1: Metric screw threads
|publisher=International Organization for Standardization
|url=http://www.iso.org/iso/catalogue_detail.htm?csnumber=3707
}}</ref> Each thread is characterized by its major diameter ''D'' and its pitch ''P''. ISO metric threads consist of a symmetric V-shaped thread. In the plane of the thread axis, the flanks of the V have an angle of 60° to each other. The outermost 1/8 and the innermost 1/4 of the height ''H'' of the V-shape are cut off from the profile.

The relationship between the height ''H'' and the pitch ''P'' is found using the following equation:<ref>{{harvnb|Oberg|Jones|Horton|Ryffel|2000|p=1706}}.</ref>

:<math>H = \cos(30^\circ) \cdot P = \frac{ {\sqrt 3}}{2} \cdot P \approx 0.866 \cdot P</math>

In an external (male) thread (e.g., on a bolt), the major diameter ''D''maj and the minor diameter ''D''min define ''maximum'' dimensions of the thread. This means that the external thread must end flat at ''D''maj, but can be rounded out below the minor diameter ''D''min. Conversely, in an internal (female) thread (e.g., in a nut), the major and minor diameters are ''minimum'' dimensions, therefore the thread profile must end flat at ''D''min but may be rounded out beyond ''D''maj.

The minor diameter ''D''min and effective pitch diameter ''D''p are derived from the major diameter and pitch as

:<math>D_\mathrm{min} = D_\mathrm{maj} - 2\cdot\frac58\cdot H = D_\mathrm{maj} - \frac{ 5 {\sqrt 3}}{8}\cdot P \approx D_\mathrm{maj} - 1.082532 \cdot P</math>

:<math>D_\mathrm{p} = D_\mathrm{maj} - 2\cdot\frac38\cdot H = D_\mathrm{maj} - \frac{ 3 {\sqrt 3}}{8}\cdot P \approx D_\mathrm{maj} - 0.649519 \cdot P</math>

==Designation==
A metric ISO screw thread is designated by the letter M followed by the value of the nominal diameter ''D'' (''Dmaj'' in the diagram above) and the pitch ''P'', both expressed in millimetres and separated by the multiplication sign, ''×'' (e.g., M8×1.25). If the pitch is the normally used "coarse" pitch listed in [[ISO 261]] or [[ISO 262]], it can be omitted (e.g., M8). Tolerance classes defined in [[ISO 965|ISO 965-1]] can be appended to these designations, if required (e.g., M500– 6g in external threads).
External threads are designated by lowercase letter, g or h. Internal threads are designated by upper case letters, H or G.

=={{anchor|ISO 261|ISO 262}} Preferred sizes==
'''ISO 261''' specifies a detailed list of preferred combinations of outer diameter ''D'' and pitch ''P'' for ISO metric screw threads.<ref>
{{cite book
|title=ISO 261:1998 ISO general purpose metric screw threads – General plan
|publisher=International Organization for Standardization
|date=17 Dec 1998
|url=http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=4165
}}</ref>

'''ISO 262''' specifies a shorter list of thread dimensions – a subset of ISO 261.<ref>
{{cite book
|title=ISO 262:1998 ISO general purpose metric screw threads – Selected sizes for screws, bolts and nuts
|publisher=International Organization for Standardization
|date=17 Dec 1998
|url=http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=4167
}}</ref>

{| class="wikitable" border="1" align="left"
|+ ISO 261 standard preferred threads
!colspan=2|Nominal diameter ''D''(mm) ISO 261
!colspan=2|Pitch ''P'' (mm)
|rowspan=19|
!colspan=2|Nominal diameter ''D'' (mm)
!colspan=2|Pitch ''P'' (mm)
|-
!1st choice ISO 262||2nd choice||coarse||fine
!1st choice||2nd choice||coarse||fine
|-
|1 || ||0.25||0.2 ||16 || ||2 ||1.5
|-
|1.2|| ||0.25||0.2 || ||18 ||2.5 ||2 or 1.5
|-
| ||1.4||0.3 ||0.2 ||20 || ||2.5 ||2 or 1.5
|-
|1.6|| ||0.35||0.2 || ||22 ||2.5 ||2 or 1.5
|-
| ||1.8||0.35||0.2 ||24 || ||3 ||2
|-
|2 || ||0.4 ||0.25 || ||27 ||3 ||2
|-
|2.5|| ||0.45||0.35 ||30 || ||3.5 ||2
|-
|3 || ||0.5 ||0.35 || ||33 ||3.5 ||2
|-
| ||3.5||0.6 ||0.35 ||36 || ||4 ||3
|-
|4 || ||0.7 ||0.5 || ||39 ||4 ||3
|-
|5 || ||0.8 ||0.5 ||42 || ||4.5 ||3
|-
|6 || ||1 ||0.75 || ||45 ||4.5 ||3
|-
| ||7 ||1 ||0.75 ||48 || ||5 ||3
|-
|8 || ||1.25||1 or 0.75 || ||52 ||5 ||4
|-
|10 || ||1.5 ||1.25 or 1 ||56 || ||5.5 ||4
|-
|12 || ||1.75||1.5 or 1.25 || ||60 ||5.5 ||4
|-
| ||14 ||2 ||1.5 ||64 || ||6 ||4
|}

{{clear}}The “coarse” pitch is the commonly used default pitch for a given diameter. In addition, one or two smaller “fine” pitches are defined, for use in applications where the height of the normal “coarse” pitch would be unsuitable (e.g., threads in thin-walled pipes). The terms “coarse” and “fine” have (in this context) no relation to the manufacturing quality of the thread.

In addition to coarse and fine threads, there is another division of extra fine, or “superfine” threads, with a very fine pitch thread. Superfine pitch metric threads are occasionally used in automotive components, such as suspension struts, and are commonly used in the aviation manufacturing industry. This is because extra fine threads are more resistant to coming loose from vibrations.{{citation needed|date=March 2012}}

==Standards==
===International===
* ISO 68-1: ISO general purpose screw threads — Basic profile — Metric screw threads.
* ISO 261: ISO general purpose metric screw threads — General plan.
* ISO 262: ISO general purpose metric screw threads — Selected sizes for [[Screw#Differentiation_between_bolt_and_screw|screws, bolts]] and [[Nut_(hardware)#Standard_metric_hex_nuts_sizes|nuts]].
* [[ISO 965]]: ISO general purpose metric screw threads — [[Tolerances]]<ref>[http://www.iso.org/iso/iso_catalogue/catalogue_ics/catalogue_detail_ics.htm?csnumber=5392] ISO 965 in the Catalogue on the Official ISO website</ref>
** ISO 965-1: Principles and basic data
** ISO 965-2: Limits of sizes for general purpose external and internal screw threads.
** ISO 965-3: Deviations for constructional screw threads
** ISO 965-4: Limits of sizes for hot-dip galvanized external screw threads to mate with internal screw threads tapped with tolerance position H or G after galvanizing
** ISO 965-5: Limits of sizes for internal screw threads to mate with hot-dip galvanized external screw threads with maximum size of tolerance position h before galvanizing

===National===
* BS 3643: ISO metric screw threads
* ANSI/ASME B1.13M: [http://catalog.asme.org/Codes/PrintBook/B113M_2005_Metric_Screw.cfm Metric Screw Threads: M Profile]

==See also==
{{multicol}}
* [[Acme thread form]]
* [[British Association screw threads]] (BA)
* [[British Standard Cycle]] (BSC)
* [[British standard fine thread]] (BSF)
* [[British standard pipe thread]] (BSP)
* [[British Standard Whitworth]] (BSW) – a British thread standard with 55° profile.
* [[Buttress thread]]
* [[Filter thread]]
* [[Garden hose#Standards and connectors|Garden hose thread]]
{{multicol-break}}
* [[National pipe thread]] (NPT)
* [[Hose coupling#NST|National thread]]
* ''[[Panzergewinde]]''
* [[Screw thread]]
* [[Square thread form]]
* [[Thread angle]]
* [[United States Standard thread]]
* [[Unified Thread Standard]] (UTS, UNC, UNF, UNEF and UNS) – a US/Canadian/British thread standard that uses the same 60° profile, but an inch-based set of diameter/pitch combinations.
{{multicol-end}}

==References==
{{reflist}}

===Bibliography===
* {{Citation | last = Oberg | first = Erik | last2 = Jones | first2 = Franklin D. | last3 = Horton | first3 = Holbrook L. | last4 = Ryffel | first4 = Henry H. | title = [[Machinery's Handbook]] | place = New York | publisher = Industrial Press Inc. | year = 2000 | edition = 26th | isbn = 0-8311-2635-3 | postscript =.}}

==External links==
* [http://www.efunda.com/DesignStandards/screws/screwm_coarse.cfm Metric coarse thread dimensions]
* [http://www.efunda.com/DesignStandards/screws/screwm_fine.cfm Metric fine thread dimensions]
* [http://www.metrication.com/engineering/threads.htm Detailed metric thread dimensions]

[[Category:Mechanical standards]]
[[Category:Screws]]
[[Category:Threading (manufacturing)]]
[[Category:ISO 68]]

2009–10 Mersin İdmanyurdu season

2012-06-19T13:39:12Z

88.251.240.54:

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Minimum-cost flow problem

2009–10 Mersin İdmanyurdu season