2,316
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→High Cu Content Copper Alloys
The reliability and electrical life of contact systems in switching devices as wellas in electromechanical and electronic components do not only depend on thecontact material. The selection of the most suitable carrier material also playsan important role.
The most frequently used ones are copper based materials. Depending on theapplication , also materials based on nickel or multi-layer composite materials,such as thermo bimetals for example, are frequently used. For specialapplications in the medium and high voltage technology, as well as for springsand snap discs for the information technology, iron or steel based materials areconsidered. These are however not included for the purpose of this data book.
Various requirements based on the enduse of the contact components have tobe met by carrier materials. Copper materials have to exhibit high electrical andthermal conductivity, good mechanical strength even at elevated temperatures,and in addition , a sufficient high resistance against corrosion. If used as springs, the carrier materials also must have good elastic spring properties. Besidesthese, the materials must, depending on the manufacturing processesemployed, also have good technological properties like ductility , to allow warmand cold forming, suitability for cutting and stamping, and be capable to bewelded, brazed or coated by electroplating.
==<!--5.1 -->Copper and Copper Alloys==
===5.1.1 Standards Overview===
Copper and copper alloys to be being used in electrical and electronic componentsare usually covered by national and international standards. DIN numbers thematerials by a prefix and/or a material number. The newer European standards(EN) refer to the material's usage products and also show a prefix and materialnumber. For reference , we also show in table 5.1 (<xr id="tab:MaterialDesignations"/>) the material designationaccording to UNS, the Unified Numbering System (USA). Other internationallyused standard and material numbers include, among others, those issued byCDA (Copper Development Association, USA), and GB (Guo Biao – China).
The most important EN as well as the US based and widely used ASTMstandards , covering the use of flat rolled copper and copper alloys in electricalcontacts , are:
{| class="twocolortable" style="text-align: left; font-size: 12px"
|-
!Standard Designation
!D e s c riptionDescription
|-
|DIN EN 1652
|-
|ASTM B 534-07 || Sec. for CuCoBe-Alloy and CuNiBe-Alloy Plate, Sheet, Strip, and Rolled Bar
|-
|}
The above DIN EN standards replace in part or completely the older DIN standards DIN 1777,
DIN 17670, DIN 1751, DIN 1791.
===<!--5.1.2 -->Pure Copper===
Copper is used in electrical engineering , mostly because of its high electrical conductivity<ref>As units for electrical conductivity MS/m and m/Ω.mm<sup>2</sup> are commonly used. Frequently – and mostly in North America – the % IACS value (International Annealed Copper Standard) is also used, where 100% is equivalent to 58 MS/m or m/Ωmm<sup>2</sup> .For the description of mechanical strength properties the units of N/mm<sup>2</sup> or MPa are most commonly used:
1 MS/m = 1 m/Ωmm<sup>2</sup>
1 MPa = 1 N/mm<sup>2</sup></ref> which with 58 MS/m (or m/Ωmm²) is only slightly below that of silver. Other advantages of copper are its high thermal conductivity, corrosion resistance, and its good ductility. The work hardening properties of ETP copper is illustrated in (<xr id="fig:StrainHardeningStrain hardening of Cu-ETP by cold working" />). The increase in strength achieved by cold working can be reversed easily by subsequent annealing. The softening properties are strongly dependent on the preceding cold working percentage ''(<xr id="fig:SofteningOfCuSoftening of Cu-ETP after annealing for 3hrs after 25% cold working"/> and <xr id="fig:Softening of Cu-ETP after annealing for 3hrs after 50% cold working"/><!--5.3-->)''.
The purity of technically pure and un-alloyed copper used for electrical applications depends on the type used and ranges between > 99.90 and 99.95
wt%. The copper types are designated mainly by their oxygen content as oxygen containing, oxygen-free, and de-oxidized with phosphorus as
described in DIN EN 1652 ''(<xr id="tab:MaterialDesignations"/> and <xr id="tab:Composition of Some Pure Copper Types"/><!--5.2-->)''.<xr id="tab:Physical Properties of Some Copper Types"/><!--Tables 5.3. --> and <xr id="tab:Mechanical Properties of Some Copper Types"/><!--5.4 --> show the physical and mechanical properties of these copper materials. According to these, Cu-ETP, Cu-OFE, and Cu-HCP are the types of copper for which minimum values for the electrical conductivity are guaranteed.
Cu-ETP is less suitable for welding or for brazing in reducing atmosphere because of the oxygen content (danger of hydrogen embrittlement).
Cu-HCP, Cu-DLP, and Cu-DHP are oxygen free copper types , de-oxidized with different phosphorus contents. With increasing phosphorus content , the
electrical conductivity decreases. Cu-OFE, also called OFHC copper, is free of oxygen and also free of de-oxidizing compounds.
<figtable id="tab:MaterialDesignations">
|}
</figtable>
<figtable id="tab:Physical Properties of Some Copper Types">
<caption>'''<!--Table 5.3:-->Physical Properties of Some Copper Types'''</caption>
<table class="twocolortable">
<tr><th><p class="s3">Material</p></th><th ><p class="s3">Density</p></th><th colspan="2"><p class="s3">Electrical</p><p class="s3">Conductivityt</p></th><th ><p class="s3">Electrical Conductivity</p></th><th><p class="s3">Thermal</p><p class="s3">Conductivity</p></th>
<th><p class="s3">Coeff. of</p><p class="s3">Linear Thermal Expansion</p></th>
<th><p class="s3">Modulus</p><p class="s3">of</p><p class="s3">Elasticity</p></th><th><p class="s3">Softening</p><p class="s3">Temperatur (approx.</p>10% loss in strength)</th><th><p class="s3">Melting</p><p class="s3">Temperature</p></th></tr>
<tr><th><p class="s3">EN- Designation</p></th>
<th >[g/cm³]</th><th>[MS/m]</th><th>[% IACS]</th><th>[μΩ· cm]</th><th>[W/(m· K)]</th>
<th>[10<sup>-6</sup>/K]</th><th>[GPa]</th><th>[°C]</th><th>[°C]</th></tr>
<tr><td><p class="s3">Cu-ETP</p></td><td><p class="s3">8.94</p></td>
<td>≥58</td>
<td><p class="s3">100</p></td><td><p class="s3">1.72</p></td><td><p class="s3">390</p></td><td><p class="s3">17.7</p></td><td><p class="s3">127</p></td><td><p class="s3">ca. 220</p></td><td><p class="s3">1083</p></td></tr><tr><td><p class="s3">Cu-OF</p></td><td><p class="s3">8.94</p></td><td>≥58</td><td><p class="s3">100</p></td><td><p class="s3">1.72</p></td><td><p class="s3">394</p></td><td><p class="s3">17.7</p></td><td><p class="s3">127</p></td><td><p class="s3">ca. 220</p></td><td><p class="s3">1083</p></td></tr><tr><td><p class="s3">Cu-HCP</p></td><td><p class="s3">8.94</p></td><td>≥54</td><td><p class="s3">93</p></td><td><p class="s3">1.85</p></td><td><p class="s3">380</p></td><td><p class="s3">17.7</p></td><td><p class="s3">127</p></td><td><p class="s3">ca. 220</p></td><td><p class="s3">1083</p></td></tr><tr><td><p class="s3">Cu-DLP</p></td><td><p class="s3">8.94</p></td><td><p class="s3">52</p></td><td><p class="s3">90</p></td><td><p class="s3">1.92</p></td><td><p class="s3">350</p></td><td><p class="s3">17.7</p></td><td><p class="s3">132</p></td><td><p class="s3">ca. 220</p></td><td><p class="s3">1083</p></td></tr><tr><td><p class="s3">Cu-DHP</p></td><td><p class="s3">8.94</p></td><td>≥46</td><td><p class="s3">80</p></td><td><p class="s3">2.17</p></td><td><p class="s3">310</p></td><td><p class="s3">17.6</p></td><td><p class="s3">132</p></td><td><p class="s3">ca. 220</p></td><td><p class="s3">1083</p></td></tr></table>
</figtable>
<figtable id="tab:Mechanical Properties of Some Copper Types">
<caption>'''<!--Table 5.4:-->Mechanical Properties of Some Copper Types'''</caption>
<table class="twocolortable" border="1" cellspacing="0" style="border-collapse:collapse">
<tr>
<table border="1" cellspacing="0" style="border-collapse:collapse"><tr><tdth><p class="s3">WerkstMaterial</p><p class="s3">EN-DesignationMaterial</p></tdth><tdth><p class="s3">EN-NumberCondition</p></tdth><tdth><p class="s3">DIN-DesignationTensile Strength</p></td><td><p class="s3">DIN-Number</p></td><td>R<p span class="s3s11">UNSm</pspan></td></tr><tr><tdp><p class="s3">Cu-ETP[MPa]</p></tdth><tdth><p class="s3">CW004A0,2% Yield</p></td><td><p class="s3">E-Cu 58Strength R</p></td><td><p span class="s3s11">p0,2.0065</pspan></td><tdp><p class="s3">C11000[MPa]</p></td></tr><trth><tdth><p class="s3">Cu-OFElongation</p></td><td><p class="s3">CW008AA</pspan class="s11">50</tdspan><td/p><p class="s3">OF-Cu[ %]</p></tdth><tdth><p class="s3">2.0040Hardness</p></td><td><p class="s3">C10200HV</p></tdth></tr><tr><td><p class="s3multirow" rowspan="4">Cu-HCPETP</pbr>Cu-OF </tdbr>Cu-HCP <tdbr>Cu-DLP<p class="s3"br>CW021ACu-DHP</ptd></td>R220</td><p class="s3"td>SE220 -Cu260</ptd></td>≤140</td><p class="s3">2.0070</ptd>≥33</td><td><p class="s3">C10300</p>40 - 65</td></tr><tr><td>R240<p class="s3"/td>Cu-DLP</ptd>240 - 300</td><td>≥180<p class="s3"/td>CW023A</ptd>≥8</td><td><p class="s3">SW65 -Cu95</ptd></tdtr><tdtr><p class="s3"td>2.0076R290</ptd></td>290 - 360</td><p class="s3"td>C12000≥250</ptd></td>≥4</tr><trtd><td><p class="s3">Cu90 -DHP110</ptd></tdtr><tdtr><p class="s3"td>CW024AR360</ptd></td>≥360</td><p class="s3">SF-Cu</ptd>≥320</td><td><p class="s3">≥2.0090</p></td><td><p class="s3">C12200</p>≥110</td></tr></table>Table 5.1: Material Designations of Some Copper Types
</figtable>
<div class="multiple-images"> <figure id="fig:StrainHardeningStrain hardening of Cu-ETP by cold working">[[File:Strain_harderingStrain hardening of Cu ETP by cold working.pngjpg|rightleft|thumb|<caption>Strain_hardening Strain hardening of Cu-ETP by cold working</caption>]]
</figure>
<figure id="fig:SofteningOfCuSoftening of Cu-ETP after annealing for 3hrs after 25% cold working">[[File:SofteningOfCuETPafterAnnealingSoftening of Cu ETP after annealing.pngjpg|rightleft|thumb|<caption>Softening of Cu-ETP after annealing for 3hrs after 25% cold working</caption>]]
</figure>
CuSn1CrNiTi and CuCrSiTi are advanced developments of the Cu-Cr-Ti precipitation materials with fine intermetallic dispersions. The materialCuNi1Co1Si also belongs into this family and has properties similar to the low alloyed CuBe materials CuAg0.1 and CuCd1 are mostly used as overhead drive cables where they have to meet sustained loads at elevated temperatures without softening.
<figtable id="tab:Mechanical Properties of Selected High Cu Content Copper Alloys"><caption>'''<!--Table 5.6; :-->Mechanical Properties of Selected High Cu Content Copper Alloys (2 teile!)'''</caption>
===<!--5.1.4 -->Naturally Hard Copper Alloys===
Alloys like brasses (CuZn), tin bronzes (CuSN), and German silver (CuNiZn), for which the required hardness is achieved by cold working , are defined as naturally hard alloys. Included in this group are also the silver bronzes (CuAg) with 2 – 6 wt% of Ag.
Main Articel: [[Naturally Hard Copper Alloys| Naturally Hard Copper Alloys]]
===<!--5.1.5 -->Other Naturally Hard Copper Alloys===
Main Articel: [[Other Naturally Hard Copper Alloys| Other Naturally Hard Copper Alloys]]
===<!--5.1.6 -->Precipitation Hardening Copper Alloys===
Besides the naturally hard copper materials , precipitation hardening copper alloys play also an important role as carrier materials for electrical contacts. By means of a suitable heat treatment , finely dispersed precipitations of a second phase can be achieved , which increase increases the mechanical strength of these copper alloys significantly.
Main Articel: [[Precipitation Hardening Copper Alloys| Precipitation Hardening Copper Alloys]]
===<!--5.1.7-->Application Properties for the Selection of Copper Alloys===
Main Articel: [[Application Properties for the Selection of Copper Alloys| Application Properties for the Selection of Copper Alloys]]
===<!--5.1.8-->Selection Criteria for Copper-Based Materials===
If current carrying capability is the key requirement, mechanical strength may have to be sacrificed as for example in carrier parts for stationary contacts. In this case, depending on the current level, pure copper or low alloyed copper materials such as CuSn0.15, or for economic reasons CuZn30, may be suitable.
For spring contact components , the interdependent relations between electrical conductivity and fatigue strength, or electrical conductivity and relaxation behavior are of main importance. The first case is critical for higher load relay springs. CuAg2 plays an important role for these applications. The latter is critical for components that are exposed to continuing high mechanical stresses like for example in connectors. The spring force must stay close to constant over the expected life time of the parts , even at elevated temperatures from the environment or current carrying. In this case , the relaxation behavior of the copper materials , which may cause a decrease in spring force over time , must be considered. Besides this , easy forming during manufacturing must be possible; this means that bending operations can also be performed at high mechanical strength values.
The increasing requirements on spring components in connectors, especially for use in automotive applications, such as higher surrounding temperatures, increased reliability, and the trend towards miniaturization led to a change of materials from traditionally CuZn30 and CuSn4 to CuNiSi alloys, for example. These CuNiSi alloys and the newer heavy duty copper alloys like CuNi1Co1 , are significantly improved with regards to mechanical strength, relaxation behavior, and electrical conductivity.
==<!--5.2 -->Nickel and Nickel Alloys==
===<!--5.2.1 -->Technical Grade Pure Nickel===
Technical grade pure nickel commonly contains 99.0 to 99.8 wt% Ni and up to 1 wt% Co. Other ingredients are iron and manganese ''(Tables <xr id="tab:Physical Properties of Nickel and Nickel Alloys"/><!--(Tab. 5.21 )--> and <xr id="tab:Mechanical Properties of Nickel and Nickel Alloys"/><!--(Tab. 5.22)''-->). Work hardening and softening behavior of nickel are shown in [[#figures11|(Figs. 5 – 6)]]<!--Figs. 5.45 and 5.46-->.
One of the significant properties of nickel is its modulus of elasticity , which is almost twice as high as that of copper. At temperatures up to 345°C nickel is ferro-magnetic.Nickel has a high corrosion resistance, is very ductile, and easy to weld and clad. It is of great importance as a backing material for multiple layer weld profiles. In addition , nickel is used as an intermediate layers layer for thin claddings, acting as an effective diffusion barrier between copper containing carrier materials and goldand gold or palladium-based contact materials.
Because of the always present thin oxide layer on its surface, nickel is not suitable as a contact material for switching contacts.
===<!--5.2.2-->Nickel Alloys===
<figtable id="tab:Physical Properties of Nickel and Nickel Alloys"><caption>'''<!--Table 5.21: -->Physical Properties of Nickel and Nickel Alloys (2 Teile!)'''</caption>
<sup>a</sup>solution annealed, and hardened
{| class="twocolortable" style="text-align: left; font-size: 12px"|-!Material!Hardness<br />Condition!Tensile Strength R<sub>m</sub><br />[MPa]!0,2% Yield Strength<br />R<sub>p02</sub><br />[MPa]!Elongation<br />A<sub>50</sub><br />[%]!Vickers<br />Hardness<br />HV!Spring Bending<br />Limit σ<sub>FB</sub><br />[MPa]!Fatigue<br />Strength σ<sub>BW</sub><br />[MPa]|-|Ni99,2|R 380|≥ 380|≥ 100|≥ 40|≥ 100|||-|NiCu30Fe|R 400<br />R 700|400 - 600<br />700 - 850|≥ 160<br />≥ 600|≥ 30<br />≥ 4|95 - 125<br />200 - 240|||-|NiBe2|R 700<sup>a</sup><br />R 1300<sup>a</sup><br />R 1500<sup>b</sup><br />R 1900<sup>b</sup><br />R 1800<sup>c</sup>|≥ 700<br />≥ 1300<br />≥ 1500<br />≥ 1900<br />≥ 1800|≥ 300<br />≥ 1200<br />≥ 1100<br />≥ 1750<br />≥ 1700|≥ 30<br />≥ 1<br />≥ 12<br />≥ 1<br />≥ 5|≥ 170<br />≥ 370<br />≥ 450<br />≥ 520<br />≥ 500| <br /> <br /> <br /> <br />≥ 1400|<br /> <br /> <br /> <br />≥ 400|}</figtable> <sup>a</sup>solution annealed, and cold rolled<br /> <sup>b</sup>solution annealed, cold rolled, and precipitation hardened<br /> <sup>c</sup>solution annealed, cold rolled, and precipitation hardened at mill (mill hardened) ===<!--5.2.3-->Nickel-Beryllium Alloys=== Because of decreasing solubility of beryllium in nickel with decreasing temperature, NiBe can be precipitation hardened similar to CuBe (<xr id="fig:Phase diagram of nickel beryllium"/><!--(Fig. 5.49)-->). The maximum soluble amount of Be in Ni is 2.7 wt% at the eutectic temperature of 1150°C. To achieve a high hardness by precipitation hardening, NiBe similar to CuBe, is annealed at 970 - 1030°C and rapidly quenched to room temperature. Soft annealed material is easily cold formed and after stamping and forming a hardening anneal is performed at 480 to 500°C for 1 to 2 hours. <figure id="fig:Phase diagram of nickel beryllium">[[File:Phase diagram of nickel beryllium.jpg|right|thumb|Figure 9: Phase diagram of nickel-beryllium]]</figure> Commercial nickel-beryllium alloys contain 2 wt% Be. Compared to CuBe2 the NiBe2 materials have a significantly higher modulus of elasticity but a much lower electrical conductivity. The mechanical strength is higher than that of CuBe2 (<xr id="fig:Precipitation hardening of NiBe2 soft at 480C"/><!--(Fig. 5.50)-->), the spring bending force limit can exceed values of over 1400 MPa and the fatigue strength reaches approximately 400 MPa. <figure id="fig:Precipitation hardening of NiBe2 soft at 480C">[[File:Precipitation hardening of NiBe2 soft at 480C.jpg|right|thumb|Figure 10: Precipitation hardening of NiBe2 (soft) at 480°C]]</figure> A further advantage of NiBe2 is its high temperature stability. Cold worked and subsequently precipitation hardened , NiBe2 can withstand sustained
temperatures of 400 - 650°C, depending on ist pre-treatment.
Similar to CuBe materials, NiBe alloys are available in various mill hardened in various conditions or also already precipitation hardened at by the manufacturer.
Nickel-beryllium alloys are recommended for mechanically and thermally highly stressed spring components. For some applications their ferro-magnetic properties can also be advantageous.
Manufacturing of triple-layer carrier materials is usually performed by cold rollcladding. The three materials cover each other completely. The advantage of this composite material group is that the different mechanical and physical properties of the individual components can be combined with each other.
Depending on the intended application , the following layer systems are utilized:
* Conduflex N <br/> CuSn6 - Cu - CuSn6 <br/>
* Cu – Fe or Steel – Cu
The high electrical conductivity and good arc mobility properties of copper are combined with the mechanical strength and magnetic properties of iron or steel. The thickness and width range of material strips are the same of the ones as those for Cu – Invar – Cu system.
The thickness ratios of the components can be selected according to the application requirements. The two outer layers usually have the same thickness.
==<!--5.4 -->Thermostatic Bimetals==
Thermostatic bimetals are composite materials , consisting of two or three layers of materials , with different coefficients of thermal expansion. They are usually bonded together by cladding. If such a material part is heated , either directly through current flow or indirectly through heat conduction or radiation, the different expansion between the active (strong expansion) and passive (low expansion) layer causes bending of the component part.
Directional or force effects on the free end of the thermostatic bimetal part is then used as a trigger or control mechanism in thermostats, protective switches, or in control circuits. Depending on the required function of the thermostatic bimetal component different design shapes are used:
*'''Straight or U-shaped strips''' for nearly linear motion
*'''Stamped and formed parts''' for special designs and applications
The wide variety of thermostatic bimetal types is specified mostly through DIN 1715 and/or applicable ASTM standards ''(<xr id="tab:Partial Selection from the Wide Range of Available Thermo-Bimetals"/><!--(Table 5.23)''-->). The different types have varying material compositions for the active and passive side of the materials. The mostly used alloys are iron-nickel and manganese-copper-nickel. Mainly used in circuit protection switches (i.e. circuit breakers) , some thermo-bimetals include an intermediate layer of copper or nickel which allows to design parts with a closely controlled electrical resistance.
<figtable id="tab:Partial Selection from the Wide Range of Available Thermo-Bimetals"><caption>'''<!--Table 5.23: -->Partial Selection from the Wide Range of Available Thermo-Bimetals'''</caption>
{| class="twocolortable" style=="text-align: left; font-size: 12px"|-!Designation<br />DIN 1715 !Designation<br />ASTM!Specific Thermal Deflection<br />[10<sup>6</sup>/K]!Sprecific<br />Electrical<br />Resistance k [μΩ·m]!Typical<br />Application Range [°C]!Application<br />Limit [°C]!Composition|-|TB 20110<br /> <br />TB 1577A<br /> <br />TB1170A<br /> <br /> <br />|TM 2<br />TM 8<br /> <br />TM 1<br /> <br />TM 3<br />TM 4|21.1<br />15.3<br />15.5<br />14.2<br />11.7<br />10.6<br />8.5|1.12<br />1.41<br />0.79<br />0.78<br />0.70<br />0.71<br />0.66| - 70 – + 260<br /> - 70 – + 260<br /> - 70 – + 370<br /> - 70 – + 370<br /> - 70 – + 425<br /> - 70 – + 480<br /> - 70 – + 425|350<br />350<br />450<br />450<br />480<br />540<br />540|Two components|-|TB 1517<br />TB 1511<br /> <br /> <br />TB 1303<br /> <br />TB 1109 | <br /> <br />TM 28<br />TM 26<br />TM 25<br />TM 24<br /> <br />|14.9<br />14.9<br />14.3<br />13.9<br />13.2<br />13.1<br />12.3<br />11.5|0.17<br />0.11<br />0.15<br />0.08<br />0.03<br />0.05<br />0.03<br />0.09| - 70 – + 260<br /> - 70 – + 260<br /> - 70 – + 315<br /> - 70 – + 315<br /> - 70 – + 260<br /> - 70 – + 315<br /> - 70 – + 315<br /> - 70 – + 380|400<br />400<br />350<br />350<br />300<br />350<br />350<br />400|Three components with Cu intermediale layer|-|TB 1555<br />TB 1435<br /> <br /> <br />TB 1425<br /> <br /> <br /> <br />| <br /> <br />TM 17<br />TM 15<br /> <br />TM 13<br />TM 11<br />TM 9|15.40<br />14.8<br />14.2<br />14.1 Design Formulas===<br />14.0<br />13.6<br />12.8<br />10.7|0.55<br />0.40<br />0.66<br />0.50<br />0.25<br />0.33<br />0.25<br />0.17| - 70 – + 260<br /> - 70 – + 260<br /> - 70 – + 370<br /> - 70 – + 370<br /> - 70 – + 260<br /> - 70 – + 370<br /> - 70 – + 370<br /> - 70 – + 370|450<br />450<br />480<br />480<br />450<br />480<br />480<br />480|Three components with Ni intermediale layer |}</figtable>
<figtable id="tab:Design Formulas for Thermostatic Bimetal Components"><caption>'''<!--Table 5.24:-->Design Formulas for Thermostatic Bimetal Components'''</caption> {| class="twocolortable" style="font-size:1em;"|-||Shape of the Thermostatic Bimetal|Deflection|Mechanical Action Force|Thermal Action Force|-|Cantilevered strip |[[File:Contilevered strip.jpg|left|234px|]] |<math>A = \frac {\alpha \Delta TL^2}{s} </math>|<math>P = \frac {cA Bs^3}{L^3} </math>|<math>P = \frac {b \Delta T Bs^3}{L} </math>|-|Dual supported strip|[[File:Dual supported strip.jpg|left|234px|]] |<math>A = \frac {\alpha \Delta T L^2}{4s} </math>|<math>P = \frac {16c AB s^3}{L^3} </math>|<math>P = \frac {4b \Delta TB s^2}{L} </math>|-|U-shaped element |[[File:U shaped element.jpg|left|220px|]] |<math>A = \frac {\alpha \Delta T L^2}{2s} </math>|<math>P = \frac {4c AB s^3}{L^3} </math>|<math>P = \frac {2b \Delta TB s^2}{L} </math>|-|Spiral|[[File:Spiral.jpg|left|220px|]] |colspan="3" style="text-align:center"|<math>A = \frac {\alpha \Delta T}{s} (f^2 - e^2 + 4 r^2 + 2 e f + 2 \pi r f) </math>|-|Helical spring|[[File:Helical spring.jpg|left|220px|]] |<math>\alpha = \frac {\alpha_{1} \Delta TL}{s} </math>|<math>P = \frac {c_{1} \alpha Bs^3}{L \cdot r} </math>|<math>P = \frac {b_{1} \Delta TBs^2}{r} </math>|-|Disc |[[File:Disc.jpg|left|220px|]] |<math>A = \frac {\alpha \Delta T (D^2 - d^2)}{5s} </math>|<math>P = \frac {16c A s^3}{D^2 - d^2} </math>|<math>P = 3,2 b \Delta T s^2 </math>|-|Reversed strip |[[File:Reversed strip.jpg|left|240px|]] |<math>A = \frac {\alpha \Delta T}{s} (y^2 - 2xy - x^2) </math>|<math>P = \frac {c ABs^2}{L^3} </math>|<math>P = \frac {b \Delta T Bs^2}{L^3} (y^2 - 2xy - x^2) </math>|-|Reversed U-shaped element|[[File:Reserved u shaped element.jpg|left|228px|]] |colspan="3" style="text-align:center"|<math>A = \frac {\alpha \Delta T}{s} [f^2 + 4 r^2 + 2 \pi r f - (e^2 - 2ex^2 - x^2) + 2f (e - x)] </math>|}</figtable> {| style="border-spacing: 20px"|<math>A</math> || Deflection in mm |<math>B</math> || Width in mm | rowspan="2" |<math>a_{1} = \frac {360}{\pi} \cdot a</math>|- |<math>\alpha</math> || Turn angle in ° |<math>D,d</math> || Diameter in mm |-|<math>P</math> || Force in N |<math>r</math> || Radius in mm | rowspan="2" |<math>b_{1} = \frac {2}{3} \cdot b</math> |-|<math>\Delta T</math> || Temperature difference in K |<math>a</math> || Specific therm. Deflection in 1/K |-|<math>s</math> ||Thickness in mm |<math>b=ac</math> ||Thermal action force constant<math> N/(mm^2 \cdot K)</math>| rowspan="2" | <math>c_{1} = \frac {\pi}{540} \cdot c</math> |-|<math>L</math> || Free moving length in mm|<math>c</math> || Mechan. action force constant in <math>N/mm^2</math>|} ===<!--5.4.2-->Stress Force Limitations=== For all calculations according to the formulas in (<xr id="tab:Design Formulas for Thermostatic Bimetal Components"/><!--Table 5.24 -->) one should check ifthe thermally or mechanically induced stress forces stay below the allowedbending force limit. The following formulas are applicable for calculating theallowable load (Force P<sub>max</sub> or momentum M<sub>max</sub>): <table class="twocolortable" style="text-align: left; font-size:12px;width:60%"><tr><td>Single side fixed strip</td> <td><math>P_{max} < \frac {\sigma Bs^2}{6L} </math> </td></tr><tr><td>Both sides fixed strip</td><td><math>P_{max} < \frac {\sigma Bs^2}{1,5L} </math></td></tr><tr><td>Spiral or filament </td><td><math>M_{max} < \frac {\sigma Bs^2}{6} </math></td></tr><tr><td>Disc </td><td><math>P_{max} < \frac {2 \sigma s^2}{3} </math></td></tr></table> <math>\sigma</math> = bending stress
==Comments==
<references/>
Kreye, H.; Nöcker, H.; Terlinde, G.: Schrumpfung und Verzug beim Aushärten von Kupfer-Beryllium-Legierungen. Metall 29 (1975) 1118-1121
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