11/47 8.2 Thermal-Expansion Methods ◆Expansion of solids is mainly in bimetallic(双金属)elements by utilizing the differential expansion of bonded(连接，结合)strips of two metals. Liquid expansion at essentially constant pressure is used in the common liquid-in-glass thermometers. Restrained expansion of liquids,gases,or vapors results in a pressure rise,which is the basis of pressure thermometers. Fahrenheit ['faeranhait]Degree:degree F,F.A scale and a unit of temperature,its defining points being 32 at the freezing point of pure water and 212 at its boiling point at atmospheric pressure,and with 180 degrees between the two.Conversion from F to C: c=5p-32 12/47 8.2.1 Bimetallic Thermometers(双金属温度计) Two strips of metal A&B of same temperature,with thermal- expansion coefficients &a,are firmly bonded together,a temperature change causes a differential expansion and the strip,if unrestrained,will deflect into a uniform circular arc with the following analytical relationship: r=t43(1+m2+(1+mm[m2+1/mml 6(aA-aB)(T2-T1)(1+m)2 (8.3) where r:radius of curvature t:total strip thickness,0.0005<t<0.125 in practice n:elastic modulus ratio EB/EA m:thickness ratio te/ta T2-T1:temperature rise Accurate results require the use of experimentally determined factors which are available from bimetal manufacturers
Expansion of solids is mainly in bimetallic(双金属) elements by utilizing the differential expansion of bonded(连接, 结合) strips of two metals. Liquid expansion at essentially constant pressure is used in the common liquid-in-glass thermometers. Restrained expansion of liquids, gases, or vapors results in a pressure rise, which is the basis of pressure thermometers. Fahrenheit [ˈfærənhait] Degree: degree F, ℉. A scale and a unit of temperature, its defining points being 32 at the freezing point of pure water and 212 at its boiling point at atmospheric pressure, and with 180 degrees between the two. Conversion from ℉ to ℃: = ૢ ( −32) 8.2 Thermal-Expansion Methods 11/47 Two strips of metal A & B of same temperature, with thermalexpansion coefficients ߙ & ߙ , are firmly bonded together, a temperature change causes a differential expansion and the strip, if unrestrained, will deflect into a uniform circular arc with the following analytical relationship: ⁄ା ା ା ା ࢚ (3.8 (ା ࢀିࢀ ࢻିࢻ where r: radius of curvature t: total strip thickness, 0.0005<t<0.125 in practice n: elastic modulus ratio ܧ/ܧ m: thickness ratio ݐ/ݐ ܶଶ − ܶଵ: temperature rise Accurate results require the use of experimentally determined factors which are available from bimetal manufacturers. 8.2.1 Bimetallic Thermometers (双金属温度计) 12/47
8.2.1 Bimetallic Thermometers 13/47 ☑Temperature=T Separate A XA>O8 B Bonded Cantilever ['kaentili::va】悬臂梁 U-shape Temperature changed Spiral Helix Washer Double helix (a)Principle of Bimetallic Thermometer (b)Variety shapes of Bimetallic Thermometer Figure 8.3 Bimetallic Sensors 14/47 8.2.1 Bimetallic Thermometers Material for B element:Invar,a nickel steel with a nearly zero [1.7x10-6 in/(in.C)]expansion coefficient. Material for A element:Originally brass,now variety of alloys depends on the mechanical and electrical characteristics required. Working range from -100~1000F (-73.3~537.8C),inaccuracy of the order of 1%of scale range for bimetal thermometers of high quality. ◆Application: -Temperature measurement; -Very widely as combined sensing and control elements in temperature-control systems,mainly of the on-off type; -Temperature compensating devices for various instruments that has temperature as interfering or modifying input; -Motion compensation due to temperature change; -Automotive sensing application,combined with conductive plastic potentiometers
(a) Principle of Bimetallic Thermometer 8.2.1 Bimetallic Thermometers Figure 8.3 Bimetallic Sensors (b) Variety shapes of Bimetallic Thermometer 13/47 8.2.1 Bimetallic Thermometers 14/47 Material for B element： Invar, a nickel steel with a nearly zero [1.7x10ି in/(in ∙ ℃)] expansion coefficient. Material for A element: Originally brass, now variety of alloys depends on the mechanical and electrical characteristics required. Working range from -100~1000℉ (-73.3~537.8℃), inaccuracy of the order of 1% of scale range for bimetal thermometers of high quality. Application: ▬ Temperature measurement; ▬ Very widely as combined sensing and control elements in temperature-control systems, mainly of the on-off type; ▬ Temperature compensating devices for various instruments that has temperature as interfering or modifying input; ▬ Motion compensation due to temperature change; ▬ Automotive sensing application, combined with conductive plastic potentiometers
15/47 8.2.2 Liquid-in-Glass Thermometers ◆Mercury is the most common liquid utilized at intermediate(中等的)and high temperatures.Freezing point of-38F(-38.9C),upper limit of 1000℉(537.8C). Other liquids and their lowest measurable temperature: 一Alcohol(酒精)，-80F(-38.9℃) 一Toluol(甲苯)，-130℉(-90C) 一Pentane(戊烷)，-330F(-201.1℃) 一Mixture of propane(丙烷)and propylene(丙烯)，-360F(-217.8C) ◆Two types: 1Total immersion:during calibration,the liquid column is completely immersed in the measured liquid.It is a bit difficult to take reading. 2 Partial immersion:during calibration,a definite amount of liquid column is immersed in the measured liquid with the remaining portion at a definite temperature. 15 16/47 8.2.2 Liquid-in-Glass Thermometers Full-immersion Partial-immersion thermometer thermometer Auxiliary thermometer (Bulb at n/2) al=70℉ 200 200 80° 80 175 175 50 Correct immersion mork on thermometer Correction兰 Correction 0.00009501200-80l=0.54℉ 0.00009(50){70-80)=-0.045℉ Figure 8.4 Total-and Partial-Immersion Thermometers
Mercury is the most common liquid utilized at intermediate(中等的) and high temperatures. Freezing point of -38℉(−38.9℃), upper limit of 1000℉(537.8℃). Other liquids and their lowest measurable temperature: ▬ Alcohol(酒精), -80℉(−38.9℃) ▬ Toluol(甲苯), -130℉(−90℃) ▬ Pentane(戊烷), -330℉(−201.1℃) ▬ Mixture of propane(丙烷 ) and propylene(丙烯), -360℉(−217.8℃) Two types: ① Total immersion: during calibration, the liquid column is completely immersed in the measured liquid. It is a bit difficult to take reading. ② Partial immersion: during calibration, a definite amount of liquid column is immersed in the measured liquid with the remaining portion at a definite temperature. 8.2.2 Liquid-in-Glass Thermometers 15 15/47 8.2.2 Liquid-in-Glass Thermometers Figure 8.4 Total- and Partial- Immersion Thermometers 16/47