隗群梅
摘? 要:該實(shí)驗(yàn)采用熱膨脹測試儀(熱膨脹測試儀DH0505)通過邁克爾遜干涉法和千分表法測量3種金屬(銅、鋼、鋁)的線膨脹系數(shù)。該文通過對(duì)實(shí)驗(yàn)數(shù)據(jù)的處理和分析,對(duì)實(shí)驗(yàn)過程中存在的問題進(jìn)行了深入的總結(jié)和探討。發(fā)現(xiàn):(1)邁克爾遜干涉測量方法的精度在理論上高于千分表法,但實(shí)際上兩種方法測量結(jié)果的相對(duì)誤差相當(dāng);(2)無論采用何種測量方法,冷卻過程中的測量結(jié)果相對(duì)誤差均小于加熱過程中的測量結(jié)果。
關(guān)鍵詞:線膨脹系數(shù)? ?誤差? ?千分表? ?邁克爾遜干涉? ?穩(wěn)態(tài)? ?瞬態(tài)
中圖分類號(hào):O4-34? ? ? ? ? ? ? ? ? ? ? ? 文獻(xiàn)標(biāo)識(shí)碼:A文章編號(hào):1672-3791(2021)07(b)-0040-04
Comparison of Two Methods of Measuring Linear Expansion Coefficient
WEI Qunmei
(College of Science, China University of Petroleum (east China), Qingdao, Shandong Province, 266580 China)
Abstract: This experiment uses a thermal expansion tester (thermal expansion tester DH0505) to measure the coefficient of linear expansion of three metals (copper, steel, aluminum) by Michelson interferometry and dial indicator method. Through the processing and analysis of experimental data, the problems existing in the experimental process are deeply summarized and discussed. It is found that: (1) The accuracy of the Michelson interferometer measurement method is theoretically higher than the dial gauge method, but in fact the relative errors of the measurement results of the two methods are equivalent; ⑵ Regardless of the measurement method, the relative error of the measurement result during the cooling process is smaller than the measurement result during the heating process.
Key Words: Linear expansion coefficients; Error; Dial indicator; Michelson interference; Steady state; Transient
線膨脹系數(shù)測量實(shí)驗(yàn)是大學(xué)物理實(shí)驗(yàn)中的基礎(chǔ)性實(shí)驗(yàn)之一,是一個(gè)熱學(xué)實(shí)驗(yàn)中微小變化量測量實(shí)驗(yàn),也是一個(gè)必須和其他測量方法相結(jié)合的實(shí)驗(yàn)。比如:采用高精度的長度測量儀(如移測顯微鏡、千分表、光柵尺等)進(jìn)行直接測量,或采用轉(zhuǎn)換法(如光杠桿、光的干涉、光的衍射和傳感器法等)進(jìn)行間接測量[1-10]。
1? 實(shí)驗(yàn)原理
線膨脹系數(shù)是指在一定溫度范圍內(nèi),溫度每升高(降低)1 ℃時(shí),固體材料在某一方向上的相對(duì)伸長(收縮)量,即:
(1)
式中α為固體的線膨脹系數(shù);L1和L2分別為物體在t1和t2下的長度,△L21=L2-L1,是長度為L的物體在溫度從t1升至t2的伸長量。在實(shí)驗(yàn)中,我們需要測量的物理量為:△L21,L,t1,t2,便可以計(jì)算得到α,達(dá)到測量的目的。由于金屬在溫度變化時(shí)長度變化的相對(duì)量都很小,而對(duì)于微小量測量要么采用高精度的測量儀器對(duì)其進(jìn)行直接測量,要么通過轉(zhuǎn)換后進(jìn)行的間接測量。下面對(duì)千分表法(直接測量)和邁克爾遜干涉法(間接測量)兩種方法分別從理論上和實(shí)際測量進(jìn)行對(duì)比研究。
2? 測量金屬線膨脹系數(shù)的測量依據(jù)
由積商函數(shù)最大誤差公式可得式(1)的最大誤差:
(2)
最大相對(duì)誤差:
(3)
若實(shí)驗(yàn)要求E<3%,式(1)中的△L21,L,t1,t2是直接測量的物理量。根據(jù)等誤差傳遞原則:
線膨脹系數(shù)實(shí)驗(yàn)儀器DH0505提供了硬鋁(α參考值23.6×10-6/℃)、黃銅(α參考值20.8×10-6/℃)和鋼(α參考值12.0×10-6/℃)3種金屬材料,以最小的線膨脹系數(shù)鋼為例進(jìn)行儀器相關(guān)精度的計(jì)算,其中L=150 mm,溫度從20~80 ℃,t2-t1=60 ℃,則:
L21=α(t2-t1)L=12.0×10-6×60×150=0.108(mm)
?L21=L21×1%≈0.001(mm)
?L=L×1%=1.5(mm)
△t2=△t1=(1/2)×(t2-t1) =(1/2)×60×1%=0.3(℃)