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本文主要探讨长度测量中,由于计量器具不符合阿贝原则,对测量中引起误差的一些认识。首先以游标卡尺为例,由于基准轴线与测量轴线不在同一轴线上,即这种测量方法不符合阿贝原则。这时,由于尺框与尺身宽度方向配合有间隙,测量时受测量力等因素的影响,引起尺框发生倾斜,从而产生了阿贝误差ΔL,如图1所示。由图1可知,产生的测量误差为ΔL=S·tanθ,由于在实际测量中所产生的θ角很小,所以tanθ≈θ,即ΔL≈S·θ如果我们检定一把测量范围为150mm、分度值为0.02mm的游标卡尺,量块名义尺寸为80mm,当基准轴线与测量轴线之间的距离为S=50mm、尺框与尺身的倾斜角为θ=100″=0.00048弧度,那么在测量时所产生的误差为ΔL≈S·θ=50×0.00048=0.024mm。
This article mainly discusses the length measurement, due to the measurement instrument does not meet the Abbe principle, some of the errors caused by the measurement. First, the vernier caliper, for example, because the reference axis and the measurement axis are not in the same axis, that is, this measurement method does not meet the Abbe’s principle. At this moment, due to the gap between the frame and the width of the ruler, there is a gap caused by the measuring force and other factors, causing the ruler to tilt, resulting in Abbe error ΔL, as shown in FIG. 1. From Figure 1, we can see that the measurement error is ΔL = S · tan θ. Since θ is very small in the actual measurement, tanθ≈θ, that is, ΔL≈S · θ. If we measure a measurement range of 150mm, The vernier caliper with an index value of 0.02 mm has a nominal gauge of 80 mm. When the distance between the reference axis and the measuring axis is S = 50 mm and the tilt angle between the scale and the blade is θ = 100 "= 0.00048 radians, The measurement error is ΔL≈S · θ = 50 × 0.00048 = 0.024mm.