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Measurement model
$$t = \left| {{M_a} - {M_b}} \right|$$ Where,
$t$ is coaxiality error;${M_a}$ is inductance sensor indication of the left side;${M_b}$ is inductance sensor indication of the right side.The uncertainty source of input including:
(1) Standard uncertainty induced by repeatability of the coaxiality of turbine components and stud standard part
$u(\left| {{M_a} - {M_b}} \right|)$ ;(2) Standard uncertainty induced by resolution of inductance probe
$u({\delta _{\left| {{M_a} - {M_b}} \right|}})$ ;(3) Standard uncertainty induced by indication error of inductance probe
$u(\Delta \left| {{M_a} - {M_b}} \right|)$ ;(4) Standard uncertainty induced by expansion coefficient difference u(δa)[11];
(5) Standard uncertainty induced by temperature difference u(δt);
(6) Standard uncertainty induced by force measurement
$u({F_{\left| {{M_a} - {M_b}} \right|}})$ ;(7) Standard uncertainty induced by shape error of three needle
$u({x_{\left| {{M_a} - {M_b}} \right|}})$ ;(8) Standard uncertainty induced by non parallel reference axis of the guide rail and stud standard parts
$u(\Delta P)$ [12];(9) Standard uncertainty induced by the reference axis which is out of vertical of the standard parts of the inductance probe and stud
$u(\Delta S)$ ;(10) Standard uncertainty induced by the measurement of the planeness of the interface due to the slight movement of the parallelogram mechanism up and down during the measurement
$u(\Delta C)$ [13];(11) The uncertainty induced by the deviation between the measured value and the actual value due to the trace movement of the parallelogram mechanism in the measurement
$u(\Delta D)$ [14];The standard uncertainty above are independent.
The Combined uncertainty is:
$$\begin{split} uc =& \displaystyle\sum\limits_{i = 1}^n {\sqrt u i} = \\ & \sqrt {{{0.2}^2} + {1^2} + {{0.71}^2} + {{002}^2}} = 1.26 \;\text{μ} {\rm{m}} \\ \end{split} $$ So the expanded uncertainty (k=2) is:
$$U = k{u_c} = 2 \times 1.26 = 2.52 \approx 2.6\; \text{μ} {\rm{m}}$$ Measurement uncertainty source and the summary of calculate results is shown in Tab.1.
Table 1. Measurement uncertainty source and the summary of calculate results
No. Measurement Uncertainty Source $ui$ Evaluation type Distribution type $ui$/μm 1 Repeatability $u(\left| {{M_{\rm{a}}} - {M_{\rm{b}}}} \right|)$ A / 0.2 Resolution $u({\delta _{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B uniformiy 0.03 2 Indication error of inductance micrometer $u(\Delta \left| {{M_{\rm{a}}} - {M_{\rm{b}}}} \right|)$ B / 0.2 3 Temperature $u({\delta _{\rm{t}}})$ B uniformiy neglected Expansion factor $u({\delta _{\rm{\alpha }}})$ B uniformiy neglected 4 Force of measurement $u({F_{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B uniformiy neglected 5 Three-needle form error $u({x_{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B Two-point 0.71 6 Installation error $u(\Delta P)$ B Two-point 1 $u(\Delta S)$ B uniformiy neglected 7 Mechanism error $u(\Delta C)$ B uniformiy neglected $u(\Delta D)$ B uniformiy neglected Combined standard uncertainty: ${u_c}$ 1.26 Expanded uncertainty(k=2): U 2.6
Development of coaxiality measurement system of turbine components and stud standard parts
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摘要: 涡轮增压器与变速箱在精密机械制造行业中应用广泛,涡轮部件及螺柱标准件的尺寸准确度是涡轮增压器和变速箱装配精度的一个重要保证,其中同轴度是涡轮部件及螺柱标准件尺寸准确度的一个关键参数,根据涡轮部件及螺柱标准件的同轴度测量需求,研制了一套涡轮部件及螺柱标准件同轴度的测量系统,并基于LabVIEW开发了测量软件。通过实验对螺柱标准件M12的同轴度进行测量并完成测量不确定度评定。实验结果显示四次测量得到的同轴度误差在6.3~6.5 μm,扩展不确定度达2.6 μm,结论表明:研制的同轴度测量系统适用于涡轮部件及螺柱标准件同轴度的高精度测量。Abstract: Turbocharger and gearbox were widely used in the precision machinery manufacturing industry. The dimensional accuracy of turbine components and stud standard parts was an important guarantee for the assembly accuracy of turbine components and gearbox, among which coaxiality was a key parameter for the dimensional accuracy of turbine components and stud standard parts. According to the demands of coaxiality measurement for turbine components and stud standard parts, a set of checking fixture was developed, and a software based on LabVIEW was built for the measurement. The coaxiality of stud standard M12 was measured by experiment and the uncertainty of measurement was evaluated. The experimental results show that the coaxiality error obtained from the four measurements is 6.3–6.5 μm, and the extended uncertainty reaches 2.6 μm. The results show that the developed coaxiality measurement system is suitable for the high precision measurement of the coaxiality of turbine parts and stud standard parts.
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Key words:
- coaxiality measurement /
- turbine components /
- stud standard part /
- uncertainty
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Table 1. Measurement uncertainty source and the summary of calculate results
No. Measurement Uncertainty Source $ui$ Evaluation type Distribution type $ui$ /μm1 Repeatability $u(\left| {{M_{\rm{a}}} - {M_{\rm{b}}}} \right|)$ A / 0.2 Resolution $u({\delta _{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B uniformiy 0.03 2 Indication error of inductance micrometer $u(\Delta \left| {{M_{\rm{a}}} - {M_{\rm{b}}}} \right|)$ B / 0.2 3 Temperature $u({\delta _{\rm{t}}})$ B uniformiy neglected Expansion factor $u({\delta _{\rm{\alpha }}})$ B uniformiy neglected 4 Force of measurement $u({F_{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B uniformiy neglected 5 Three-needle form error $u({x_{\left| {{{\rm{M}}_{\rm{a}}}{\rm{ - }}{{\rm{M}}_{\rm{b}}}} \right|}})$ B Two-point 0.71 6 Installation error $u(\Delta P)$ B Two-point 1 $u(\Delta S)$ B uniformiy neglected 7 Mechanism error $u(\Delta C)$ B uniformiy neglected $u(\Delta D)$ B uniformiy neglected Combined standard uncertainty: ${u_c}$ 1.26 Expanded uncertainty(k=2): U 2.6 -
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