Performance Investigation of CMM Measurement Quality Using Flick Standard

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">CMM fitting algorithms</td><td align="center">LSQ</td><td align="center">ME</td><td align="center">MC</td><td align="center">MI</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">Combined standards uncertainty, <svg height="11.9625" id="M40" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 14.725 11.9625" width="14.725" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M515 96q-37 -44 -84.5 -76t-71.5 -32q-12 0 -18 7t-6 34t10 75l19 89h-2q-87 -113 -181 -176q-43 -29 -83 -29q-46 0 -46 63q0 31 9 67l52 222q7 36 -1 36q-10 0 -76 -50l-13 24q47 45 92 71.5t67 26.5q18 0 21 -16.5t-8 -65.5l-56 -242q-16 -67 13 -67q41 0 114 74
t114 146l32 145l74 26h11q-52 -199 -80 -347q-8 -39 6 -39q7 0 32 17.5t47 39.5z" id="x1D462"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.213,11.762)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
</svg></td><td align="center">0.52650</td><td align="center">0.52555</td><td align="center">0.52650</td><td align="center">0.523873</td></tr><tr><td align="left">Expanded uncertainty <svg height="18.112499" id="M41" style="vertical-align:-5.03986pt" version="1.1" viewbox="0 0 32.612499 18.112499" width="32.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M751 650l-6 -28q-53 -1 -69 -12.5t-24 -38.5q-23 -85 -43 -192l-13 -69q-34 -181 -130 -262q-79 -65 -185 -65t-171 57q-87 77 -54 258l42 232q12 58 0.5 73t-75.5 19l8 28h263l-6 -28q-63 -5 -78 -18t-26 -74l-41 -226q-25 -135 22 -201t139 -66q99 0 161.5 68t91.5 217
l11 57q28 149 28 193q0 28 -19 38t-79 12l6 28h247z" id="x1D448"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.038,15.187)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,18.094,15.187)"><path d="M474 0h-214v26q32 4 39 12t-5 28l-74 117q-39 -58 -64 -106q-16 -25 -10 -35t44 -16v-26h-186v26q46 6 64 17t48 49t85 120l-87 136q-23 36 -40 47t-58 16v26h199v-26q-31 -4 -36.5 -12.5t9.5 -29.5l59 -93q37 56 58 94q13 23 7 30t-40 11v26h183v-26q-47 -5 -65 -13.5
t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" id="x78"></path></g><g transform="matrix(.012,-0,0,-.012,23.711,15.187)"><path d="M169 380l92 53q26 16 49 16q80 0 128.5 -56t48.5 -133q0 -108 -72.5 -180.5t-176.5 -91.5q-38 1 -69 18v-131q0 -57 13 -70t71 -18v-27h-236v27q49 5 61 17t12 61v452q0 48 -9.5 58.5t-56.5 16.5v24q66 11 145 43v-79zM169 346v-270q37 -39 94 -39q63 0 101.5 50
t38.5 134q0 78 -38.5 123t-95.5 45q-45 0 -100 -43z" id="x70"></path></g>
</svg></td><td align="center">1.0526</td><td align="center">1.0511</td><td align="center">1.0526</td><td align="center">1.0478</td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left">Average of <svg height="18.112499" id="M42" style="vertical-align:-5.03986pt" version="1.1" viewbox="0 0 32.612499 18.112499" width="32.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M751 650l-6 -28q-53 -1 -69 -12.5t-24 -38.5q-23 -85 -43 -192l-13 -69q-34 -181 -130 -262q-79 -65 -185 -65t-171 57q-87 77 -54 258l42 232q12 58 0.5 73t-75.5 19l8 28h263l-6 -28q-63 -5 -78 -18t-26 -74l-41 -226q-25 -135 22 -201t139 -66q99 0 161.5 68t91.5 217
l11 57q28 149 28 193q0 28 -19 38t-79 12l6 28h247z" id="x1D448"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.038,15.187)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,18.094,15.187)"><path d="M474 0h-214v26q32 4 39 12t-5 28l-74 117q-39 -58 -64 -106q-16 -25 -10 -35t44 -16v-26h-186v26q46 6 64 17t48 49t85 120l-87 136q-23 36 -40 47t-58 16v26h199v-26q-31 -4 -36.5 -12.5t9.5 -29.5l59 -93q37 56 58 94q13 23 7 30t-40 11v26h183v-26q-47 -5 -65 -13.5
t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" id="x78"></path></g><g transform="matrix(.012,-0,0,-.012,23.711,15.187)"><path d="M169 380l92 53q26 16 49 16q80 0 128.5 -56t48.5 -133q0 -108 -72.5 -180.5t-176.5 -91.5q-38 1 -69 18v-131q0 -57 13 -70t71 -18v-27h-236v27q49 5 61 17t12 61v452q0 48 -9.5 58.5t-56.5 16.5v24q66 11 145 43v-79zM169 346v-270q37 -39 94 -39q63 0 101.5 50
t38.5 134q0 78 -38.5 123t-95.5 45q-45 0 -100 -43z" id="x70"></path></g>
</svg></td><td align="center" colspan="4">1.0510</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Evaluation of uncertainty budget in roundness deviation measurements.

Journal of Quality and Reliability Engineering

tab4

Table 4

Table 4: Performance Investigation of CMM Measurement Quality Using Flick Standard 