{"id":574,"date":"2021-12-06T19:24:07","date_gmt":"2021-12-06T19:24:07","guid":{"rendered":"https:\/\/moodle.localhost\/wp\/?page_id=574"},"modified":"2024-05-15T04:05:02","modified_gmt":"2024-05-15T04:05:02","slug":"grindng-bulletin-5","status":"publish","type":"page","link":"https:\/\/metcomtech.com\/fr\/grindng-bulletin-5\/","title":{"rendered":"Bulletin de meulage #5"},"content":{"rendered":"\n<h5 class=\"wp-block-heading\">What exactly is \u2018Work Index\u2019 and how can I make use of it?<\/h5>\n\n\n\n<p class=\"has-small-font-size\">&#8216;Work Index&#8217; is to measuring energy in size reduction what the &#8216;meter&#8217; is to measuring distance. It is a standard measure that brings all size reduction circuits onto a common basis for comparison. It starts with Bond&#8217;s Work Index equation:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[W ={WI } \\times ({ 10\\over\\sqrt{P80}\\ }\\space-\\space { 10\\over\\sqrt{F80}\\ })\\]<script src=\"https:\/\/metcomtech.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/metcomtech.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\">W is the work (energy) input per ton. F80 is the 80% passing size of the circuit feed, and P80 is the 80% passing size of the circuit product, in microns. For example, a grinding circuit is processing 450 t\/h (of dry feed) with a mill drawing 3,150 kW (at the pinion). The circuit feed is 80% passing 2,500 \u03bcm, and the circuit product is 80% passing 212 \u03bcm.\u00a0\u00a0<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">The Work Input, W  \\[ {W}\\space{=} \\space{ 3150 \\space kW\\over 450 \\space t\/h}  \\space {=}  \\space {7.00} \\space kWh\/t\\]<\/div>\n\n\n\n<p class=\"has-small-font-size\">&nbsp;&nbsp;Then WIo, the &#8220;Operating Work Index&#8221; of this circuit, is calculated as follows:<br><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{ 7.00 \\space kWh\/t} \\space {=} \\space {WIo } \\times ({ 10\\over\\sqrt{212 \u03bcm}\\ } \\space-\\space { 10\\over\\sqrt{2500 \u03bcm}\\ })\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{ 7.00 \\space kWh\/t} ={WIo } \\times  { 0.4868 }\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{WIo}  = \\frac  {7.00}  { 0.4868}\\space {kWh\/t}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{WIo}  = 14.38 \\space {kWh\/t}\\]<\/div>\n\n\n\n<p>So for this circuit on this ore,<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{W}={14.38} \\times ({ 10\\over\\sqrt{P80}\\ } \\space-\\space { 10\\over\\sqrt{F80}\\ })\\]<\/div>\n\n\n\n<p class=\"has-small-font-size\">We can now estimate the needed W if, for example, we accept a grind P80 of 250 \u03bcm.<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{W}={14.38} \\times ({ 10\\over\\sqrt{250 \u03bcm}\\ } \\space-\\space { 10\\over\\sqrt{2500 \u03bcm}\\ })\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{W}={6.22} \\space kWh\/t \\]<\/div>\n\n\n\n<p class=\"has-small-font-size\">So with the same mill power we can increase the tonnage to:<\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[{6.22}  = \\frac  {{3150}\\space{kW}}  {{ x}\\space {tph}}\\]<\/div>\n\n\n\n<div class=\"wp-block-columns has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-f7558fb0f9f1aca9afbb408b6c59342c is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-medium-font-size is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-mathml-mathmlblock\">\\[ {{ x}\\space {=} \\space{ 506} \\space{tph}}\\]<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\">Estimating the new production rate by changing one of the variables is just one of the ways you can use this equation. Note that if we make the feed size very large, the term 10\/\u221aF80 would approach a value of zero. If at the same time we make the P80 equal to 100 \u03bcm, the term 10\/\u221aP80 would equal one, and W, the Work Input would equal the Work Index. So the Work Index of this circuit is the equivalent amount of energy (W) it would use to reduce this ore from a very large size to a P80 of 100 \u03bcm. For any circuit, whether a crushing circuit, a rod mill, or a closed ball mill circuit, the\u00a0<strong>Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 \u03bcm.<\/strong>\u00a0Just as the meter is used to measure and compare distances, the &#8216;Work Index&#8217; thusly measures and compares energy usage of size reduction processes.<\/p>\n\n\n\n<p class=\"has-small-font-size\">The Bond Work Index equation is indeed a process engineering tool for the ages. This bulletin describes its form and basic uses. Another bulletin will describe how Bond used it to prescribe mill power requirements for new projects by measuring the Work Index of the ore, and subsequently how to use it to calculate and compare circuit efficiencies.<\/p>\n\n\n\n<p class=\"has-small-font-size\"><strong>Reference: <\/strong>F.C. Bond, &#8220;Crushing and Grinding Calculations&#8221;,&nbsp;<em>British Chemical Engineering<\/em>, June, 1961, pp.378-385.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-buttons is-horizontal is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-03627597 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/metcomtech.com\/#GrindingBulletin\">See more Grinding Bulletins<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What exactly is \u2018Work Index\u2019 and how can I make use of it? &#8216;Work Index&#8217; is to measuring energy in size reduction what the &#8216;meter&#8217; is to measuring distance. It is a standard measure that brings all size reduction circuits onto a common basis for comparison. It starts with Bond&#8217;s Work Index equation: W is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-a1-main-template","meta":{"footnotes":""},"class_list":["post-574","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/pages\/574","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/comments?post=574"}],"version-history":[{"count":43,"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/pages\/574\/revisions"}],"predecessor-version":[{"id":2542,"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/pages\/574\/revisions\/2542"}],"wp:attachment":[{"href":"https:\/\/metcomtech.com\/fr\/wp-json\/wp\/v2\/media?parent=574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}