27:null 28:["$","title",null,{"children":"FSW Tool Parameters | jason a. grafft | Observable"}] 2d:T165a,Plot.plot({ marks: [ // Domain // Plot.ruleX(params.drawing.domain.x), Plot.ruleY(params.drawing.domain.y), // Reference Marks // // Left-hand edge of probe tip Plot.lineY( [ {"x": params.tool.midline - tool_parameters_form.pr, "y": tool_parameters_form.te}, {"x": params.tool.midline - tool_parameters_form.pt, "y": tool_parameters_form.te - tool_parameters_form.bit_length} ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 2 } ), // Right-hand edge of probe tip Plot.lineY( [ {"x": params.tool.midline + tool_parameters_form.pr, "y": tool_parameters_form.te}, {"x": params.tool.midline + tool_parameters_form.pt, "y": tool_parameters_form.te - tool_parameters_form.bit_length}, ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 2 } ), // Tool centerline Plot.lineX( [ {"x": params.tool.midline, "y": params.drawing.domain.y[1]}, {"x": params.tool.midline, "y": params.drawing.domain.y[0]} ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 1, strokeDasharray: [7,3,3] } ), // Workpiece surface Plot.lineY( [ {"x": params.drawing.domain.x[0], "y": 0}, {"x": params.drawing.domain.x[1], "y": 0} ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 1, strokeDasharray: [7,3,3] } ), // Tool Shoulder [L,midline] Plot.lineY( [ {"x": params.tool.midline - tool_parameters_form.pr, "y": tool_parameters_form.te}, { "x": params.tool.midline - tool_parameters_form.pr - tool_parameters_form.shoulder_width, "y": tool_parameters_form.te - tool_parameters_form.shoulder_width * Math.sin(tool_parameters_form.alpha) } ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 2 } ), // Tool Shoulder [midline,R] Plot.lineY( [ {"x": params.tool.midline + tool_parameters_form.pr, "y": tool_parameters_form.te}, { "x": params.tool.midline + tool_parameters_form.pr + tool_parameters_form.shoulder_width, "y": tool_parameters_form.te - tool_parameters_form.shoulder_width * Math.sin(tool_parameters_form.alpha) } ], { x: "x", y: "y", stroke: "#1ecbe1", strokeWidth: 2 } ), // Parameters // // S Plot.lineY( [ {"x": l_shoulder_x_intercept, "y": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt}, {"x": params.tool.midline, "y": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt} ], { x: "x", y: "y", stroke: "#8d2cd3", strokeDasharray: [3] } ), // Probe Root Raidus (P_R) Plot.lineX( [ {"x": params.tool.midline - tool_parameters_form.pr, "y": tool_parameters_form.te}, {"x": params.tool.midline + tool_parameters_form.pr, "y": tool_parameters_form.te}, ], { x: "x", y: "y", stroke: "#f00f21", strokeDasharray: [3] } ), // Probe Tip Radius (P_T) Plot.lineX( [ {"x": params.tool.midline - tool_parameters_form.pt, "y": tool_parameters_form.te - tool_parameters_form.bit_length}, {"x": params.tool.midline + tool_parameters_form.pt, "y": tool_parameters_form.te - tool_parameters_form.bit_length} ], { x: "x", y: "y", stroke: "#62ea44", strokeDasharray: [3] } ), // Tool penetration depth (t) Plot.lineY( [ {"x": l_shoulder_x_intercept, "y": 0}, {"x": l_shoulder_x_intercept, "y": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt} ], { x: "x", y: "y", stroke: "#ff9f2b", strokeDasharray: [3] } ), // Probe tip radius length (t_T) Plot.lineY( [ {"x": params.tool.midline, "y": tool_parameters_form.te - tool_parameters_form.bit_length}, {"x": params.tool.midline, "y": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt} ], { x: "x", y: "y", stroke: "#fc0e0a", strokeWidth: 2, strokeDasharray: [1, 2] } ), // Probe tip segment [L,midline] Plot.arrow( [ { "x1": params.tool.midline - tool_parameters_form.pt, "y1": tool_parameters_form.te - tool_parameters_form.bit_length, "x2": params.tool.midline, "y2": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt } ], { x1: "x1", y1: "y1", x2: "x2", y2: "y2", bend: true, headLength: 0, sweep: "+y", stroke: "#1ecbe1", bend: 33 } ), // Probe tip segment [midline,R] Plot.arrow( [ { "x1": params.tool.midline + tool_parameters_form.pt, "y1": tool_parameters_form.te - tool_parameters_form.bit_length, "x2": params.tool.midline, "y2": tool_parameters_form.te - tool_parameters_form.bit_length - tool_parameters_form.tt } ], { x1: "x2", y1: "y2", x2: "x1", y2: "y1", bend: true, headLength: 0, sweep: "-y", stroke: "#1ecbe1", bend: 33 } ) ] })2e:T76b,| Current Value | Parameter | Description | |:-----:|:-----:|:---| | ${tool_parameters_form.alpha} rad | ${tex`\alpha`} | Shoulder taper angle | | ${+frustrum_probe_half_angle.toFixed(2)} rad | ${tex`\beta`} | Frustrum probe half angle | | ${+l_shoulder_x_intercept.toFixed(2)} mm | ${tex`S`} | Effective shoulder radius| || ${tex`S_{T}`} | Truncated tapered shoulder minor diameter | | ${tool_parameters_form.pr} mm | ${tex`P_{R}`} | Probe root radius | | ${tool_parameters_form.pt} mm | ${tex`P_{T}`} | Probe tip radius | || ${tex`R_{T}`} | Probe tip ball radius | || ${tex`R_{C}`} | Convex shoulder radius | | ${tool_penetration_length} mm | ${tex`t`} | Tool penetration length | | ${tool_parameters_form.te} mm | ${tex`t_{E}`} | Shoulder embed distance | | ${tool_parameters_form.tt} mm | ${tex`t_{T}`} | Probe tip radius length |2f:[] 2b:{"id":"891ad490c88000bb","slug":null,"title":"FSW Tool Parameters","thumbnail":"b3edf5306fd265d24d275e8c48b10f67f7127ce67b53396cbb1b685aa9bd0874","access_level":"public","create_time":"$D2023-10-03T17:30:53.357Z","update_time":"$D2023-10-10T14:32:24.022Z","view_time":null,"first_public_time":"$D2025-11-13T01:35:19.833Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"33d714a841c4dfd5","login":"jagrafft","name":"jason a. grafft","avatar_url":"https://avatars-next.observableusercontent.com/50bfa5f99ef282cce89216516d1b5d3a73b8b6d3cc0bd65b3d18608b9b3f8957","tier":"starter_2024"},"version":941,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"69c7ef7870d59485","login":"jagrafft","name":"jason a. grafft","avatar_url":"https://avatars-next.observableusercontent.com/50bfa5f99ef282cce89216516d1b5d3a73b8b6d3cc0bd65b3d18608b9b3f8957","tier":null}],"members":[{"type":"individual","id":"69c7ef7870d59485","login":"jagrafft","name":"jason a. grafft","avatar_url":"https://avatars-next.observableusercontent.com/50bfa5f99ef282cce89216516d1b5d3a73b8b6d3cc0bd65b3d18608b9b3f8957","tier":null,"role":"editor"},{"type":"team","id":"33d714a841c4dfd5","login":"jagrafft","name":"jason a. grafft","avatar_url":"https://avatars-next.observableusercontent.com/50bfa5f99ef282cce89216516d1b5d3a73b8b6d3cc0bd65b3d18608b9b3f8957","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"FSW Tool Parameters","cells":[{"id":0,"value":"# FSW Tool Parameters","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"viewof tool_parameters_form = Inputs.form({\n bit_length: Inputs.range([0.5,2.5], {\n label: html`Bit Length`,\n step: 0.1,\n value: 1\n }),\n shoulder_width: Inputs.range([0.5,3], {\n label: html`Shoulder Width`,\n step: 0.1,\n value: 1\n }),\n alpha: Inputs.range([-Math.round(Math.PI/2, 1), Math.round(Math.PI/2, 1)], {\n label: html`${tex`\\alpha`} (rad)`,\n step: 0.1,\n value: 0.0\n }),\n pr: Inputs.range([0.1,2.5], {\n label: html`${tex`P_{R}`} (mm)`,\n step: 0.1,\n value: 0.3\n }),\n pt: Inputs.range([0.1,2.5], {\n label: html`${tex`P_{T}`} (mm)`,\n step: 0.1,\n value: 0.3\n }),\n te: Inputs.range([-2,2], {\n label: html`${tex`t_{E}`}^* (mm)`,\n step: 0.1,\n value: 0\n }),\n tt: Inputs.range([0,1.0], {\n label: html`${tex`t_{T}`} (mm)`,\n step: 0.05,\n value: 0\n }),\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":905,"value":"$${html`^* - Inverted presentation. Does not affect calculations.`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"$2d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"$2e","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":718,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":824,"value":"$${tex`geo = \\frac{2\\pi}{3}\\left[\\frac{S^3-P_{R}^3}{\\cos\\alpha} + \\frac{t\\left((P_{R}+P_{T})^2-P_{R}P_{T}\\right)}{\\cos\\beta}+P_{T}^3\\right] = \\frac{2\\pi}{3}\\left[\\frac{${+l_shoulder_x_intercept.toFixed(2)}^3-${tool_parameters_form.pr}^3}{\\cos(${tool_parameters_form.alpha})} + \\frac{${tool_penetration_length}\\left((${tool_parameters_form.pr} + ${tool_parameters_form.pt})^2-(${tool_parameters_form.pr}\\times ${tool_parameters_form.pt})\\right)}{\\cos(${+frustrum_probe_half_angle.toFixed(2)})} + ${tool_parameters_form.pt}^3\\right]`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":927,"value":"$${tex`= \\frac{2\\pi}{3}\\left[\\frac{${Math.pow(+l_shoulder_x_intercept,3)}-${Math.pow(tool_parameters_form.pr,3)}}{${Math.cos(tool_parameters_form.alpha)}} + \\frac{${tool_penetration_length}\\left(${Math.pow((tool_parameters_form.pr + tool_parameters_form.pt),2)}-${tool_parameters_form.pr * tool_parameters_form.pt}\\right)}{${Math.cos(+frustrum_probe_half_angle)}} + ${Math.pow(tool_parameters_form.pt,3)}\\right]`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":848,"value":"$${tex`= ${(2*Math.PI)/3}\\left[\\frac{${Math.pow(+l_shoulder_x_intercept, 3)- Math.pow(tool_parameters_form.pr,3)}}{${Math.cos(tool_parameters_form.alpha)}} + \\frac{${tool_penetration_length * Math.pow((tool_parameters_form.pr + tool_parameters_form.pt)-(tool_parameters_form.pr * tool_parameters_form.pt),2)}}{${Math.cos(+frustrum_probe_half_angle)}} + ${Math.pow(tool_parameters_form.pt,3)}\\right]`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":887,"value":"$${tex`= ${(2*Math.PI)/3}\\left[${(Math.pow(+l_shoulder_x_intercept, 3)- Math.pow(tool_parameters_form.pr,3)) / Math.cos(tool_parameters_form.alpha)} + ${(tool_penetration_length * Math.pow((tool_parameters_form.pr + tool_parameters_form.pt)-(tool_parameters_form.pr * tool_parameters_form.pt),2)) / Math.cos(+frustrum_probe_half_angle)} + ${Math.pow(tool_parameters_form.pt,3)}\\right]`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":894,"value":"$${tex`= ${(2*Math.PI)/3}\\left[${((Math.pow(+l_shoulder_x_intercept, 3)- Math.pow(tool_parameters_form.pr,3)) / Math.cos(tool_parameters_form.alpha)) + ((tool_penetration_length * Math.pow((tool_parameters_form.pr + tool_parameters_form.pt)-(tool_parameters_form.pr * tool_parameters_form.pt),2)) / Math.cos(+frustrum_probe_half_angle)) + Math.pow(tool_parameters_form.pt,3)}\\right] = ${((2*Math.PI)/3)*(((Math.pow(+l_shoulder_x_intercept, 3)- Math.pow(tool_parameters_form.pr,3)) / Math.cos(tool_parameters_form.alpha)) + ((tool_penetration_length * Math.pow((tool_parameters_form.pr + tool_parameters_form.pt)-(tool_parameters_form.pr * tool_parameters_form.pt),2)) / Math.cos(+frustrum_probe_half_angle)) + Math.pow(tool_parameters_form.pt,3))}`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":908,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":808,"value":"$${tex`\\tau_{flow} = \\frac{T}{geo}`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":714,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":294,"value":"params = new Object({\n drawing: {\n domain: {\n x: [-3.5,3.5],\n y: [-3.5,3.5]\n }\n },\n tool: {\n midline: 0,\n te: -tool_parameters_form.te\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":675,"value":"frustrum_probe_half_angle = Math.atan(((tool_parameters_form.te - tool_parameters_form.bit_length) - tool_parameters_form.te) / (params.tool.midline - tool_parameters_form.pt - params.tool.midline - tool_parameters_form.pr))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":525,"value":"l_shoulder_x_intercept = ((X) => {\n // var magnitude = Math.sqrt((Math.pow(X[1][0] - X[0][0], 2) + Math.pow(X[1][1] - X[0][1], 2)))\n var m = (X[1][1] - X[0][1])/(X[1][0] - X[0][0])\n // var theta = Math.atan(m)\n // y = mx + b => b = y - mx\n var y_intercept = X[1][1] - m*X[1][0]\n // x = (y-b)/m = (0-b)/m\n var x_intercept = (-y_intercept)/m\n\n if (isNaN(x_intercept)) {\n return Math.abs(X[1][0])\n } else if (Math.abs(x_intercept) === Infinity) {\n return Math.abs(X[1][0])\n } else {\n return Math.abs(x_intercept)\n }\n // return { m: m, y_intercept: y_intercept, x_intercept: x_intercept }\n // return { magnitude: magnitude, m: m, y_intercept: y_intercept, x_intercept: x_intercept, theta: theta }\n})([\n [params.tool.midline - tool_parameters_form.pr, tool_parameters_form.te],\n [params.tool.midline - tool_parameters_form.pr - tool_parameters_form.shoulder_width, tool_parameters_form.te - tool_parameters_form.shoulder_width * Math.sin(tool_parameters_form.alpha)]\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":610,"value":"tool_penetration_length = Math.abs(tool_parameters_form.te - tool_parameters_form.bit_length)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2c:"$2b:body"