31:T6cf,# Importance In sheet metal fabrication, there is a miss understanding of what the flat projection in drawings is to be used for. ## Two cases If in the design you can specify all the bending processes (machine, material, thickness, angle, die, punch and process) then the flat can be used for cutting the part. If it's something to be defined by the manufacturer after the design is made. Then the flat projection made from the design is a rough idea for quotation, roughly what is the material needed and to validate for self interferences in the flat projection. The manufacturer is the one responsible for making the correct flat projection according to the internal radius, dies, processes, etc. that will affect the K-factor for each bend thus the flat projection. ## Misconceptions ** Using the K factor from the design software **: The design software doesn't know what manufacturing process you will use thus using 0.33 for everything won't give you the right Bend Allowance thus the Flat Projection. ** Using the K factor from the CNC software **: The CNC software doesn't know the exact properties of the material you will use. Thus using 0.33 for everything won't give you the right Bend Allowance thus the Flat Projection. If the CNC software is giving you a K factor, is just hoping that you won't notice the difference. ** Using the K factor from the Machine vendor **: Again it's supposed to vary between materials. # Right approach Make a test procedure for the specific case you will bend. And reverse engineer the K factor, so that the real part will have the right flat projection. # What you will find here Here you will find a proof of the errors found for each misconception and tools to make your own tests.32:Ta4b,{ // todo, make a function that generates the text // apply a transform that makes two of them side by side const t = 3; const r_i = 3.5; const r_i_vs = 3.4; const k = 0.45; const k_vs = 0.45; const r_tol = 0.7; const ba_tol = 0.5; const pi = Math.PI, cos = Math.cos, sin = Math.sin; const A = (90 * pi) / 180; const BA = (r_i + t * k) * A; const BA_vs = (r_i_vs + t * k_vs) * A; const t_comp = t * k; const r_comp = r_i + t_comp / 2; const comp_color = "red"; const t_tens = t * (1 - k); const r_tens = r_i + t - t_tens / 2; const tens_color = "blue"; const r_k = r_i + k * t; const min_tol_color = "green"; const max_tol_color = "orange"; const r_min_tol = r_i_vs - r_tol / 2; const r_max_tol = r_i_vs + r_tol / 2; const ba_min_tol = BA_vs - ba_tol / 2; const ba_max_tol = BA_vs + ba_tol / 2; return svg` `; }33:Ta74,{ const t = thickness; //const r_i = 3.4; //const r_i_2 = 3; const r_diff = (r_i_2 - r_i) * 1; const r_o = r_i + t; const r_o_2 = r_i_2 + t; //const k = 0.3; const tk = t * k; //const k2 = 0.5; const tk2 = t * k2; const r_k = r_i + tk; const r_k_2 = r_i_2 + tk2; const pi = Math.PI, sin = Math.sin, cos = Math.cos; const A = (Adeg * pi) / 180; const large = A >= (180 * pi) / 180; const BAmax = r_o * pi; const BA = calcBA(A, r_i, k, t); const BA2 = calcBA(A, r_i_2, k2, t); const tol = getTol("m", BA); const L = 300; const tolL = getTol("m", L); return svg` `; }34:[] 2f:{"title":"Sheet Metal K-factor (and Bend Allowance)","cells":[{"id":0,"value":"# Sheet Metal K-factor (and Bend Allowance)\n\nThis is a set of tools to calculate, visualize and estimate the effects of the K factor in sheet metal bending.\n\nIncludes a tool to do experiments for the K factor for your particular test measurements.\n\n- [wikipedia: Bending (metalworking)](https://en.wikipedia.org/wiki/Bending_%28metalworking%29)\n- [Omnicalculator: k-factor](https://www.omnicalculator.com/construction/k-factor)\n- [trumpf: Bending Tools](https://www.trumpf.com/filestorage/TRUMPF_Master/Products/Services/01_brochures/TRUMPF-bending-tools-catalog-EN.pdf)\n- [Xometry: Bending Radius Table](https://xometry.pro/en/articles/sheet-metal-bend-radius-table-calculator/)\n- [WilsonTool: Air Bending Force Chart](https://wilsontool.com/en-us/resources/air-bending-force-chart)","pinned":false,"hidden":false,"mode":"md"},{"id":612,"value":"# Din rule for\n\nDIN-6935-1975\n\neq(3)\n\n${tex.block`2k = 0.65 + \\frac{1}{2} log\\left(\\frac{r}{t}\\right)`}","pinned":false,"hidden":false,"mode":"md"},{"id":620,"value":"function dinRule(r, t) {\n const log = Math.log;\n return (0.65 + 0.5 * log(r / t)) / 2;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":624,"value":"dinRule(5.3, 3.05)","pinned":true,"hidden":false,"mode":"ojs"},{"id":97,"value":"$31","pinned":false,"hidden":false,"mode":"md"},{"id":94,"value":"# TO DO\n\n- [x] Include the graphic for bend allowance\n- [x] Show in the graphic the effect of a wrong estimation (ri and k)\n- [ ] Make an example of a company that uses the default of 0.33\n- [ ] Make a plot of different radiuses, thicknesses angles, etc.\n- [ ] Compare to the rules of thumb\n- [ ] Show the errors\n- [ ] Compare to a DIN 2768 Standard for errors","pinned":false,"hidden":false,"mode":"md"},{"id":6,"value":"## Bend Allowance\n\nThe BA can be estimated using the following formula, which incorporates the empirical K-factor:\n\n${tex.block`\nBA = A \\left( R + (K \\times T \\right))\n`}","pinned":false,"hidden":false,"mode":"md"},{"id":12,"value":"function calcBA(A, R, K, T) {\n return A * (R + K * T);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":491,"value":"# OSSB\n\nOutside Setback is the distance from the apex to the tangent of the outside radius.\n\n${tex.block`OSSB = \\tan\\left(\\frac{A}{2}\\right)(R+T)`}","pinned":false,"hidden":false,"mode":"md"},{"id":504,"value":"function radians(A) {\n return (A * Math.PI) / 180;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":489,"value":"function calcOSSB(A, R, T) {\n const tan = Math.tan;\n return tan(A / 2) * (R + T);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":518,"value":"# Bend Deduction\n\n${tex.block`BD = 2*OSSB - BA`}","pinned":false,"hidden":false,"mode":"md"},{"id":511,"value":"function calcBD(A, R, T, K) {\n // This function receives the angle in radians but the error is in degrees\n if (typeof A !== \"number\" || A <= 0 || A > 180)\n throw new Error(`Angle must be between 0 and 180 degrees, not ${A}`);\n if (typeof R !== \"number\" || R <= 0 || R === Infinity)\n throw new Error(`Radius must be positive, not ${R}`);\n if (typeof T !== \"number\" || T <= 0 || T === Infinity)\n throw new Error(`Thickness must be a positive number, not ${T}`);\n if (typeof K !== \"number\" || K < 0 || K > 1 || K === Infinity)\n throw new Error(`K factor must be a number between 0 and 1 not ${K}`);\n const BA = calcBA(A, R, K, T);\n const OSSB = calcOSSB(A, R, T);\n return 2 * OSSB - BA;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":509,"value":"calcOSSB(radians(72), 3.5, 3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":516,"value":"calcBD(radians(90), 3.5, 3, 0.33)","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"// Example\n// Angle\t90°, Radius\t10.0, K-factor\t0.33, Thickness\t10\n// Bend allowance\t20.89\ncalcBA((90 * Math.PI) / 180, 10, 0.33, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":520,"value":"function labExperiment(flatLength, legA, legB, R, bendingAngle, T) {\n const A = radians(bendingAngle);\n const OSSB = calcOSSB(A, R, T);\n const BA = flatLength - (legA + legB - 2 * OSSB); //calcBA(A, R, T, K)\n const K = calcK(A, R, BA, T);\n return K;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":522,"value":"labExperiment(20, 10.5, 12, 1.5, 90, 1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":14,"value":"## K-factor\n\nThe following equation relates the K-factor to the bend allowance\n\n${tex.block`\nK = \\frac{-R + \\frac{BA}{ A}}{T}.\n`}","pinned":false,"hidden":false,"mode":"md"},{"id":21,"value":"function calcK(A, R, BA, T) {\n return (-R + BA / A) / T;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":27,"value":"// Example\n// Angle\t90°, Radius\t10.0, Bend allowance\t20.89, Thickness\t10\n// Yields K-factor\t0.33\ncalcK((90 * Math.PI) / 180, 10, 20.8916, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":32,"value":"## Generic K factors\n\n### Air bending\n\n\n| Radius | Soft materials (Al) |\tMedium materials (Al) | Hard materials (Steel) |\n| --- | --- | --- | --- |\n| 0 to thickness | 0.33 |\t0.38 | 0.40 |\n| Thickness to 3 × thickness | 0.40\t| 0.43 | 0.45\n| Greater than 3 × thickness | 0.50 |\t0.50 | 0.50\n\n### Bottoming\n| Radius | Soft materials (Al) |\tMedium materials (Al) | Hard materials (Steel) |\n| --- | --- | --- | --- |\n| 0 to thickness | 0.42 |\t0.44 | 0.46\n| Thickness to 3 × thickness |\t0.46 | 0.47 | 0.48\n| Greater than 3 × thickness | 0.50 | 0.50 | 0.50\n\n### Coining\n| Radius | Soft materials (Al) |\tMedium materials (Al) | Hard materials (Steel) |\n| --- | --- | --- | --- |\n| 0 to thickness | 0.38 | 0.41 | 0.44\n| Thickness to 3 × thickness | 0.44 | 0.46 | 0.47\n| Greater than 3 × thickness | 0.50 | 0.50 | 0.50","pinned":false,"hidden":false,"mode":"md"},{"id":30,"value":"function generic_K_factors(Material, Process, T, R) {\n const db = {\n \"Air bending\": {\n Soft: [0.33, 0.4, 0.5],\n Medium: [0.38, 0.43, 0.5],\n Hard: [0.4, 0.45, 0.5]\n },\n Bottoming: {\n Soft: [0.42, 0.46, 0.5],\n Medium: [0.44, 0.47, 0.5],\n Hard: [0.46, 0.48, 0.5]\n },\n Coining: {\n Soft: [0.38, 0.44, 0.5],\n Medium: [0.41, 0.46, 0.5],\n Hard: [0.44, 0.47, 0.5]\n }\n };\n const radius_case = R <= T ? 0 : R <= 3 * T ? 1 : 2;\n const materials = Object.keys(db[\"Air bending\"]);\n const processes = Object.keys(db);\n if (!materials.includes(Material)) {\n throw Error(`Material should be one of : ${materials} not ${Material}`);\n }\n if (!processes.includes(Process)) {\n throw Error(`Process should be one of : ${processes} not ${Process}`);\n }\n return db[Process][Material][radius_case];\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":38,"value":"generic_K_factors(\"Soft\", \"Air bending\", 1, 3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":48,"value":"# Air bending approximation\n\nThe following formula can be used in place of the table as a good ''approximation'' of the K-factor for air bending:\n\n${tex.block`K = \\frac{\\log \\min\\left(100, \\frac{\\max(20 R, T)}{T}\\right)}{2 \\log 100}`}\n","pinned":false,"hidden":false,"mode":"md"},{"id":54,"value":"function K_air_bending(R, T) {\n const log = Math.log,\n min = Math.min,\n max = Math.max;\n return log(min(100, max(20 * R, T) / T)) / (2 * log(100));\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":58,"value":"K_air_bending(3, 1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":343,"value":"# Tolerances (ISO 2768)\n\nPermissible deviations in mm for ranges in nominal lengths\n\n| nominal lengths | f (fine) | m (medium) | c (coarse) | v (very coarse)\n|---|---|---|---|---|\n| 0.5 up to 3 |\t±0.05\t| ±0.1\t| ±0.2\t| – |\n| over 3 up to 6 |\t±0.05\t| ±0.1\t| ±0.3\t| ±0.5\n| over 6 up to 30 | ±0.1\t| ±0.2\t| ±0.5\t| ±1.0\n| over 30 up to 120 | ±0.15\t| ±0.3\t| ±0.8\t| ±1.5\n| over 120 up to 400 | ±0.2\t| ±0.5\t| ±1.2\t| ±2.5\n| over 400 up to 1000 | ±0.3\t| ±0.8\t| ±2.0\t| ±4.0| \n| over 1000 up to 2000 | ±0.5\t| ±1.2\t| ±3.0\t| ±6.0\n| over 2000 up to 4000 | – | ±2.0 | ±4.0 | ±8.0","pinned":false,"hidden":false,"mode":"md"},{"id":352,"value":"function getTol(tol_class, length) {\n const db = {\n f: [0.05, 0.05, 0.1, 0.15, 0.2, 0.3, 0.5, null],\n m: [0.1, 0.1, 0.2, 0.3, 0.5, 0.8, 1.2, 2.0],\n c: [0.2, 0.3, 0.5, 0.8, 1.2, 2.0, 3.0, 4.0],\n v: [null, 0.5, 1.0, 1.5, 2.5, 4.0, 6.0, 8.0]\n };\n const tol_classes = Object.keys(db);\n if (!tol_classes.includes(tol_class)) {\n throw new Error(\n `Classes should be one of: ${tol_classes} not ${tol_class}`\n );\n }\n if (length < 0.5) {\n throw new Error(\n `this standard doesn't cover length ${length} because it's less than 0.5`\n );\n }\n const limits = [3, 6, 30, 120, 400, 1000, 2000, 4000];\n for (let i = 0; i < limits.length; i++) {\n if (length <= limits[i]) {\n return db[tol_class][i];\n }\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":356,"value":"getTol(\"v\", 6.1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":85,"value":"# Visualization\n\nNear the inner radius the material is in compression (blue) and near the outer radius the material is in tension (red).","pinned":false,"hidden":false,"mode":"md"},{"id":63,"value":"ri = 3.5","pinned":true,"hidden":false,"mode":"ojs"},{"id":65,"value":"t = 3","pinned":true,"hidden":false,"mode":"ojs"},{"id":67,"value":"L = [10, 10]","pinned":false,"hidden":false,"mode":"ojs"},{"id":91,"value":"K_factor = 0.44","pinned":true,"hidden":false,"mode":"ojs"},{"id":459,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"id":463,"value":"","pinned":true,"hidden":false,"mode":"ojs"},{"id":392,"value":"viewof thickness = Inputs.range([0, 6], {\n label: \"Thickness\",\n step: 0.01,\n value: 3\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":382,"value":"viewof r_i = Inputs.range([0, 6], {\n label: \"Internal radius\",\n step: 0.01,\n value: 3\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":251,"value":"viewof k = Inputs.range([0, 1], { label: \"K factor\", step: 0.01 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":255,"value":"viewof Adeg = Inputs.range([0, 180], { label: \"Angle °\", step: 0.1 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":384,"value":"viewof r_i_2 = Inputs.range([0, 6], {\n label: \"Internal radius real\",\n step: 0.01,\n value: 3\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":310,"value":"viewof k2 = Inputs.range([0, 1], { label: \"K factor real\", step: 0.01 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":146,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}