Repairing the MSE Mirrors Steve Scott Howard Yuh Bob Granetz + Cast of thousands MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt Status We are pursuing solutions based on both metal and glass mirrors. Glass (Yuh): design of new support “ring” structure is completed. No glass-to-metal contact. Use existing mirrors. Mirror is supported along its entire periphery No bolts used through the mirror  no tensile forces Steel and telfon should arrive tomorrow. Water-jet cutting starts tomorrow – hopefully. Machining starts Thursday (?) May hold off a day or two for stress analysis (Rui) Metal (Scott): design nearing completion Major issues are disruption forces  minimize thickness. But then need to support mirror during polishing. Rib design seems to satify both requirements. Have some initial bids for polishing and coating – waiting for more. MSE mirror repair 6jan03.ppt

Simple estimate of disruption forces during disruption V = df / dt = A (cos q) dB/dt = 0.12 * 0.20 * 0.71 * 1000 = 17 volts E = V / perimeter = 17 / 2*(0.12+0.20) = 26.6 volts / meter = 1.4 106 / Ohm-m I = sE * 0.03 * 0.002 = 2235 Amps Force = I Bt * length = 2235 * 8 Tesla * 0.12 = 2145 Newtons Moment = 2 * Force * (L/2) = 2 * 482 * (0.2/2) = 429 Newton-m English Units: Force = 482 pounds Moment = 190 foot-pounds 12 cm 3 cm dB/dt = 1000 T/s 20 cm 0.2 cm dB/dt F = I x B x 0.12 m Edge view Bt 20 cm F = I x B x 0.12 m MSE mirror repair 6jan03.ppt

Better estimate of currents during disruption Integrate induced current over an ensemble of small rectangles. b = 15 cm For each rectangle, compute differential force = I x B * length x y dB/dt = 1000 T/s a = 23 cm h= 0.2 cm Result: Fb = b3 h (dB/dT) Bt cos(q) / 12 r (1+ (b/a)2) Example: a = 0.23, b = 0.15, h = 0.002, dB/dt = 1000, B = 8, cos(q) = 0.71, r = 72 x 10-8 Ohm-meters  Fb = 3113 Newtons = 700 Pounds. MSE mirror repair 6jan03.ppt

Force on screws that affix mirror to back-plate F = 3113 N 2210 Vertical stress = 2210 N / area of screw / number of screws. Assume 2 screws, 2mm diameter. Area = 3.14 10-6 m2 Stress = 2210/ 3.14 10-6/2. = 3.5 108 Pascal = 350 MPa. For two 3mm screws, Stress = 235 MPa 2210 q “… Therefore, when designing stainless steel parts, a value of 30,000 psi (207 mPa) is considered the limiting stress for determining safety factors.” http://www.dezurik.com/AppData_PDF/10_60_1.pdf F = 3113 N 2210 Note: there is no shear stress on bolts because there is an equal and opposite force on the other side of the plate. backing plate 2210 flange MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt Conceptual Stainless Steel Mirror M2 for Motional Start Effect Diagnostic on Alcator C-Mod Flat surface: final grinding and coating by vendor. Substrate: single-piece of austenetic steel rough-machined by MIT Shape is an ellipse with ends cut off 6.142 Small (approx 1 mm) 45o bevel along entire top edge 5.748 All dimensions are approximate Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

M2 Mirror: front view of coated surface Polished / coated area 3.071 9.055 2.874 6.142 2.874 3.071 Leave sharp 90o edge – no chamfer 5.748 Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M2 Mirror: rear view Rim = 0.5 cm thickness typ. Fill with metallic mixture having a low melting Temperature (200oF) Leave extra support for bolts 23.0 cm 15.6 cm How many bolt holes, and what size? Tapped holes (not through-holes) -- how many, and what size? 0.2 cm 14.6 cm Removable polishing inserts Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov 0.5 cm MSE mirror repair 6jan03.ppt

How much support is req’d during polishing? P = Polishing pressure (60 PSI?) Deflection = 0 along rim h a Maximum deflection (at center) = 0.1875 P (1-n2) a4 / (E h3) (MKS) For stainless steel, E = 207 109 and n = 0.3 In funny but usable units: Deflection (# 660 nm wavelengths) = 0.086 PPSI a4(cm) / h3(mm) Example: 10 wavelengths, 60 PSI, a = 2.0 cm  h = 2.4 mm Conclusion: to keep maximum deflection below 10 wavelengths, need support every Couple of cm, and a thickness of order 2 mm. MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt Conceptual Stainless Steel Mirror M3 for Motional Start Effect Diagnostic on Alcator C-Mod Substrate: single-piece of austenetic steel rough-machined by MIT. Final grinding, smoothness and coating by vendor. 9.055 5.748 Small (approx 1 mm) 45o bevel along entire top edge Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt Conceptual Stainless Steel Mirror M2 for Motional Start Effect Diagnostic on Alcator C-Mod Flat surface: final grinding and coating by vendor. Substrate: single-piece of austenetic steel rough-machined by MIT Shape is an ellipse with ends cut off 15.6 cm Small (approx 1 mm) 45o bevel along entire top edge 14.6 cm 1 cm All dimensions are approximate Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt Conceptual Stainless Steel Mirror M3 for Motional Start Effect Diagnostic on Alcator C-Mod Substrate: single-piece of austenetic steel rough-machined by MIT. Final grinding, smoothness and coating by vendor. 23.0 cm 14.6 cm 7.05 cm 1 cm 1.305 cm Small (approx 1 mm) 45o bevel along entire top edge Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

M2 Mirror: front view of coated surface Polished / coated area 7.8 cm 23.0 cm 7.3 cm 15.6 cm 7.3 cm 7.8 cm Leave sharp 90o edge – no chamfer 14.6 cm Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt All dimensions are approximate M2 Mirror: rear view Rim = 0.5 cm width typ. Pillars 0.5 cm x 0.5 cm Spaced about 2.0 cm on-center Note: total rim thickness = 1.0 + 0.160 (button) + 0.159 (original plate) + Dx (for polishing, tbd) 2mm-wide slices 23.0 cm Leave extra support for bolts How many bolt holes, and what size? 15.6 cm Tapped holes (not through-holes) -- how many, and what size? Pillar (typ) rim 0.5 cm 0.2 cm 14.6 cm 0.1587 1.319 + Dx cm 0.5 cm Backing plate Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov Machine pillar faces flush with face of back MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt All dimensions are approximate M2 Mirror: rear view Rim = 0.2 width Pillars 0.2 x 0.2 Spaced about 2.0 cm apart Note: total rim thickness = 1.0 + 0.160 (button) + 0.159 (original plate) + Dx (for polishing, tbd) = 1.319 cm = 0.519 + Dx 23.0 cm Leave extra support for bolts Try for bolts about 3mm diameter? 6.142 Tapped holes (not through-holes) -- how many, and what size? Pillar (typ) rim 0.2 0.078 5.748 0.519 + Dx 0.2 Backing plate Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov Machine pillar faces flush with edge of rim MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: front view Polished / coated area 11.5 cm 23.0 cm 14.6 cm 9.91 cm 3.70 cm Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: front view Polished / coated area 4.528 9.055 5.748 cm 3.902 1.457 Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: front view Polished / coated area 11.5 cm 23.0 cm 14.6 cm 9.91 cm 3.70 cm Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: rear view 6.55 cm Rim width = 0.5 cm Pillars 0.5 cm x 0.5 cm 6.47 6.97 1.242 1.11 Rib width = 0.5 cm 11.5 cm 6.47 1.242 23.0 cm Cuts through rim: 0.2 cm wide 1.262 14.6 cm 1.242 1.262 9.91 cm 6.97 6.47 7.3 cm Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov 3.70 cm MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: rear view 6.55 cm Rim width = 0.5 cm Pillars 0.5 cm x 0.5 cm 6.47 6.97 1.242 1.11 Rib width = 0.5 cm 11.5 cm 6.47 1.242 23.0 cm Cuts through rim: 0.2 cm wide 1.262 14.6 cm 1.242 1.262 9.91 cm 6.97 6.47 7.3 cm Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov 3.70 cm MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: rear view 6.55 cm Rim width = 0.5 cm Pillars 0.5 cm x 0.5 cm 6.47 6.97 Rib width = 0.5 cm 11.5 cm 6.47 23.0 cm Cuts through rim: 0.2 cm wide 14.6 cm Check thickness… 9.91 cm 6.97 ? ? 6.47 0.2 0.078 0.519+Dx 7.3 cm Machine face of pillars to be flush with rim Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov 3.70 cm MSE mirror repair 6jan03.ppt

MSE mirror repair 6jan03.ppt M3 Mirror: rear view Rim width = 0.2 Pillars 0.2 x 0.2 2.744 Rib width = 0.2 4.528 Space pillars about 0.75-0.8 inches apart. 3-4 pillars per region should suffice. 2.542 9.055 5.748 3.902 Check thickness… 2.744 0.078 0.2 0.519+Dx 2.874 Machine face of pillars to be flush with rim and ribs Steve Scott 617-253-8695. sscott@psfc.mit.edu or sscott@pppl.gov 1.457 MSE mirror repair 6jan03.ppt

Force on srews that affix mirror to back-plate Deflection of end-loaded cantilever beam, length L, Width = w, thickness = t, force = F I = = w * t3 / 12 Deflection = Force * L3 / 3EI = 4 F (L/t)3 / (wE) E = 207 109 Here, L = 0.1, w = 0.12, t = 0.002, F = 2145, So deflection = 0.04 meters  force must be taken by the screws. F = 2145 N q Argument below is bogus Shear force = F sin(q) = f * 0.71 = 1523 Newtons Shear force per screw = 1523 / n (n = # screws on top segment) Assume a 2mm diameter screw: area = 3.1 10-6 m2 Shear stress = 1523 / (3.1 10-6 )/ n = 4.91 108/n newtons/m2 Assume 2 screws: shear stress = 2.5 108 newtons/m2 ? = 68% of ultimate shear strength? MSE mirror repair 6jan03.ppt

Force on srews that affix mirror to back-plate F = 3113 N Deflection of end-loaded cantilever beam, length L, Width = w, thickness = t, force = F I = = w * t3 / 12 Deflection = Force * L3 / 3EI = 4 F (L/t)3 / (wE) E = 207 109 Here, L = 0.1, w = 0.12, t = 0.002, F = 2145, So deflection = 0.04 meters  force must be taken by the screws. 2210 2210 q Vertical stress = 1523 N / area of screw/ number of screws. Assume 2 screws, 2mm diameter. Area = 3.14e-6 m^2 Stress = 1523./ 3.14e-6/2. = 2.4 108 Pascal = 240 MPa. For two 3mm screws, Stress = 107 MPa F = 3113 N No shear stress on bolts because there is an equal And opposite force on the other side of the plate. 2210 2210 From: http://www.dezurik.com/AppData_PDF/10_60_1.pdf “Therefore, when designing stainless steel parts, a value of 30,000 psi (207 mPa) is considered the limiting stress for determining safety factors.” MSE mirror repair 6jan03.ppt