Analysis of PSD Optical System Mounting Requirements, Assignments of Chemistry

Download Analysis of PSD Optical System Mounting Requirements and more Assignments Chemistry in PDF only on Docsity! B. Anderton Opti 521 Fall ‘08, HW 10 pt 1 Pg. 1 of 8 Last Saved on 12/9/2008 5:58:00 AM PSD Lens Mount and Assembly Analysis Overview A variety of calculations regarding lens mounting and assembly requirements revealed an appropriate barrel material (stainless steel) and operating environment (maximum stresses and loads) appropriate for this design’s assembly tolerances. Results of this analysis were used to suggest an assembly procedure for this lens (that gives the overall 0.07λ accuracy specified). Analysis summary and breakdown See Appendix A for detailed calculations pertinent to each of the subsequent sections. Athermalization: Overall coefficient of thermal defocus sysβ was determined so that a barrel material could be specified for which the resulting RMSWE (for that thermal effect alone) is within the 0.04λ specification. Stainless steel was chosen as a barrel material satisfying this requirement. Clearance required for temperature expansions: Based on the barrel material specification, the net lateral clearance required for temperature fluctuations was calculated and found to be comparatively negligible. Thermal compressive force (along optical axis): The effect of system compression along the optical axis was calculated, using appropriate equations from technical references (Yoder). Results revealed comparatively insignificant forces (compared to clamping forces and others). Shock: Using lens 1 as the mass basis, the 100G shock force was determined to be 6 N. This corresponded to a 5 MPa compressive shock stress, well within the 168 MPa compressive stress at failure. (This 168 MPa resulted from extrapolating [the maximum 1 ksi long-term tensile stress value] from long-to-short-term and tensile-to-compressive, via appropriate rule-of-thumb scaling factors [4 and 6, respectively].) Steady-state allowable force (clamping): Using the same expression, the steady-state force causing 168 MPa compressive stress was determined to be 428 N. Operating environments involving forces approaching this order of magnitude should be avoided. Torque on clamp ring: Appropriate expressions from Vukobratovich revealed a torque specification of 3 N cm⋅ based on shock force preload (at Yoder’s suggestion). The suggested torque is 5 N cm⋅ to reduce shock instability risks. Tilt clearance gap: The calculated positional accuracy corresponding to the 0.1 degree tilt accuracy (from homework 3) for each lens was found to be on the order of 50 mμ . B. Anderton Opti 521 Fall ‘08, HW 10 pt 1 Pg. 2 of 8 Last Saved on 12/9/2008 5:58:00 AM Such is beyond the capabilities of standard drop-in mounts; nylon set screws are instead recommended to constrain tilt motion for each lens (3 per lens). Calculating mount locations: Various calculations were included to depict system geometry in the event that geometrical dimensions are desired. Assembly procedure 1. Inspect components for cleanliness and quality (including fatigue). 2. Partially screw in 6 nylon set screws (3 per lens) 3. Carefully insert lens 2 in the barrel with suction cup. 4. Remove lens residue (if required) from lens 2 5. With indicator/alignment-telescope, center the lens (with the 3 set screws). 6. Insert spacer 7. Carefully insert lens 1 into barrel with suction cup. 8. Remove lens residue (if required) from lens 1 9. With indicator/alignment-telescope, center lens 1 (with the 3 set screws). 10. Thread in and torque retaining ring to 5 N-cm. 11. Assemble detector and detector mount (with one 0.55 mm and ten 5 μm shims) 12. Test focus with WFE-characterizing test. Adjust shims, re-assemble PSD mount, and re-test. 13. Repeat 12 until overall design requirement of 0.07λ RMSWE is achieved. Design schematic Although detailed geometrical dimensions (including tangential mount angles) were not determined for the high-level of view provided in this report, it was deemed useful to at least provide a schematic system overview. The following diagram indicates (not-to- scale) system setup following proper assembly. ShimsBarrel Nylon screws Spacer Threaded retaining ring Lens 2 Lens 1 Bolts PSD and mount Figure 1: Schematic of properly-assembled system B. Anderton Opti 521 Fall ‘08, HW 10 pt 1 Pg. 5 of 8 Last Saved on 12/9/2008 5:58:00 AM Shock • Consider shock on lens 1 (most massive since it’s thickest) • Lens 1 approx. mass (disk of 5 mm thickness, 5 g/cm3 density): 0.0061 kg • Shock force: ma = 6.013 N • Stress under shock (1st order, normal incidence) o Reference Yoder, pg. 758 o 1,max 2 0.798c K F K L σ ≈ , 1K and 2K factors from Yoder, pg. 748 11 smallest 1 1 8.53m 2 58.6mm K D −= = = ⋅ 2 2 glass 11 1metal 2 glass metal 1 1 1.64 10 PaK E E ν ν − −− −= + = ⋅ lens 0.0785mL Dπ= = o Evaluates to ,max 5.04 MPacσ = from shock • Recalling that o tensile/compressive stresses related by comp tensile6σ σ≈ ⋅ and o long-term/short-term allowable stresses related by short long4σ σ≈ ⋅ o Rule-of-thumb for tensile,long term,MAX 1000psi 7 MPaσ − = = • The above means MAX allowable short-term compressive stress is 7 MPa 6 4 168MPa⋅ ⋅ = , much higher than our max compressive 5 MPa, so we’re OK with tangential stainless steel mounts. Steady-state allowable force (clamping) • We calculate the shock force F causing 1,max 2 0.798 168MPac K F K L σ = = . • We find clamp,max 428 NF = . Torque on clamp ring • Reference: Vukobratovich pg. 212 • preload0.2M d F= ⋅ ⋅ • Assume preload shock 6 NF F= = : 0.2 25mm 6 N 0.03 N m 3 N cmM = ⋅ ⋅ = ⋅ = ⋅ o This preload was suggested in Yoder, pg. 185 • To ensure that the lens doesn’t move under shock loading, we’ll set the applied torque to 5 N cm⋅ (almost twice as much and a round number). B. Anderton Opti 521 Fall ‘08, HW 10 pt 1 Pg. 6 of 8 Last Saved on 12/9/2008 5:58:00 AM Tilt clearance gap • See figure at right (of approximate lens); main effect (for small θ is drop of corner by amount sin 2 th θ≈ where t is lens thickness). • From HW3, max allowable tilt was 0.1 deg, so (for t = 5mm) this corresponds to allowable 0.044mmh = or 44μm. • This is infeasible; use nylon screws to center the lens instead. Calculating mount locations • Note that o ( )223 2, 2, 2 / 2front frontx R R D= − − o ( )222 2, 2, 2 / 2back backx R R D= − − o ( )221 1, 1, 1 / 2back backx R R D= − − o These give mount locations and could be used to determine dimensions on sketches. • Also note that since the PSD has 5μm compensation, shims could be used to extend this compensation over a large axial range. o Suggested values: one 0.55 mm and ten 5 μm shims. θ BFD x2x1 L2 tangent L2 flat L1 tangent x3 B. Anderton Opti 521 Fall ‘08, HW 10 pt 1 Pg. 7 of 8 Last Saved on 12/9/2008 5:58:00 AM Appendix B: Matlab code for computations The numerical results in appendix A were determined with the following code. It is included for the reader’s ability to examine the effect from changing inputs (barrel material, shock requirements, etc.) % constants G = 9.8; ppm = 1e-6; fprintf(1,'\n\n\n########## inputs ##########\n\n'); accel_max = 100*G % G's deltaTemp_max = 20 % maximum operational range, deg. C deltaTemp_op = 5; % daily operational rhange, deg. C sigma_tensMaxAllowLong = 1000 * (70e9/10e6) alpha_lens = 6.7*ppm n_lens = 1.620702 dndT_lens = 2.7*ppm rho_lens = 2.5e-3/1e-6 % kg/m^3 nu_lens = 0.2 % vuko, pg. 211 E_lens = 81e9 alpha_barrel = 10.1*ppm E_barrel = 200e9 nu_barrel = 0.3 lens1_F_radius = 58.6e-3 lens1_B_radius = -277e-3 lens1_thickness = 5e-3 lens1_diameter = 25e-3 lens2_F_radius = -97e-3 lens2_B_radius = -174e-3 lens2_thickness = 4e-3 lens2_diameter = 24e-3 lensSpacing = 1.0e-3 dia_EP = 20e-3 f_total = 100e-3; lambda_wavelen = 632.8e-9 BFD = 93.824e-3 fprintf(1,'\n\n\n########## calcs ##########\n\n'); % Basics Fn = f_total/dia_EP % Athermal design lens1_phiFront = (n_lens - 1)/lens1_F_radius; lens1_phiBack = (1 - n_lens)/lens1_B_radius; f1 = (lens1_phiFront + lens1_phiBack - ... lens1_thickness/1 * lens1_phiFront * lens1_phiBack)^(-1) lens2_phiFront = (n_lens - 1)/lens2_F_radius; lens2_phiBack = (1 - n_lens)/lens2_B_radius; f2 = (lens2_phiFront + lens2_phiBack - ... lens2_thickness/1 * lens2_phiFront * lens2_phiBack)^(-1) beta_lens = alpha_lens - 1/(n_lens - 1) * dndT_lens beta_sys = beta_lens*( abs((1/f1)/(1/f_total)) + abs((1/f2)/(1/f_total)) ) deltaZ = (alpha_barrel - beta_sys)*f_total*deltaTemp_op