Discussion of Tolerances

1. Discussion of Tolerances November 12, 1998 Pixel Mechanics D. Bintinger, LBNL E. Anderssen, LBNL/CERN

2. Tolerance Scheme • Mechanics should not significantly add to inherent Pixel resolution • Goal: 15m to 18m in Azimuth • Two possible Approaches • A.) Fabricate with loose tolerances and rely on track alignment (particles) • B.) Fabricate with very tight tolerances to minimize track alignment effort • Desire to fall closer to option B than A, but certainly in between • Desire to use Stave as fundamental alignment unit to minimize track fitting effort for 1500 modules with 6 DOF • This discussion only applies to the specific geometry of the stave Tolerances presented are with view in mind that Stave is a well know unit D. Bintinger LBNL

3. Relation of Assembly to Tolerances Only fundamental requirements are Module placement, and Stability Fundamental to Module but Unrelated to rest • Modules Placed on Local Support • Minimum accuracy required for module to module registration • All modules are to E3s, within 1 pixel width of desired position • Modules Surveyed on Local Support • Modules’ Positions are determined relative to stave mounts and each other • CMM Accuracy limits fundamental accuracy of this measurement to E5 m (one s for CMM) • Local Support placed in Shell/Disk • Last time to physically measure module location • CMM Accuracy limits fundamental accuracy here as well. • Powered on in operating environment (Flow, CME, CTE, etc) • Changes location of modules from surveyed position • X-Ray survey in powered on condition (arbitrary accuracy) • Stability/Repeatability • Gradient of stability motions should be less than accuracy/calibration-time-constant Add in Quadrature Change of State Not Statistical Affects Fundamental Performance Consider that this rationale requires a thorough X-ray Survey D. Bintinger LBNL

4. Comments on “Change of STATE” • Should not be treated as stochastic variation, however if small, affects can be estimated by adding in quadrature • The change from nominal is not statistically based, but highly correlated with temperature/% moisture and does not average to zero • This could be viewed as “Systematic” error and “removed” if well understood • Operation in Powered Up Configuration only • Measurements in Power-Off configuration only • Movement from last measured positions occurs in definite “repeatable” fashion, but stability affects accuracy of X-Ray survey • X-Ray survey could “remove” the offset caused by powering up, but would require changing from Stave-based to Module-based alignment (13 times the number of parameters)--this sets limit of stave deflection from nominal • If X-Ray survey is not done, and errors are near limit • Static and Power-up deflections become very important for convergence of alignment software at start-up of ATLAS Repeatability and Stability should be on the same order D. Bintinger LBNL

5. Relating Survey to Position • Last measurement of Stave is in Half Shell • Going to full shell, center ring sags 2m* • Negligibly affects staves • Supporting from ends, Barrel sags 50m* • This is static, and affects barrel uniformly, equivalent to moving detector axis • All static deflections and assembly tolerances “disappear” after X-ray survey and/or track alignment *Figures may change based on detail design D. Bintinger LBNL

6. Map Global Tolerance to Stave Dimension • Global Tolerances based on 3 effects • Tilt angle • Module does not change dimension as it moves (DR maps to DF ) • Low momentum tracks have bend radius (negligible) • Global Tolerances are mapped to stave coordinates • Lateral Tolerance is approximately equal to Azimuth tolerances (projectively: cos(tilt) y 1) • Out of plane (normal) motion of stave maps to azimuth via tilt angle--azimuthal tolerance sets limit on out of plane motion, not Radial Tolerance Stave azimuth lateral normal 5m Limits Normal excursion radial Tolerance Box E Normal (requires touch) Try to define tolerances in terms easy to measure on CMM Nominal Dimension D. Bintinger LBNL

7. Construction Tolerances • Modules within E3s will be within 1 pixel width of nominal • Global--only tight enough to allow unambiguous alignment of modules dimensions are 1s values except as noted • Lateral: 15 m • Normal: 20 m B-Layer 25 m Layers 1,2 • Z: 50 m • Planarity: E10 m (limits not 1s) • Rotation about normal axis: .34 mrad • Rotation about longitudinal axis: 1.8 mrad B-Layer 3.6 mrad Layers 1,2 • Rotation about horizontal axis 0.5 mrad B-Layer 1.0 mrad Layers 1,2 • Values are Relative to Stave fixtured for assembly (vac-chuck?) • Radial and Azimuth map to normal and lateral directions, z is along stave--tilt affects can be ignored • Need to understand assembly loading and spring back as related to tolerances D. Bintinger LBNL

8. Stave Survey Tolerances • Knowledge of module positions w.r.t. stave coordinate system • Designed so that Stave can act as alignment unit • Global Tolerance R, Azimuth, Z • These tolerances in quadrature add 6.6m to the pixel resolution I.e.(152 + 6.62)1/2 • Lateral: 5 m • Normal: 10 m B-Layer 15 m Layers 1,2 • Z: 25 m • Planarity: E10 m (limits not 1s) • Rotation about normal axis: .17 mrad • Rotation about longitudinal axis: 1.8 mrad B-Layer 3.6 mrad Layers 1,2 • Rotation about horizontal axis 0.5 mrad B-Layer 1.0 mrad Layers 1,2 • Measured with Stave in simulated mounting configuration • Need to consider the influences of measuring forces for contact measurements • Errors in z-position for a module in a shingled configuration map to r • Tolerances at these levels exceed confidence limits of available CMM’s D. Bintinger LBNL

9. Movement Tolerances • Movement due to coolant flow, power-up, cool-down, drying, w.r.t. Stave Coordinate system • Global Tolerances as tied to Pixel Size • These add another 6.6m in quadrature to pixel resolution: ((152 + 6.62) + 6.62)1/2 = 17.7m • Lateral: 5 m • Normal: 10 m B-Layer 15 m Layers 1,2 • Z: 25 m • Planarity : E10 m (limits not 1s) • Rotation about normal axis: .17 mrad • Rotation about longitudinal axis: 1.8 mrad B-Layer 3.6 mrad Layers 1,2 • Rotation about horizontal axis 0.5 mrad B-Layer 1.0 mrad Layers 1,2 • Tolerance on Stability can be directly tied to these numbers • Stability motions not to exceed half the value of the above numbers absolute • OR --- • Require that motions are not to exceed above numbers between software alignments (order 1-day)--This requires module-based alignment. • Motion of Stave in excess of specified tolerances precludes its use as a functional alignment element D. Bintinger LBNL

10. Approximation Possible to estimate response through analysis of a single degree of freedom oscillator Input acceleration PSD assumed to be a constant 1mg2/Hz A fundamental mode at 100 Hz would have a response of ~25mm rms, 1 sigma Q of stave materials has not been measured Simple analysis indicates that vibration on the order of 100Hz yields 1sigma errors on the order of our tolerances This is not well qualified for stave structures, but is of the correct order These numbers actually exceed tolerance limit further work needs to be done to quantify this better Comment on Vibration Tolerance Rationale Estimate based 1DOF Oscillator RMS Motion mm Hz D. Bintinger LBNL

11. Conclusions • Rational basis for tolerancing of assembly and deformations has been employed to set limits on errors tied to the physical precision of the detector • Tolerances on motion are more stringent than originally thought • Survey tolerances are at limit of CMM’s available • Stability, Vibration, and Hygrothermal strains are, at present understanding, each in excess of allowances D. Bintinger LBNL