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Surface Variation and Mating Surface Rotational Error in Assemblies

Surface Variation and Mating Surface Rotational Error in Assemblies. Taylor Anderson UGS June 15, 2001. outline. Introduction Periodicity in surface variation Characterization of surfaces Quantifying assembly variation Conclusions. introduction.

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Surface Variation and Mating Surface Rotational Error in Assemblies

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  1. Surface Variation and Mating Surface Rotational Error in Assemblies Taylor Anderson UGS June 15, 2001

  2. outline • Introduction • Periodicity in surface variation • Characterization of surfaces • Quantifying assembly variation • Conclusions

  3. introduction • Every product manufacturer in the world is chasing the product quality “Holy Grail” • Effective Product Lifecycle Management must include variation analysis and tolerance management • ADCATS and others are working to make this as painless as possible

  4. component variation • Size or location variation • Form or shape variation • Feature orientation variation • Surface roughness variation

  5. real-world surface variation • All real surfaces contain SOME variation. • Surface variation can cause assembly variation. • Surface variation can propagate through assemblies.

  6. assembly variation • Component size variation • Component feature location variation • Component form or shape variation

  7. accumulation of variation Geometric variations propagate through an assembly as imperfect shapes and surfaces contact each other.

  8. propagation of variation • Assembly joints (contacts) have: • Kinematic degrees of freedom • Feature variation degrees of freedom • Feature variation propagates along kinematically constrained degrees of freedom F F K F Y K Y K X X F K F

  9. research objectives 1. Characterize surface variation 2. Correlate rotational error magnitude due to surface variation

  10. periodicity in surface variation • Many manufacturing processes are periodic Milling, turning, machined molds, etc. • Many factors affect periodicity Spindle speeds / feed rates Vibration and/or deflection of: cutting tool material being cut fixturing assemblies machine tool

  11. periodicity in surface variation Surface variation can be characterized as a sum of several sinusoids. Surface Profile

  12. extracting periodic information signal amplitude surface variation amplitude surface variation time distance sampling interval sample length • Sum of periodic variations appears in nature • Vibratory systems • Optics • Signal processing • Acoustics • others… signal processing

  13. Fourier analysis method • Fixed sampling interval • Fixed sampling rate • Store ( t , y ) pairs • Time coordinate • Amplitude coordinate Time Variation Frequency Spectrum y y t n T

  14. Fourier analysis method AutoSpectrum Surface

  15. wavelength is not enough… C.L.2 C.L.1 l l / C.L.

  16. max rotation depends on l / C.L. < l l C.L.2 C.L.1 C.L.2 C.L.1 l dimensionlessparameter Scalable when rotation is less than 5 degrees. (small angle theorem)

  17. non-dimensionalizing rotation Characteristic Length = C.L. Tolerance Zone

  18. non-dimensionalizing rotation Characteristic Length = C.L. Tolerance Zone Tolerance Zone f = actual rotational error f f

  19. non-dimensionalizing rotation Characteristic Length = C.L. Tolerance Zone () Zone = b ArcTan C.L. b = standardized rotational error b

  20. non-dimensionalizing rotation Characteristic Length = C.L. Tolerance Zone Tolerance Zone f b is dimensionless b (standardized) f (actual)

  21. research methodology Simulation Application Known sinusoidal inputs Manufactured surfaces Surface generation program Video microscope Collect simulated surface data Collect real surface data Analyze rotational error Interpret results

  22. theoretical surface simulation • Random sinusoidal inputs for: • Form variation (wavelength, amplitude, phase) • Waviness variation (wavelength, amplitude, phase) • Roughness variation (wavelength, amplitude, phase) Inputs Simulated Surfaces 200 data points per sample 4000 samples per Monte Carlo simulation Assembly Simulation

  23. manufactured surface analysis Raw Data Digital Enhancement Assembly Simulation

  24. max rotational error vs. l / C.L. f b Max Rotation Magnitude / Beta l / C.L. 0.5 1.0 10.0 Wavelength / Characteristic Length

  25. max rotational error vs. l / C.L. 0.80 1.00 1.20 3.00 0.66 5.00 0.50 0.25 longer wavelengths Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length

  26. max rotational error vs. l / C.L. Zone #1: l / C.L. < 0.5 Zone #2: l / C.L. > 0.5 and l / C.L. > 1.0 Zone #3: l / C.L. > 1.0 Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length

  27. phase distribution assumption Probability that a given C.L. will encounter a given phase is uniformly distributed. Goal is statistical understanding of the distribution of rotational errors for various values of l/C.L. C.L. C.L. C.L. C.L.

  28. max rotational error vs. l / C.L. Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length

  29. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length

  30. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length ≤ 0.50

  31. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 0.50

  32. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 0.66

  33. distribution for l / C.L. = 0.66 66%=0 66% in spike +0.72 +0.72 2 1 3 Amplitude 1 4 0% Phase 100% 2 3 Frequency 0 Amplitude 4

  34. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 0.80

  35. distribution for l / C.L. = 0.80 25%=0 +1.70 +1.70 25% in spike 2 1 Amplitude 1 4 3 0% Phase 100% 2 3 Frequency 0 Amplitude 4

  36. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 1.00

  37. distribution for l / C.L. = 1.00 +2.35 +2.35 3 1 2 Amplitude 1 4 0% 100% 2 Phase 3 Frequency 0 Amplitude 4

  38. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 1.20

  39. distribution for l / C.L. = 1.20 +2.32 3 1 2 Amplitude 1 4 0% Phase 100% 2 3 Frequency 0 Amplitude 4

  40. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 3.00

  41. distribution for l / C.L. = 3.00 +1.05 3 1 Amplitude 2 1 4 0% Phase 100% 2 3 Frequency 0 Amplitude 4

  42. rotational error vs. l / C.L. vs. phase Phase Max Rotation Magnitude / Beta 0.5 1.0 10.0 Wavelength / Characteristic Length 5.00

  43. distribution for l / C.L. = 5.00 +0.63 1 3 Amplitude 2 1 4 0% Phase 100% 2 3 Frequency 0 Amplitude 4

  44. rotational error distributions • Distributions different at every l / C.L. • Distributions are highly non-normal • Logical, gradual change in shape l / C.L. < 0.5 l / C.L. = 0.66 l / C.L. = 0.8 l / C.L. = 1.0 l / C.L. = 1.2 l / C.L. = 3.0 l / C.L. = 5.0 l / C.L. = 

  45. conclusions • This graph describes an UPPER BOUND on rotational error at a given value of l / C.L. Max /  l / C.L. 0.5 1.0 10.0 • Given uniformly distributed phase, these distributions describe the STATISTICAL PROBABILITY of a given rotational error at a given value of l / C.L.  0 3 1

  46. conclusions • Only SOME values of l / C.L. are relevant to assemblies • l / C.L. greater than 0.5 • l / C.L. less than 4.0 (higher for some applications) • Translates to geometric form variations • Roughness and waviness may be neglected

  47. conclusions • Characterization using a sum of sinusoids is sufficient Most easily sampled frequencies are most important Very high and very low frequencies are actually least relevant • Non-dimensionalized graphs are scalable May be used for any size geometry • Form variation will dominate rotational error • Variation amplitude and rotation magnitude are linearly correlated within realm of small angle theorem

  48. contributions • Rigorous mathematical relationships between periodic surface variation and rotational errors in assemblies • Surface variation simulation model • Application of Fourier transform to surface periodicity extraction • Three regions of rotational behavior • Non-dimensionalized rotation graphs • Monte Carlo simulation of distributions • Small angle theorem applicability

  49. recommendations • Model new distributions for use in CATS • Fine-tune the frequency spectra extraction • Characterize manufacturing processes • Specify geometric tolerances based on selection of a characterized manufacturing process

  50. Thank You !

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