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DS-005-Tolerance Design

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  • 1. GATEWAY Tolerance Design Department of Mechanical Engineering, The Ohio State Sl. #1 University
  • 2. GATEWAY Design Specifications and Tolerance • Develop from quest for production quality and efficiency • Early tolerances support design’s basic function • Mass production brought interchangeability • Integrate design and mfg tolerances Department of Mechanical Engineering, The Ohio State Sl. #2 University
  • 3. GATEWAY Definition “The total amount by which a given dimension may vary, or the difference between the limits” - ANSI Y14.5M-1982(R1988) Standard [R1.4] Department of Mechanical Engineering, The Ohio State Sl. #3 University Source: Tolerance Design, p 10
  • 4. GATEWAY Affected Areas Engineering Tolerance Product Design Quality Control Manufacturing Department of Mechanical Engineering, The Ohio State Sl. #4 University
  • 5. GATEWAY Questions • “Can customer tolerances be accommodated by product?” • “Can product tolerances be accommodated by the process?” Department of Mechanical Engineering, The Ohio State Sl. #5 University
  • 6. GATEWAY Tolerance vs. Manufacturing Process • Nominal tolerances for steel • Tighter tolerances => increase cost $ Department of Mechanical Engineering, The Ohio State Sl. #6 University
  • 7. GATEWAY Geometric Dimensions • Accurately communicates the function of part • Provides uniform clarity in drawing delineation and interpretation • Provides maximum production tolerance Department of Mechanical Engineering, The Ohio State Sl. #7 University
  • 8. GATEWAY Tolerance Types • Size • Form • Location • Orientation Department of Mechanical Engineering, The Ohio State Sl. #8 University
  • 9. GATEWAY Size Tolerances Department of Mechanical Engineering, The Ohio State Sl. #9 University
  • 10. GATEWAY Form Tolerances Department of Mechanical Engineering, The Ohio State Sl. #10University
  • 11. GATEWAY Location Tolerances Department of Mechanical Engineering, The Ohio State Sl. #11University
  • 12. GATEWAY Orientation Tolerances Department of Mechanical Engineering, The Ohio State Sl. #12University
  • 13. GATEWAY Tolerance Buildup Department of Mechanical Engineering, The Ohio State Sl. #13University
  • 14. GATEWAY Statistical Principles • Measurement of central tendency − Mean − Median − mode • Measurement of variations − Range LSL X USL − Variance − Standard deviation 3σ tolerance Department of Mechanical Engineering, The Ohio State Sl. #14University
  • 15. GATEWAY Probability • Probability − Likelihood of occurrence • Capability − Relate the mean and variability of the process or machine to the permissible range of dimensions allowed by the specification or tolerance. Department of Mechanical Engineering, The Ohio State Sl. #15University
  • 16. GATEWAY Tolerance SPC Charting Department of Mechanical Engineering, The Ohio State Sl. #16University Figure Source: Tolerance Design, p 125
  • 17. GATEWAY Tolerance Analysis Methods • Worst-Case analysis • Root Sum of Squares • Taguchi tolerance design Department of Mechanical Engineering, The Ohio State Sl. #17University
  • 18. GATEWAY Initial Tolerance Design Initial Tolerance Design Department of Mechanical Engineering, The Ohio State Sl. #18University Figure Source: Tolerance Design, p 93
  • 19. GATEWAY References • Handbook of Product Design for Manufacturing: A Practical Guide to Low-Cost Production, James C. Bralla, Ed. in Chief; McGraw-Hill, 1986 • Manufacturing Processes Reference Guide, R.H. Todd, D.K. Allen & L. Alting; Industrial Press Inc., 1994 • Standard tolerances for mfg processes − Machinery’s Handbook; Industrial Press − Standard Handbook of Machine Design; McGraw-Hill − Standard Handbook of Mechanical Engineers; McGraw-Hill − Design of Machine Elements; Spotts, Prentic Hall Department of Mechanical Engineering, The Ohio State Sl. #19University Figure Source: Tolerance Design, p 92-93
  • 20. GATEWAY Worst-Case Methodology • Extreme or most liberal condition of tolerance buildup • “…tolerances must be assigned to the component parts of the mechanism in such a manner that the probability that a mechanism will not function is zero…” - Evans (1974) Department of Mechanical Engineering, The Ohio State Sl. #20University
  • 21. GATEWAY Worst-Case Analysis m WCmax = ∑ (N p i + Tp i ) i=1 m WCmin = ∑ (N p i − Tp i ) i=1 • Ne + Te => Maximum assembly envelope • Ne - Te => Minimum assembly envelope of Mechanical Engineering, The Ohio State Department University Sl. #21 Source: “Six sigma mechanical design tolerancing”, p 13-14.
  • 22. GATEWAY Assembly gaps m Gmax = N e + Te − ∑ (N p i − Tp i ) i=1 m Gmin = N e − Te − ∑ (N p i + Tp i ) i=1 m Gnom = N e − ∑ (N p i ) i=1 Department of Mechanical Engineering, The Ohio State Sl. #22University
  • 23. GATEWAY Worst Case Scenario Example Department of Mechanical Engineering, The Ohio State Sl. #23University Source: Tolerance Design, pp 109-111
  • 24. GATEWAY Worst Case Scenario Example Department of Mechanical Engineering, The Ohio State Sl. #24University Source: Tolerance Design, pp 109-111
  • 25. GATEWAY Worst Case Scenario Example • Largest => 0.05 + 0.093 = 0.143 • Smallest => 0.05 - 0.093 = -0.043 Department of Mechanical Engineering, The Ohio State Sl. #25University Source: Tolerance Design, pp 109-111
  • 26. GATEWAY Non-Linear Tolerances y = f (x1, x 2 , x 3 ,...x n ) ∂f ∂f ∂f ∂f Toly = tol1 + tol2 + tol3 + ...+ toln ∂x1 ∂x 2 ∂x 3 ∂x n ∂f ∂f ∂f ∂f Nomy ≈ x1 + x2 + x 3 + ...+ xn ∂x1 ∂x 2 ∂x 3 ∂x n Department of Mechanical Engineering, The Ohio State Sl. #26University Wource: “Six sigma mechanical design tolerancing”, p 104
  • 27. GATEWAY Root Sum-of-Square • RSS • Assumes normal distribution behavior 1 −(1/ 2)[x− μ )/σ ]2 f (x) = e σ 2π Department of Mechanical Engineering, The Ohio State Sl. #27University Wource: “Six sigma mechanical design tolerancing”, p 16
  • 28. GATEWAY RSS method • Assembly tolerance stack equation f (x) = T + T + T + ...T 1 2 2 2 3 2 n 2 Department of Mechanical Engineering, The Ohio State Sl. #28University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 29. GATEWAY Pool Variance in RSS Tol σ adjusted = 3Cp ⎛ Te ⎞ ⎛ Tpi ⎞2 m 2 σ gap = ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cp ⎠ i=1 ⎝ 3Cpi ⎠ Department of Mechanical Engineering, The Ohio State Sl. #29University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 30. GATEWAY Probability Q − Gnom ZQ = σ gap ⎛ m ⎞ Q − ⎜ N e − ∑ N pi ⎟ ⎝ ⎠ ZQ = i=1 ⎛ Te ⎞ ⎛ Tpi ⎞ 2 2 m ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cp ⎠ i=1 ⎝ 3Cpi ⎠ Department of Mechanical Engineering, The Ohio State Sl. #30University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 31. GATEWAY Probability for Limits Gmin − Gnom ZG min = ⎛ Te ⎞ 2 m ⎛ Tpi ⎞ 2 ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cp ⎠ i=1 ⎝ 3Cpi ⎠ Gmax − Gnom ZG max = ⎛ Te ⎞ 2 m ⎛ Tpi ⎞ 2 ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cp ⎠ i=1 ⎝ 3Cpi ⎠ Department of Mechanical Engineering, The Ohio State Sl. #31University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 32. GATEWAY Dynamic RSS Gmin − Gnom ZG min = ⎛ Te ⎞ 2 m ⎛ Tpi ⎞ 2 ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cpk ⎠ i=1 ⎝ 3Cpk i ⎠ Gmax − Gnom ZG max = ⎛ Te ⎞ 2 m ⎛ Tpi ⎞ 2 ⎜ ⎟ + ∑⎜ ⎟ ⎝ 3Cpk ⎠ i=1 ⎝ 3Cpk i ⎠ Department of Mechanical Engineering, The Ohio State Sl. #32University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 33. GATEWAY Nonlinear RSS ⎛ ∂f ⎞ 2 2 ⎛ ∂f ⎞ 2 2 ⎛ ∂f ⎞ 2 2 ⎛ ∂f ⎞ 2 Toly = ⎜ ⎟ tol 1 + ⎜ ⎟ tol 2 + ⎜ ⎟ tol3 + ...+ ⎜ ⎟ toln ⎝ ∂x1 ⎠ ⎝ ∂x 2 ⎠ ⎝ ∂x 3 ⎠ ⎝ ∂x n ⎠ Toli σ adjusted = 3Cpki Department of Mechanical Engineering, The Ohio State Sl. #33University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 34. GATEWAY RSS Example • Largest => 0.05 + 0.051 = 0.101 • Smallest => 0.05 - 0.051 = -0.001 Department of Mechanical Engineering, The Ohio State Sl. #34University Wource: “Six sigma mechanical design tolerancing”, p 128
  • 35. GATEWAY Taguchi Method Input from the voice of the customer and QFD processes Select proper quality-loss function for the design Determine customer tolerance values for terms in Quality Loss Function Determine cost to business to adjust Calculate Manufacturing Tolerance Proceed to tolerance design Department of Mechanical Engineering, The Ohio State Sl. #35University Wource: “Six sigma mechanical design tolerancing”, p 21
  • 36. GATEWAY Taguchi • Voice of customer • Quality function deployment • Inputs from parameter design − Optimum control-factor set points − Tolerance estimates − Initial material grades Department of Mechanical Engineering, The Ohio State Sl. #36University Wource: “Six sigma mechanical design tolerancing”, p 22
  • 37. GATEWAY Quality Loss Function • Identify customer costs for intolerable performance • Quadratic quality loss function Ao L(y) = k(y − m) = (y − m) 22 Δo Department of Mechanical Engineering, The Ohio State Sl. #37University Wource: “Six sigma mechanical design tolerancing”, p 208
  • 38. GATEWAY Cost of Off Target and Sensitivity • Cost to business to adjust off target performance • Sensitivity, β Ao Ao φ= A = [β (x − m)]2 A Δ Department of Mechanical Engineering, The Ohio State Sl. #38University Wource: “Six sigma mechanical design tolerancing”, p 226-227
  • 39. GATEWAY Manufacturing Tolerance Ao ⎛ Δ o ⎞ Δ= ⎜ ⎟ A⎝β⎠ Department of Mechanical Engineering, The Ohio State Sl. #39University
  • 40. GATEWAY Summary • Importance of effective tolerances • Tolerance Design Approaches − Worst-Case analysis − Root Sum of Squares − Taguchi tolerance method • Continual process • Involvement of multi-disciplines Department of Mechanical Engineering, The Ohio State Sl. #40University
  • 41. GATEWAY Credits • This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC-9109794). Contributing members include: • Gary Kinzel…………………………………. Project supervisor • Phuong Pham.……………. ………………... Primary author Reference: “Six Sigma Mechanical Design Tolerancing”, Harry, Mikel J. and Reigle Stewart, Motorola Inc. , 1988. Creveling, C.M., Tolerance Design, Addison-Wesley, Reading, 1997. Wade, Oliver R., Tolerance Control in Design and Manufacturing, Industrial Press Inc., New York, 1967. Department of Mechanical Engineering, The Ohio State Sl. #41University
  • 42. GATEWAY Disclaimer This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement. Department of Mechanical Engineering, The Ohio State Sl. #42University

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