Abstract
Being versatile and fast, a co-ordinate measuring machine is used for the measurement of worm. A best-fit surface is obtained from the measured points by a surface fitting method, which minimizes the root mean square of normal deviations. For this problem in discrete space, an iterative optimization algorithm based on an orthogonal array is developed. On minimizing the objective function, the deviations of worm parameters from the specified values are obtained. The algorithm is validated using input data points generated from a straight-sided in axial section worm (ZA worm) with known errors. The proposed algorithm requires fewer objective function evaluations and the result is highly repeatable as there are no random operations involved.
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Abbreviations
- b :
-
half bottom width of worm groove
- L :
-
lead
- L m :
-
range reduction factor
- M :
-
number of measured points
- m :
-
module
- nd :
-
normal deviation
- n x , n y , n z :
-
unit normal vector along coordinate directions
- N :
-
normal vector
- N x , N y , N z :
-
normal vector along coordinate directions
- Nc :
-
number of chromosomes
- Ng :
-
number of genes per chromosomes
- Nd :
-
number of binary digits per gene
- p :
-
screw parameter (lead per radian)
- p a :
-
axial pitch
- Pcross :
-
cross over probability
- Pmute :
-
mutation probability
- r b :
-
root radius of worm
- r p :
-
probe radius
- S r :
-
range of search
- x c ,y c , z c :
-
real surface coordinates (contact point)
- x m , y m , z m :
-
measured coordinates (probe center point)
- x w ,y w , z w :
-
worm surface coordinates (ideal)
- z f :
-
form number of worm
- ΔL :
-
error in lead
- Δ α:
-
error in pressure angle
- α:
-
axial pressure angle
- γ:
-
lead angle at reference diameter
- u,θ:
-
surface parameters
- μ:
-
root mean square of normal deviations (objective function)
References
Bangalore HMT (2003) Production technology. Tata McGraw-Hill, India
Watson HJ (1970) Modern gear production, 1st edn. Pergamon Press, Oxford
Litvin FL, Hsiao CL, Ziskind MD (1998) Computerized over-wire (ball) measurement of worms, screws and gears. Mech Mach Theory 33(6):851–877
Merrit HE (1992) Gear engineering. Wheeler, India
Murthy TSR, Abdin SZ (1980) Minimum zone evaluation of surfaces. Int J Mach Tool Des Res 20:123–136
Xiong YL (1990) Computer aided measurement of profile error of complex surfaces and curves: theory and algorithms. Int J Mach Tools Manuf 30(3):339–357
Menq C, Chen FL (1996) Curve and surface approximation from CMM measurement data. Comput Ind Eng 30(2):211–225
Qiu H, Cheng K, Li Y, Yan Li, Wang J (2000) An approximation to form deviation evaluation for CMM measurement of 2D curve contours. J Mater Process Technol 107:119–126
Deb K (2002) Optimization for engineering design. Prentice-Hall of India, India
Lee KH, Yi JW, Park JS, Park GJ (2003) An optimization algorithm using orthogonal arrays in discrete design space for structures. Finite Elem Anal Des 40:121–135
Ross PJ (1989) Taguchi techniques for quality engineering. McGraw-Hill, Singapore
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Mohan, L.V., Shunmugam, M.S. An orthogonal array based optimization algorithm for computer-aided measurement of worm surface. Int J Adv Manuf Technol 30, 434–443 (2006). https://doi.org/10.1007/s00170-005-0097-7
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DOI: https://doi.org/10.1007/s00170-005-0097-7