A simple method is presented for analysis of contact stresses and deformation conditions between the bearing balls, screw, and nut of the ball screw mechanism. The method is based on representation of contact geometry and curvature analysis of contacting surfaces using a generalization of the medial axis transform (MAT) to tubular surfaces. Simplified Hertzian contact solutions are obtained using the curvature information. The results are approximate but do include the effect of complex thread profiles as a result of the helical grooves and are suitable for mechanical design purposes.

1.
Blum
H.
,
1973
, “
Biological Shape and Visual Science, Part 1
,”
J. Theoret. Biol.
, Vol.
38
, pp.
205
287
.
2.
Blum
H.
, and
Nagel
R.
,
1978
, “
Shaped Description Using Weighted Symmetric Axis Features
,”
Pattern Recognition
, Vol.
10
, pp.
67
180
.
3.
Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M., 1993, Advanced Mechanics of Materials, 5th edition, John Wiley & Sons, pp. 713–715.
4.
Hamrock
B. J.
, and
Brewe
D.
,
1983
, “
Simplified Solution for Stresses and Deformations
,”
Journal of Lubrication Technology
, Vol.
105
, pp.
171
177
.
5.
Levit
G. A.
,
1963
a, “
Recirculating Ball Screw and Nut Units
,”
Machines and Tooling
, Vol.
XXXIX
, No.
4
, pp.
3
8
.
6.
Levit
G. A.
,
1963
b, “
Calculations of Recirculating Ball Screw and Nut Transmission
,”
Machines and Tooling
, Vol.
XXXIV
, No.
5
, pp.
9
16
.
7.
Lin
M. C.
,
Ravani
B.
, and
Velinsky
S. A.
,
1994
a, “
Kinematics of the Ball Screw Mechanism
,”
ASME Journal of Mechanical Design
, Vol.
116
, No.
3
, pp.
849
855
.
8.
Lin
M. C.
,
Velinsky
S. A.
, and
Ravani
B.
,
1994
b, “
Design of the Ball Screw Mechanism for Optimal Efficiency
,”
ASME Journal of Mechanical Design
, Vol.
116
, No.
3
, pp.
856
861
.
9.
Nackman
L. R.
,
1982
, “
Curvature Relations in Three-Dimensional Symmetric Axes
,”
Computer Graphics and Image Processing
, Vol.
20
, pp.
43
57
.
10.
Nackman
L.
, and
Pizer
S.
,
1985
, “
Three-Dimensional Shape Description Using the Symmetric Axis Transform 1: Theory
,”
IEEE Transactions on Pattern Analysis and Machine Intelligence
, Vol.
PAMI-7
, No.
2
, pp.
187
202
.
11.
Pegna, J., 1987, “Variable Sweep Geometric Modeling,” Doctoral Dissertation, Department of Mechanical Engineering, Stanford University, December, p. 180.
12.
Pratt
M. J.
,
1990
, “
Cyclides in Geometric Design
,”
CAGD
, Vol.
7
, pp.
221
242
.
13.
Srinivas
Y. L.
, and
Dutta
D.
,
1994
, “
Intuitive Procedures for Constructing Geometrically Complex Objects using Cyclides
,”
Computer Aided Design
, Vol.
26
, No.
4
, April, pp.
327
335
.
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