Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

다국어 초록 (Multilingual Abstract)

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adoptedin the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed indetail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of thegear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic systemwith rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effectof static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Underdesign power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer.

The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, butthe effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonicresonance, and the static transmission error may excite the even sub-harmonic resonance respectively.

참고문헌 (Reference)

1 C. Weber, "The deformation of loaded gears and the effect on their load carrying capacity" Department of Scientific and Industrial Research 1951

2 K. Aizoh, "Research on super high speed gearing : 5th report, dynamic behavior of helical gears" 39 : 1682-1689, 1973

3 K. Aizoh, "Research on super high speed gearing : 4th report, influence of lubricating method on the dynamic tooth - fillet – stress" 39 : 1043-1052, 1973

4 K. Aizoh, "Research on super high speed gearing : 3rd report, influence of pitch error on the dynamic stress at tooth fillet and on the dynamic loading on a tooth flank" 38 : 2709-2715, 1972

5 K. Aizoh, "Research on super high speed gearing : 2nd report, influence of profile errors on the circumferential vibration of a gear set" 38 : 2701-2708, 1972

6 K. Aizoh, "Research on super high speed gearing : 1st report, running characteristics of super high speed gear testing machine" 38 : 2692-2700, 1972

7 M. Tavakoli, "Optimum profile modifications for the minimization of static transmission errors of spur gears" 108 (108): 86-94, 1986

8 H. -H. Lin, "On dynamic loads in parallel shaft transmissions: Part I---Modelling and analysis" 110 : 221-225, 1988

9 C. Gill-Jeong, "Nonlinear behavior analysis of spur gear pairs with a one-way clutch" 301 : 760-776, 2007

10 A. Kahraman, "Non-linear dynamics of a spur gear pair" 142 : 49-75, 1990

11 A. Kahraman, "Non-linear dynamics of a geared rotor-bearing system with multiple clearances" 144 : 469-506, 1991

12 D. C. Johnson, "Modes and frequencies of shafts coupled by straight spur gears" 4 : 241-250, 1962

13 H. N. Ozgüven, "Mathematical models used in gear dynamics - a review" 121 : 383-411, 1988

14 H. Milan, "Linear and nonlinear damping in dynamics of gear mesh of the parametric systems with impacts" 14 : 91-104, 2007

15 A. Kahraman, "Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system" 146 : 135-156, 1991

16 D. C. H. Yang, "Hertzian damping, tooth friction and bending elasticity in gear impact dynamics" 109 : 189-196, 1987

17 F. Hiroki, "Fundamental research on gear noise and vibration (6th Report, Generation Mechanism of Radial and Axial Vibration of Spur Gears)" 16 : 1094-1107, 1973

18 A. Kahraman, "Effect of involute contact ratio on spur gear dynamics" 121 : 112-118, 1999

19 S. Chen, "Effect of backlash on dynamics of spur gear pair system with friction and time-varying stiffness" 45 : 119-124, 2009

20 G. V. Tordion, "Dynamic stability of a twostage gear train under the influence of variable meshing stiffnesses" 99 : 785-791, 1977

21 R. W. Gregory, "Dynamic behaviour of spur gears, ARCHIVE" 178 : 207-226, 1963

22 R. Cornell, "Compliance and stress sensitivity of spur gear teeth" 103 : 447-459, 1981

23 E. Buckingham, "Analytical mechanics of gears" McGraw-Hill Book Co 1949

24 S. M. Wang, "Analysis of nonlinear transient motion of a geared torsional" 96 : 51-59, 1974