An Analytic Algorithm of Time-varying Mesh Stiffness of Helical Gears Considering Temperature Effect

Lin Tengjiao, Zhao Zirui, Jiang Feiyang, Chen Bingkui

Abstract

Taking a helical gear pair as the research object，the analytic algorithm of time-varying mesh stiffness of helical gears with temperature was proposed based on slicing method and integral thought. In this algorithm，the tooth profile deformation caused by change of tooth contact temperature，elastic deformation of tooth contact，bending，shear，axial compression and the wheel were taken into account. The accuracy of the algorithm was verified by using finite element method. Then the influence of working parameters，such as friction coefficient，input torque and input speed，on the mesh stiffness of gears was analyzed. The results show that the mesh stiffness of teeth increases in the whole meshing process after considering the influence of temperature. Besides，the body temperature and instantaneous flash temperature of helical gears increase with the increase of friction coefficient，input torque and input speed，so the single mesh stiffness and the mean of total mesh stiffness increase. The research results can provide a theoretical basis for accurate and efficient dynamic analysis of the high-speed and heavy-duty gear system.

Keywords:  helical gears,  temperature effect,  time-varing mesh stiffness,  potential energy method

PDF

References

CUI L L，ZHAI H，ZHANG F B. Research on the meshing stiffness and vibration response of cracked gears based on the universal equation of gear profile [J] . Mechanism and Machine Theory， 2015，94：80—95.

CHAARI F，FAKHFAKH T，HADDAR M. Analytical modelling of

spur gear tooth crack and influence on gear mesh stiffness[J] . European Journal of Mechanics- A/Solids，2009，28(3) ：461—468.

LIANG X H，ZUO M J，PANDEY M. Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set[J] . Mechanism and Machine Theory，2014，76：20—38.

WAN Z G，CAO H R，ZI Y Y，et al. Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears [J] . Mechanism and Machine Theory， 2015，92：447—463.

WAN Z G，ZI Y Y，CAO H R，et al. Time -varying mesh stiffness algorithm correction and tooth crack dynamic modeling [J] . Journal of Mechanical Engineering，2013，49(11) ：153—160.(In Chinese)

LIU W，LI R，ZHANG J H，et al. Study on correction algorithm of time -varying mesh stiffness of helical gears and its influencing factors [J] . Journal of Hunan University (Natural Sciences) ， 2018，45(2) ：1—10.(In Chinese)

COOLEY C G，LIU C G，DAI X，et al. Gear tooth mesh stiffness：A comparison of calculation approaches [J]. Mechanism and Machine Theory，2016，105：540—553.

LIANG X H，ZHANG H S，ZUO M J，et al. Three new models for evaluation of standard involute spur gear mesh stiffness [J]. Mechanical Systems and Signal Processing，2018，101：424—434.

FERNNDEZ A，VIADERO F，IGLESIAS M，et al. A model for the study of meshing stiffness in spur gear transmissions[J]. Mechanism and Machine Theory，2013，61：30—58.

FERNNDEZ A，IGLESIAS M，DE -JUAN A，et al. Gear transmission dynamic：effects of tooth profile deviations and support flexibility[J] . Applied Acoustics，2014，77(3):138—149.

MA H，ZENG J，FENG R J，et al. An improved analytical method for mesh stiffness calculation of spur gears with tip relief [J] . Mechanism and Machine Theory，2016，98：64—80.

GOU X F，QI C J，CHEN D L. Nonlinear dynamic modelling and analysis of gear system with tooth contact temperature [J] . Journal of Mechanical Engineering，2015，51(11)71—77.(In Chinese)

LUO B，LI W，LI L S. Research on thermal stiffness of gear based on thermoelastic coupling [J] . Journal of Central South University(Science and Technology)，2017，48(12) ：3209—3215. (In Chinese)

LI G H. Theoretical and applied research of thermal deformation of complicated components with regular camber [D]. Hefei：College of Mechanical Engineering，Hefei University of Technology，2006：54—70. (In Chinese)

LI R F. Stiffness analysis and modification method of gear transmission [D]. Chongqing：Chongqing University Press，1998： 128—133.(In Chinese)

Refbacks

• There are currently no refbacks.