Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

Numerical simulation of tumor-induced angiogenesis influenced by the extra-cellular matrix mechanical environment

To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix （ECM） was treated as a thin plane. The displacement of ECM is obtained from the force balance equation consisted of the ECs traction, the ECM visco-elastic forces and the exter- nal forces. Simulation results show that a layered capillary network is obtained with a well vascularized region at the periphery of the tumor. The present model can be used as a valid theoretical method in the basic researches in tumorinduced angiogenesis.

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve,one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed,and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model,which could predict the flow behavior of the tested steels at different tempering temperatures more efficiently,was established.The relationship between mobile dislocation density and strain hardening exponent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse proportional function were adopted to describe the mobile dislocation,and two mathematical models were established to describe the relationship between tempering temperature and strain hardening exponent.Nonlinear regression analysis was applied to the Arrhenius type model,hence,the activation energy was determined to be 37.6kJ/mol.Moreover,the square of correlation coefficient was 0.985,which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve,the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus,the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.