A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Stabilization of a Lateric Clay from Burkina Faso with Cement-Metakaolin for an Application in Road Construction

The objective of this work is to obtain a composite of clay-cement-metakaolin having good mechanical properties and geotechnical. To do this, a lateritic clay from Burkina Faso referenced ALK was characterized by various methods (X-ray diffraction, infrared spectrometry, thermal analysis and Inductively Coupled Plasma, Atomic Emission Spectrometry) in order to be used as a base course after adding cement and metakaolin. The results of the mineralogical characterization of this clay showed that it is composed of kaolinite (65.7 wt.%), quartz (19.3 wt.%) and goethite (10.8 wt.%). The geotechnical tests carried out showed that ALK is moderately plastic with a plasticity index Ip = 22%. The optimum moisture content and the maximum dry density are respectively 15.9% and 1.76 g∙cm-3. Simple compressive strength and splitting tensile strength are Rc = 1.59 MPa and ft = 0.149 MPa respectively. The California Bearing Ratio (CBR) index at 95% is 40% and above the minimum value of 30% shows that ALK can be used as a sub-base course in road construction. The addition of cement and metakaolin in various proportions improved the CBR index and the mechanical strength of the composites produced. This improvement is due to the formation of hydrated calcium silicate (CSH) resulting from the pozzolanic reaction between the portlandite of the cement and the amorphous silica of the metakaolin. Thus the 2 wt.% metakaolin and 6 wt.% cement formulation with a 95%CBR index of 81% is suitable for the development of a base course in road construction.

The Relationship between Natural Resources and Population Development in Liaocheng City

According to the relevant data about the land resources and population in Liaocheng City from 1999 to 2008, by using the research method of bearing capacity of natural resources, the thesis analyzes the relationship between natural resources and dynamic change of population in Liaocheng City. The results show that the farmland tends to diminish on the whole, and forests, garden land, urban-rural settlements and land for enterprises and mining increase slowly. Based on the analysis of the dynamic relationship between land resources and population, we conclude that the land resources still can bear the current population in Liaocheng City, but the population development inflict critical pressure on the forest resources and water resources.