The rotor of a Roots blower is the key component relating to its capability, so the profile design of the rotor in a Roots blower is extremely important. We focused on the modelling and verification for a novel Roots blower tooth profile based on the performance analysis. By comparing the area utilization coefficient and the ratio of several traditional rotor profiles, we proposed a new rotor profile. Then, we further accomplished the mathematical modelling of the proposed rotor profile and the computational fluid dynamics(CFD) simulation, and obtained the Roots blower outlet flow monitoring curves. Finally, we verified the characteristics by a physical experiment.
Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system's dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error(DTE) fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system's dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.
To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.
