Quasi-Static and Dynamic Behaviors of Helical Gear System with Manufacturing Errors

Time?varying mesh stiffness(TVMS) and gear errors include short?term and long?term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is usually neglected in the traditional quasi-static and dynamic behaviors analysis of gear system. This paper investigates the influence of short?term and long?term components of manufacturing errors on quasi?static and dynamic behaviors of helical gear system considering the coupling relationship between TVMS and gear errors. The TVMS, loaded static transmission error(LSTE) and loaded composite mesh error(LCMS) are determined using an improved loaded tooth contact analysis(LTCA) model. Considering the structure of shaft, as well as the direction of power flow and bearing location, a precise generalized finite element dynamic model of helical gear system is developed, and the dynamic responses of the system are obtained by numerical integration method. The results suggest that lighter loading conditions result in smaller mesh stiffness and stronger vibration, and the corresponding resonance speeds of the system become lower. Long?term components of manufacturing errors lead to the appearance of sideband frequency components in frequency spectrum of dynamic responses. The sideband frequency components are predominant under light loading conditions. With the increase of output torque, the mesh frequency and its harmonics components tend to be enhanced relative to sideband frequency components. This study can provide effective reference for low noise design of gear transmission.

Effect of Manufacturing Errors on Static Characteristics of Externally Pressurized Spherical Air Bearings

Externally pressurized spherical air bearings are the key component of the three-axis air bearing table, and the manufacturing errors of the bearing affects the performance of the air bearing table. However, the manufacturing errors are unavoidable, and the pursuit to enhance the manufacturing accuracy will increase the cost greatly. In order to provide some theoretical guideline for the tolerance choice in the design of the externally pressurized spherical air bearings with inherent compensation, the effects of several manufacturing errors on the static characteristics of the air bearing are studied. Due to the complex geometry of the computational domain, an unstructured meshing technology is used for mesh generation. A finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations. A modified SIMPLE algorithm which is suitable for compressible flows is applied to solve the discretized governing equations. The effects of the dimension error and the roundness error of the ball head and the ball socket on the static characteristics are investigated. The investigation result shows that the positive dimension error and the oblate spheroid-type roundness error of the ball head as well as the negative dimension error and the prolate spheroid-type roundness error of the ball socket can improve the bearing capacity and static stiffness of the air bearings by reducing the mass flow. The calculation method proposed in this paper fits well for the general principle, which can be extended to the characteristics analysis of other air bearings.

Practical Calculation of Thermal Deformation and Manufacture Error in Surface Grinding

The paper submits a method to calculate thermal deformation and manufacture error in surface grinding. The author established a simplified temperature field model, and derived the thermal deformation of the ground workpiece. It is found that there exists not only a upwarp thermal deformation, but also a parallel expansion thermal deformation. A upwarp thermal deformation causes a concave shape error on the profile of the workpiece, and a parallel expansion thermal deformation causes a dimension error in height. The calculations of examples are given and compared with presented experiment data.

A New Finite Element Model with Manufactured Error for Additive Manufacturing

Additive manufacturing(AM),adding materials layer by layer,can be used to produce objects of almost any shape or geometry.However,AM techniques cannot accurately build parts with large overhangs,especially for the large features close to horizontal,hanging over the void.The overhangs will make the manufactured model deviate from the design model,which will result in the performance of the manufactured model that cannot satisfy the design requirements.In this paper,we will propose a new finite element(FE)analysis model that includes the manufacturing errors by mimicking the AM layer by layer construction process.In such FE model,an overhang coefficient is introduced to each FE,which is defined by the support elements in the lower layer.By mimicking the AM process from the bottom layer to the top layer,all the FE properties are updated based on their overhang coefficients,which makes the computational model be able to predict the manufactured model with manufacturing errors.The proposed model can be used to predict the performance of the AM objects in the design stage,which will help the designers to improve their design by the simulation results.

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Planet pin position errors significantly affect the mechanical behavior of planetary transmissions at both the power-sharing level and the gear tooth meshing level,and its tolerance properties are one of the key design elements that determine the fatigue reliability of large aviation planetary systems.The dangerous stress response of planetary systems with error excitation is analyzed according to the hybrid finite element method,and the weakening mechanism of large-size carrier flexibility to this error excitation is also analyzed.In the simulation and analysis process,the Monte Carlo method was combined to take into account the randomness of planet pin position errors and the coupling mechanism among the error individuals,which provides effective load input information for the fatigue reliability evaluation model of planetary systems.In addition,a simulation test of gear teeth bending fatigue intensity was conducted using a power flow enclosed gear rotational tester,providing the corresponding intensity input information for the reliability model.Finally,under the framework of stress-intensity interference theory,the computational logic of total formula is extended to establish a fatigue reliability evaluation model of planetary systems that can simultaneously consider the failure correlation and load bearing time-sequence properties of potential failure units,and the mathematical mapping of planet pin positional tolerance to planetary systems fatigue reliability was developed based on this model.Accordingly,the upper limit of planet pin positional tolerance zone can be determined at the early design stage according to the specific reliability index requirements,thus maximizing the balance between reliability and economy.

Effects of manufacturing errors on the characteristics of a polymer vertical coupling microring resonator

The effects of manufacturing errors on transmission characteristics are analyzed for a polymer vertical coupling microring resonator.Calculated results show that the errors cause a shift and shape change of the transmission spectrum compared to the designed case without errors.Furthermore,accumulation and compensation for the errors is researched.In order to realize the normal filtering for the fabricated microring resonator device,some allowed errors are discussed.

Influence of leading edge with real manufacturing error on aerodynamic performance of high subsonic compressor cascades

To investigate the influence of real leading-edge manufacturing error on aerodynamic performance of high subsonic compressor blades,a family of leading-edge manufacturing error data were obtained from measured compressor cascades.Considering the limited samples,the leadingedge angle and leading-edge radius distribution forms were evaluated by Shapiro-Wilk test and quantile–quantile plot.Their statistical characteristics provided can be introduced to later related researches.The parameterization design method B-spline and Bezier are adopted to create geometry models with manufacturing error based on leading-edge angle and leading-edge radius.The influence of real manufacturing error is quantified and analyzed by self-developed non-intrusive polynomial chaos and Sobol’indices.The mechanism of leading-edge manufacturing error on aerodynamic performance is discussed.The results show that the total pressure loss coefficient is sensitive to the leading-edge manufacturing error compared with the static pressure ratio,especially at high incidence.Specifically,manufacturing error of the leading edge will influence the local flow acceleration and subsequently cause fluctuation of the downstream flow.The aerodynamic performance is sensitive to the manufacturing error of leading-edge radius at the design and negative incidences,while it is sensitive to the manufacturing error of leading-edge angle under the operation conditions with high incidences.

A Particle-in-cell scheme of the RFQ in the SSC-Linac

A 52 MHz Radio Frequency Quadrupole （RFQ） linear accelerator （linac） is designed to serve as an initial structure for the SSC-Linac system （injector into Separated Sector Cyclotron）.The designed injection and output energy are 3.5 keV/u and 143 keV/u,respectively.The beam dynamics in this RFQ have been studied using a three-dimensional Particle-In-Cell （PIC） code BEAMPATH.Simulation results show that this RFQ structure is characterized by stable values of beam transmission effciency （at least 95%） for both zerocurrent mode and the space charge dominated regime.The beam accelerated in the RFQ has good quality in both transverse and longitudinal directions,and could easily be accepted by Drift Tube Linac （DTL）.The effect of the vane error and that of the space charge on the beam parameters have been studied as well to define the engineering tolerance for RFQ vane machining and alignment.

Vibration Characteristic Analysis and Experiment of Non-Rigid Airship with Suspended Curtain

In order to evaluate the vibration characteristics of non-rigid airship with suspended curtain,we introduce vibration characteristic analysis method of the inflatable membrane structure.Modal numerical method of the inflatable membrane structure under the pressure difference is validated by the model testing of the inflatable cantilever tube.The finite element model of 75 m airships is established to simulate the vibration characteristics subjected to only pressure difference and the resultant force of weight and buoyancy.The nonlinear static deformation and stress analysis are investigated for two kinds of equilibrated configurations with various pressure differences,as well as the vibration characteristics.The structural efficiency of the suspended curtain is investigated through the force transfer ratio at the assumed equilibrated point.The effects of manufacture error of the suspended cable length on the structural behavior are analyzed.The results indicate that the local area of airship envelope connected to the suspended cable is a weak part.Various pressures and pressure gradients have significant effects on the global airship structure and the suspended curtain.The suspended curtain is effective to transfer the equilibrated force from the bottom to the top of airship envelope.Manufacture error of the suspended cable length could result in obvious deformation of local airship envelope.The presented work is valuable to the structural engineering design of stratospheric airship.