Jia Chun Lin

Uncertainty Analysis of Helical Deviation Measurements

The helix is a complex geometrical element. During the process of a dynamical measurement of the helical deviations, many factors, including the machine and the environment, lead to measurement errors. Although ISO as well as national standards stipulate the tolerances and assessment methods for helical deviations, these standards contribute little to the uncertainty calculations concerning such measurements. According to the Guide to the Expression of Uncertainty in Measurement (GUM), all measurement results must have a stated uncertainty associated to them. But in most cases of helical deviation measurements, no uncertainty value is given, simply because no measurement uncertainty calculation procedure exists. For the case of helical deviation measurements on a Computer Numeric Control (CNC) polar coordinate machine, this paper analyses in detail all kinds of factors contributing to the measurement uncertainty, and gives the calculation procedure of the measurement uncertainty of helical deviation. As an example, the calculation of the measurement uncertainty of the helical deviations of a worm is presented.

Study of the Dynamic Behavior of Face Gear Transmission System

According to the gear meshing theory, the tooth surface equation of orthogonal face gear is derived and the mathematical model is established. Also the model was provided for simulating the bevel gear transmission system concerning the time variant stiffness and face gears errors under static load and cyclic loads. Through the model the computerized analysis of speed, angle and acceleration of gear real tooth surface could be accomplished. Rattle as discussed under condition of different static loads and the constant cyclic loads.

Least Squares Association of Geometrical Features by Automatic Differentiation

Least squares association of geometrical features plays an important role in geometrical product specification and verification. Most existing algorithms for the least squares association today usually do not give the covariance matrix associated with the parameters of the respective geometrical feature. The reason is that the complexity of these algorithms can be very high, because partial differential quotients are needed. If the necessary partial difference quotients are calculated by hand and subsequently coded into an algorithm, there is a high risk to introduce unwillingly errors. This paper shows how the least squares algorithm can automatically be generated solely from the equation specifying the distance function of the measured points from the geometrical feature.

Super-Large Gear Measurement Using Laser Tracker and CMM

As general methods can no longer be used to measure super-large gears, their manufacturing accuracy, performance and quality cant be guaranteed. In this paper, after introducing the characteristics, measuring requirement and the state of arts of inspection of super-large gears, a laser tracker and CMM based measuring technology, proposed by Shi, was presented, and the key techniques were discussed. By taking full advantage of the characteristics of a laser tracker and a coordinate measuring apparatus, the super-large gears positioning problem, which was to determine the relationship between the instrument and workpeice, was solved. Thus, the gears profile, helix, and topology error etc. could be measured. Experiments have been carried out to verify the effectiveness of the method. The results showed that the proposed method could be used to measure super-large gears with the diameters up to 10m.

Finite Element Modality Analysis of Face Gear

For improving the dynamic characteristics and reliability of the face gear, the finite element of the face gear was established with NX Advanced Simulation based on the theory of vibration mechanics and finite element method. the former 12 ranks of natural frequencies and shapes were calculated by using NX. Nastran solver, The results provided a direct theoretic basis for improving the design of the face gear. And it laid a foundation of dynamic response calculation of face gear at the same time.

Design for H type co-planar precision stage based on closed air bearing guideway with vacuum attraction force

The accuracy of traditional two-dimensional precision stage is limited not only by the accuracy of each guideway but also by the configuration of the stage. It is not easy to calculate and compensate the total accuracy of the stage due to the complicated influence caused by the different position of the slides. An air bearing guideways with vacuum attraction forces has been designed with closed slide structure to enhance the stiffness and avoid the deformation caused by the weight of slide and workpieces. An H style two-dimension ultra-precision stage with co-planar structure has been developed based on the air bearing guideways to avoid the multi-influence by the axes. Driven by linear motors, the position of the workpiece is encoded by length scales with resolution of 50nm and thermal expansion of 0.6 μm/m/°C (0 °C to 30 °C). The travel span of the stage is 320x320mm, during which each axis has a positioning accuracy of ±1μm, a repeatability of ±0.3μm and a straightness of ±0.5μm. The stage can be applied in precision manufacturing and measurement.

Optimized Face Gear and its Bending Stress Analysis

According to the simulation of the face gear in UG, the research established the model of face gear. A perfect model that can be used in ANSYS was obtained through reserve modeling. The blending situation of three models of face gear was analyzed in ANSYS. The blending stresses distribution area and the influence on gear teeth bending stresses of different parameters i.e. modulus, width and number of teeth were discussed. And the discipline of the bending stresses under these parameters was got. It provides a new analysis method to research the characteristics of stress of face gear.

Uncertainty Calculation of Roundness by Automatic Differentiation

According to the Guide to the Expression of Uncertainty in Measurement (GUM), all measurement results must have a stated uncertainty associated to them. But in most cases of roundness measurement either no uncertainty value is given, or the calculation is not based on the model of the respective association criterion for the geometrical feature, because no suitable measurement uncertainty calculation procedure does exist. For the case of roundness measurement in coordinate metrology, this paper will suggest algorithms for the calculation of the measurement uncertainty of the roundness deviation based on the two mainly used association criteria LSC and MZC. The calculation of the sensitivity coefficients for the uncertainty calculation can be done by automatic differentiation, in order to avoid introducing additional errors by the traditional difference quotient approximations. The proposed methods are exact and need as input data only the measured co-ordinates of the data points and their associated uncertainties.