Study On Gear Reliability Design Based On Weibull Distribution

With three distributed parameters compounding arbitrarily, Weibull distribution can fit a great variety of curves, which can be used to describe various distribution pattern, however, complexity of its distribution function bring inconvenience to applying, thus, random variable is assumed to normal distribution, exponential distribution, etc, and seldom Weibull distribution. Weibull distribution parameter estimation and reliability design method with random variable is assumed to Weibull distribution were studied, and I strive to make it conveniently applied in engineering. To bring about the desired result, the fllowing matters were researched in the dissertation.1. Many kinds of typical methods for Weibull parameter estimation were introduced, and an improved moment estimation method and a failure rate estimation method were put forward. The improved moment estimation method no longer needs table look-up operation consequently it is more easily to program and more accurate. The outstanding characteristic of failure rate estimation method are adopting recursion arithmetic, have no use for initial value, easy constringency, exclusive computational solution. A visualized programme by Visual C++estimating Weibull distribution parameters was developed, that can estimate Weibull distribution parameters in various method, and is easy to used by engineers and technicians.2. The groovy design methods about involute cylindrical gear, involute cone gear and double-circular-arc gear were introduced, and a visualized programme was developed by Visual C++. Based on the groovy design methods and assumed all the random variable to be Weibull distribution, the reliability design methods were studied. A visualized programme designing gears was developed by Visual C++, that is easy to used by engineers and technicians.3. The modeling method of involutes and root fillet curves was studied. The finite element model of gears was established accurately. The contact stress in tooth flank and the bending stress in teeth root were computed, which were contrast with the results in routine method. The difference of them and its causation were analyzed. 4. A mechanical component may fail in many modes that are usually not independent. There is generally not a joint probability density function to describe these correlated failure modes. Thus, it is difficult to compute the reliability with considering the correlations between the failure modes.①The relationship between ultimate state functions in different failure modes is established by utilizing linear regression method. A double integration modal for reliability of mechanical components with dependent failure modes is built according to stress-strength interference model.②It is supposed that all ultimate state functions in multi-failure modes are weibull distribution. A computation module for total reliability is established. A kind of computation method for reliability sensitivity in multi-failure modes is built based on that in single failure mode.③According to the definitions of the sensitivity and partial derivative, the mathematical models about the reliability sensitivity are put forward and solved by Monte Carlo method. How to obtain an appropriate sampling size and increment is discussed. Without considering the relationship between the failure modes, the distribution patterns of random variables and the ultimate state functions, the reliability and sensitivity in the correlated failure modes can be obtained by utilizing Monte Carlo method. Thus this method can be used widely and validate the theoretical methods.