Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes qui...Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.展开更多
In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations an...In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameterαrelated to a minimum length.Then,by solving the geodesic deviation equations explicitly with appropriate boundary conditions,we show thatαin the effective metric affects both the radial and angular components of the geodesic equation,particularly near the singularities.展开更多
In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions t...In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51205286,51275348)
文摘Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.
基金supported by a Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,NRF-2019R1I1A1A01058449supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2020R1H1A2102242)。
文摘In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameterαrelated to a minimum length.Then,by solving the geodesic deviation equations explicitly with appropriate boundary conditions,we show thatαin the effective metric affects both the radial and angular components of the geodesic equation,particularly near the singularities.
文摘In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.
