This paper presents an analytical model for predicting the magnetic field performance of permanent magnet synchronous motor with permanent magnet cutting. In order to satisfy the boundary conditions, the defective permanent magnet is equivalent to a double-layer sector permanent magnet, and the size of the sector-shaped permanent magnet is determined, this process is obtained by an equivalent magnetic circuit model. Then, the motor is divided into four sub-domains: inner sector permanent magnet sub-domain, outer sector permanent magnet sub-domain, air gap sub-domain and stator slot sub-domain. Under the boundary conditions, the analytical solution and harmonic decomposition of the air gap magnetic flux density and cogging torque for several different permanent magnet cutting sizes under no-load condition are obtained by solving the Poisson equation and Laplace equation with the method of separating variables. The analytical model is verified by the finite element method. The results show that the error between the analytical method and the finite element method is less than 6%, and the solution time of the analytical method is only 0.59% of the finite element method, the chamfered structure proposed in the paper reduces the cogging torque amplitude 35%. Therefore, this method can provide powerful help for the initial design of permanent magnet motors.INDEX TERMS Sub-domain model, Cutting permanent magnet, Magnetic circuit method, Magnetic flux density.

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Nowadays, the speed of data generation is growing rapidly. The analysis and mining of data on enterprise websites can bring business value to enterprises. There are many ways for users to access a website. What the real-time analysis system of user behavior from the perspective of big data needs to do is to collect all the access ways of users, and finally get a real-time dynamic effect map through technical storage, statistics, analysis. Through the analysis of the effect map, we can know which way users visit the website and which way is the main one, so as to serve as a reference for enterprise product promotion. In particular, because the resulting renderings are dynamic and real-time, with the passage of time, the amount and percentage of each access mode will change, from which we also can know the change trend of access mode, so as to adjust the promotion strategy in time.