There are a lot of physical processes in the binary systems during the evolution. Many processes have influence on the rotation of the components toward synchronization or non-synchronization. In the case of synchronous rotation, the interior of the components rotates rigidly. It exists, hence, differential rotation in the components only during the asynchronous rotation of the systems. According to the Tayler-Spruit dynamo, the generation of magnetic fields in stars are due to the existence of differential rotation. Therefore, the existence of magnetic fields in binary systems is closely related to the asynchronous rotation. A method considering the actions of many physical processes simultaneously is proposed here to calculate the spin and orbital periods in binary systems, which include mass exchange, stellar wind and mass overflow from outer Lagrangian point. By this method we can get whether the binary is in synchronization during evolution.The results of detailed computations with this method indicate that the spin and orbitperiods can be reached near synchronization in a short time, but it takes long time to reach completely synchronization if the system have reached synchronous rotation, stellar wind and volume change cased by evolution have little influence on synchronization during main sequence. As mass exchange started, the synchronization rotation can be changed into non-synchronization rotation for semi-detached binaries. There exist, therefore, differential rotations and magnetic fields in the components. However, the degree of asynchronous is different for the primary and secondary. It means that the strength of differential rotation and magnetic field may be different in both of the components. For contact binary systems, tidal effect are so strong that mass exchange can not case obvious asynchronous rotation. The evolution tracks in HR diagram of synchronization and non-synchronization are also compared with each other, the result show that the model considers non-synchronization moves to high luminosity and high temperature during mass exchange stage. Finally, the result is compared with observational date and the non-synchronization after tidal-lock timescale in binaries can be explained by this model.
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