从简单模型入手探究陀螺仪在磁场中的减速问题

2019年中国大学生物理学术竞赛中,非铁磁性导体材料制的陀螺仪在磁场中减速问题的研究没有限定任何具体参数,不易根据麦克斯韦方程得到全面统一的答案.本文从无限长导体圆柱模型入手,通过合理的近似,推导得到了陀螺仪转轴与磁场方向垂直和平行两种条件下,电磁阻力矩与磁感应强度、角速度、电导率等参数依赖关系的表达式,进而给出了磁场方向相对陀螺仪转轴任意取向时陀螺仪减速阻尼系数满足的一般关系,并通过量纲分析验证了公式的合理性.实验部分设计引入直流电动机提供驱动转矩,分析测量数据可以证明,基于基本模型得到的电磁阻力矩公式可以较为准确的描述实际的陀螺仪减速过程.

Exploration of the deceleration process of gyroscope in magnetic field starting from a simple model

The 12th problem of 2019 China Undergraduate Physics Tournament(CUPT)was to study the deceleration of a gyroscope made of nonferromagnetic conductor materials when placed in a magnetic field.There is no specific parameter to be qualified in the question,which is difficult to be solved comprehensively and uniformly by Maxwell’s equation.Starting from the infinite long conductor cylindrical model in this paper,the formulae of electromagnetic resistance moment depends on magnetic induction strength,angular velocity,conductivity,and other parameters are obtained.The deriving process of these formulae is going under the condition that the direction of the magnetic field is vertical or parallel to the gyroscope’s shaft with reasonable approximation.Then the general relation of gyroscope deceleration damping coefficient is given when the direction of the magnetic field is relative to any direction of the gyroscope’s shaft with the rationality verified through the dimensional analysis.In the experimental part,an experimental facility driven by a DC motor is designed,and the analysis of measurement data shows that the formulae of the electromagnetic resistance moment obtained from the basic model can describe the actual gyroscope deceleration process more accurately.