Optimization of transition curve of casing cavity of profiled chamber flow sensor

Profiled chamber flow sensor is a newly-designed rotary displacement flow sensor. Its stator has an inner chamber with two circular arc surfaces and two noncircular arc surfaces. The shape curve of the noncircular arc surfaces is defined as transition curve, which directly affects the performance characteristics of the sensor. This paper deals with an optimization method for determining the transition curves. At first, design considerations on the transition curves including their geometric features and requirements of kinematics and dynamics are discussed, and a set of derivation constraints are formulated. Next, based on the constraints, the goal functions in polynomial forms with 3, 5, 7, 9°, are deduced. Finally, by comparing velocity, acceleration and jerk of the derived functions, optimal results for the transition curves are provided.