Modellering av roterende legeme

The objective of this work was to make a mathematical model of a 155 mm spin-stabilised projectile that has the possibility to correct its own trajectory. To obtain course correction the idea is to change the fuse with a course-correction fuse (CCF). This CCF is connected to the shell through two roll bearings. In this way, the CCF and the shell can have different spin velocities. A mathemtical model has been developed that describe the projectile’s movements in six degrees of freedom. This model corresponds to a regular projectile and was validated against a firing table [8] with acceptable results. Then it was tested with forces on the CCF to test when the shell became unstable. The result was going to be used to find an ok size on the fins. The projectile seems to handle around 140 N perpendicular to its length axis, on the tip of its CCF. This model was then modified to include the spin of the CCF, and describes now the projectile’s seven degrees of freedom. The CCF is equipped with two sets of fins from [1]. One set of fins controls the angular velocity of the CCF, while the other set controls the course correction of the projectile. It has been done a few tests with various fin sizes to find out how big they might be before the projectile gets unstable. The results show that the fins that are designed in [1] are well within the limits of how big they can be before the projectile gets unstable. It is not practical to deliberately aim so that you must regulate the course from the beginning. Normally you aim at a target and you correct drift along as the projectile flies. If the guidance starts 10 seconds after start, simulations show a course-correction ability of over 1000 meter in deflection, and over 500 meters in range. This ability will be decreased with increasing delay in the startup of the guidance system. These simulations were done with a constant torque between the CCF and the shell. In the reality this torque will vary. It is difficult to get a god simulation result with this varying torque without a good representation of the guidance system, and it was therefore decided to run simulations with a fixed torque between the CCF and the shell. This report includes an expression to calculate the torque from the roll bearings and an expression to calculate the torque from a generator. It is recommended that these equations be tested and eventually implemented when a regulation system is available. In this way the model will be as complete as possible.