20 19 how to draw cam edge curve with Matlab in the national mathematical modeling competition for college students

To solve the first problem, stabilize the tubing pressure at 100MPa.

The first question:

First of all, we use matlab to curve fit the data in Annex 3, in order to get the relationship between pressure and density through integral inversion. Then it is found that the fitting effect of cubic and quartic is the best, but matlab can't deduce it, and finally the quadratic expression is selected. After obtaining the relationship between pressure and density, a single-objective optimization model with the minimum total pressure offset as the objective function is established, and the numerical value is obtained every 0.0 1ms under different pre-oiling time conditions by using search algorithm (probably simulation), and the optimal situation is found.

The optimal situation we consider is not the minimum deviation in a certain direction, but the fluctuation stability as much as possible. So in our condition, we write the up-and-down offset as offset.

The second question:

It is mainly to increase the pressure in the pipe from 100MPa to 150MPa. We divide it into 5 1 process, calculate the total refueling time, and achieve the effect of uniform pressurization. Because the gas pressure and concentration in each process are different, the refueling time to the next process is also different. Because the purpose is to increase evenly, we allocate the refueling time to each process according to a certain proportion. (What proportion is the algorithm); Then 2, 5, 10 change the parameters in the same way.

Aiming at the second problem, the pressure in the oil pipe is stabilized at 100MPa by changing the angular velocity of the cam.

Firstly, the curve fitting in Appendix II is carried out, and the piecewise function relationship between needle valve lift and time is obtained, and the expression of orifice area is obtained through calculation. From this calculation, the estimated oil quality of the choke within 100ms is 31.6423 mg; ;

Then, the curve fitting in Appendix I is carried out, and the relationship between polar angle and polar diameter is obtained. Then, through the transformation relationship between pressure and density, it is estimated that the oil intake mass of the oil pump is 74.7228mg when the cam rotates once. In order to stabilize the air pressure in the pipe, that is, the oil intake mass is roughly equal to the oil output mass, an estimated angular velocity can be calculated at this time, and then the error rate of 0.0 1rad/s is taken up and down based on this estimated angular velocity, and the optimal angular velocity can be found through the search algorithm.

In view of the third question, the situation of the oil filler.