I would suggest that you reconsider your specification of a $40\, \rm mm$ focal length and a 40 mm diameter which even for a simple lens is not so easy.
If it was a simple thin lens with both surfaces having a radius of curvature $R$ then you could use the lens maker's formula $\frac 1 f = (n-1)\left (\frac 1R + \frac 1R \right )$, where $n$ id the refractive index of the glass and $f$ the focal length of the lens to evaluate the necessary radius of surfaces to produce a lens with focal length $40\, \rm mm$.
If $n=1.5$ the this gives $R= 40\, \rm mm$ giving a maximum aperture, which the lens a sphere, of $80\, \rm mm$.
Given that the simplest achromatic doublet is a converging lens followed by a diverging lens you are not going to get the aperture that you desire with a focal length of $40\,\rm mm$.
I have simplified matters in that you can get lens made of materials with higher refractive indices but the point I am making is that you need to change the aperture and/or the focal length to more realistic values.
Telescope makers design achromatic lenses and here is an example of what is involved although the examples that are given are for lenses with a focal length greater than your specification.
Good microscope objectives have a number of lens as can be seen in this diagram
which is taken from this website which gives a good overview of what is required.
I would imagine that as a start (and end) for a school project you should start with a simple combination of two commercially available lens, one a biconvex lens and the other as a plano-concave lens a shown below?
which is taken from the Wikipedia article achromatic lens.
If you want the component lens to look like a single lens then you must make sure that the radii of curvature of adjacent sides are as close to one another as possible and given that there will be imperfections you should consider using a suitable oil between the lenses to reduce the effect of such imperfections.