BEFORE REMOVING THE CONE AND COIL ASSEMBLY, MAKE NOTE OF THE LOCATION OF THE BRAIDED LEADS TO MAINTAIN CORRECT POLARITY DURING RE-ASSEMBLY.  A DOUBLE A (AA) BATTERY CAN BE USED TO CHECK POLARITY.  WITH THE POSITIVE OF THE BATTERY CONNECTED TO THE RED TERMINAL AND THE NEGATIVE TO THE BLACK, THE CONE SHOULD MOVE UPWARD, AWAY FROM THE BASKET.

Annuli (surrounds) can be purchased from several online places and one such place does have several videos showing the process  without removing the cone and coil assembly.  This is easy due to the perfection of the mold injected annuli which are close to being perfectly round and much more rigid than 1/8^th inch foam.  However, that procedure does leave some possibility of error. which could easily result in failure.  It's based on the assumption that the spider will maintain parallelism between the coil and the pole piece; it will maintain some close semblance of concentricity.  With luck, it will but it's not a good assumption upon which to rely. (see photo 18)  One distributor does make mention of the procedure shown in photo 18 in their videos. 

The above procedures are necessary despite their faults because many speakers today don't allow the dust cap to be removed without damaging the speaker.  In short, they're not intended to be repaired by the consumer and for good reason.

Unfortunately, such purveyors of speaker replacement parts don't and can't supply parts for vintage speakers such as the Wharfedale W15 due to it's odd size.  Its size places it just slightly larger that a 12" and smaller than a 15" but not a 14", the latter being mentioned because JBL did have a 14" speaker.

Some numbers.  A standard 12" unit has an effective piston area of 83 sq.in. and a standard 15" has an effective piston area of 133 sq.in.  The Wharfedale W15 has an effective piston area of 95 sq.in.  This is only 14% greater than that of a 12" and 71% that of a 15". The W15 measurement is taken from the outside of the mounting bolt tabs which challenges logic because that measurement is 15.625".

Those previously mentioned videos can be see here.   Simply Speakers   At the top of the page just right of center is an icon labeled "Our Videos"  Their website is worth the time to peruse.

The 1/8^th inch foam needed to replace the original foam can be purchased from THE FOAM FACTORY

This shows the points between which to measure for the inside diameter (ID) of the stencil used to cut the annulus from the foam sheet.  The ID will be about 2mm in diameter smaller but this results in a 1mm difference in radius and is of no consequence. The smaller ID will allow the foam (red) to sit closer to the cone; it will compress easily at the junction of the cone and the flange.  The basket is used to measure the outside diameter (OD)

My collection of plastic shim stock of various thicknesses

The small strips in the plastic box are used to finally lock the coil to the pole piece

The annulus marked on the foam.  A box cutter type knife is a good tool to use as these blades are extremely sharp.  A new blade is recommended because if there is any nik in the blade from previous use, it will snag the foam.

A 12" speaker can be used to hold the stencil in place.  A dinner plate can also be used.  Ones fingers may not be a good idea as the stencil can and probably will move as your fingers are relocated around the stencil.

Hold the tool so the blade edge is at an acute angle to the foam as possible.  Apply very little pressure when drawing the tool.  Too much pressure will allow the blade tip to dig into the wood and impede its smooth motion.

Cuts of about 6 inches can be made easily.

The black ring around the outer circumference of the stencil is felt tip ink, not the foam. 

The inner edge should be taped to prevent stencil movement when your fingers are repositioned.

This has already been cut as the photo was taken after.

The black ring around the outer circumference of the stencil is felt tip ink, not the foam.  It can also be seen in photos 3 and 4

PHOTO 6

After removing the cone assembly, clean the basket.  Use sandpaper or a wire brush or wheel to roughen the outer ring whereupon the annulus and gasket will be affixed and also the area whereupon the spider will be affixed.  This will ensure a good glue bond.

Acetone will remove residual foam and glue from the cone edge.  The brush is used to apply glue to the spider plate as a squeezable bottle will be awkward to use there.

If you're handy with such a bottle, a nice thin bead can be applied to the cone prior to affixing the annulus.  the brush can be used to spread the glue evenly over the contact area of the annulus.

Be sure to center the annulus around the cone.  If it too far off center, you may have to trim the outer edge to make it fit onto the basket.

The cone assembly is my last of 4 purchased around '72 from Wharfedale in England when I lived in NY.  The foam is a newer concoction that has lasted to this day.  The magnet is from a W15 that was damaged beyond repair in the 80's by a careless owner.  The alnico magnet is cracked also and severely weakened. Pity.

The paper strips are shims since many enthusiasts today don't necessarily have plastic shim stock.  The paper is ordinary printer paper, 20 pound and is 0.004" thick.  These pieces measure 1.25" wide by 5.5" long.

The pink strips are to further lock the coil to the pole piece as trying squeeze another long shim of paper is extremely difficult.

The following instructions may seem detailed but the intent was that they be understood for one who has not done this.

First, roll the paper as shown so it's diameter is smaller than that of the coil.

Slip the first shim into the coil.  Remember to align the lead wires to the terminal strip.  Wiggle the strip down as far as it will go.

Insert the second strip so the opening is about 1/3^rd the circumference (120^o) from the previous.

And, the third strip.  This one may be a little more difficult.  If you see a defect as shown in the photo at 12 o'clock, your fingernail or a pencil tip will tuck it into the gap.

The three shims.  This will almost lock the coil.  By rotating your finger around the inside of the coil while gently pressing down on the cone apex and/or the shims, the three shims should creep down ensuring they are below the bottom of the top plate as seen in the next photo.

At this point, there is still the ability to rotate the cone and coil assembly to align the braided lead wires with the terminal strip.

Inserting the smaller shims can be done easily by slightly wetting a finger and sliding the shim down between the other shims and the pole piece.  Insert the second shim diametrically across from the first and avoid the gap in the inner shim.

The third and fourth shims will offer a little more resistance.  A little pressure applied with your finger as the shim is slid down will facilitate this.

Check that the spider (centering device) is flat and not concave or convex.

Of course, the green gasket will not be on the speaker.  This one is a completed unit for demo purposes.  The idea here is to ensure parallelism of the cone and coil assembly's axis to that of the pole piece.

If the straight edge presses down on the cone flange, add some pieces of cardboard to the mounting tabs to get about 1mm or so clearance.  Then, check both sides of the cone under the straight edge for equal distance between the edge and the flange.

Now, rotate the wedge to the other two tabs (don't forget the cardboard spacers if used) and check for the same gap as previously noticed.  If equal to the previous, you're all set to glue the spider and annulus to the basket.  The spider can be gently lifted enough to apply the glue with a small artist's brush.  Don't be stingy here. Check the cone edge spacing 

The foam can be lifted to apply the glue with a small artist's brush.  If the cone gets moved continue to apply the glue and then reset the cone.  Don't panic.  The Titebond wood glue takes about 10 minutes to get tacky.  Apply a very thin amount as just enough is needed to hold the annulus.  You don't want to flood the pores of the foam because once this sets, it will inhibit a good fit of the gasket.

Don't tug at or stretch the foam

After about 20 minutes, the glue will have set enough to test the adherence of the annulus to the basket by gently applying upward pressure from the underside of the foam.  Once confirmed, the shims can be removed.

If all went well, the flange of the cone should just touch the edge with the edge resting on the aluminum basket as seen in photos 20 and 21 below, not on the green felt gasket as seen in the photo above.

Free motion of the cone can now be verified by applying gentle upward and downward pressure to the cone, the pressure being evenly applied to two points diametrically opposed.

A bead of glue can now be applied to the foam and the gasket installed.  Place a board on the gasket and add some weight.  After a few minutes, if desired, the speaker can be inverted to allow its full weight to press onto the gasket until the glue fully sets.  The dust cap can then be installed.

All done

The spider is not glued in photos 20 and 21