Turn off the riding lawn mower when the gas tank is less than half full. Set the gear selector to "Neutral".
Slowly tilt the riding lawn mower back until the mower is resting on the back bumper. Get assistance for this step, as riding mowers are very heavy.
Locate the drive wheel underneath the mower, which looks like a little rubber tire, next to the engine shaft drive disk. This is the rear differential, which is attached to the mower with shim locks and a top hat-shaped cover.
Remove the bolts that hold the differential casing onto the mower using an adjustable wrench. Set the bolts aside and then remove the bolts that hold the ring gear onto the assembly.
Turn the axles while tapping the axles with a hammer and a piece of wood until the axles are loose. Slide the axles out.
Remove the axle assembly from the differential casing and take the ring gear carrier out of the axle assembly by removing the bolts.
Mark the carrier and the ring gear where the two are connected with a marker to make reassembly easier.
Pull the spider gears off the differential housing carrier and clean with brake cleaner and a rag. Wipe dry with a clean rag until the spider gears are completely clean. Do not leave dirt or debris in the gears, as this will interfere with the welding process.
Place the spider gears in a vise and tighten the vise so that the gears are held firmly. Cover the bearing on each end with a heat-resistant protective covering, such as a piece of leather.
Prepare the welding torch by setting the torch to the correct setting. One recommendation for welding spider gears on a rear differential is a MIG, TIG, or arc welder, 0.30 wire with the heat setting on high.
Turn on a welding torch and create a bead between each set of teeth on the spider gears. Move slowly and keep the beads relatively small in size.
Let the spider gears cool completely when finished. Use a sand blaster or metal file to sand down or remove any welding splatters from areas other than the spider gear teeth.
File down any beads that are too large and prevent the spider gears from being assembled correctly.
Replace the spider gears in the carrier and apply medium-grade adhesive to the bolts that reconnect the carrier on the mower prior to reassembling the parts.
Hold the top-hat cover over the rear differential housing and tighten the bolts with a torque wrench. Reassemble the rest of the rear differential assembly.
Remove the fill plug, fill with 80 to 90 gear oil and replace the fill plug before using the mower.