I had the same problem on the same model. This problem seems fairly common for this model engine. I had to take the engine apart to find that the governor gear had blown apart inside the engine. Luckily, the engine was not damaged by the shrapnel. To repair this problem I had to:
A) Remove the mower deck
B) Disconnect the battery
C) Drain the oil and gas from the engine and tank
D) Disconnect all electrical connections between the mower and the engine
E) Remove throttle and choke assembly
F) Unbolt the engine from the chassis (4 bolts)
G) Remove the V-Belt (Drive belt)
H) Remove the Engine Pulley
I) Remove the engine from the chassis
J) Remove the head cylinder No. 1 (10 bolts)
K) Remove the Governor Gear and all shrapnel from the engine
L) Replace the governor gear assembly
M) Replace the Crankcase gasket
N) Replace the Oil seal (PTO side)
O) Remove the oil pump shaft
P) Reattach the head cylinder No. 1 (Lubricate gasket)
Q) Re-install the oil pump shaft
- You get the idea; from here put everything back where it goes. A tip to remember is never force the head cylinder into place, and replace the locktite on the bolts for the head cylinder. This involves exposing the crankshaft and you don't want any dirt or debris in this chamber. If I missed any steps I apologize; I don't know everyone's familiarity with engines. My advice is if you are not comfortable with the inside of an engine, a repair shop may be a good option. The repair cost would probably be around $200. The parts according to B&S come to about $21.10.
Parts required (Original Briggs & Stratton Part Numbers) :
Craftsmen Tractor - Model 917.272441
B&S Engine - Model 407777, Type Number 0121-E3
394348 - Gear-Governor
690945 - Gasket-Crankcase
690947 - Seal-Oil (PTO Side)
It is strongly recommended to replace the gasket, though if you are careful you can save the existing gasket. The Oil Seal (PTO Side) is for good measure. The Governor Gear is the actual broken assembly.
Brandon Brooks, September 2008