Olympic champion Chad Le Clos won the men's 200m butterfly gold at the World Swimming Championships in Barcelona.
18, who won four golds at London 2012, also claimed gold in the women's 200m freestyle.
South African Le Clos, 21, clocked one minute 54.32 seconds to claim the world title and add to the gold he won in London last year.
both qualified for the 50m backstroke finals.
Quigley finished fourth in the first semi-final with a time of 28.02, while Davies also touched the wall fourth in the second with 28.05.
Le Clos, who beat decorated American swimmer Michael Phelps to the 200m butterfly Olympic title last year to famously
prompt an ecstatic response
from his father Bert, beat Poland's Pawel Korzeniowski, with China's Wu Peng third.
"It is the first time I have won a world title, so it is a landmark moment for me," said Le Clos. "Also, I wanted to win this title to mark the anniversary of my Olympic title a year on."
Franklin, whose gold was her third in Barcelona, clocked 1:54.81 to finish ahead of Federica Pellegrini of Italy and France's Camille Muffat.
won the men's 800m freestyle gold, with Michael McBroom of the US second and Canada's Ryan Cochrane third.