Never, the Abacus existed more than 5000 years before Babbage was born and Babbage never had any need for one.
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Charles Babbage and it was first made for military use
Charles Babbage
While Charles Babbage did invent a calculator as well as what is considered the first programmable computer, he did not invent the abacus. This basic counting tool was invented in China around 3000 B.C. Babbage most certainly would have known of the abacus, indeed he likely would have used one himself, but it is not a tool of his original design.
Charles Babbage's most famous assistant was Ada Lovelace.
Charles Babbage is buried in Kensal Green Cemetery in London, England.