“They have been very arrogant to the workers,” said Rich Rankin, the U.A.W.’s director for the region. He added that the environment remained challenging, but organizers had seen rising enthusiasm for their efforts since a rally late last month.
Athena Hou, the chief legal officer of Fuyao Glass America, said the company denied the accusations “categorically” and dismissed them as part of a misinformation campaign by the union.
“Our company’s policies are benchmarked against other manufacturers and are administered fairly and equally,” she wrote in an email.
The vote is widely seen as an indication of how Chinese companies that are building or buying factories in the United States might handle the delicate subject of labor relations. Unions in China are strictly controlled by the Communist Party. Unauthorized strikes or demonstrations are often quickly shut down.
“This is part of the whole growing pains of going global,” said Bill Russo, a former chief executive of Chrysler China who is now a Shanghai-based automotive consultant. “You’re going to have to deal with different cultures and different labor-management relations.”
Still muscular at 71 after a youth of strenuous manual labor, Mr. Cao has a cheerful disposition and cites Andrew Carnegie, the American industrialist and philanthropist, as an inspiration. But he turned rueful when discussing the unionization push and other challenges that he had not fully expected when he opened the giant Ohio factory, even blaming excessive union power for America’s industrial decline.
“To be brutally honest, up to this moment, my investment in the U.S. has brought no good to Fuyao,“ he said in May.
A small number of Chinese companies — such as Fuyao and Qingdao Haier, the appliance maker, with a plant in South Carolina — have opened factories in the United States. Most of the time, Mr. Cao said, “people like me would rather stay in China than go to the U.S.”
Still, others may follow thanks to politics and the potential for President Trump to impose trade restrictions. Chinese factories also face surging labor costs at home and high energy costs.
Fuyao entered the United States market with a less aggressive stance toward state governments or unions than many companies.
In contrast with big companies like Taiwan’s Foxconn, which wrung $3 billion in tax credits from the state of Wisconsin to build a factory there, Fuyao ended up with a relatively modest $12 million in state and local assistance.
Unlike such foreign automakers as BMW, Toyota and Nissan, which built factories in Southern states with laws that make it hard to unionize, Fuyao took few precautions at first to avoid unionization. The company selected Ohio, a state with laws friendly to unions. Mr. Cao said Fuyao had hired the initial workers for its factory without trying to screen them for pro-union tendencies. He focused instead on the superb infrastructure at the Ohio site, a former General Motors factory near Dayton.
In Moraine, workers complain of a strict attendance policy that punishes them for absences with legitimate explanations, like having a sick child, and of being criticized or disciplined by managers for offering constructive input.
Fuyao managers have seized on a federal indictment alleging that a U.A.W. and a Fiat Chrysler official had pocketed funds from a jointly run training center to argue that the union is fundamentally corrupt. “It’s one more thing they can throw at us,” said Mr. Rankin, of the union.
Mr. Cao was born in Shanghai at the end of World War II to the co-owner of a famous department store. As Communist armies approached Shanghai four years later, the family fled by ship to this area of southeastern China, near his father’s hometown, but lost almost all their possessions.
In his autobiography, he describes how he dropped out of school in sixth grade. The headmaster at the village school had publicly humiliated him, and Mr. Cao retaliated by sneaking to a space above the latrine and urinating on the headmaster’s head.
As a teenager, Mr. Cao and his family nearly starved during the famine in the early 1960s that killed tens of millions of Chinese, after Mao’s disastrous Great Leap Forward industrialization experiment wrecked the country’s agricultural and industrial base. For three years, they survived by eating mostly powdered peanut shells. His mother became bedridden from malnutrition and nearly perished.
Mr. Cao went into smuggling with his father, using bicycles to transport rationed tobacco for illegal resale. That business failed when the authorities confiscated his father’s bicycle and the tobacco. Mr. Cao ended up on a reservoir construction labor crew, hauling dirt back and forth in hand carts while walking as many as 35 miles a day.
Around the time of Mao’s death in 1976, Mr. Cao helped set up a commune-owned small business to make the glass facings for water meters. Mr. Cao and several friends later bought a stake in the business and persevered.
When Mr. Cao almost broke a car windshield by accident in the mid-1980s, he learned that China made virtually no car windows or windshields, which had to be imported at great expense. Mr. Cao set up Fuyao Group in 1987 here in southeastern China’s Fujian province and quickly cashed in as growing affluence led tens of millions of Chinese to buy their first cars.
Fuyao has also been shipping rising volumes of windshields and windows halfway around the world to American assembly plants. American automakers, particularly G.M., urged Fuyao to set up production in the United States to shorten their supply chains, Mr. Cao said.
Despite Fuyao’s troubles in Ohio, Mr. Cao sees a reason for Chinese factories to open in the United States.
“I personally think that the U.S. should industrialize again,” he said. “You can’t just rely on a global supply chain. The cost of producing in China is catching up with the cost of producing in the U.S.”