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• A novel method for machining double-enveloping worms is proposed. • The whirl-machining tool is generated using a straight-lined blade. • Normal deviations in surface topology are investigated. • Virtual cutting simulation on worm machining is conducted. • The generated worm gear drive is achieved through the proposed process. Double-enveloping worms (DEWs) are widely used in many applications, especially in space-saving and high-reduction ratio equipment. DEWs have a higher transmission efficiency and contact ratio than non-enveloping worms. In this study, a general method to manufacture enveloping worms using a whirl-machining process is proposed. The whirl-machining tool profile is provided from a straight-lined blade, which is tilted with an angle the same as the lead angle of the worm. The whirl-machining model is developed by a relative-motion coordinate system of a proposed CNC machining machine. The cutting simulations, surface topologies, and normal deviations for worms are demonstrated with different pitch radius of gear, lead angles, and cylindrical worms. In order to determine the practicability and accuracy of the developed model, six numerical examples are performed. A virtual cutting simulation was conducted on the worm using VERICUT. The results verify the benefits of the proposed method in DEW manufacturing. [ABSTRACT FROM AUTHOR]