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The paper considers computing the stress-strain state of a workpiece during drawing with wall thinning through a die with a small taper angle. A manufacturing process for a sleeve usually includes several drawing operations, whereas recommendations for the final drawing operation are a low extent of deformation and using dies with a small taper angle of (2°--4°). We present a diagram for drawing with wall thinning, delineating all deformation stages recorded on the chart showing force as a function of tool path. We computed the stress-strain state and deformation in the workpiece wall during the final operation of drawing through a die with a small taper angle α ≤ 4°. We provide equilibrium equations in toroidal coordinates and compute stress-strain state parameters and extents of deformation for the axisymmetric problem statement. No longer assuming a plane strain state, we compute the stress-strain state and extent of deformation in the workpiece wall during drawing with wall thinning through a die with a small taper angle α = 2°--4°. We show that at the stage when intermediate product walls are formed, for a small taper angle it is reasonable to consider the process of drawing with wall thinning to be monotone.

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