This study aims to improve the accuracy of the pulling force estimation by establishing the variable friction model of the dry-lubricated split sleeve when cold working an aluminum 2024-T3 hole. The variable friction model was empirically obtained from the friction experimental setup simplified from the split-sleeve cold expansion process. The contact-pressure-dependent variable friction model was derived through a systematic design of experiments approach with three different normal stress conditions, namely low normal stress (220 MPa), medium normal stress (440 MPa), and high normal stress (660 MPa), to cover the range of normal stresses occurred in the cold expansion process. A full quadratic response surface model was drawn for the friction coefficient's nonlinear relationship between the mandrel and the lubricated sleeve, depending on the normal stresses. The variable friction model was verified with 3-dimensional friction test finite-element (FE) simulations. This FE modeling validates the variable friction model to predict the pulling forces with a sound agreement between the estimated and experimentally obtained values. We conducted split-sleeve cold expansion experiments to obtain the pulling force profile. Two 3-dimensional (3D) FE numerical analyses of the same split-sleeve cold expansion process were conducted using the variable friction model and a constant frictional coefficient of 0.05. The pulling force profiles from the FE modeling with the variable friction model closely align with those from the experiments to show the four distinct regions.