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Due to its exceptional mechanical properties, 18CrNiMo7-6 alloy steel is one of the preferred materials for producing critical components, such as high-speed heavy-duty gearboxes. To study the relationship between cylindrical grinding parameters (e.g., workpiece speed, wheel speed, and grinding depth) and responses (i.e., grinding force, temperature, and surface residual stress), dimensional analysis and finite element simulation of cylindrical grinding were performed in this paper. A mathematical model for predicting the grinding force and residual stress of cylindrical grinding was proposed, and numerical and experimental verifications of cylindrical 18CrNiMo7-6 alloy steel were carried out. The numerical verification results showed that the maximum relative errors of the model for predicting the grinding force and residual stress were 7.9% and 11.2%, respectively. The experimental results revealed that the maximum absolute errors were 1.31 N and 33.7 MPa, respectively. To consider the simplification between finite element simulation and experiments, a modified model was proposed, with the errors of 5.4% and 8.6% for grinding force and residual stress, respectively. The results of this study indicate that the proposed model can guide practical grinding operations and help optimize machining parameters, improve production efficiency, and achieve high-quality machining results. [ABSTRACT FROM AUTHOR]