The distribution of undeformed chip thicknesses is the kinematic “copy” of grain space distribution on a workpiece and has an important influence on the grinding results. In this study, a wheel topography model is developed that can be integrated with a workpiece model, a kinematic model and a calculation model of undeformed chip thickness of a single grain to obtain the distribution of undeformed chip thicknesses. In order to verify the integrated model, a single-layer brazed diamond grinding wheel is fabricated, and the topography measurements of the grinding wheel are conducted. The measured data are used in the integrated model to perform a simulation; the simulation results are consistent with the test results. At the same time, the model is verified with grains that are uniformly distributed. Then, simulations utilizing the integrated model are used to thoroughly study the grinding process. The distribution of grain protrusion height can be controlled by radial numerical dressings on the grinding wheel. Thus, the role of the distribution of grain protrusion height on the undeformed chip thickness distribution can be quantified by using radial numerical dressings on the grinding wheel. Additionally, the relationship between the average value of the distribution of undeformed chip thicknesses, hmean, and the surface roughness can be determined by simulation. It is shown that the surface roughness can be controlled quantitatively by radial numerical dressings on the wheel. •A universal model for the undeformed chip thickness distribution is established.•The model for maximum undeformed chip thickness is only a special case of the universal model.•The surface roughness can be quantitative controlled by adjusting the grain protrusion height distribution.