# On-Machine Precision Form Truing and In-Situ Measurement of Resin-Bonded Spherical Diamond Wheel
## 4 Results and Discussion  
Figure 9a shows the measured line-profile of the spherical diamond wheel after diamond roller truing. The spherical diamond wheel is stationary during the measuring process. The measuring radius and the two-dimensional (2D, along the generatrix direction) form-truing error of the spherical diamond wheel can be obtained by least square fitting. As affected by the abrasive grain size and the  
Figure 8: Surface morphology of the form-trued spherical diamond wheel. Figure 7: Principle of biarc curve-fitting error analysis for the spherical diamond wheel: (**a**) profile fitting of the left side, (**b**) profile fitting of the right side. surface micro-roughness, the measuring radius possesses a certain deviation from the actual radius, which needs to be compensated according to the ground surface form error of the test specimen. The 2D form-tuning error of the spherical diamond wheel is the deviation between the measured surface profile and the fitted curve. As shown in Figure 9b, the obtained 2D form-tuning error is approximately 40 \(\upmu\)m, which is slightly less than the average grain size of the spherical diamond wheel. In order to validate the accuracy of the in-situ measurement results, the 2D form-truing error of the spherical diamond wheel are also measured by stylus profilometer (Form Talysurf PGI 1240, Taylor Hobson Ltd., Leicester, UK), as shown in Figure 10. By comparing the error curves in Figures 9b and 10, it is observed that the two measurement results have a high degree of consistency, especially the high-frequency form error of the spherical diamond wheel. The high-frequency error signals in the measurement results mainly originate from the protruding diamond grains and bond pits on the surface of the spherical diamond wheel. These grains and pits are extremely random and can be expressed by the signal amplitude in the measurement results. In addition, the amplitude detected by the stylus profilometer is less than that of the laser scan micrometer. Due to the limitation of the profiler probe size and shape, it cannot detect the bottom of the pits in the contact measurement process, this may generate an error in the peak to valley value. The 2D form-truing errors obtained by both the laser scan micrometer and the stylus profilometer cannot accurately characterize the form accuracy of the grinding wheel, as only the protruding diamond grains on the whole grinding wheel surface is functional for the ground surface form accuracy. The highest point of the protruding diamond grains on the rotation circumference of the spherical diamond wheel is the actual effective profile in the grinding process. Therefore, the surface profile can  
Figure 10: The form-truing error detected by a stylus profilometer. Figure 9: Line-profile of the form-trued spherical diamond wheel: (**a**) measurement results and data fitting, (**b**) 2D from-truing error. better reflect the form accuracy of the spherical diamond wheel rather than the line-profile. One of the advantages of non-contact measurement is that the spherical diamond wheel can rotate in the detection process to obtain the surface profile. Figure 11 shows the surface profile information of the form-trued spherical diamond wheel detected by the laser scan micrometer under a rotation speed of 600 rpm. It can be seen from Figure 11a that the measured profile of the spherical diamond wheel is in good consistency with the fitted curve. However, the rotation of the spherical diamond wheel causes continuous change and rapid fluctuation of the measured surface, the high-frequency signals are introduced into the measured results. These high frequency signals contain not only the form error in the rotation direction but also noise signals. According to the original form error signals shown in Figure 11b, the maximum amplitude exceeds 150 \(\upmu\)m. In order to obtain the effective information about the enveloping profile of the protruding diamond grains, the noise signals are removed by low-pass filtering.