# On-Machine Precision Form Truing and In-Situ Measurement of Resin-Bonded Spherical Diamond Wheel
## 1 Introduction  
The spherical diamond wheels can be used for the grinding of complex surfaces, such as aspheric surfaces, off-axis surfaces, free-form surfaces, and also play a significant role in the optical manufacturing industry [1, 2]. However, ultra-precision grinding is only possible provided that a periodic form truing of the diamond wheels is conducted over the whole grinding cycle [3, 4]. The resin-bonded spherical diamond wheels are especially beneficial for obtaining better ground surface quality but are more susceptible to wear [5]. A high-efficiency on-machine precision form truing process and a form-truing error in-situ measurement method are therefore necessary to reduce the influence of grinding wheel wear on the resulting accuracy of the grinding surface profile, thus allowing for efficient and precision grinding of complex surfaces of hard and brittle materials [6]. On-machine precision form truing is primarily aimed to eliminate the errors caused by installation, manufacturing, wear, and other factors of the grinding wheel [7]. The error elimination could improve the rotation and profile accuracy of the grinding wheels, which is crucial for obtaining good surface accuracy and quality [8, 9]. The common form-truing methods that can be used for resin-bondeddiamond wheels include diamond pen truing, pulsed laser truing, abrasive block truing, diamond roller truing, etc. [10]. The single point diamond pen can achieve the purpose of truing by extruding it on the grinding wheel surface and shedding the bond materials [11]. This method is simple, but the diamond pen wears out quickly when truing large diamond wheels. In addition, the single point diamond pen is not suitable for truing grinding wheels with complex profile [12]. The pulsed laser truing method can sharpen and profile the grinding wheel in radial and tangential directions, respectively [13,14]. Although it can be used for truing resin-bonded grinding wheels, the resulting form accuracy is usually not impressive. The main difference between abrasive block truing and diamond roller truing lies in the truing tools. For abrasive block truing, in order to make the grinding wheel bond materials wear and fall off to achieve the truing purpose, sintered corundum and green silicon carbide truing tools on the diamond wheel are often used [15]. Due to the rapid wear of the abrasive block truing tools, it is difficult to control the form-truing accuracy of the grinding wheels. However, abrasive block truing has the advantages of low cost, small truing force, and good sharpening effect [16]. The diamond roller can achieve from truing of the grinding wheels by both grinding and rolling effects under high rotation speed [17]. The coarse-grained electroplated diamond wheels are generally used for diamond roller truing, which results in a large truing force and has high requirement on the rigidity of the truing spindle, tool spindle, and machine tool. As the diamond roller is resistant to wear, it is easy to control the grinding wheel shape, and the resulting truing efficiency is high [18]. Although the truing and dressing techniques of resin-bonded diamond wheels have been widely reported, relatively few reports focusing on the precision form truing of spherical diamond wheels. [PERSON] et al. [19] applied the generating method to precision form truing of a micro-spherical diamond wheel, where the cup truer and the grinding wheel rotate around their respective axes and make axial feed to generate the spherical surface of the grinding wheel. By this method, the profile \(PV\) (peak to valley) value of the grinding wheel with a diameter of 1 mm is approximately 1-2 \(\upmu\)m. Based on the generating method, the cup truer can be replaced with an electrode tool for truing the metal bonded spherical diamond wheels. [PERSON] et al. [20] applied the electrical discharge truing method to profile a metal-bonded spherical diamond wheel with a diameter of 3.8 mm.