1 Overview The goal of machining is to pursue the best combination of machining accuracy, cost and efficiency. In order to achieve this goal, one of the key technologies that urgently needs to be researched and developed is the online measurement technology of machining accuracy. Especially under the conditions of multi-variety small-batch production, the research on advanced online measurement technology is of great significance, because online measurement is an important part of machining measurement integration technology and an important means to ensure part quality and improve productivity. Foreign countries have long recognized the importance of online measurement technology and have carried out a lot of research, and it has been widely used in actual production. Online measurement of part machining accuracy is divided into two situations: one is to directly measure the workpiece machining surface during the machining process, and the required accuracy index can be obtained as soon as the machining process is completed[1]. This is the most ideal situation for online measurement; the other is that after the machining process is completed, the workpiece is still installed on the machine tool, and the workpiece is measured with a reasonable measuring instrument[2]. In ultra-precision machining, the influence of thermal deformation on machining accuracy is not negligible. Therefore, constant temperature oil spraying or cutting fluid cooling is necessary during machining. In the case of coolant and high workpiece speed, there is currently no sensor with a measurement accuracy of 0.01μm. Therefore, in ultra-precision machining, the detection of part machining accuracy mainly adopts the traditional offline measurement method. In many cases, the cost of offline measurement is equal to or even exceeds the cost of part machining. Based on the above reasons, this paper studies the second case to realize online measurement of parts. Its essence is to use the lathe as a coordinate measuring machine. Since the motion accuracy of the moving parts of the submicron ultra-precision lathe developed is very high, even higher than the motion accuracy of many measuring instruments and measuring machines, if the machine tool and suitable measuring instruments are organically combined, the online measurement of part machining accuracy can be realized. In this way, the machine tool can be used for machining and measurement, which expands the application range of the machine tool and solves the problem of part measurement [3]. The current trend in machining quality assurance is to replace offline measurement and statistical quality control entirely with online measurement, bringing quality assurance closer to the machining process and ensuring that parts are qualified as soon as they leave the machining equipment. Of course, this requires a prerequisite: the efficiency and accuracy of online measurement must be guaranteed. This allows for comprehensive decision-making and necessary compensation to be achieved with minimal time delay. Therefore, researching online measurement technology for part machining accuracy has significant practical implications. 2. Error Source Analysis Affecting Online Measurement Accuracy The purpose of online measurement is to check whether the accuracy indicators of the machined parts meet the requirements. If they meet the requirements, the workpiece is removed; otherwise, necessary compensation machining is performed until the workpiece's machining accuracy is qualified. We know that to accurately measure the machining accuracy of a part, the accuracy of the measuring equipment must be one order of magnitude higher than the accuracy of the part being measured, i.e., 10 times higher. In ultra-precision machining, the machining environment and the online measurement environment are not significantly different. To ensure the accuracy of online measurement, error compensation is the only way. That is, online measurement of uncompensated parts using error compensation can guarantee measurement accuracy (error compensation can improve the machining accuracy of the part by one order of magnitude). However, measuring compensated parts using error compensation cannot meet the 10-fold principle. Nevertheless, the accuracy of online measurement on the lathe is already high enough after applying error compensation, making it still meaningful. Of course, when the lathe is used as a coordinate measuring machine, the online measurement accuracy is also affected by the accuracy of the measuring sensors, the measurement strategy, and the data processing strategy. Many advanced technologies were employed in the design and manufacturing of this lathe (using a T-type layout) to reduce or eliminate the impact of thermal deformation errors on the lathe's motion accuracy. For example, the lathe uses an air-static spindle and selects white jade as the material for the spindle and bearings; the lathe slide uses air-static guideways; the spindle box, slide, bed, and guideways are all made of granite; and the machining temperature is controlled at 20±0.1℃. Therefore, the main source of error affecting measurement accuracy is the machine tool's geometric errors, totaling 21 items: 6 errors for each moving part and three mutual positional errors between the three axes. These 21 errors are shown in the table below. Accurate and rapid identification of error sources is fundamental to achieving high-precision online measurement. Considering the similar motion patterns of the measurement and machining processes (the tool is replaced by a sensor or measurement probe, and their error compensation models are also similar), the impact of error sources in non-error-sensitive directions on measurement accuracy can be ignored. That is, the effects of δ(x), γ(x), δY(z), γ(z), δY(Ф), and α(Ф) on measurement accuracy are not considered separately. Furthermore, βXZ does not affect measurement accuracy (it is affected by αZФ). (Including βXФ), during the machine tool evaluation process, the spindle rotation accuracy was measured. The measured results showed that the radial runout error δX(Ф) and axial runout error δZ(Ф) of the spindle were both <0.05μm, which is smaller compared to the slide straightness error (δZ(x)≤0.18μm/100mm, δX(z)≤0.20μm/100mm). The spindle runout error β(Ф) was also very small. Therefore, when measuring the machining accuracy of parts online, the influence of spindle rotation error on the measurement accuracy is not considered separately. Of course, if you want to measure large-size parts (large-size plane mirrors) with high precision online, the spindle rotation error (such as β(Ф)) must be considered. 3. Error Source Identification and Modeling This lathe mainly processes cylindrical, end, conical, and spherical parts. Without considering spindle rotation error, only X-axis error compensation is needed when measuring the shape or cylindricity error of the generatrix of a cylindrical surface online; Z-axis error compensation is needed when measuring an end face online; and both Z-axis and X-axis error compensation are needed when measuring conical and spherical surfaces online. In this case, the error compensation model must be two-dimensional. Of course, three capacitive sensors can also compensate for the influence of spindle rotation error on measurement accuracy. There are generally two methods for identifying the error compensation amount: one is to first identify various error sources offline and obtain the error compensation amount at each point in the machine tool machining space through a certain synthesis rule (such as homogeneous coordinate transformation); the other is to obtain the error compensation amount by measuring the machined surface of the part. The first method is time-consuming, and the assumptions in the modeling process affect the modeling accuracy. The second method can only compensate for the specific measured part and cannot expand the compensation area to the entire machining area. This paper combines the two methods to identify the error compensation amount, ensuring both accuracy and saving time.