1 Overview

The primary goal of machining is to achieve the best balance between precision, cost, and efficiency. To reach this objective, one of the most critical technologies that require urgent research and development is online precision measurement, especially in environments characterized by small-batch and multi-species production. Online measurement plays a crucial role as it is an essential component of integrated process and measurement technology, and serves as a key method for ensuring part quality and boosting productivity. Internationally, the importance of online measurement technology has been widely recognized, with extensive research and numerous applications in industrial settings.

Online measurement of part machining accuracy can be categorized into two main scenarios. The first involves directly measuring the workpiece surface during the machining process, allowing for the acquisition of the required accuracy index once the process is complete. This is the ideal situation for online measurement. The second scenario occurs after the machining is finished, where the workpiece remains on the machine tool, and a suitable measuring instrument is used to assess its dimensions. In ultra-precision machining, thermal deformation significantly impacts accuracy, making constant temperature oil cooling or controlled cutting fluid temperature essential. However, at high rotational speeds, even a 0.01μm sensor may not be sufficient. As a result, traditional offline measurement methods are still predominantly used in ultra-precision machining, often resulting in costs equal to or exceeding those of the machining itself.

Given these considerations, this paper focuses on the second scenario to enable online measurement of parts, essentially using the lathe as a coordinate measuring machine. Due to the extremely high precision of submicron ultra-precision lathes, their movement accuracy surpasses many conventional measuring instruments. When the machine tool is combined with appropriate measuring devices, it becomes possible to perform online accuracy measurements, enabling the machine to serve both as a processing and measurement tool. This expands the application scope of the machine tool while addressing part measurement challenges. The current trend in machining quality assurance is to move towards online measurement, replacing offline methods and statistical quality control to ensure that only qualified parts are removed from the machine. This requires efficient and accurate online measurement systems capable of making timely decisions and necessary compensations.

2 Error Source Analysis Affecting Online Measurement Accuracy

The purpose of online measurement is to verify whether the machined part meets the required precision standards. If it does, the part is removed; otherwise, necessary compensation is applied until the desired accuracy is achieved. To accurately measure machining precision, the measuring equipment must have an accuracy level one order of magnitude higher than the part being measured. In ultra-precision machining, the processing and online measurement environments are similar, so error compensation is essential to ensure measurement accuracy. Without error compensation, online measurement cannot guarantee the accuracy of the part, but with proper compensation, the accuracy of the lathe's online measurement remains significant.

When using a lathe as a coordinate measuring machine, the online measurement accuracy is also influenced by the sensor's precision, measurement strategy, and data processing approach. Advanced design and manufacturing techniques, such as T-shaped layouts, are employed to minimize thermal deformation errors. For example, air-static pressure spindles, white jade materials, and granite components are used to enhance accuracy. Temperature control is maintained at 20±0.1°C, reducing the impact of environmental factors. The primary error sources affecting measurement accuracy are the machine tool’s geometric errors, totaling 21 items—six per moving part and three mutual position errors between axes. Identifying these error sources is crucial for achieving high-precision online measurements, as some errors have minimal impact on accuracy and can be ignored.

Lathe 21 Error Source List

No. Symbol Geometry Meaning No. Symbol Geometry

1 δx(x) X-axis positioning error 12 γ(z) Z-axis pitch error

2 δy(x) X-axis Y-axis straightness error 13 δx(Ф) Spindle X-bounce

3 δz (x) Z axis straightness error 14 δy (Ф) Spindle Y traverse

4 α(x) X axis rollover error 15 δz (Ф) Spindle Z direction gyration

5 β(x) X axis yaw error 16 α ( Ф) Spindle rotation angle X error

6 (x) X-axis tilt error 17 β (Ф) Spindle rotation Y rotation error

7 δz(z) Z-axis positioning error 18 γ(Ф) Spindle rotation around Z rotation error

8 δx(z) Z X axis straightness error 19 αz 主轴 spindle and Z axis parallelism error

9 δy(z) Z axis Y linearity error 20 βx 主轴 spindle and X axis squareness error

10 α(z) Z axis rollover error 21 βxz X axis sum Z axis perpendicularity error

11 β(z) Z axis yaw error

3 Error Source Identification and Modeling

The lathe primarily processes cylindrical surfaces, end faces, tapers, and spherical parts. For online measurement of cylindrical surfaces, X-direction error compensation is required, while Z-direction compensation is needed for end face measurements. For more complex shapes like tapers and spheres, both X and Z directions require simultaneous compensation. Error compensation models must be two-dimensional, and capacitive sensors can help mitigate spindle rotation errors. There are typically two methods for identifying error compensation: off-line identification using homogeneous coordinate transformation rules, and direct measurement of the machined surface. While the former is time-consuming, the latter is limited to specific parts. This paper combines both approaches to improve accuracy and efficiency.

3.1 Error Source Identification

1. X-direction error compensation amount identification: Six error sources affect X-direction measurement accuracy: δX(z), αZФ, β(z), α(z), δX(x), and β(x). The X-direction error compensation amount is expressed as:

δX=δX(x)+δX(z)+αZФ.z+β(z).WZ+α(z).Wh+β(x).TZ (1)

Where z is the distance from the origin of the Z-slide, WZ is the distance of the measuring point from the suction cup in the Z direction, TZ is the distance from the Z-sensor to the center of gravity of the X-slide, and Wh is the vertical distance from the center of gravity of the measuring point to the Z-slide.

To identify the error sources, a cylindrical surface is turned in the Z direction, and the busbar error is measured. From this, four error sources—δX(z), αZФ, β(z), and α(z)—can be identified. The error compensation amount is calculated as:

Δ-column X=δX(z)+αZФ.z+β(z).WZ+α(z).Wh (2)

Figure 1 Cylindrical busbar error measurement

Equation (1) and (2) show that δX(x) and β(x) need to be identified. δX(x) is ensured by the lathe's full closed-loop system, while β(x) is measured offline using a laser device. Thus, the X-direction error compensation amount when measuring is:

Δx=f(x,z)=δ Column X+β(x).TZ (3)

2. Z-direction error compensation identification: Six error components affect Z-direction measurement accuracy: δz(x), β(z), βxФ, α(x), β(x), and δz(z). The error compensation amount is expressed as:

Δz=δz(x)+βxФ.x+α(x).Th+β(x).TX+β(z).WX+δz(z) (4)

When measuring the end face, four error sources—βxФ, δz(x), α(x), and β(x)—affect the accuracy. The error compensation amount is calculated as:

Δ plane X=δ(x)+βxФ.x+α(x).Th+β(x).Tx (5)

To identify these sources, a 200mm diameter end face is turned, and the prism is mounted on the tool post. The sensor measures the straightness, and the least squares method is used to fit the angle between the laser and the X slide motion. The error compensation amount is obtained as:

δ=δ pass-δ straight

From equations (4) and (5), β(z) and δz(z) are identified. β(z) is measured offline, while δz(z) is ensured by the lathe's full-closed-loop system. The Z-direction error compensation amount when measuring the end face is:

Δz=f(x,z)=δ face Z+β(z).TX (6)

3.2 Error Source Modeling

Using a BP neural network, any nonlinear function can be approximated with high accuracy, making it ideal for error compensation modeling. This paper uses MATLAB5.1's neural network toolbox to build an online measurement error compensation model. The hidden layer uses the "tansig" function, and the output layer uses the "purelin" function.

1. X-direction error compensation modeling: The Z position of the slide plate is the input, and δ column X is the output. Neural network A fits the function δ1X=δ column X=f(z). The X position is the input, and β(z).TZ is the output, with neural network B fitting δ2X=β(z).TZ=f(x).

Fig. 2 Topological diagram of single input and single output neural network

2. Z-direction error compensation modeling: The X position is the input, and δ surface Z is the output. Neural network C fits δ1Z=δ plane Z=f(x). The Z position is the input, and β(z).TX is the output, with neural network D fitting δ2Z=β(z).TX=f(z).

In practice, the commonly used area is 100mm×100mm, with 51×51 sampling points (2601 training samples). The training sample calculation method is as follows:

X-axis error compensation amount training sample calculation: When measuring δ-column X, sampling points (δ-column X(zj), zj) are obtained, with zj=0, 2, 4,..., 100 (mm). Similarly, for β(x).Tz, 51 points are sampled within 0–100mm. The training sample for X-direction error compensation is:

δ(xi,zj)=δ2X(xi)+δ1X(zj) xi,zj=0,2,4,...,100(mm) i,j=0,1,2,...,50;

The same applies to Z-direction error compensation, with the training sample being:

δZ(xi,zj)=δ1Z(xi)+δ1Z(zj) xi,zj=0,2,4,...,100(mm) i,j=0,1,2,...,50;

The neural network training sample in the lathe machining space is [(δX(xi,zj), δZ(xi,zj)), (xi,zj)]. A double-input, double-output neural network is used to fit the online measurement error compensation amount. The model and its topological structure are shown in Figure 3.

Fig. 3 Topology diagram of double-input, double-outlet neural network

4 Online Measurement Experiments and Results Analysis

To validate the model, online measurements were performed on two machined parts using an inductor with 0.01μm accuracy. First, a cylindrical surface (busbar 100mm) was turned, and the straightness error was measured online. The result was 0.26μm (0.10μm after processing). With the spindle mounted on the codewheel, the cylindrical error was 0.38μm (0.21μm after compensation), compared to 0.40μm on a TAYLOR cylindrimeter.

Second, an end face (diameter 100mm) was turned, and the flatness error was measured online. The non-compensated flatness error was 0.80μm, and after compensation, it dropped to 0.12μm. The flatness measurement principle involved reducing the spindle speed to 60r/min and using a capacitance sensor. The sensor's trajectory followed an Archimedean spiral, with the polar equation ρ=-(θ+π)/2π, where θ=2πt (0≤t≤48s). The rectangular coordinate parameter equation was derived, and the sampling interval was set to 0.1s, collecting 481 points. After error compensation, the deviation distribution was calculated using the least squares method to determine the flatness error.

The results showed that the online measurement accuracy improved significantly after error compensation. If the spindle rotation error is also compensated, the accuracy would be even higher. However, without a high-precision probe, it is currently not possible to measure spherical surfaces online. With the right sensor and software, the lathe could function as a high-precision coordinate measuring machine.

5 Conclusion

The experimental results demonstrate that the neural network-based error compensation model proposed in this paper effectively improves online measurement accuracy. The model is simple, accurate, and easy to implement in practical applications. A well-designed training sample can cover the entire machining space, enabling automated online measurement. The measuring sensor or probe can be stored on the tool holder, and the conversion between tool and sensor can be done automatically. The ultimate goal of manufacturing technology is to ensure part accuracy entirely through the machine tool itself, integrating machining and measurement technologies. Online measurement technology is a vital means for quality assurance and productivity improvement in machining. Despite ongoing challenges, such as the development of high-precision sensors and optimization of data processing strategies, online measurement holds great promise for future applications.

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