Keywords

1 Introduction

Machine tools are exposed to thermal influences that can reduce the machining accuracy. The development phase and operational phase of milling machines require evaluating the accuracy of motion in order to guarantee high machining accuracy. Tactile measuring methods using linear displacement sensors (defined in DIN ISO 230-3), circular shape tests with double ball bars (defined in DIN ISO 230-4) or, less frequently, test work pieces (TWP) are current standards for this purpose. The TWPs according to VDI 2851, NAS 913, ISO 10791-7 and VDI/DGQ 3441 are used to determine reversal span, positioning accuracy, interpolation properties, quadrant reversal, form and dimensional deviations based on standardized or recommended testing procedures. However, these TWPs do not allow for separating thermally induced geometrical errors of a machine tool from other error proportions [1]. Tactile measurements are not applicable during machining. Various test work pieces have been proposed [2,3,4], to measurement TCP displacements as a function of time. But recording the progressions of thermally induced motion errors and deviations of position over the course of a production shift remain unknown. Therefore, the Collaborative Research Centre “Transregio 96” (CRC) developed a compact TWP to measure thermally induced TCP errors during three axes milling operations over a time span of 6 h. This paper introduces the TWP and compares the TWP results to tactile measurements with linear displacement sensors according to DIN230-3.

2 Experimental Setup and Methods

Section 2 describes the developed TWP, the experimental setup, the procedure of validation measurements as well as data acquisition and processing.

2.1 Test Work Piece (TWP)

The imprint of TCP displacements into the TWP caused by the kinematic and static properties of the machine tool as well as the effects of process forces and wear had to be minimized. In addition, it was necessary to record the TCP displacements as a function of time until thermal steady state of the machine tool is reached.

The TWP has three reference surfaces corresponding to the X-, Y-, and Z-axis of the machine tool, which are machined at the beginning of an experiment. They represent the geometric initial state of the machine tool.

Fig. 1.
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Test work piece with ref. Surfaces and shape elements before and after measurements

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To map the TCP position, shape elements, corresponding to the X-, Y-, and Z-axis of the machine tool, are machined. The distance between a shape element and its corresponding reference surface translate into TCP-displacements at specific times during the experiment (Fig. 1). In order to log a detailed TCP displacement progression, the TWP possesses 25 shape elements for each translational direction (X, Y and Z). When manufacturing these shape elements, tool wear can have a negative effect on the shape accuracy. Therefore, the actual diameter of the tool is recorded in the TWP five times during the experiment by manufacturing counter lines 1 to 5 (Fig. 1). The rear side of the TWP is identical to that of the front side. Thus, two test trials can be recorded on the same part, e.g. running the machine tool once with and once without activated correction methods as introduced in [5,6,7].

2.2 Machine Tool DMU 80

The TWP tests were conducted on a 5-axis milling machine (DMG DMU 80 eVo linear). Only the three translational axes of the machine tool were active during the experiments. Machining was performed without compressed air or cooling lubricants. Machine-internal thermal correction methods (spindle length and translational axes) were deactivated during the experiments. The TWP was machined with an end mill for aluminium with the following set of cutting parameters (Table 1):

Table 1. Tool properties and cutting parameters.
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2.3 Test Setup

Two fixtures made of Fe65Ni35-Invar hold the measuring probes (MP). The test work piece was mounted on the machine tool table as shown in Fig. 2 and 3.

Fig. 2.
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Test setup on DMU80 machine tool: a) front view, b) top view.

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Tactile Measurement

Once triggered by contact, the measuring probes recorded the TCP displacements every 200 ms. The dwell time during this measurement is one minute. During this time, each probe recorded approx. 300 values. Afterwards, the median value was calculated.

The sensors were aligned in such a way that point zero (middle of the measuring range) was in the same plane as the corresponding shape elements of the TWP. This clamping position minimizes thermally effective lengths, which would limit the comparison of the TCP displacements recorded on the TWP and the measuring probes. Furthermore, this reduces the linearity error and thereby increases the measuring accuracy of the measuring probes. The probes in z direction contact the bottom of the tool holder. The probes in X and Y direction contact the tool shaft. This avoids a tool change to switch to a mandrel for measuring purposes.

Fig. 3.
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Experiment setup on machine tool table: sensor positions and coordinate system.

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Table 2 is an overview of the sensors used:

Table 2. Measured values, sensor features and measuring positions.
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Table 3 shows the measurement uncertainties of the measuring equipment used:

Table 3. Manufacturer information on measurement uncertainties of the measuring equipment.
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2.4 Test Execution

Two variations of the same experiment were performed, each with two trials, on consecutive days. For each trial, the machine tool was prepared in the afternoon of the previous day; the machine tool was set to the desired state (running or switched off) and the trial started on the next morning. The two experiments differ in the type of load case, that was applied, to simulate different machining scenarios.

Test Procedure

Each experiment starts with milling the TWP reference surfaces including the first tool wear groove. In a second step, the initial set of shape elements (Fig. 1) for translational errors in the x, y and z direction is machined. Third, the CNC moves tool to contact the probes for tactile measurement. In step four, the machine tool performs a motion sequence defined by load cases from industrial applications (see “artificial load cases”). Subsequently, the next set of shape elements is manufactured and tactile measurements are conducted. The procedure starts from step three is repeated for all 25 shape element sets.

Artificial Load Cases

Two artificial load cases were designed to induce thermal loads into the machine tool in order to simulate two different machining scenarios without actually machining. Thereby, the machine tool heats up or cools down, to create thermally induced positioning errors (Fig. 1 and Fig. 4).

Fig. 4.
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Expected temperature changes of machine tool components under load case #1 and #2.

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The machine tool performed axis movements and spindle rotations. Thermal loads result from friction and electrical losses of the feed drives during movement and acceleration of the feed axes and motor spindle. The measurement intervals were defined in such a way that short measurement intervals were used for periods with high temperature gradients and large measurement intervals for low temperature gradients. Table 4 shows the different measurement intervals, for the two artificial load cases that were investigated:

Table 4. Measuring intervals
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Load Case 1: “Single Part Production”

This load case simulates the production of individual components with intermediate idle times. The machine tool experiences alternating thermal loads and standstill, so that the temperature of the feed and spindle components rises and falls alternately. The machine tool is switched off on the evening of the previous day and is at thermal equilibrium with the environment at the start of the experiment in the morning.

Load Case 2: “Continuous Manufacturing”

This load case simulates series production. The machine tool is subjected to a continuous, almost constant load with the exception of short dwell times during the tactile measurements. The temperature of the feed and spindle components rises continuously until the machine is in a steady state. In the following experiments, the machine tool was switched-on at the evening of the previous day (all feed axes in position control). Therefore, the machine tool was not in a state of thermal equilibrium with the environment at the beginning of the test. The planned motion sequence heats the machine including the feed axes and the main spindle. It simulates a representative machining process. The motion sequence consists of cyclic acceleration and braking processes of the feed axes and the main spindle. The TCP moves on spiral paths in the X-Y plane of the machine.

2.5 Experiment Evaluation

Removing material with the end mill tool imprints the TCP displacement directly on the TWP surface. A thermal compensation calculation of the TWP must be performed, to account for the thermally induced geometry changes during the trial. On the condition that the TWPs thermal expansion was compensated and that tool wear and its thermal expansion were negligible, the displacement obtained by measuring one specific TWP shape element is defined as the actual TCP displacement of the machine tool at the time of machining this specific shape element. The goal of the experiment was to compare two different measuring methods. Because tactile and TWP based TCP displacement measurements were conducted at a different location on the machine table and at different points in time, this entails uncertainties and difficulties in comparing the measurement data obtained by the two methods. Therefore, the measurement data were processed in the following way: First, a thermal compensation calculation was performed for all values and then an Offset was calculated to match the progressions of the two sets of data (TWP and MP). This procedure allows for comparing the progressions of the measured values of the two measuring methods.

Measurement of TWP on a Coordinate Measuring Machine

A coordinate measuring machine (CMM) is required to measure the geometry of the TWP. Wiemer et al. have shown that high-precision coordinate measuring machines provide a measurement uncertainty of about ±0.6 μm. Because two measurements are necessary to calculate the distance between reference surface and shape element, the maximum error can be up to ±1.2 μm [6]. The evaluation is carried out by calculating the above-mentioned distances for all 25 sets of shape elements and the four groove widths (for tool wear determination). To reduce the influence of the surface roughness of the surfaces of the machined TWP, five measuring points per surface were to be measured and averaged.

Compensation of Thermal Expansion of TWP and Fixtures on Measurement Results

The aluminium TWP expands and shrinks with temperature changes (23.1 * 10–6/K at 20 ℃ which requires a thermal correction of measured values.

Table 5 shows the expected linear expansion due to temperature change on the TWP:

Table 5. Calculated displacement of the TWP surfaces due to thermal expansion.
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The tactile probe fixture 1 was made out of Invar (thermal expansion negligible). But for technical reasons, it was mounted on a 100 mm high steel block. Therefore, the probe’s measured displacements in the Z direction require thermal correction as well. The temperature at fixture 1 was recorded every minute. The temperature at fixture 1 was recorded every minute. Using the expansion coefficient of steel (13.9 * 10–6/K at 20 ℃), the measured displacement values were corrected by a factor of 1.39 µm/K. For comparison of tactile and TWP measurement, the offset for a given trial and direction was calculated from the difference in the median of two corresponding displacement variables (e.g. XTWP and XMP) for all measured values. Table 6 shows the calculated offset values:

Table 6. Differences in median values between TWP and MP (Offset values for MP values).
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3 Measured TCP Errors Due to Thermal Influences

3.1 Determined TCP Error Values

The results demonstrate that the progression of the recorded TCP displacements, determined by means of the TWP and the measuring probes, are consistent.

Load Case 1

Load case 1 showed increasing displacements during the (simulated) machining part of the load case in the first part of the experiment. Afterwards, during the transition to the cooling phase, the measured displacements decreased. During the second (simulated) machining part of the experiment, the displacements increased again due to the renewed increase in thermal load on the machine tool, as shown in Fig. 5.

Fig. 5.
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Measured TCP displacements for load case 1: a) trial #1 and b) trial #2.

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Load Case 2

The parameters for load case 2 were selected to ensure continuous heating of the machine tool and to reach a steady state towards the end of the experiment. The measured displacements increased during the experiment and approached a maximum, as shown in Fig. 6:

Fig. 6.
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Measured TCP displacements for load case 2: a) trial #1 and b) trial #2.

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3.2 Comparison of the Deviation in the Determined TCP Error Values for TWP and Measuring Probe Measurements

The difference between the measured values with the TWP and the measuring probes was less than ±2 µm (Fig. 7). The maximum total measurement uncertainty of the test setup is ±2 µm. The red dashed lines indicate the upper and lower limits of measurement uncertainty. With the exception of a few outliers, all measured value differences fall within this range.

Fig. 7.
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Differences in TCP displacements measured with the TWP and with the measuring probes for the two load cases. The dotted line represents the maximum measurement uncertainty of the sensors.

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4 Discussion

The experimental results show that the TWP is suitable for measuring thermally induced TCP displacements during milling with a high accuracy. During machining of the shape elements on the TWP, the machine tool’s TCP displacement is transferred to the TWP by means of material removal. Therefore, it can be defined as a direct measurement of the machine tool’s TCP. There are three factors, which can influence the accuracy of this direct measurement: the thermal expansion of the tool, of the TWP and tool wear. The radial tool wear was recorded several times during the test and the tool diameter change was below 0.5 µm. The temperature and resulting shape change of the TWP during each trial was taken into account. Influences that could not be determined in a practicable way were the tool temperature itself and the actual TWP temperature field (temperature was measured on one side of the TWP only). In addition to the measurement inaccuracies, specified by the manufacturers of the measuring equipment (Table 3), the following negative influences on the measurement accuracy caused by the test setup were identified:

  1. a)

    At the beginning of the measurement, the reference surfaces on the TWP are machined. This operation takes approx. 60 s. The end of this operation is the moment of the maximum heat flow into the TWP and the tool. The resulting thermal expansion leads to dimension deviations of the reference surfaces. Since, the reference surfaces serve as a reference for the measurement of the shape elements on a CMM, this phenomenon might cause a measurement uncertainty, which was not quantified.

  2. b)

    During the application of load case and machining of the shape elements, the motor spindle is running and heats up. During the measurement with the measuring probes, the motor spindle does not rotate and cools down. It is expected, that due to the deactivated thermal spindle length compensation, the spindle would begin to shorten. This effect was observed in the z direction displacement, measured by the probes. It reached up to 1.5 µm during the one-minute measuring period (Fig. 8).

Fig. 8.
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The displacement of the measuring probe in the Z-direction as a function of time

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Table 7 shows outliers and likely causes:

Table 7. Overview of identified outliers and presumption of cause.
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5 Conclusion

Comparing the TCP positioning errors obtained by from the developed TWP with results from measuring probes showed deviations of only ±2 µm. Up to 25 TCP displacements (with 3 spatial components each) can be recorded with the TWP.

The preparation and post-processing as well as the execution of tests by means of the TWP require shorter set-up time than conventional probes. No other measuring equipment than temperature sensors are required. Even inexperienced machine operators can carry out measurements with the TWP. It is a user-friendly, time-efficient, and cost-effective alternative to conventional measuring methods. Since the TWP must be fixated on the machine table, the measurement of TCP displacements is limited to a plane at a distance of 85 mm above the machine table. The applicability of the TWP is limited to the measurement of translatory errors on 3-axis milling machines. The user needs access to a CMM to measure the shape elements on the TWP.

Since only low cost temperature sensors are used, there is no danger of damaging sensitive measuring equipment by chips and cooling lubricants. Therefore, a measurement can be carried out simultaneously to the machining of components.

The TWP was developed to validate the effectiveness of thermal compensation and correction methods on milling machines. The experiments confirmed its suitability for this application.