In Situ Machine Tool Walking on Large Workpieces: Improvement of Machining Accuracy by Compensating Orientation Dependent Position Error

Chang-Ju Kim; Dae-Hyun Kim; Seung-Kook Ro

doi:10.57062/ijpem-st.2024.00192

Abstract

For manufacturing and repair operations involving large parts, such as aircraft components and wind turbines, in situ machine tools have been recognized as an effective solution. This study introduces a new design concept for a machine tool capable of walking on large workpieces, along with a geometrical error model that independently accounts for the effects of gravitational load. Its distinctive serial kinematic mechanism provides both high flexibility for walking and a large work envelope for machining. The feasibility of this design concept is validated through evaluation tests on mobility and cutting, demonstrating the accuracy typically required in aerospace manufacturing.

Keywords: Machine tool · In situ machining · Machining accuracy · Large workpiece

1 Introduction

Machining large parts in aircraft, ship hulls, wind turbines, and nuclear power plants typically require machine tools that are larger than parts themselves. The use of such large machine tools is necessary for conducting heavy cutting or achieving high accuracy. However, movable machines that are smaller than target workpieces can offer energy and cost advantages over large workshop machine tools in manufacturing new parts or conducting maintenance and repair operations on post-production parts [1]. Growing production rates in the aerospace industry also has led to an increasing demand for more flexible and productive solutions [2].

Among the various types of small machine tools for large parts introduced so far [1], self-propelled machines can be divided into two groups: ground-based and walking machine tools [3]. Serial kinematic industrial robots [2, 4] or parallel kinematic machines [5], in the first group, move on the ground around large parts on a mobile platform or a track.

These machines are used mainly for manufacturing large parts, such as airplane wing panels, and have high productivity and processing capability, but they are usually too heavy for in situ operations on a part.

Machine tools in the second group have been developed mainly for post-production in situ operations on e.g. airplane skins. Most of the serial kinematic walking machines in this group are based on gantry-type machine construction [6] to have high structural stiffness, but have drawbacks such as limited motion flexibility and tool accessibility. In contrast, parallel kinematic walking machines [7,8] balance structural stiffness and motion flexibility, but are not ideal for high productivity, and complicated motion control may limit widespread use. To further widen applications of in situ machine tools, improvements in motion flexibility, tool accessibility and productivity are desired.

This study presents (a) a novel design concept of an in situ machine tool that can walk on steep slopes and (b) a new geometric error model to compensate for the position error varying with the machine’s angular orientations. The machine’s unique serial kinematic mechanism provides both freedom of movement similar to that of parallel kinematic walking machines and the large work envelope that is an advantage of industrial robots. The primary target of the machine in the current phase of development is to achieve the machining accuracy generally required in aerospace manufacturing, about 0.3 mm [9], by overcoming low structural stiffness with error compensation.

2 Design Concept and Performance Evaluations of the Walking Machine Tool

2.1 Design of the Primary Structure

A main design concept of the developed machine is adopting a rotational motion axis in between two linear feed drive systems to realize both highly flexible walking motion and a large machining area while maintaining enough structural stiffness for machining operations. In contrast to gantry-type machines and parallel kinematic machines the stacked-stage type serial kinematic structure of this machine allows locating the spindle head on the periphery of the machine, which enables the tool accessing hard-to-reach areas, such as corners and edges of the workpiece. In addition the wide range of tool reach makes implementation of an automatic tool change possible and this leads to high productivity.

The primary structure of the machine consists of two rectangular frames connected with linear motion axes, X and Y, and a rotational motion axis, C (See Fig. 1). Three vertical axes—Z₁, Z₂ and Z₃—fixed on the upper frame lift the machine body during the walking motion. One of the vertical axes, Z₁, with the spindle head, synchronizes with the X and Y axes during machining operations while the other Z axes are stationed at the top position [10].

The upper or lower frame clamps on a smooth, curved surface with a radius of curvature of 2 m or larger, with three ball-jointed foot modules, each of which has three individual vacuum clamps. The spindle is linked to the Z₁ axis via a large spherical and a journal bearing so it can be tilted to the surface normal direction and raised up during walking motion.

Linear axes driven by servo motors and ballscrews can travel 400 mm along the X and Y axes and 200 mm along the Z axes at a maximum speed of 30 m/min. The C axis unit, composed of a reduction gear and a servo motor, can rotate 120 at a maximum speed of 5 rpm. The spindle, with the power of 0.6 kW, torque of 0.1 Nm and maximum speed of 60,000 rpm, holds a tool of 6 mm diameter with a pneumatically actuated tool clamp. The vision camera or the laser line scanner fixed next to the spindle detects reference features on the workpiece to identify the location of the machine relative to the workpiece.

The machine weighs about 95 kg and can be contained in a circle of 1.2 m diameter. The tool can access the primary 0.4 × 0.4 m Cartesian coordinate (X, Y) area for machining and extra polar coordinate (Y, C) areas for referencing or tool changes as illustrated in Fig. 1.

2.2 Evaluation of Walking Performances

The walking motion for moving the machine base is realized with a 4-step sequence (Fig. 2):

1. With the lower frame clamped on the surface, raise all three feet of the upper frame.
2. Move the upper frame to an intermediate stepping position using the X, Y and C axis motions.
3. Lower all Z axes to the surface, switch the vacuum engagement from the lower to upper feet, lower the Z axes further to lift the lower frame from the surface, and move the lower frame to the desired position.
4. Raise all Z axes until the lower feet touch the surface and switch the vacuum engagement back to the lower frame. Raise Z₂ and Z₃ further to the end to avoid collision during machining.

An evaluation test for mobility shows that the prototype machine can be firmly clamped on a vertical wall and walk as designed.

One step motion takes about 30 seconds on the vertical wall and carries the machine up to 0.3 m of linear distance (0.6 m/min) or 1/8 turn of rotation (0.25 rpm). When the inclination angle is low traveling speed can be faster with precaution procedures for drop prevention bypassed. Positioning error of walking motion is about 0.5 mm on the horizontal plane but increases to 3 mm at high angles due to structural flexibility and slips of the vacuum clamps during foot exchanges.

2.3 Evaluation of Cutting Performances

The machining capability of the machine was tested by milling 7075 aluminum alloy workpieces with two-flute end mills 6 mm in diameter at 10,000 rpm and 120 mm/min feedrate at the axis center position (Fig. 3(a)). The axial depth varied from 0.1 to 0.5 mm with full radial immersion. Measured cutting forces confirmed that the machine can withstand at least 80 N in the lateral direction. The surface roughness and the machining error due to cutting forces measured 0.7 μm Ra and 0.12 mm, respectively, at the axial depth of 0.5 mm.

Drilling performance was tested on 5 mm thick 6061 aluminum plate with 5 mm diameter TiAlN coated carbide tools at 20,000 rpm and 0.7 mm/min feedrate (Fig. 3(b)). A single tool could drill more than 80 holes without significant degradation in hole quality.

The influences of the following error sources on hole center position were evaluated: (a) referencing error after walking motion, (b) position repeatability, and (c) geometric position error. The referencing error, mainly due to the uncertainty of the machine vision measurement, is measured about 20 μm. Position repeatability of 30 μm and drill wandering motion results in about 0.1 mm overall position accuracy after error compensation when the machine is on a horizontal plane.

The position error, however, increases significantly when the machine is tilted at a high angle because of a change in the gravity load on the machine structure. The conventional geometric error models, which are based on the assumption that the direction of gravity does not change against the machine base, are not applicable when the angular orientation of the machine changes drastically. Therefore, it is necessary to build a new geometric error model which considers the effect of gravity independently.

3 Compensation of Orientation Dependent Position Error

3.1 Geometric Error Model Considering the Direction of Gravity

The kinematic and the gravity–induced error of a conventional machine tool are generally treated together as a quasi-static geometric error [11] and it can be described with a translational error vector, e =(δ_x, δ_y, δ_z), changing as a function of axis position, p = (p_x, p_y, p_z).

The quasi-static error vector, e_QS, can be expressed with Eq. (1) when the gravity is pointing to –Z direction of a machine:

(1)

eQS(p)=eK(p)-eGZ(p)

where e_K is the kinematic error caused by imperfect geometry and dimensions of machine components and e_GZ is errors due to gravity load when the direction of gravity is aligned to the machine’s Z axis.

When the direction of gravity varies relative to the machine’s reference axis, Eq. (1) can be generalized with a unit directional vector of gravity, g = (g_x, g_y, g_z):

(2)

e(p,g)=eK(p)+eGX(p)·gx+eGY(p)·gy+eGZ(p)·gz

where e_GX and e_GY are errors due to gravity load when the gravity vector is aligned to the X and Y axis of the machine, respectively. Eq. (1) is a special case of the generalized equation when the gravity vector is g₀ = (0, 0, −1).

By combining Eqs. (1) and (2) the kinematic error term can be replaced with the quasi-static error which can be directly measured:

(3)

e(p,g)=eQS(p)+eGX(p)·gx+eGY(p)·gy+eGZ(p)·(gz+1)

If the four principal error vectors—e_QS, e_GX, e_GY, e_GZ—at grid points in the work envelope are identified, then the geometric error at a certain axis position and a machine orientation can be calculated by linear interpolation.

3.2 Identification of Principal Error Vectors

Among two common approaches for error model calibration, analytical methods based on reversal techniques and best-fit methods [12], a best-fit method was applied for this machine because of nonlinear behaviors in machine components such as vacuum clamps and a not perfectly rigid workpiece.

The machine vision camera (Laon people LPMVC-EE500, 1.2 M pixel, 54fps) fixed on the spindle head measured the geometric position error in the X and Y directions by finding the center of 8 × 8 holes evenly spaced with 50 mm pitch on the reference plate, and the capacitive gap sensor (Lion C1-A, range: 500 μm, sensitivity: 0.04 V/μm) measured the Z direction error simultaneously (Fig. 4(a)). This measurement was repeated at 15 different angular orientations of the machine base defined in Figs. 4(b) and 4(c).

The measured sets of geometric errors overlapped in Fig. 4(d) show that translational errors can be as large as 1.3 mm in the lateral direction and 7.8 mm in the vertical direction, especially when the machine is tilted to a high angle and the spindle head extends to the end of the stroke.

The quasi-static error vectors, e_QS, were directly measured when the machine was in a horizontal plane (α = 0°). The other three principal error vectors—e_GX, e_GY, e_GZ—were identified by minimizing the sum of 14 root mean squares of difference between the measured position error and the one calculated with Eq. (3). The identified principal error vectors are shown in Fig. 5.

When compensating the measured errors with the calibrated error model the maximum lateral and vertical error reduces to 0.3 and 0.9 mm, respectively (Fig. 4(d)). This validates the feasibility of the proposed error model and also the calibration procedure.

3.3 Drilling Test with Error Compensation

To confirm the effectiveness of the developed error model drilling test was conducted with (a) compensation based on only the quasi-static geometric errors and (b) compensation based on the proposed model. Fig. 4(c) shows the machine orientations used for this drilling test along with the ones for the model calibration test. 4 × 4 holes at the grid points illustrated in Fig. 6(a) were drilled with the same cutting conditions described in Section 2.3 and their center positions were measured with a CMM. Position errors at each grid point were averaged over 9 different machine orientations. The measurement results show that compensation based on the proposed error model can improve hole position accuracy to the targeted level of accuracy in drilling (Fig. 6(b)).

Error compensation is implemented by adjusting the command value of the machining program with the error value calculated in advance instead of using the controller’s compensator. This method is effective in drilling where the position of the tool is important, but for milling where the tool trajectory is important, the 3D error mapping function of the controller should be utilized. In this case, in order to apply the proposed error model, it would be necessary to calculate the error map and update the error compensation table of the controller whenever the machining machine moves and changes its posture.

4 Conclusions

This study presents a new design concept for in situ machine tools that can walk on a large workpiece and conduct milling or drilling operations. The main advantages over existing systems include that the machine, weighing 95 kg, has a large work envelope of 0.4 × 0.4 × 0.2 m³ and the axis configuration allows the spindle to access hard-to-reach areas. Evaluation tests demonstrated that the machine can walk at 0.6 m/min on a vertical wall, end-mill aluminum workpieces with 6 mm diameter tools to surface roughness of 0.7 μm Ra withstanding up to 80 N of cutting forces, and drill 5 mm diameter holes at 0.7 mm/min feedrate.

The study also proposed a geometric error model to compensate for the position error induced by gravity load. The feasibility of the design concept and the effectiveness of the proposed model was demonstrated by showing that the position accuracy of drilled holes after compensation is at the level generally required in aerospace manufacturing regardless of the machine orientation.

However, the developed machine tool still has the following limitations. It is too heavy for an operator to easily operate, and the structural rigidity of the floor interface is low, so a displacement of several mm occurs at the machining point without error compensation. The proposed error model has been applied to improve the intermittent positioning accuracy in processes such as drilling, but a more complex compensation technique needs to be developed for error compensation that occurs during continuous movement such as milling. In addition, it is difficult to perform hole machining or milling vertically on a curved floor with a three-axis linear feed. Therefore, the development of mobile machine tools in the future will proceed in the following directions: (1) introducing an actively tilting spindle head to machine curved workpieces, (2) improving the machining accuracy of milling by pre-compensating the tool path, and (3) improving cutting performance by reducing the weight and reinforcing the rigidity.