Sudhanshu Nahata, PhD, mechanical design engineer, ASML, and O. Burak Ozdoganlar, PhD, Ver Planck professor of mechanical engineering, Carnegie Mellon University (CMU)
In micromachining, the majority preference is to specify tolerances in microns and sub-microns, but how does one meet the prescribed tolerances using the tool at hand? There is no formula that works for everyone: each micromachine tool (MMT) is different, has a different spindle unit mounted on its unique structural frame and uses a different set of cutting tools. Therefore, it is reasonable to assume that each MMT is capable of holding different tolerances. The capability of an MMT to hold a tolerance depends on various factors such as manufacturing/assembly errors of the spindle shaft and bearings, tool attachment errors and machine dynamics, all of which ultimately relate to the observed cutter offset at the tool tip. This article explores cutter offset in detail, understands the factors that promote it and discusses ways to avoid its undesired influence on micromachined parts.
The focus is on a three-axis MMT capable of micromilling using microtools. The diameter of said microtools commonly ranges from a few tens of microns (for example, 0.02 mm) to a few hundred microns (for example, 0.5 mm). The smaller the tool is, the higher the rotation speed required to meet the required cutting speeds. For this reason, modern MMTs are usually equipped with high-speed and ultra-high-speed spindles that can rotate as fast as 280,000 rpm. The lower rpm spindles generally have ceramic bearings and the higher rpm spindles tend to have air bearings.
In micromilling, one of the important factors in achieving accuracy is how true the cutting edges are held to their ideal locations during cutting. Ideally, the cutting edges rotate in a circle with a diameter equal to the geometric tool diameter. However, this is seldom the case. The cutter often possesses a radial offset, which increases the effective tool diameter and therefore causes inaccuracies in the micromachining process. In addition, the finite stiffness of the micro tools, coupled with the stiffness of the spindle structure, further affects accuracy. These radial offsets at the tool tip can sometimes be larger than the diameter of the cutting tool itself, which is undesirable.
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Figure 1: A series of thin triangular walls (at a prescribed width of 100 µm) micromilled in brass. The wall thickness is 79.2 µm.
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Figure 1: A series of thin triangular walls (at a prescribed width of 100 µm) micromilled in brass. The wall thickness is 79.2 µm.
Before proceeding further, it is important to clarify the term ‘cutter offset’. It is also referred to as radial runout, total indicator reading, tool concentricity and radial throw of the tool axis, which are similar but not the same. Often, radial runout is used to denote the total radial displacement of the cylindrical surface of the cutting tool during a complete rotation (see figure 2a). This displacement is usually measured along a single radial direction, which results in a single numerical value, half of which is considered as the radial offset. This definition assumes a constant radial offset between the geometric axis of the tool and the true axis of rotation during the entire rotation of the tool, which is not correct. Moreover, radial runout does not possess an orientation that is equally or more important than the magnitude.
To assess the kinematic trajectory of the cutting edges, it is necessary to determine the real-time trajectory of the tool axis (in a 2D cutting plane) with respect to the true axis of rotation as the tool rotates. Since radial runout is a single (constant) number, it cannot represent the real-time radial offset of the tool axis as the tool rotates. This 2D motion is accurately captured by the “radial throw of the tool axis,” which denotes the “distance between the geometric axis of a part (or test artefact) connected to a rotary axis and the axis average line (true axis of rotation), when the two axes do not coincide”1. This is also highlighted in figure 2a.
Figure 2: (a) The difference between radial runout and radial throw: radial runout is represented by the total deviation of the rotating surface along the direction of measurement, and radial throw is represented by a rotating vector connecting the true rotation axis and the geometric axis of the cutting tool. (b) The radial throw vector possessing a magnitude (ρ(θ)) and an orientation (η(θ)).
One might wonder why the cutter offset or the radial throw changes as the tool rotates. The conventional macro-scale milling machines run their spindles between 3,000 and 20,000 rpm, where dynamics are not as big a concern as thermals. However, in micro-scale milling, as the process deals with ultra-high-spindle speeds, there are important dynamic effects that cause the radial throw to vary as the tool rotates. In other words, these effects cause the overall shape of the cutting trajectory to be elliptical rather than the commonly assumed circular. These dynamic effects, along with the static effects, need to be well understood to predict the performance of an MMT. There are two major contributors to the radial throw: (1) kinematic errors, and (2) speed-dependent dynamic effects.
The contribution of kinematic errors to the radial throw includes tool attachment error, inherent spindle error motions, spindle shaft misalignment due to manufacturing/assembly and geometric inaccuracy of the microtools. Generally, these errors are added as a tolerance stackup to obtain the resulting radial throw at any axial location of the tool. Assuming it is a geometrically perfect cutting tool, the result of the tolerance stackup is a potential misalignment between the tool axis and the true axis of rotation, which affects the effective tool diameter. In other words, the effective tool diameter is the geometric diameter of the tool, plus any radial offset caused due to static or dynamic effects.
The radial throw of tool axis is a vector described by a magnitude and an orientation (see figure 2b). Both the magnitude and the orientation are a function of the rotational angle and play an important role in the calculation of effective tool diameter. The contribution of the magnitude is relatively easier to imagine, namely the lower it is, the closer the effective tool diameter to its geometric tool diameter. The radial throw magnitude is further broken down into an eccentricity and a tilt, the latter being more problematical as it keeps growing with the length of the tool (see figure 3).
Figure 2: (a) The difference between radial runout and radial throw: radial runout is represented by the total deviation of the rotating surface along the direction of measurement, and radial throw is represented by a rotating vector connecting the true rotation axis and the geometric axis of the cutting tool. (b) The radial throw vector possessing a magnitude (ρ(θ)) and an orientation (η(θ)).
Figure 3: The increase in radial throw magnitude with axial location of the tool, taking into consideration both eccentricity and tilt.
The radial throw orientation, on the other hand, is relatively unfamiliar but plays an equal role in determining the effective tool diameter. The orientation helps in determining the phase angle, which is used when adding the magnitude to the geometric radius of the cutting tool. This calculation becomes straightforward when the orientation of radial throw is defined with respect to the cutting edge of the tool (see figure 4a). As an example, when the radial throw vector aligns with the cutting edges (i.e., η=0 deg.), the effective tool diameter maximises, and it gradually decreases as the orientation increases from 0 to 90 deg. (see figure 4b).
Figure 4: (a) The difference between the ideal (geometric) tool diameter and the effective tool diameter. (b) The variation in effective tool diameter as a function of radial throw orientation at two different magnitudes (5 µm and 10 µm). The geometric tool diameter is 254 µm.
The resulting radial throw at the tool tip is a summation of various error sources, making it difficult to decipher. Yet, when measured enough times, the trend becomes visible; generally, both the magnitude and the orientation follow a normal distribution. One does not have much control over minimising the magnitude of radial throw unless the geometric inaccuracies of the cutting tool are the cause. However, the orientation of radial throw is dependent on how the cutting edges are oriented with respect to the radial throw vector. Therefore, one solution is to locate the average location of the phase angle (of the radial throw vector) for the tool-collet-spindle arrangement and clamp the cutting tool such that the cutting edges are located farther away from this phase angle. This can be done by making a mark on the collet or the rotor where the average phase angle is located. In a nutshell, careful clamping of the cutting tool maximises the orientation of radial throw, thereby minimising the effective tool diameter. Figure 5 shows how controlling the radial throw orientation improves accuracy of the micromachining process4.
Figure 5: The effective tool diameter with varying radial throw magnitude and orientation. The geometric tool diameter is 254 µm.
The speed-dependent dynamics of the spindle structure cause the radial throw to strongly depend on the spindle speed. Therefore, static measurements of the radial throw do not hold true when the spindle is running at its operational speeds. There are two main effects playing a role: (1) increase in the unbalance response of the rotating elements, which varies as a square of the spindle speed, and (2) variation in the stiffness of the spindle structure with spindle speed1. The unbalance response of the rotating elements is relatively straightforward to imagine. Any amount of unbalance results in centrifugal forces, where higher speeds cause higher forces and hence, higher radial motion.
On the other hand, the dynamic stiffness of the spindle structure is interesting and has a substantial influence on the micromilling process. The commonly used spindle speeds, affording between 50,000 rpm and 200,000 rpm, correspond to a frequency range between 833 Hz and 3333 Hz. It is common to have the natural frequency of the spindle structure either within this frequency range or very close to it. This causes the radial throw to modulate as the spindle frequency changes corresponding to the frequency-dependent stiffness (see figure 6). More often, the frequency-dependent stiffness is dissimilar among different radial directions, especially closer to the natural frequency of the spindle structure5–6. As a result, the modulation of radial throw is different in different radial directions, which causes a more general elliptical radial throw1–2.
Figure 6: The effect of spindle structure dynamics on the resulting magnitude of radial throw. The bump around 100,000 rpm in the radial throw magnitude is a result of the natural frequency of the spindle.
These dynamic effects should be taken into consideration when choosing spindle type, namely a low-stiffness air bearing spindle or a high-stiffness ball bearing spindle, and spindle speed as, for example, it is common to observe different accuracies at two different spindle speeds for the same spindle system.
The measurement of radial throw requires two perpendicular probes targeting the geometric axis of the cutting tool. Although dial indicator-based approaches are common, they cannot be used for micro-scale spindles as measurements at rotational speed is required. For this reason, a non-contact laser-based system is considered appropriate. The radial throw measurements must be conducted at two different axial locations to obtain the tilts. To obtain an approximation value of the speed-dependent stiffness of the spindle structure, a tap test is usually undertaken. However, it should be noted that the tap test also needs to be conducted at operational speeds for higher accuracy5.
The radial throw affects many aspects of the micromachining process. First and foremost, it affects the achievable precision from a specific MMT. If the effective tool diameter is known prior to machining, one can make necessary adjustments in the G-code to compensate a portion of it. Even then, the limited stiffness of the tools results in bending, which is difficult to predict and compensate. Second, radial throw causes one of the cutting edges to experience more tool engagement, which means that it eventually wears faster then the others. Third, a difference in tool engagement means further variations in the cutting force, which could affect the surface finish of the workpiece7. These effects cannot be avoided but can be minimised by characterising the MMT to take informed decisions and maximising the radial throw orientation.
Conclusion
A machinist needs to make many decisions before machining and those decisions need to be based on a thorough understanding of the machining process. The objective of this article has been to impart understanding of the various factors that play a role in determining rotational accuracy of MMTs, since it is ultimately responsible for determining the achievable accuracy and repeatability. Although runout is the commonly used term, radial throw (magnitude and orientation) is more accurate and comprehensive as it captures the more general motions of the tool axis. Both the magnitude and the orientation of radial throw play a substantial role in determining the effective tool diameter. As well as the kinematic (static) effects, it is also important to characterise the dynamic effects on radial throw; this is because depending on the tool and spindle speed, the radial throw can be more than the diameter of the tool itself, which is not desirable.
ASML
References
1ISO 230-7:2015 Test code for machine tools -- Part 7: Geometric accuracy of axes of rotation. Available at: bit.ly/2DGAb2M
2Nahata, S., Onler, R., Shekhar, S., Korkmaz, E. and Ozdoganlar, O.B. (2018). Radial throw in micromachining: measurement and analysis. Precision Engineering, volume 54, pp.21-32.
3Nahata, S., Onler, R., Korkmaz, E. and Ozdoganlar, O.B. (2018). Radial throw at the cutting edges of micro-tools when using ultra-high-speed micromachining spindles. Procedia Manufacturing, volume 26, pp.1517-1526.
4Nahata, S., Onler, R. and Ozdoganlar, O.B. (2019). Radial throw in micromilling: a simulation-based study to analyze the effects on surface quality and uncut chip thickness. Journal of Micro and Nano-Manufacturing, volume 7, issue 1, p.010907.
5Bediz, B., Gozen, B.A., Korkmaz, E. and Ozdoganlar, O.B. (2014). Dynamics of ultra-high-speed (UHS) spindles used for micromachining. International Journal of Machine Tools and Manufacture, volume 87, pp.27-38.
6Lu, X., Jamalian, A. and Graetz, R., 2011. A new method for characterizing axis of rotation radial error motion: part 2. Experimental results. Precision Engineering, volume 35, issue 1, pp.95-107.
7Lee, K. and Dornfeld, D.A. (2004). A study of surface roughness in the micro-end-milling process. Laboratory for Manufacturing and Sustainability (LMAS), University of California (UC), Berkeley. Available at: bit.ly/2UTh2Af