Five-Axis Motion Systems

In Part I and Part II, I have talked about a soft cutting tool controller and a 3D CAM software product for ruled surface cutting. They solved the problem of optimized programming of waterjet cutting. However, we will need some sort of motion systems (e.g., five-axis motion systems) to implement the sophisticated cutting motion, including small-angle tilting motion to compensate for geometrical errors caused by the soft cutting tool as well as the large-angle tilting motion needed for cutting a three-dimensional part. So this article will talk about the five-axis motion systems currently on the market and their pros and cons. 

Waterjet cutting, especially with abrasive, became popular in the 90s of last century. Back then, almost all the waterjet cutting machines were only two or three axes machines. They were used for material blanking and floor tile cutting. Precision was not important then. People considered taper errors as an inherent part of waterjet cutting. A five-axis machine was rare, but did exist, for the sole purpose of cutting parts with beveled angles.

With the steady growth of waterjet cutting applications, cutting precision became more and more important. OMAX Corporation took the lead to promote waterjest to the market of precision cutting, by introducing a smart waterjet cutting controller that used a waterjet cutting model for optimization of cutting speeds. As the waterjet technology evolution came to the new century, Flow International Corporation came up with a five-axis waterjet machine that can eliminate taper from waterjet cutting. The combination of these two technologies pushes waterjet cutting to a new height and fosters a rapid growth of the worldwide waterjet cutting market. Since then, many kinds of five-axis waterjet machines have been introduced to the market to satisfy the needs of both cutting parts with large beveled angles and cutting precise parts without taper. Today, the five-axis machine has become standard in the waterjet cutting industry.

Almost all the five-axis waterjet machines in today’s market are constructed with orthogonal XYZ axes plus a tilting mechanism. The tilting mechanism includes two tilting axes mounted on the Z axis. The tilting axes are typically labeled with the letter A or B or C. The orthogonal XYZ axes may be designed and built differently, but they all belong to classical motion systems and people arequite familiar with them. Therefore they will be not covered in this article. To help users to understand different five-axis waterjet machines, this article will be focused on different tilting mechanisms on the market.

I will start with the simplest tilting mechanism, “A-B tilting mechanism,” as shown in Figure 1.

This tilting mechanism has two orthogonal tilting axes. The tilting axis parallel to the X axis is labeled with the letter A, and the one parallel to the Y axis with B. The two orthogonal tilting axes intersect at the point labeled as ISP, which is above the tool center point (TCP) with a distance of TCPD.

The advantages of this tilting mechanism include simplicity of its mechanical structure and its consequential low cost. Another advantage is its simple motion algorithm. However, the biggest disadvantage of this tilting mechanism is that the intersection point (ISP) does not coincide with the tool center point (TCP).To prevent the TCP from straying off the cutting path when the cutting head is tilting, compensating XYZ motions are necessary. These compensating motions can be calculated as
follows:
DX = TCPD ∙ sin γ ∙ cos ψ (1)
DY = TCPD ∙ sin γ ∙ sin ψ (2)
DZ = TCPD ∙ (1- cos γ) (3)

For example, assuming TCPD=100 mm, γ=30° and ψ=45°, the values of compensation motions are: DX=DY=35.36 mm, DZ=13.40 mm. When the cutting head comes to a corner or an arc with a small radius on the cutting path, the cutting head should stop momentarily or have only a small amount of movement. However, if tilting is also required, compensation XYZ motions are inevitable and can be large. These compensation motions could cause unnecessary dwell time or slow cutting speed or jerks from unexpected acceleration/decelerations.

Therefore, this type of tilting mechanism is typically used only for applications where tilting angles are small (e.g., under 10°), precision is not important, and low cost is a high priority. Whenever possible, the distance TCPD should be minimized.
Because it is only used in small tilting angles, a coil of high pressure tubing can be used to accommodate the motion of the cutting head, as shown in Figure 1 (page 14). 

From the discussions above, one should realize the importance of having the intersection point (ISP) to coincide with the tool center point (TCP). I will now discuss a tilting mechanism that accomplishes this goal. This tilting mechanism is shown in Figure 2.

From Figure 2, one would notice that the C axis is parallel to the Z axis, and the A axis is on the XZ plane, but not parallel to the X axis. Instead, the A axis has an inclined angle of α measured from the Z axis. In fact, it is not even necessary for the A axis to lie on the XZ plane at the initial posture. It can lie on the YZ plane or any other vertical plane that contains Z axis. Some people call this
type of tilting mechanism the “A-C tilting mechanism.” For the purpose of classification, it is instead named “Ai-C tilting mechanism” (where “i” stands for “inclined”) in this article. Based on the schematic in Figure 2, it is obvious that the intersection point (ISP) coincides with the tool center point (TCP), which is a greaadvantage because compensating XYZ motions are not needed.

In this mechanism, the A axis is independently responsible for the tilting angle γ and the C axis is responsible for the orientation angle of ψ, which also depends on the tilting angle γ. Some people take advantage of this characteristic and make the Aaxis manually driven. As a result, a four-axis motion system is created, which can be used for performing beveled cutting with a fixed tilting angle.

Its motion algorithm is not as simple as that of the “A-B tilting mechanism,” but is still manageable. Its greatest advantage is its capability of tilting a large angle. By rotating the A axis to the lowest position, the maximum tilting angle can be as large as double the inclined angle α. For example, when α=45°, the maximum tilting angle will be 90° (i.e., the cutting head will lie on the horizontal plane at its lowest position). Its greatest disadvantage comes from the fact that, for a given tilting angle γ, the orientation angle ψ completely relies on the rotation of the C axis. After cutting a complete conical surface or any closed contour with beveled angles, the C axis will rotate a full 360°.

To avoid twisting the motor cables, abrasive feeding tubing, air supply tubing, etc., a common practice is to rewind the C axis after a certain amount (e.g., ±360° or ±540°) of rotation. This will increase unproductive time. Furthermore, when cutting a sharp corner on a part with a certain beveled angle, the XYZ and the A axes will stop at the corner until the C axis rotates an angle equal to the included angle of the sharp corner. This will further increase the unproductive time and also cause an overcut at the corner. Even though this can be improved by using some advanced algorithms or by adding a fillet at the corner to avoid a complete stop at the corner, the amount of C axis rotation is inevitable and will reduce productivity to some degree. Because it can be used in large tilting angles, high pressure swivels are used to connect high pressure tubing to accommodate the motion of the cutting head, as shown in Figure 2 (page 16).

To overcome the problems of the previous two tilting mechanisms described, an innovative design was developed [1]. This design features a triple linkage mechanism. For the sake of classification, it is called the “A-B triple linkage tilting mechanism,” as shown in Figure 3.

Among the three linkage arms, two use ball joints and the other one uses universal joints. If all three linkage arms use ball joints,
the cutting head would have extra freedom of twisting. But this unique design uses two perpendicular motor drives as the yokes of the universal joint, which provides constraint for this extra twisting freedom. It is interesting to note that the ISP does not coincide with the TCP either in this tilting mechanism. However, the compensation motions are much smaller than those in the “A-B tilting mechanism.” For example, for a 9° tilting angle, the maximum horizontal compensation motion is about 2 mm [1] (vs. about 11 mm for the “A-B tilting mechanism”). So even though this design does not completely get rid of compensation motions, it does significantly reduce their amounts and it completely avoids the shortcomings of the “Ai-C tilting mechanism” because there is no vertical C axis. Therefore, this design has the highest productivity among these three tilting mechanisms. Its shortcomings come from its complexity. First of all, its motion algorithm is extremely complicated. It requires solving 15 nonlinear equations numerically [1]. Secondarily, its mechanical structure is also very complex, leading to difficulty and high cost
in manufacturing. Thirdly, it is only suitable for small angle (e.g., under 10°) tilting applications. In applications of precision cutting, it is necessary to do error mapping and use software to further compensate for the accumulated errors from part tolerance. Similar to the “A-B tilting mechanism,” a coil of high pressure tubing is used to accommodate the motion of the cutting head [1].

The tilting mechanism is one of the technical areas that receives the most attention for innovation in the waterjet industry. Figure 4  shows yet another innovative design. This design features a horizontal A axis and an inclined B axis, as well as a parallelogram mechanism to transform the A axis motion to the TCP. Therefore, it is named as “A-Bi parallelogram tilting mechanism.”

Even though the ISP of A and B axes does not coincide with the TCP directly, with the transformation of the parallelogram mechanism, a virtual intersection point ISP does coincide with the TCP. Therefore, it completely gets rid of the compensation motions as well as the shortcomings that come with a vertical C axis. There is no rewinding. There is no worry for cable twisting. There is no dwell time at sharp corners or slow motions at small arcs. Its motion efficiency surpasses all other three tilting mechanisms. It also allows a relatively large tilting angle (e.g., 45°). But to accommodate the motion of large angle tilting, four high pressure swivels are used to construct a linkage mechanism, as shown in Figure 4. 

Its greatest shortcoming also comes from its complexity. The complexity of its motion algorithm is second only to the “A-B triple linkage tilting mechanism.” Multi-solutions of nonlinear equations present a great challenge in choosing proper initial trial values during the numerical calculation. The complexity of the mechanical structure creates about the same level of difficulty in machining and cost as that of the “A-B triple linkage tilting mechanism.” Similarly, in applications of precision cutting, it is also necessary to use error mapping and software compensation for the accumulated errors from part tolerance.

Innovations in the waterjet industry recently resulted in the addition of another twist in creating a new tilting mechanism (shown  in Figure 5). With an inclined A axis and an inclined B axis, it is named “Ai-Bi tilting mechanism."

In this tilting mechanism, the coincidence of the ISP with the TCP completely eliminates compensation motions. Because there is no vertical axis, the shortcomings in the “Ai-C tilting mechanism” are avoided. Its productivity is among the highest. Its mechanical structure is also relatively simple. The complexity of its motion algorithm is medium. Its maximum tilting angle depends on the inclined angles of α and β. The angles of α and β are not required to be the same. For example, the tilting mechanism shown in the left side of Figure 5 is with α=30°and β=45°, respectively, and the theoretical maximum conical tilting angle is 22°. Since the tilting mechanism shown in Figure 5 is only used in small tilting angles (within 10°), a coil of high pressure tubing is used. For large tilting angles, high pressure swivels are likely needed.

I have discussed five different tilting mechanisms that are currently used in the waterjet cutting market. For the convenience of comparison, their pros and cons are listed in Table 1 at the end of this article.

 In summary, if you want a low cost tilting mechanism, you can consider the “A-B tilting mechanism.” If you need to cut large beveled angles, you should consider the “Ai-C tilting mechanism.” If you need precision and motion efficiency, avoid these two and consider the other three tilting mechanisms. If you need a balance between large tilting angles and precision, you should consider the “A-Bi parallelogram tilting mechanism.” If you need a balance between simplicity and precision, you should consider the “Ai-Bi tilting mechanism.”

As a disclaimer, these classifications and recommenda-tions are just my personal opinions based on qualitative analysis and they are for your reference only. All waterjet manufacturers have their own considerations and designs of tilting mechanisms that are proper for their circumstance. 

In fact, the performance of a five-axis machine largely depends on the control system that gives it life.

 With advanced algorithms, a five-axis waterjet machine can precisely remove taper and eliminate or reduce unproductive time. Otherwise, its usage may be limited to imprecise beveled cutting. A good design plus proper machining and assembling can make a tilting mechanism with a complex mechanical structure have compactness, precision, convenience in maintenance, and relatively low cost, etc. A poor design, as well as improper machining and assembling, can cause a simple tilting mechanism to be
imprecise, unreliable, and unusable. 

Again the author sincerely welcomes feedback, corrections, and discussions. Feedback can be received at my email address: zengjiyue@lionstek.com. 

■ References:
[1] J. Zeng, J. Olsen, C. Olsen, and B. Guglielmetti, “TAPER-FREE ABRASIVE WATERJET CUTTING WITH A TILTING HEAD”, Proceedings of 2005 WJTA American Waterjet Conference, August 21-23, 2005, Houston, Texas, Paper 7A-2.