Fixture Design

The fixture design used for the research is described in this section. The focus of the research was on the management of these fixtures in the production system, and not on the fixture design itself. The fixture design provided a conceptual platform upon which the research could be implemented and tested.

Modularity has proven to be a successful method of practical implementation for mass customisation;

as suggested by Gershenson et al. [20] and Fogliatto et al. [2] with respect to parts; and Bi and Zhang [4] with respect to fixtures. This is true for cellular manufacturing systems, where reconfigurable modular fixtures can be designed for flexibility within a part family, producing fixtures with greater effectiveness for the particular task [36]. Thus, a modular fixture design was chosen for use in the research.

A grid hole base plate with dowel pin modules was the selected design; similar to those displayed in Figure 2.3 and Figure 2.4. The base plate comprised of a square block of dimensions 200 mm×200 mm×16 mm; with an 8×8 array of through holes, each 10 mm in diameter. Dowel pins of diameter 10 mm and length 40 mm were used as modules. Pin configurations were assembled upon the base plate by inserting the dowel pins into the base plate array in an arrangement that was appropriate

33 for securing the part. Figure 3.2 shows the pin configuration required to secure a large, triangular part.

Figure 3.3, thereafter, shows how this part would fit within the pin configuration.

Figure 3.2: Pin configuration for large triangle part (isometric view)

Figure 3.3: Large triangle part on fixture (isometric view)

The force applied by the tool in an end milling process can be calculated by Equation 3.1 [92]:

𝑇 = 0.05𝐾_𝑑𝐹_𝑓𝐹_𝑇𝐵𝑊 + 0.007𝐾_𝑑𝐷²𝐽𝑊 (3.1) Where:

T = thrust (N)

Kd = work material factor, based on material hardness (BHN) Ff = feed factor, based on feed (mm/rev)

FT = thrust factor, based on drill diameter (mm)

B = chisel edge factor for thrust, based on chisel edge to drill diameter ratio W = tool wear factor, based on operation type

D = drill diameter (mm)

J = chisel edge factor thrust other, based on chisel edge to drill diameter ratio

A sample calculation was performed to investigate the force caused by an end milling process with 2.4 mm diameter drill bit, operated at a feed rate of 0.05 mm/rev on aluminium alloy material. The calculation is shown in Equation 3.2, with parameters obtained from tables in [92]:

Pin Module Base plate

Unfinished Part

34 𝑇 = 0.05(7000)(0.091)(2.02)(1.235)(1.1) + 0.007(7000)(2.4)²(0.01)(1.1)

(3.2) 𝑇 = 90.51 𝑁

Equation 3.1 shows the thrust to be proportional to the diameter of the drill bit. A drill bit size of 2.4 mm for the engraver yielded a force of 90.51 N, which was deemed acceptable for the fixture design upon examination. The decreased drill bit size of engravers would also yield reduced vibrations in comparison to larger drill bits more commonly used for end milling processes (> 10 mm) [93]. The pin configuration, thus, prevented rotation and translation of the part in the X-Y plane. The design was deemed sufficient for the engraving process that the plaque would undergo.

The fixture design was limited by the resolution of the base plate array. The 8×8 dimensions of the array was arbitrarily selected, estimated from past designs [3], [4], [11]. The use of custom modules could have improved the resolution limitation of the base plate array. It was decided that pin modules would be used instead, for the purpose of simplifying the quantification of pin configuration comparisons for the scheduling method (Section 6.7). Despite the practical limitations of the fixture design, the base plate array could theoretically accommodate a total of 2⁶⁴ unique pin configurations. Several of these pin configurations would be unusable in practice (such as those with one pin, or those with 64 pins).

The research considered pin configurations within the range of 8 – 16 pins per configuration. Only four pins were required to prevent rotation and translation in the X-Y plane for most shapes. The range of 8 – 16 pins was selected by testing observations of various arbitrarily-shaped parts upon a template of the base plate array; it was concluded that no more than 16 pins would be required to properly secure almost any part shape from translation or rotation in the X-Y plane. The exception to this conclusion was the circle shape, where prevention of rotation was independent of the number of pin modules used for its configuration. This special case required an interference fit with the dowel pin modules to prevent rotation via friction with the dowel pin module circumference.

The number of available pin configurations were calculated from the summation of the associated binomial coefficients, as shown in Equation (3.3).

𝐶 = ∑ 𝑛!

𝑘! (𝑛 − 𝑘)!

𝑏

𝑘=𝑎

(3.3) Where:

C = total number of unique pin configurations n = total number of holes

k = number of pins evaluated a = minimum number of pins used b = maximum number of pins used

The total number of usable unique pin configurations available was calculated to be 7.1325×10¹⁴ — a very high number. While full customisability would theoretically mean an infinite number of possible configurations, the customisability of the fixture design was deemed sufficiently high for the purposes required for the research implementation.

The fixture design fulfilled the Physical and Affordability requirements (see Section 2.3). The Tolerance and Constraint requirements were fulfilled for the pin configurations that satisfied the

35 practical customisability afforded by the base plate array. The other fixture design requirements (Usability and Collision Prevention) are beneficial to the robust operation of the fixture, which was beyond the scope of the research.

Table 3.1: Fixture specifications

Parameter Value

Fixture type description Modular grid hole base plate design with dowel pin modules

Base plate dimensions 200 m×200 mm×16 mm square plate

Base plate array dimensions 8×8 holes (64 holes total);

10 mm diameter through holes Dowel pin module dimensions 40 mm height×10 m diameter Theoretical customisability of fixture 2⁶⁴ unique pin configurations Pin range selected for research implementation 8 – 16 pins per configuration

Practical customisability of fixture 7.1325×10¹⁴ unique pin configurations