3.1.
Introduction
As the aim of this thesis is to develop the stylus system of micro-CMM that consists of dimension in sub-10 µm, the influence factors to develop the stylus at that scale need to be identified. In general, it is a challenging task to scale down styli from the smallest commercially-available dimensions (of the order of 100 µm) to a diameter of 50 µm or less. Many issues which are not relevant at the macro-scale, will be significant at the micro- and nano-scale. Therefore, in this chapter, a set of design rules will be introduced that address the influence factors affecting micro-CMM measurements at micro- and nano-scale. This set of design rules developed for the eventual manufacture of stylus systems with diameters of the order of 10 µm. These influence factors are all interlinked; hence, for a better description of design rules, the influence factors have been divided into five categories. The suggested categories of influence factors are geometrical consideration, forces during measurement, physical condition, material selection, and manufacturing process and technique. This design rules are written in a general way, intended to be universal enough to be a guideline in designing the stylus system for many micro-CMM applications.
3.2.
Geometrical consideration
3.2.1 Background
The selection of geometrical dimensions of the stylus system is crucial in fulfilling an increasing demand for high aspect measurement of miniatures product using micro-CMMs. This is because, a stylus with suitable combination of geometrical dimension of stylus shaft and stylus tip will help to optimise other influence factors such as the stiffness of the stylus, effect of forces and probing speed during measurement and hence the measurement error is expected to be minimum in value. However, selection of geometrical dimension of the stylus also depend on the application of the stylus itself and hence, to an extent, compromises between some influence factors are needed. For instance, to have a high aspect ratio
67 measurement, the effective length of the stylus should be increased. Consequently, the stiffness will be decreased and a larger error in measurement may occur.
In this section, the design rules on stylus shaft and stylus tip dimensions including length and diameter will be identified and explained. Although only few papers discuss the geometrical considerations of stylus system (see chapter 2), it can be understood that these influence factors are unwritten general rules known by researchers. Therefore, the general views on the stylus shaft and tip dimensions and aspect ratio of the stylus will be formalised in section 3.2.2 and 3.2.3. In addition, the mathematical relationship between diameter of stylus shaft and tip, and effective length of stylus will be explained in 3.2.4.
3.2.2 Diameter of Stylus shaft and stylus tip
To start the technical discussion associated with the geometry considerations of the stylus system, the geometrical dimension of the stylus shaft and the stylus tip are the first aspect to be discussed. Based on ISO 10360 [18], the stylus tip is the component of the stylus system that establishes a contact with the measured workpiece while the stylus shaft is the component that connects the stylus tip to the probing sensor. Normally, the design of stylus shaft has two parts, which are the upper part of the stylus shaft and the effective part of the stylus shaft as shown in Figure 3.1. The upper part of the stylus shaft function as a holder of the stylus for connection to the probing system while the effective stylus shaft transmits the position of the stylus tip during measurement to the probing sensor.
The first design rules relate to the diameter of the stylus tip. The diameter of the stylus tip sphere must be smaller than the dimensions of any entrance features of the surface to be measured. Furthermore, the diameter of the stylus tip should be bigger than the diameter of the effective stylus shaft. These two common rules have been implemented by researchers and scientists in terms of design and selection of the stylus system for micro-CMMs. These rules have been mentioned specifically in some literature [32] [5]. As features of workpieces or measured surfaces get smaller, the current stylus systems for micro probes will not be able to measure them. As a result, nowadays, increasing research focuses on shrinking the stylus system for micro probes. Other reason to have smaller diameter of stylus shaft compared to stylus tip is to allow flexibility in the direction of approach relative to the probe body of the stylus tip in measuring the workpiece. In addition, the centre of the stylus tip sphere should
68 be manufactured aligned with the centre axis of the stylus shaft. Alternatively, if this design rule or this condition cannot be achieved, the difference in distance between the centre of the stylus tip and the centre axis of the shaft has to be specified and applied in the measurement.
Figure 3.1: structure of stylus system 3.2.3 Effective length and Aspect ratio
The aspect ratio of the stylus should be higher than the aspect ratio of the features that it is intended to be measured. The maximum aspect ratio of the measured surface needs to be determined before selecting the suitable aspect ratio of the stylus for micro probes. As in Figure 3.2, the aspect ratio is defined as the length divided by the width. Generally, for the stylus system, there are two types of definition of aspect ratio for stylus shaft; effective aspect ratio and mechanical aspect ratio. The effective aspect ratio describes the overall aspect ratio of the stylus that is involved in the measurement. In this case, the effective aspect ratio of the stylus is defined as the effective length of stylus divided by the diameter of the stylus tip. In contrast, the mechanical aspect ratio demonstrates the properties of the stylus shaft. Therefore, the mechanical aspect ratio of the stylus is defined as the effective length divided by the diameter of the stylus shaft. Note also that, for a few designs and applications of the stylus, the aspect ratio is defined by the total length of the stylus rather than effective length of stylus. Thus, the effective length and diameter of the stylus shaft, and the diameter of stylus tip are the important parameters in defining the aspect ratio of the stylus for micro probes. Ideally, the stylus shaft should be as short as possible to increase the stiffness of the stylus [32], hence, avoiding stick slip phenomena in measurement. This means that a low aspect ratio of stylus will be seen as a ‘good’ stylus for general manufacture. However, the demand to measure high aspect ratio of the features conflict with this idea of the good stylus. Thus, there are considerable to produce the stylus that is stiff enough, free from stick slip
Upper shaft Effective shaft
69 problem, and that is able to measure the high aspect ratio of the features on the measured surface. The selection of appropriate effective aspect ratio of stylus is also crucial to avoid collisions between the stylus shaft and the edge of some features of measured workpieces due to the deflection of the stylus during probing. Thus, the determination of the maximum effective aspect ratio of a stylus used in a measurement is influenced by the applied contact forces, the elastic deflection of stylus and the material properties of the stylus tip and the measured workpiece. Therefore, the maximum effective aspect ratio is expected to vary depending on the material of the stylus tip and measured workpiece. Further explanation of the effect of forces and material properties will be described later in section 3.3 and section 3.5.
Figure 3. 2: Aspect ratio of the measured surface and stylus
3.2.4 Relationship between stylus tip diameter, effective length and diameter of stylus shaft
In the previous discussion, the general rules related to the diameter of the stylus tip, diameter and length of the stylus shaft have been reviewed. For the next discussion, the mathematical relationship between diameter of the stylus shaft, length of the stylus shaft and diameter of the stylus tip will be formulated. These derivations draw directly on several well-known theoretical models and so first-principles detail is mostly omitted here. The first equation is based on the Hertz theory of the acceptable probing force [25]. Note that section 3.3.2.1 provides discussion on the practical probing force. This equation is also known as the equation of allowable probing force, has previously been formulated as [26]:
70
𝐹
𝑝= 21
𝜎3 𝑟𝑡2𝐸∗2
(3.1)
Where,
Fp : Allowable probing force,
rt : Radius of stylus tip,
E* : Reduced Young’s modulus, σ : Material’s yield strength
Any bending or other distortion of the stylus shaft during probing, resulting from a probing force, constitutes an error in transmitting the position of the stylus tip to the rest of the probe. So, a second equation is used to define the amount of elastic deformation of the stylus shaft expected under acceptable probing force [2]. Lateral displacement of the free end of the shaft relative the fixed end is the only significant error term and it will be dominated by bending effects for all practicable aspect ratios. Then, using simple elastic deflection beam theory with the assumptions that the stylus shaft is a laterally end-loaded uniform cylindrical cantilever gives: