Five main categories of influence factors in developing styli for micro-CMM with dimension below 100 µm have been discussed. These influence factors are important measurement performance and must be considered carefully, especially in micro- and nano-scale work. This is because, many factors, which are not relevant at the macro-scale, will become significant at the micro- and nano-scale. For example, low contacting forces during micro-CMM measurement are often desirable to ensure no significant surface damage occurs. However, a low force probing introduces susceptibility to surface interaction forces, such as surface tension from adsorbed water layers, resulting in surface stiction effects both parallel and normal to the surface and consequently in reduced measurement consistency. In addition, other parameters such as the stiffness of the stylus shaft and form error of stylus tip which are not necessarily so significant in macro scale measurement, will always be important factors to be determined in the micro and nanoscale. As discussed earlier, in micro-scale measurement, the stiffness plays important roles not only in determining the sensitivity of the measurement and minimising the stick slip error during scanning, it also critical in selecting the appropriate probing speed of the micro CMM. The form error of the stylus tip needs to be small or to be determined (ideally, both) in order to minimise the systematic errors.
102 As mentioned earlier, all of these main categories of influence factors are interrelated. A new, wide-ranging set of design rules has been developed here from the main influence factors. Some of these design rules are general and qualitative rules while some can be quantitatively modelled. For instance, the relationship between the geometrical dimensions of the stylus, allowable probing force, surface interaction force, elastic deformation and stiffness of stylus shaft can be calculated and estimated using specific equations. However, the best values for factors such as stylus speed, surface form for the stylus tip and abrasive wear characteristics at the stylus tip could not be determined by a specific mathematical equation, depending in too complex ways on the other influence factors. Furthermore, maximum safe tip force and control parameter in manufacturing process can be determined practically during experiments prior to setting up ‘routine’ measurements.
In the detail investigation, the effects of forces are the main critical factors influencing the design of a new stylus with a dimension less than 100 µm. In summary, besides introducing a measurement error, the ultimate effect of forces in measurement could damage the surface of the workpiece and stylus tip sphere. Also, the stylus shaft might be broken, or its excessive bending might cause collision between the stylus shaft and the measured workpiece. Therefore, to avoid these conditions, the ideas of allowable probing force and maximum safe tip force are introduced to be limiting factors in selecting an appropriate applied contact force in measurement. These two forces are different in nature. The allowable probing force concerns the interaction between stylus tip sphere and the measured workpiece, whereas the maximum safe tip force concerns the (bending) strength of the stylus shaft under a certain applied force. Whilst the value of the maximum safe tip force of any stylus is expected to be constant, the material properties of the stylus tip and measured workpiece are the limiting factors of the allowable probing force, as discussed in section 3.5. This means that the value of the allowable probing forces varies depending on the measurement tasks. Therefore, it is crucial for a maximum safe tip force to be known for a particular situation, because it will be a limiting factor in selecting a working range of allowable probing force, and, hence, in designing the measurement task. This is based on the practical assumption that the value of maximum safe tip force should be higher than allowable probing force as described in section 3.3.4. In addition, the value of maximum safe tip force is difficult to estimate from theoretical equations.
103 Allowable probing force is also used in formulating the relationship between the diameter of the stylus tip, effective length and diameter of the stylus shaft, as illustrated in equation (3.5) in section 3.2.4. From this equation (3.5), a suitable diameter of the stylus tip can be calculated from the input parameter of the effective length and diameter of the stylus shaft. In addition, this equation can also be altered to determine the appropriate diameter of the stylus shaft. Also, this equation is intended to be a guideline in determining the geometry of the styli as the result of this equation will be used to define the maximum values of their dimensions. The solution of this equation is quadratic and more than one value is expected from it. As long as the values from these equations obey the design rule (ii) in section 3.2.5, they can be used in the estimation of the dimensions of the geometry for styli.
Equation (3.5) is also indirectly demonstrates the relationship between the maximum effective aspect ratio with the allowable probing force, elastic deflection of the stylus and the material selection of the measured workpiece and stylus tip sphere. As this equation only considered the condition where the maximum elastic deflection is equal to or less than the allowable stylus deflection, only an input value of effective length that obey this condition will give result value of diameter of stylus tip or stylus shaft. Otherwise the output value will contradict with design rule (ii) in section 3.2.5. Therefore, the maximum effective aspect ratio can be predicted through this equation when the maximum stylus deflection is equal to allowable stylus deflection. Moreover, since the material properties of both stylus tip and measured workpiece are considered in formulating the allowable probing force (which is used in the calculation of maximum stylus deflection), the maximum effective aspect ratio also depends on both materials. Hence, the maximum effective aspect ratio will be different when a different material is selected as a measured workpiece or stylus tip. Nevertheless, when using a stylus which have effective aspect ratio that does not satisfy equation (3.5) and hence, in theory, not obey the design rule (xiii) in section 3.3.5, other influence factors should be considered. For instance, during actual measurement, the deflection of the stylus must be ensured not to exceed the allowable stylus deflection and the applied force imparted on the stylus should be monitored below the allowable probing force. Furthermore, the approach probing speed also needs to be carefully selected, so that the impact and overtravel forces can be minimised.
104 As the intention of this project is to develop micro-styli with dimensions in the sub-10 µm range, the sum of forces exerted to the styli has to be a small value. To reduce this sum of forces, the stiffness at the region of contact (in the metrology loop), mass and speed of the probe should also be reduced. However, several challenges will arise. By reducing this stiffness, the stick slip effects during scanning will be increased, which can also cause a probing error. Moreover, when the dimension of the styli is in the micro-scale range, the sum of the surface interaction forces is larger compared to gravitational forces, which might cause a similar measurement error to the stick slip phenomena. Therefore, the surface interaction forces need to be investigated in detail. In contrast, as discussed in section 3.4.2, in order to reduce the impact forces, the effective mass of the probing system is inversely proportional toward its speed and therefore, both of them cannot be reduced at the same time. Another challenge is to fulfil the current demand in producing the high aspect ratio micro-styli with dimensions in sub-10 µm region. This is because the stiffness of the stylus shaft should be higher than the stiffness at the probing sensor in order to increase the sensitivity of measurement and resistance towards bending of the stylus. A higher stiffness of the stylus shaft can be achieved by reducing its aspect ratio.
Another key fact to remember is that some of the parameters in the design rules can only be examined when the styli are attached to their probing systems. These include the probing force, impact and overtravel force, stylus speed and stick slip effect during scanning. In contrast, some parameters can be examined on the styli itself without paying any direct attention to the probing system. For instance, the form error of the stylus tip, the stiffness of stylus shaft, control parameters of the manufacturing process and the maximum safe tip force are some of the parameters in this category.
In this chapter, the discussion on the influence factors that lead to the design rules for new stylus systems are based on the general functions expected of stylus systems for tactile probing with micro-CMMs. For a specifically functionalised type of stylus, such as vibration styli in which a stylus is vibrating during measurement, other specific influence factors related to its specific function (for example, its natural frequency) need to be considered.
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