Forces during
Scanning
Surface
interaction force
Bending Force
Maximum safe tip
73 3.3.2 Force during single point probing
Force exerted during the cycle of single point probing can be categorised according to several phenomena as illustrated in Figure 3.4. As a touch triggering probe [104] [105][106] is a common and widely used in conventional CMM, it is a good example to explain the overview of force during single point probing. Nevertheless, as the type and operation of the sensor mechanism varies among current available probing system in the market, some of the forces described for touch trigger probe, may not occurduring particular examples of single point probing.
Figure 3.5 is graph of a behaviour of force applied to a touch trigger probe and a behaviour of the velocity of the CMM, which both behaviours observed against time during process of approach, contact and retract cycle of single point probing. It shows that the Impact force occurs at time t1 when the stylus tip first contacts the surface. After the first
contact with the surface, the tip will bounce several times before the contract is registered and a signal is sent to the micro-CMM controller after time t2. To prevent macroscopic plastic
deformation between probe tip and the surface, the velocity during second and subsequent collisions must be smaller than first contacts. This impact force has a strong relationship with the probing speed, the effective mass at the probe tip and material properties of the stylus system [107][21].
74 Overtravel force occurs after initial contact at time t1 until the time t3 where the probe
has stopped moving toward the surface [107]. This force occurs due to the stiffness at stylus tip (later, the detail of stiffness will be explained in section 3.4.4). In Figure 3.5, notice that there are overlapping regions between overtravel force and impact force between time t1 and t2.
The effect of surface tension from adsorbed films should also be considered during probing. Thus, a surface interaction force should be added to the probing force. There are four major types of surface interaction force: the Van der Waals force; the Casimir force; the electrostatic force; and the hydrostatic force. The effect of this surface force during measurement is very significant in micro scale measurement. The surface interaction force depends on the environmental condition such as temperature and humidity [21].
3.3.2.1. Allowable Probing force
The forces exerted during single point probing is often known as probing force or, in some literature, contact force. It could consist of one or a combination of impact force, overtravel force and surface interaction forces. It might also involve other force which is not specified above, such as a triggering force (depending on the type and sensor mechanism of the probe). In the majority of the research conducted in this field, the value of the probing force is one of the main parameters that has been reported. This is because an excessive probing force will cause damage to the surface of the stylus tip or measured workpiece.
Clearly, with the development of stylus tips for micro-CMMs having sub-micrometres scale, the probing forces need to be reduced in order to prevent plastic deformation either on the surface of the stylus tip or the measured workpiece. However, there are arguments about the value of probing force that should be applied without damaging the stylus tip or the surface of test workpiece. Generally, Dai [29] states that the value probing force should be in order of micro-newton. Leach et al [32]has suggested that probing force should be less than 0.1 mN, while Liebrich [30] stated that the maximum value of probing force is 0.2 mN. Fan [108] also suggests that the probing force should be less than 1 mN. In contrast, the existing styli of micro-CMMs have various values of probing force. For instance, probing force for the METAS stylus system is less than 0.5 mN, for the NPL capacitive stylus system is 0.1 mN, and for the TUE/Gannen stylus system is less than 0.4 mN. All of these three stylus
75 systems use a stylus tip greater than 100 Β΅m in diameter. For stylus systems with stylus tip diameter less than 100 Β΅m such as PTB/Werth fiber Probe and Mitotuyo UMAP stylus system, the value of probing force is recorded in the micronewtons range. This wide variation in the design values of the probing force can be understood in practical term. In order to avoid damaging on either surface, the selection of probing force depends on the material properties, the radius of the stylus tip itself and the compliance of the probe system.
To estimate the appropriate probing force to be applied in a measurement, a theoretical value which is called the allowable probing force is introduced. The allowable probing is defined (using ideas from Hertz contact theory) as the force where the shear stress at a point somewhat below the surface exceeds a critical value and plastic deformation starts[22][26]. It can be calculated using equation (3.1) from section 3.2.4 [26]. However, this definition is difficult to measure in practised, and therefore, it is used only as a theoretical guideline in the selection of the suitable force applied to a measurement. Alongside this theoretical definition is exerted force, the combination values of all components of probing forces, which should not exceed the value of allowable probing force as calculated in the equation (3.1). This is because, with the consideration of the material properties and the requirements of the stylus tip diameter in this equation, calculated value of allowable probing force is expected to be the maximum force that can be applied in order for the stylus to operate in the elastic region (or the stresses occurring during contacting process do not exceed the plastic deformation condition of both surfaces). The detailed explanation of the relationship of material properties with allowable probing force will be described in section 3.5.
3.3.2.2. Impact force
In single point probing, introduced in section 3.3.2, impact force is the first force that occurs when the stylus tip contacts the surface under test. This impact force has been discussed in detail by Pril [22], Meli [26] and Bos [21][107]. The impact force has been recognised as a force resulting from the almost instantaneous stopping of the tip (while the probe continues to have some forward velocity) and the effective mass of the probe at the point of contact. The effective mass in this scope covers the net effect at the tip of all the masses and moments of inertia of the probing systems that are involved in accelerating the
76 probe tip including any components attached to it [22][107]. The impact force has been expressed [21][22][26] :
πΉ
πππ= β
125 36π
π‘ 3βπ£
6πΈ
ππππ
π‘ 5(3.6) With, 1 πΈπππ
=
1βπ£12 πΈ1+
1βπ£22 πΈ2(3.7) Where,
Fimp : Impact force
mt : Effective Mass at stylus tip
βv : Stylus speed
rt : Radius of stylus tip
Ered : Reduced Youngβs modulus
E1 : Youngβs modulus for material of stylus tip sphere
E2 : Youngβs modulus for material of measured surface v1 : Poison ratio of material for material of stylus tip sphere
v2 : Poison ratio for material of measured surface
According to the relationship in equation (3.6), the impact force is greatly influenced by the mass of the stylus, the stylus speed, material properties and diameter of the stylus tip. In developing the smaller stylus, the impact force needs to be reduced to prevent plastic deformation during probing. Hence the mass of the stylus and the stylus speed also need to be reduced. Nevertheless, the mass of the stylus and the stylus speed are the two parameters which are not directly proportional to each other. These parameters and the relationship between them will be discussed in detail in section 3.4.2.
3.3.2.3. Overtravel force
As briefly described in section 3.3.2, overtravel force occur after an initial contact between the stylus tip and the measured surface. Once a small, pre-set deflection of the stylus has been registered to the probing system to trigger the position measurement, the micro CMM will be instructed to stop, but the micro CMM, and so the probe body, needs some travel distance to decelerate before it can come to a complete stop. This travel distance is called overtravel distance and causes the overtravel force. The overtravel force is resulted from overtravel distance and the effective stiffness at the stylus tip. Assuming, reasonably,
77 that the effective stiffness is constant over the distances involved, the overtravel force is [22][107]
πΉ
ππ£π‘= πΆ
π‘π₯
ππ£π‘(3.8)
Where,
Ct : Effective stiffness at stylus tip
xovt : overtravel distance
The overtravel distance, mainly depends on the movement parameters of the micro- CMM and its probing system. Because the overtravel distance is defined as the distance travelled by the stylus tip from initial contact until the micro-CMM has finished decelerating, an assumption that the machine acceleration is approximately constant allows it to be expressed simply as [22]: