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geometry, the material properties and the temperature rise in the contact zone Lee and Schaffer developed a model based on the idea that the material shears plastically along a plane to form the chip Their model assumed the material to be ideally plastic, that is, the yield stress did not depend on the strain rate and the strain (no hardening), and elastic stresses and strains were not considered [6] It is important to have knowledge of the forces and power involved in cutting operations for the following reasons [7]: 1 Power requirements have to be determined so that a motor of a suitable capacity can be installed in the machine tool 2 Data on forces are necessary for the proper designing of machine tools for cutting operations that avoid an excessive distortion of the machine elements and maintain the desired tolerances for the machined part 3 The work piece s ability to withstand the cutting forces without any excessive distortion has to be determined in advance The forces acting on the tool in orthogonal cutting are shown in Figure 310 The cutting force, Fc, acts in the direction of the cutting speed, V, and supplies the energy required for cutting The thrust force, Ft, acts in the direction normal to the cutting velocity, that is, perpendicular to the work piece These two forces produce the resultant force, R The resultant force can be resolved into two components on the tool face: a friction force, F, along the tool-chip interface, and normal force, N, perpendicular to it The resultant force is balanced by an equal and opposite force along the shear plane and is resolved into a shear force, Fc, and normal force, Fn The coefficient of friction in metal cutting generally ranges from about 05 to 20, thus indicating that the chip encounters a considerable frictional resistance while climbing up the face of the tool Although the magnitude of the forces in actual cutting operations is generally of the order of a few hundred newtons, the local stresses in the cutting zone and the pressures on the tool are very high because the contact areas are very small A general discussion of the forces acting during metal cutting is presented by using an example of a typical turning operation When a solid bar is turned, there are three forces acting on the cutting tool [3]: Tangential Force This acts in a direction tangential to the revolving workpiece and represents the resistance to the rotation of the workpiece In a normal operation, the tangential force is the highest of the three forces and accounts for about 98% of the total power required by the operation Longitudinal Force This acts in a direction parallel to the axis of the work piece and represents the resistance to the longitudinal feed of the tool The longitudinal force is usually about 50% as great as the tangential force As the feed velocity is usually very low in relation to the velocity of the rotating workpiece, the longitudinal force accounts for only about 1% of the total power required.

i =1

(17.4)

Evaluating the thermal via resistance as a function of trace plating variability, a 0.015 mm thick plated via with the same dimensions as the preceding will have a thermal resistance of 73 C/W. Thus, the thermal performance of a PCB is sensitive to variations in the plating thickness of its thermal vias. To ensure thermal via performance, the plating thickness in the via should be checked. This is usually performed by parallel polishing down from the surface of the PCB rather than through a cross-sectional polishing of the via. When cross-sectioning a via, if sectioning plane does not intersect the exact center of the via, an incorrect plating thickness will be measured; this problem does not occur when parallel polishing into the depth of the PCB.

I measured the current consumption of the device when in use and when the device was put in powered-down sleep mode.

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Component Spacing on the PCB There is a finite spreading thermal resistance to any PCB as a function of its thickness and the number of planes in the PCB. Eq. 17.5 is a simple equation to calculate the in-plane thermal conductivity of a PCB as a function of the spreading plane thicknesses versus the FR-4 material layers. For example, if a 1.57 mm thick FR-4 board has a single solid thermal spreading plane that is 0.036 mm thick, the effective in-plane thermal conductivity of the plane is 8.9 W/m- C. This is substantially lower than the thermal conductivity of pure Cu, which is 386 W/m- C. Therefore, thermal spreading through the PCB with a single plane will be worse than thermal spreading through a plate of Cu with the same thickness as the PCB. keffective = ki ti

Radial Force This acts in a radial direction from the centerline of the work piece and is generally the smallest of the three, often about 50% as large as the longitudinal force Its effect on power requirements is very small because the velocity in the radial direction is negligible g = rake angle = a f = shear plane angle

(17.5)

keffective = the PCB s effective in-plane thermal conductivity ki = the thermal conductivity of the ith layer ti = the thickness of the ith layer

The net effect of the limited spreading resistance of a PCB is that component temperatures will rise as they are clustered more tightly on a PCB of a given size and construction. For example, Table 17.2 shows the maximum component temperature of four small devices on a

TABLE 17.2 Case Example of Component Temperature versus PCB Spacing Component spacing (mm) 50 25 12.5 8 Maximum temperature ( C) 81.6 84.4 92.9 98.4

Fig 311: The shear plane in metal cutting [2]

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