**8. Hole bottom-chamfer error: description and possible correction**

The hole-drilling method is based on the theoretical assumption that the drilled hole is perfectly cylindrical at any drilling increment. Perfect cylindrical holes are used in finite element models, by various authors, for the determination of the calibration coefficients.

The ASTM standard makes some recommendations regarding the geometry of the end mill in relation to both the radial clearance angles of the cutting edges on the end face of the cutting tool (<1°) and the taper angle (<5°). These requirements were introduced by the standard in order to avoid any ambiguity in determination of the depth and measurement of the hole diameter.

Unfortunately, the carbide inverted-cone end mills used for performing the hole-drilling measurements could have a small chamfer at their cutting extremities that generates a small chamfer in the bottom of the hole (**Figure 8**). This small chamfered extremity of the end mill reduces wear and facilitates chip ejection during drilling.

This chamfer influences the strain signals and consequently the calculation of residual stresses. The effect of the hole bottom chamfer has a higher impact on the first depth increments where the chamfer of the end mill generates a hole with a smaller diameter than the nominal diameter. Furthermore, in the case of nonuniform stress distribution, the geometric variation in the hole shape in the first depth increments determines errors not only in the first calculation depths but also in successive calculation depths.

In order to reduce the effect of the hole-bottom chamfer, it is advisable to use a type of cutter with the smallest chamfer available or use the high-speed orbital drilling technique. The method is based on the orbital movement of the end mill as it advances. While producing the same diameter as a center-drilled hole, this technique employs an end mill with a smaller diameter and consequently creates a smaller bottom chamfer.

If the above is not possible, it is necessary to correct the errors generated by the presence of the chamfer.

A first solution for this correction was proposed by Scafidi et al. [17] carrying out an analysis based on the Boundary Element Method. By introducing the gage circle diameter, the drilled hole diameter and the bottom-hole fillet radius, the authors developed a method based on the correction of acquired strains. Subsequently,

#### **Figure 8.**

*(a) Section of a drilled hole with a hole-bottom chamfer, (b) Typical carbide inverted-cone end mill used for the hole drilling method.*

*Recent Advancements in the Hole-Drilling Strain-Gage Method for Determining Residual Stresses DOI: http://dx.doi.org/10.5772/intechopen.90392*

Blödorn et al. [19] recalculated the ASTM E837 coefficient for blind uniform stress using an FEM model with a hole bottom chamfer.

More recently, the generalized integral method based on the influence functions [8, 9] has been enriched with a new database of displacements, which considers the chamfer as a new geometrical parameter of the finite element model.

For a certain value of the ratio between the height of the hole chamfer and the radius of the drilled hole, this methodology allows the correction of calculated stress for blind holes and non-uniform stress distributions.

**Figure 9** shows the finite element model in which the hole bottom chamfer was simulated to evaluate its influence.

The presence of the hole-bottom chamfer influences the calculation of the stresses.

**Figure 10** gives an example of the influence of a hole bottom chamfer on the reconstruction of a pure shear stress distribution. In the first part of the depth of the analysis, it is clearly seen that the chamfer determines an under-estimation of the actual stress, especially in the first depth increments. On the contrary, in the second part of the depth of the analysis, the results show an over-estimation of the calculated stresses.

#### **Figure 9.**

based on 5 different thicknesses (2.7 D, 1.0 D, 0.6 D, 0.3 D, 0.2 D); once the thickness is defined, the displacements are interpolated between the two closest

**8. Hole bottom-chamfer error: description and possible correction**

The hole-drilling method is based on the theoretical assumption that the drilled hole is perfectly cylindrical at any drilling increment. Perfect cylindrical holes are used in finite element models, by various authors, for the determination of the

The ASTM standard makes some recommendations regarding the geometry of the end mill in relation to both the radial clearance angles of the cutting edges on the end face of the cutting tool (<1°) and the taper angle (<5°). These requirements were introduced by the standard in order to avoid any ambiguity in determination

Unfortunately, the carbide inverted-cone end mills used for performing the hole-drilling measurements could have a small chamfer at their cutting extremities that generates a small chamfer in the bottom of the hole (**Figure 8**). This small chamfered extremity of the end mill reduces wear and facilitates chip ejection

This chamfer influences the strain signals and consequently the calculation of residual stresses. The effect of the hole bottom chamfer has a higher impact on the first depth increments where the chamfer of the end mill generates a hole with a smaller diameter than the nominal diameter. Furthermore, in the case of nonuniform stress distribution, the geometric variation in the hole shape in the first depth increments determines errors not only in the first calculation depths but also

In order to reduce the effect of the hole-bottom chamfer, it is advisable to use a type of cutter with the smallest chamfer available or use the high-speed orbital drilling technique. The method is based on the orbital movement of the end mill as it advances. While producing the same diameter as a center-drilled hole, this technique employs an end mill with a smaller diameter and consequently creates a

If the above is not possible, it is necessary to correct the errors generated by the

A first solution for this correction was proposed by Scafidi et al. [17] carrying out an analysis based on the Boundary Element Method. By introducing the gage circle diameter, the drilled hole diameter and the bottom-hole fillet radius, the authors developed a method based on the correction of acquired strains. Subsequently,

*(a) Section of a drilled hole with a hole-bottom chamfer, (b) Typical carbide inverted-cone end mill used for*

available thickness values.

calibration coefficients.

during drilling.

in successive calculation depths.

smaller bottom chamfer.

presence of the chamfer.

**Figure 8.**

**70**

*the hole drilling method.*

of the depth and measurement of the hole diameter.

*New Challenges in Residual Stress Measurements and Evaluation*

*Finite Element Model used for the evaluation of the calibration coefficients considering the presence of the hole-bottom chamfer.*

*Residual stresses in the case of pure shear stress, with (dashed line) and without (solid line) the hole-bottom chamfer.*
