## Case Study: Machine distortion modeling

We’ve recently uploaded a new case study on the topic of part distortion caused by machining. Distortion is a significant problem faced by many industries, especially where rigorous dimensional tolerances are required. When not appropriately accounted for, distortion can lead to significant economic loss and should be managed for effective design and production. Continue reading Case Study: Machine distortion modeling

## Machining distortion modeling

Part distortion during machining is a significant problem in many industries, particularly where rigorous dimensional tolerances are required. Distortion of finished parts can lead to significant economic loss and should be managed for effective design and production. This case study demonstrates some of the basic concepts related to the impact of residual stress on part distortion during machining. A representative problem is defined, and a model is used to estimate part distortion due to machining of raw material containing bulk residual stress.

This study considers a 304.8 x 203.2 x 12.7 mm (12.0 x 8.0 x 0.5 inch) aluminum plate as the starting raw material for the analysis. From the plate an example part will be machined that has the same in-plane dimensions as the starting plate (304.8 mm x 203.2 mm) and includes a 2.54 mm (0.1 inch) thick frame around a 2.54 mm (0.1 inch) thick web.

Raw plate and final part geometry. Non-bracketed dimensions are in inches and bracketed dimensions are in mm.

Aluminum plate is often stress relieved by stretching, and typically exhibits low levels of residual stress post-stress relief. For the sake of this analysis, the raw material is assumed to have the residual stress distribution shown in Figure 2a (similar to the residual stress measured by Prime and Hill [1]). The residual stress values are low compared to the yield strength of the material, ranging from about -20 to 20 MPa (-3 to 3 ksi).

In addition to the bulk residual stress present in the raw material, the machining process also induces stress. The machining-induced residual stress assumed for this demonstration is shown in Figure 2b, and exhibits a typical distribution with compressive residual stress near the machined surface that spans over a thin layer (0.2 mm) before it reaches magnitudes near zero. The peak compressive residual stress at the machined surface is -50 MPa (~ 7.3 ksi). The bulk residual stress in Figure 2a is assumed to be present in the raw plate for the analysis, while the machining-induced residual stress in Figure 2b is applied locally to the machined surfaces.

(a) Bulk residual stress (similar to [1] along rolling and transverse direction, (b) idealized machining induced residual stress

A finite element model including the bulk and machining-induced residual stresses was used to predict the distortion of the finished part. The model is elastic and superposes bulk and machining residual stress to provide an equilibrium solution. Figure 3a shows the deformed shape (using a magnification factor of 30 to better illustrate the deformation). The displacement pattern shows bowing of the finished part with respect to its intended shape, with positive displacements near the center. A 2D map of the displacement of the bottom surface of the finished part is shown in Figure 3b. Line plots along the x direction at y = 101.6 mm and along the y direction at x = 152.4 mm are shown in Figure 3c. The distortion range is approximately 1.4 mm. It is important to note that even though the bulk residual stress in the raw material is low (about 5% of the yield strength), it still has potential to cause significant distortion in finished parts, as illustrated here.

(a) Undeformed/deformed 3D shape of final part with zoffset = 0, (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top

Since the raw plate is thicker than the final part, the final part can be extracted from different positions through the thickness of the raw plate (e.g., Figure 4). The position from within the raw plate that the final part is removed from can have a significant impact on the distortion (due to the different bulk residual stress levels at different locations through the thickness). The position is defined by an offset distance from the bottom surface of the raw plate, zoffset. In the first example, the zoffset = 0, i.e., the bottom surface of the final part is aligned with the bottom surface of the raw plate (z = 0).

Location of machining of baseline/final part within the raw plate

The model used here can be modified to consider different part placements within the raw material in a straightforward manner. A significantly different result was obtained considering zoffset = 2.54 mm (0.1inch), which is shown in Figure 5. An opposite pattern of distortion is observed in Figure 5a compared to the case where zoffset = 0 (Figure 3a). The 2D map shown in Figure 5b shows displacements that range from 1.1 mm to -0.6 mm. Figure 5c shows the displacement along the left-right and bottom-top paths, and includes the results obtained with zoffset = 0 for comparison. Compared to zoffset = 0, zoffset = 2.54 mm exhibits displacement along the x direction that ranges from positive-negative-positive values and with higher magnitudes. The displacement along the y direction is similar for both offsets, but have opposite signs.

(a) Undeformed/deformed 3D shape of final part with zoffset = 2.54 mm (0.1inch), (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top comparing zoffset = 0 and 2.54 mm

Another aspect that influences the part distortion is the thickness of the web of the large pocket. The previous results considered a thickness of 2.54 mm (0.1inch), as illustrated in the final part drawing in Figure 1. Reducing the thickness to 0.635 mm (0.025inch) and considering the zoffset = 0 configuration causes significant changes in the results, as observed in Figure 6. A similar pattern of distortion is observed in Figure 6a and Figure 6b compared to Figure 3a and Figure 3b, however the magnitudes of displacement are significantly lower. A line plot comparing the results obtained with both thicknesses is shown in Figure 6c. Overall, the model with reduced thickness (red lines) provides lower displacement magnitudes along both paths (left-right and bottom-top) compared to the initial model with 2.54 mm thickness, and exhibits peak displacement that is lower by about 50%.

(a) Undeformed/deformed 3D shape of final part with zoffset = 0, (b) 2D map of leveled displacement of bottom surface, (c) line plots along paths from left-right and bottom-top comparing thickness = 0.635 mm (0.025inch) and 2.54 mm (0.1inch)

This case study provided an example problem for the estimation of part distortion due to residual stress release from machining, considering a typical bulk residual stress distribution and machining-induced residual stress distribution. The results show significant part distortion, even though the considered bulk residual stress had very low magnitude compared to the yield strength of the material. The results also show that part distortion varies significantly depending on the machining location within the raw stock material.

For more information concerning this case study or any of the residual stress measurement techniques employed at Hill Engineering, feel free to contact us.

[1] M. B. Prime and M. R. Hill, “Residual stress, stress relief, and inhomogeneity in aluminum plate,” Scripta Materialia, pp. 77-82, 2002.

## Hill Engineering introduces ExpressRS

 For materials engineers, designers, and managers seeking residual stress measurements, Hill Engineering is a trusted source for a broad range of best-in-class measurement capabilities. But while we always strive to deliver quality results in a timely manner, sometimes a job requires a faster than normal turn-around. This is why we’ve introduced ExpressRSTM, a service geared toward expedited delivery of residual stress measurement results. Continue reading Hill Engineering introduces ExpressRS

## Case Study Highlight: 3D Scanner

Hill Engineering recently installed a Nikon ModelMaker H120 3D scanner, which is proving to be very useful in our laboratory. In addition to scanning services we now offer to outside parties, we’ve also implemented this technology into our residual stress measurement processes. This new capability allows us to produce faster, more accurate results than ever before. Continue reading Case Study Highlight: 3D Scanner

## 3D Scanning

3D scanners are powerful tools with many applications ranging from dimensional inspection to reverse engineering. Typically, 3D scanners are used to create a 3D representation of the geometry of a complex part. Initially the part geometry may be represented by thousands or millions of individual points. These points can then be used to reconstruct a model of the part.

Many of our projects at Hill Engineering benefit from 3D scanning technology. In addition, Hill Engineering offers 3D scanning services for others on a fee-for-service basis. Some typical applications that require the use of a 3D scanner include:

• Quality assurance inspection: checking the geometry of manufactured parts to ensure consistency with drawing requirements
• Reverse engineering: generating a CAD model of a physical object for use in future design or manufacturing
• Machining distortion: evaluating the effects of different machining and manufacturing processes on the final machined shape of parts
• Engineered residual stress: evaluating the effects of residual stress surface treatments on the deformation of parts

At Hill Engineering we use a Nikon ModelMaker H120 3D scanner. The cutting-edge ModelMaker H120 incorporates blue laser technology, ultra-fast frame rate, specially developed Nikon optics and the ability to measure the most challenging materials. The following is a summary of the system specifications:
• Measuring range: 78.75 inches (2.0 m)
• Measurement accuracy: 0.0011 inches (0.028 mm)
• Minimum resolution: 0.0014 inches (0.035 mm)

Figure 1 – Photograph of Nikon ModelMaker H120 scanning a case

The illustrations below show example 3D scans that illustrate the capability of the Nikon ModelMaker H120 3D scanner. The first example shows an image taken from a 3D scan of a cordless drill. The second example shows a comparison between a scan of a new computer mouse and a used computer mouse. The colors show the regions of wear from continued use (red is worn).

Figure 2 – Illustration of a 3D scan of a cordless drill

Figure 3 – Comparison between a 3D scan of a new mouse and a used mouse showing regions of wear

Inspecting your parts using state-of-the-art 3D laser scanners provides the geometric insight needed to take the right engineering and quality assurance decisions. Hill Engineering’s in-house 3D scanning services provides a fast and reliable solution to meet your 3D scanning needs. Results are supplied in the form of easy-to-interpret graphic reports, complemented with complete measurement datasets. Please contact us with additional questions about 3D scanning services.

## Residual stress biaxial mapping validation

Hill Engineering recently published new research detailing our efforts to validate the PSR biaxial mapping technique for residual stress measurement.

This new technique generates two-dimensional maps of additional residual stress components over the same plane as the original contour method measurement. The paper is titled Assessment of Primary Slice Release Residual Stress Mapping in a Range of Specimen Types and appears in the November 2018 volume of Experimental Mechanics. Continue reading Residual stress biaxial mapping validation

## Meet our new 3D scanner

 We at Hill Engineering are always looking for ways to improve the accuracy and efficiency of our laboratory. That’s why we recently acquired a 3D scanner for our laboratory, which will aid in many aspects of our residual stress measurement processes, as well as enable us to provide further services to our customers. In the newest video on our YouTube channel , we discuss some of the highlights of this tool. Continue reading Meet our new 3D scanner

## Overview of a strain gage

We talk about strain gages a lot in our blogs, vlogs, and all over our website. That’s because strain gages are a crucial element of the work we do at Hill Engineering. Our little rectangular friends are very important sensors for residual stress measurements. That something so small can be so important is astounding, but how exactly do strain gages work? Continue reading Overview of a strain gage