This paper presents a semi-automated grinding system for the postprocessing of metalcastings. Grinding is an important procedure in the “cleaning room” of a foundry, where the removal of gate contacts, parting line flash, surface defects, and weld-repaired areas is performed, and almost always manually. While the grinding of repetitive locations on medium to high production castings can be automated using robotics or otherwise, it is not as practical for larger castings (e.g., > 200 kg) that are typically produced in smaller production volumes. Furthermore, automation is even more challenging in that the locations of the required grinding are not a constant depending on the unique conditions and anomalies of each pouring of a component. The proposed approach is intended for a simple x−y−z positioner (gantry) device with a feedback controlled grinding head that enables automated path planning. The process begins with touch probing of the surfaces that contain the anomaly requiring grinding, and then the system automatically handles the path planning and force control to remove the anomaly. A layer-based algorithm for path planning employs a search-and-destroy technique where the surrounding geometry is interpolated across the grind-requiring surface patch. In this manner, each unique condition of the casting surface after initial torch or saw cutting can be handled cost effectively without the need for human shaping and the egregious ergonomic problems associated. Implementation of the proposed grinding control is prototyped at a lab scale to demonstrate the feasibility and versatility of this strategy. The average error for the prototype was on the order of 0.007 in (0.2 mm) with a flatness of the ground surface within 0.035 in (0.9 mm), which is within the cleaning room grinding requirements, as per ISO and ASTM dimensional and surface tolerance requirements. A significant contribution of the work is the layer-based algorithm that allows an effective automation of the process planning for grinding, avoiding robot programming or numerical control code generation altogether. This is a key to addressing the largely unknown and unpredictable conditions of, for example, the riser contact surface removal area on a metalcasting.

## Introduction

Most metalcastings, especially those made in sand molds, require some grinding after they are removed from their molds. This grinding is used to remove the riser and gating contacts, smooth the parting line, weld repaired areas, and correct any other surface anomalies, such as burnt on sand [1]. This type of grinding in the “cleaning room” of the foundry falls into the off-hand grinding category, meaning the material is either held by the operator or the weight of the material is enough to prevent it from moving during the grinding process. Aluminum oxide grinding wheels up to 300 mm in diameter are commonly used in industry for these applications with no cutting fluids [2]. Figure 1 shows examples of anomalies on castings addressed by cleaning room grinding. The goal is to improve the surface so it as good as the surrounding surfaces will be left in the condition as produced by the sand mold.

For high volume products, grinding is often automated with a dedicated machine or a robot. However, these automation solutions are not feasible for lower volume products. For instance, the steel casting industry produces a wide variety of lower volume products from 1 to 100,000 pounds (0.45 to 45,000 kg). Grinding robots and automatic machines are widely used to grind risers and parting lines, for example, on high volume castings because they are known locations and can be programmed per computer model data. These machines are not flexible enough to deal with grinding at unexpected locations. To grind on a different type of casting, changes must be made to the program, and sometimes the machine itself. For castings over 1000 pounds (450 kg), challenges are presented in regard to fixturing, as the weight of the casting may inhibit the ability to properly orient the part and adequate fixtures needed to orient the casting in multiple positions would be cost prohibitive. For many metalcasting foundries producing a variety of such castings, it is not cost effective to invest in such machines. Furthermore, unlike grinding gating and riser contacts in which the location is known, the location of other geometric anomalies on the surface of the part is unexpected, which makes full automation of identifying anomalies and differentiating them from part features a difficult task.

On the positive side, cleaning room grinding finish requirements are on an order of magnitude less stringent as other grinding; the main goal of cleaning room grinding is to remove extra material and make the surface generally smooth and blended [3]. As opposed to surface grinding which regularly delivers precision on the order of 0.001 in (0.0254 mm), cleaning room grinding needs are on the order of 0.1 in (2.54 mm).

Other than a few special cases, cleaning room grinding in steel foundries, as well as low production cast iron foundries, is performed by operators manually manipulating the grinder and applying force to remove material on complex shaped castings. This is a significant ergonomic problem because of the high amount of force required for the operator to exert on the casting, poor positioning to access grinding areas, and vibration from the grinding process [4]. This results in high employee turnover and a wide variation in grinding processing time [5]. Some castings are over-ground, leading to a waste of time and energy, while some are not ground sufficiently, leading to rework.

Previous work on automating the grinding process has focused much effort on two important issues: force control and path planning. Many automated grinding machines have transitioned from a standard “fixed-feed” operation to “controlled force;” this is beneficial to accommodate for any deflection in the grinding apparatus and wear to the wheel [6]. These scenarios can make the ground surface unpredictable causing areas to be over- or underground [7]. Studies on robotic grinding have discussed ways to control the grinding force, path plan, and surface finish for the grinding operation [812]. These approaches depend on computer-aided design (CAD) data and are generally not flexible enough to handle the variation of cleaning room grinding. In other work, intelligence was added to the machines to improve strategies to grind on known casting geometries and anomalies [13], some of which may have control of fourteen axes [14]; however, only limited research exists pertaining to planning on unknown surfaces. Some examples of these include using fuzzy neural networks to find the real force direction from noise signals [15], impedance control to determine the desired force in an unknown environment [16], fuzzy hierarchical coordination and neural control based on position and force control to map unknown surfaces [17], and image recognition defect detection [18]. One study examined automated robotic deburring on an unknown contour using geometrical projection method to plan the trajectory [19]; however, much of this work was directed at surface grinding in which only a thin layer of material is removed, and the geometry of the surface remained virtually unchanged. In contrast, cleaning room grinding removes extra material not part of the desired geometry.

This paper proposes a semi-automated solution for cleaning room grinding. Some geometric input is required to isolate the anomaly, in this example touch probing, and then the system automates its removal by monitoring grinding force to determine the path plan with minimal air grinding. The key to the solution is a path planning algorithm that avoids nearly all preprocess planning tasks (e.g., robot programming or numerical control code generation) that has relegated the industry to deploying a high-turnover labor force for manual grinding in an undesirable location of the metalcasting foundry.

## Solution Method

The proposed process begins with the identification of the “anomaly” that needs to be ground and a desired state for that surface. Currently, visual inspection of castings by an operator is required to identify anomalies; this method is very efficient as humans can easily adapt to product diversity. Research has been conducted to automate the isolation of anomalies and differentiating them from casting features by identifying the underlying geometry [20,21]; however, full automation is not feasible at this time. In this work, it is similarly assumed that an operator will identify the area requiring grinding. After information regarding the location to be ground is obtained, an automated grinding process will remove the anomaly. Section 2.1 details the proposed process for semi-automation of cleaning room grinding.

### Control Approach.

The main control strategies for this semiautomatic grinding system include process planning, path planning, and force control (Fig. 2). Process planning guides the operator through the data input steps (where is the anomaly, what is the surrounding geometry). For this process, the orientation angle of the grinding wheel, boundary points encircling the anomaly, and reference points that sample the surface onto which the anomaly is to be blended must be defined. Path planning and force control are strategies based on this data input and then real-time feedback from the system guides the desired tool path and applies the effective force during grinding.

The orientation angle θ of the grinder is used to position the grinder to the correct orientation during point sampling and grinding, so the grinder can access the anomaly and maximize the width of the wheel in contact with the surface. The angle is also used to define the working coordinate system (WCS). In the WCS, the Xw axis is parallel to the axis of the grinding wheel, the Yw axis is in the plane of the grinding wheel, and the origin remains the same as that of the machine coordinate system. Grinding is to be performed primarily along the Yw axis; thus, an attempt must be made to position the grinder perpendicular to the surface of the casting so the grinding force can be effectively applied to remove the anomaly and the anomaly boundary can be projected onto the XwYw plane. The relationship between the two coordinate systems, machine versus grinding wheel, can be seen in Fig. 3.

The next step is for the operator to input two sets of sampling points: (1) boundary points and (2) reference points (Fig. 4). The containment boundary points surround the anomaly and define the path planning containment boundary for the traversal of the grinding wheel. The operator does not necessarily have to touch the surface of the part to input these points since all boundary points are projected to the Xw−Yw plane to form a convex polygon B.

The reference points are points sampled on the surface of the casting surrounding the anomaly that are input by the operator. These points are used to model the interpolated geometry under the anomaly region. The desired surface can be derived from these scattered points to the entirety of the containment boundary [22]. If the desired surface is planar, at least three nonlinear points should be chosen surrounding the anomaly. If the desired surface is nonplanar, multiple points are sampled using methods considering surface noise [23,24]. By not mandating a specific number of points and spacing of the points, the system is flexible to allow the foundry to specify the error level based on specific requirements of its castings. Additionally, for nonplanar surfaces, the desired surface in the containment boundary should be calculated from interpolation using methods such as triangulation. Other common methods of interpolation for point clouds include b-spline and Kriging, which require more complex mathematical algorithms that can increase computational time [25]. Although various techniques can be applied, the surface patches in this work are generated using Delaunay triangulation based cubic interpolation, which can be coded in matlab (griddata) using the points surrounding the anomaly to estimate the underlying geometry. Further, it is anticipated that grind-requiring patches (like those under a riser contact) would not reside on a surface that could not be simply interpolated with a C2 surface across. That is, a curvature matching patch (i.e., b-spline), contained by the boundary points, will fit within the anticipated accuracy requirement. Note that this is only feasible because of the relatively low precision requirement in cleaning room grinding. For example, when asked to grind a riser contact patch smooth, the expectation is that ±2 to 3 mm is sufficient. Any surface requiring precision finishing would have had machining allowance added by the tooling designer and would then likely be sent to computer numerical control (CNC) machining or turning operations for final finishing. However, extrapolation is not feasible due to the relative complexity of casting geometries (likely not simply analytic surfaces, but rather freeform topology); therefore, the reference geometry must be assumed to surround and represent the underlying geometry below the anomaly. In other words, the assumption is made in such a way that the automated grinder must do what the manual laborer does: Blend the anomaly until it matches curvature with the surrounding geometry. All the reference points are projected to the X−Y plane to form another convex polygon R, which contains all the reference points. To assure that the desired surface can be interpolated, polygon R must contain all of polygon B formed from the boundary points. In this work, the underlying surface geometry is approximated using a griddata method from matlab; of course, numerous surface creation methods could be used and it is outside the scope of this paper on grinding path planning.

### Real-Time Path Planning.

In CNC machining, path planning is based on known elements including the CAD geometry, part location, stock size, shape, and location. If these elements can be estimated for cleaning room grinding, the path planning methods used in CNC machining could be deployed; however, this would result in a considerable amount of air grinding and increase the time to grind. Alternatively, determining where the undesirable material (anomaly) is and is not along the path would decrease grinding time significantly (i.e., Can the grinding wheel sense contact with the anomaly peaks and valleys?). This can be achieved by monitoring the grinding force (feedback), but to react by changing the path planning in a layer-based fashion. That is, if the grinding wheel runs into a bulk of material at a particular offset height, then it will move to an upper layer and continue until it reaches the peak of the geometry (i.e., search-and-destroy).

To decide the step size to move up or down, layers are created within the boundary of polygon B (Fig. 5). The interpolated underlying surface is first offset in the direction normal to the surface for a small distance d0 to create layer 1; this distance is chosen based on the surface tolerance of the casting, which is typically 0.1 in (2.54 mm) which is based on the ISO 8062-3 Dimensional Tolerance Standard [26] and ASTM A802 for surface specifications [27]. Layer 1 is defined in this manner to allow for some slight variation in the final grinding pass without overgrinding. Layer 1 is then offset for subsequent layers with thickness d; therefore, each layer has the same contour of the desired surface. The parameter d is determined by the maximum thickness of material the grinder can process without exceeding the set grinding force. These layers are calculated using Eq. (1).

Grinding starts from an initial point in layer 1, as shown in Fig. 6(a). The initial point is a point on the boundary with the lowest xw value (Eq. (2)). If there is more than one point with the lowest xw value, the point with the lowest yw value among these is chosen (Eq. (3)). Layer 1 is the only layer the grinder must traverse the entire area within the boundary. For the other layers, grinding is performed only where required.

Force feedback is used to monitor the position of the grinder and the grinding force in real-time. As shown in Fig. 6(b), if the force exceeds the maximum, the grinder will move through upper layers until the force is within the acceptable range and continue to grind in that layer. When the system detects a sudden decrease of force, it signals that the grinder has moved off the anomaly in the current layer, so it will change direction (Fig. 6(c)) as dictated by a staircase tool path strategy. Grinding will continue on a peak entity until it is reduced through layer 1 (Fig. 6(d)) when it will seek another surface to grind and the process is repeated until all peaks are reduced through layer 1 (Fig. 6(e)). The stair case tool path (also known as Zig–Zag or direction parallel tool path planning) is created in real time in the different layers, as illustrated in Fig. 7.

As such, the system searches through z heights and reduces material across the entirety of the x−y space within the anomaly boundary (Eq. (4)). Once all upper layers are completed, the wheel will always return to layer 1 to continue its previous path. It is for this reason the approach is deemed search and destroy; the wheel is given real time guidance to seek all peaks of the anomaly across all layers and all traces along the staircase path in x−y. Along the way, the real-time path planning method generates the next step based on the position and force feedback during grinding (Eqs. (57)). The location of the next point with respect to the WCS is calculated as follows:

Layer surfaces:
$SL={finterp({R1,R2,…})(L=1)foffset(S1,d0)(L=2)foffset(S2,(L−2)×d)(L>2)$
(1)
initial point:
$n=1L1=1x1=min(xB1,xB2)$
(2)

$y1=min(yBi|xBi=x1)$
(3)

$z1=fz(x1,y1,L1,SL1)$
(4)
For any n = k (k > 1):
$(xk,yk,r)=fstair(xk−1,yk−1,{B1,B2,…})$

$r={1if the stair case tool path in the current layer is finished0else$
(5)

(6)

$zk=fz(xk,yk,Lk,SLk)$
(7)

where SL is the offset surface in layer L where S1 is the desired surface; finterp is the function used to interpolate the desired surface [22]; foffset is the function used to offset the surfaces; {R1, R2} is the set of reference points from process planning; L is the current layer number; d0 is the thickness of layer 1; d is the thickness of other layers; {B1, B2} is the set of boundary points; xBi, yBi are, respectively, the x, y value of the boundary point Bi; fz(x, y, L, SL) means to look for the z value of the point(x, y) in known surface SL; n is the nth point (step) from start; (xn, yn, zn) is, respectively, the nth x, y, z location; Ln and Fn are, respectively, the layer and force at the nth step; Fmax is the maximum force of the grinding wheel; fstair means using the stair case tool path to find the next x, y location.

In all layers, with the exception of layer 1, the grinder does not have to be positioned exactly at the z location for each (x,y,z) point calculated along the tool path. So long as the grinding force does not exceed the set limit, no additional modification of the z location is needed. This speeds up the grinding process, since in all layers, aside from layer 1, waviness that does not exceed a layer depth is deemed acceptable. This is, again, similar to industry practice of grinding, or rough machining; it does not as much matter what the surface condition is like in-process, only the final finishing pass is critical. The goal when grinding in layer 1 is to create a smooth surface within the surface tolerance of the casting [26]. Since layer 1 was set based on the surface tolerance, when the surface is smooth within layer 1, the grinding operation can be stopped. To achieve a smoothed final surface, more precise position control is used in layer 1 to reduce the waviness which positions the grinder to a more exact z level for the (x, y) location (tighter controls on force/locational precision). As a practical issue, a calibration point P0(x0, y0, z0) is set on a flat, hard plate fixed to the system assembly used to calibrate the grinding wheel. Before and during the grinding operation, the grinding wheel must touch off this point to measure the diameter of the wheel, since the wheel will wear over time. The overall path planning process flow is illustrated in Fig. 8.

### Force Control.

Wheel speed, feed rate, and grinding force are important parameters that influence the depth of cut and material removal rate significantly [28]. In this paper, the wheel speed is kept constant, while the grinding force and feed rate will be controlled. The grinding force can be split into three components: the tangential force Ft, responsible for power dissipation; the normal force Fn, the most important factor in material removal; and the side force Fa, resulting in sideways movement of the wheel. The grinding forces considered in this work focus on the normal force. The normal force and feed rate of surface grinding, which are directly correlated, are typically kept constant because the same depth of material is removed in each pass of the grinder. In cleaning room grinding, the depth of material to be removed may vary; requiring more grinding force. Therefore, the force must be a variable but limited to an absolute maximum grinding force set at an experiential value |Fmax|, which is the maximum force that will prevent wheel failure. This is valid for all layers above layer 1. In layer 1, a more precise force control method is needed to achieve a smoother surface; therefore, reducing the feed rate would be ideal compared to decreasing maximum grinding force setting Fmax; this is because the force in the finishing layer might exceed the maximum force causing the grinder to move to an upper layer, making the process less efficient. The force control strategy in this system applies the desired force and monitors the force to maintain safe operation. The system calculates the desired force to be applied based on the desired surface, the next location, and the current force feedback signal, as illustrated in Fig. 9. The system converts the desired force into the signal to the force control device.

## Implementation

A lab prototype was built to verify the automatic grinding system and algorithms of this proposed method. Since it would not be practical to grind actual steel castings with this prototype system, the system was designed to grind epoxy test parts with similar geometries. This section will cover the system structure and force applying device in addition to experimental results from a test piece. The system structure shown in Fig. 10 includes a three axes 13.8 × 11.4 × 6.9 in (350 × 290 × 175 mm) gantry system, an industrial probe attached to the apparatus to obtain reference points during the user input stage, a rotary tool to simulate a grinder that is mounted via a spring/damper, and an LC500 linear variable digital transducer (LVDT) used to translate deflection to force by its spring constant. As explained previously by monitoring the force feedback (in this case LVDT deflection), one can decide to move the device up or down through the layer stack through the process planning algorithm. For grinding on an unknown surface, the system must apply an effective force but also be able to avoid grinding wheel damage when it collides with an unexpected surface; therefore, this spring/damper/LVDT system mounted on the Z axis guides layer location in real time. Other than manual touch probing control via an attached joystick, the prototype system could automatically traverse simulated part samples representing scaled casting anomalies.

To validate the system, epoxy test pieces 3.0 × 3.0 in square (75 × 75 mm) were automatically ground to demonstrate the effectiveness of the proposed approach. The geometry of the test pieces contained anomalies of various geometries and quantities that would require the device to traverse up and down through processing layers. The test pieces were then laser scanned before and after grinding using an Optix 400 L laser scanning system. Figure 11 shows the original test models in addition to the comparison between the ground test pieces and ideal models. Using a surface-to-surface deviation mapping in Geomagics, an average error on the order of 0.007 in (0.2 mm) with a flatness of the ground surface within 0.035 in (0.9 mm) was achieved for flat underlying geometries, with error on the order of 0.012 in (0.3 mm) for concave and convex underlying geometries, which is well within reason of the tolerance required by the metalcasting industry of ∼0.078 in (2 mm). Obviously, the lab setup falls well short of an industrial grinding process, but was intended to validate the overarching solution for automated path planning. Further scaleup and testing on a larger positioner, appropriate grinding wheel, and metalcastings would be required for the evaluation at a higher technical readiness level.

## Conclusions

Mechanization of cleaning room grinding is needed to improve efficiency when producing low volume products, which are particularly prevalent in the steel casting industry. Current automatic machines are not able to accommodate grinding of unexpected anomalies. In this paper, the characteristics of cleaning room grinding problems are investigated and a layer-based path planning method was developed to remove unknown anomalies. In addition, a hybrid position and force control strategy was presented, which can perform grinding in an unknown environment and make real time decisions and drive the grinding wheel across the anomaly until it is effectively blended to the approximated surface. A simple lab implementation of the proposed semiautomatic grinding system validated the automated path planning method and potential effectiveness of this approach. By using the semiautomatic grinding system, ergonomics in cleaning room grinding and the overall quality of ground castings could be improved. Although potentially limited in scope (cleaning room grinding), the proposed solution addresses an underserved category of grinding that unfortunately lacks a cost effective and flexible automation solution.

## Acknowledgment

Research was sponsored by the U.S. Army Benet Laboratories and was accomplished under Cooperative Agreement Number W15QKN-06-R-0501. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of U.S. Army Benet Laboratories or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation heron.

This material is based upon work supported by the U.S. Department of Energy. Any opinions, findings, or conclusions and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Department of Energy.

The authors wish to acknowledge technical support and fabrication provided by Kevin Brownfield and Mike Renze. Technical editing services were provided by Michelle Stallard (Voelker) of Iowa State University.

## Funding Data

• Office of Energy Efficiency and Renewable Energy (Grant No. DE-FC36-04GO14230).

## References

References
1.
Spinner
,
D.
,
Peters
,
F.
, and
O'Shaughnessy
,
K.
,
2001
, “
Considerations for a More Efficient Cleaning Operation
,”
Mod. Cast.
,
91
(1), pp.
29
31
.
2.
Harwood
,
B.
,
2017
, private communication.
3.
Bex
,
T.
,
1992
, “
Cleaning Rooms Gain Efficiency
,”
Mod. Cast.
,
82
(4), p.
32
.
4.
AFS
,
2007
, “
,”
Mod. Cast.
,
9
(3), p.
49
.
5.
Butler
,
T.
,
2016
, “
Justify Automatic Grinding to Raise Profitability, Solve Cleaning Room Staff Issues: One Investment Option Offers an Effective Solution to Production, Quality, and Management Dilemmas
,”
Foundry Manage. Technol.
,
144
(1),
p
. 33.
6.
Malkin
,
S.
, and
Guo
,
C.
,
2008
,
Grinding Technology: Theory and Application of Machining With Abrasives
,
Industrial Press
,
New York
, pp.
142
151
.
7.
Cheng
,
K.
,
2008
,
Machining Dynamics: Theory, Applications and Practices
,
Springer
,
London
, p.
290
.
8.
Pagilla
,
P. R.
, and
Yu
,
B.
,
2001
, “
Adaptive Control of Robotic Surface Finishing Processes
,”
American Control Conference
(
ACC
), Arlington, VA, June 25–27, pp.
630
635
.
9.
Erlbacher
,
E. A.
,
2000
, “
Force Control Basics
,”
Ind. Rob. Int. J.
,
27
(
1
), pp.
20
29
.
10.
Wang
,
Y. T.
, and
Jan
,
Y. J.
,
2000
, “
A Robot-Assisted Finishing System With an Active Torque Controller
,”
IEEE International Conference on Robotics & Automation
(
ICRA
), San Francisco, CA, Apr. 24–28, pp.
1568
1573
.
11.
Trygve
,
T.
,
Lien
,
T. K.
, and
Sannaes
,
P. K.
,
2001
, “
Robot Control System for Grinding of Large Hydro Power Turbines
,”
Ind. Rob. Int. J.
,
28
(
4
), pp.
328
334
.
12.
Dimo
,
H. O.
,
Dewen
,
J.
,
Zhang
,
J.
, and
Gruver
,
W. A.
,
2001
, “
Vibration Control of a Redundant Robot for Grinding
,”
IEEE International Conference on Systems
, Man and Cybernetics (
ICSMC
), Tucson, AZ, Oct. 7–10, pp.
389
394
.
13.
Nandi
,
A. K.
, and
Pratihar
,
D. K.
,
2004
, “
Automatic Design of Fuzzy Logic Controller Using a Genetic Algorithm—to Predict Power Requirement and Surface Finish in Grinding
,”
J. Mater. Process. Technol.
,
148
(
3
), pp.
288
300
.
14.
Altintas
,
Y.
,
2012
,
Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations and CNC Design
,
2nd ed.
,
Cambridge University Press
, New York, pp.
190
195
.
15.
Kiguchi
,
K.
, and
Fukuda
,
T.
,
2000
, “
Position/Force Control of Robot Manipulators for Geometrically Unknown Objects Using Fuzzy Neural Networks
,”
IEEE Trans. Ind. Electron.
,
47
(
3
), pp.
641
649
.
16.
Jung
,
S.
,
Hsia
,
T. C.
, and
Bonitz
,
R. G.
,
2004
, “
Force Tracking Impedance Control of Robot Manipulators Under Unknown Environment
,”
IEEE Trans. Control Syst. Technol.
,
12
(
3
), pp.
474
483
.
17.
Yin
,
Y.
,
Hu
,
H.
, and
Xia
,
Y.
,
2004
, “
Active Tracking of Unknown Surface Using Force Sensing and Control Technique for Robot
,”
Sens. Actuators, A
,
112
(
2–3
), pp.
313
319
.
18.
Abramovich
,
G.
,
Weng
,
J.
, and
Dutta
,
D.
,
2005
, “
Adaptive Part Inspection Through Developmental Vision
,”
ASME J. Manuf. Sci. Eng.
,
127
(
4
), pp.
846
856
.
19.
Chen
,
S.-C.
, and
Tung
,
P.-C.
,
2000
, “
Trajectory Planning for Automated Robotic Deburring on an Unknown Contour
,”
Int. J. Mach. Tools Manuf.
,
40
(
7
), pp.
957
978
.
20.
Voelker
,
M. M.
, and
Frank
,
P. E.
,
2017
, “
Development of a Digital Standard to Specify Surface Requirements of Cast Metal Surfaces
,”
Mater. Perform. Charact.
,
6
(1), pp. 130–143.https://www.astm.org/DIGITAL_LIBRARY/JOURNALS/MPC/PAGES/MPC20160014.htm
21.
Voelker
,
M. M.
,
2016
, “
Quantitative Surface Inspection Methods for Metal Castings
,”
Master's thesis
, Iowa State University, Ames, IA.http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=6175&context=etd
22.
Chan
,
E. S.
, and
Ong
,
B. H.
,
2001
, “
Range Restricted Scattered Data Interpolation Using Convex Combination of Cubic Bezier Triangles
,”
J. Comput. Appl. Math.
,
136
(
1–2
), pp.
135
147
.
23.
Shannon
,
C. E.
,
1949
, “
Communication in the Presence of Noise
,”
,
37
(
1
), pp.
10
21
.http://nms.csail.mit.edu/spinal/shannonpaper.pdf
24.
MathWorks
,
2017
, “
Griddata
,”
Interpolate Scattered Data—MATLAB Griddata
, MathWorks, Natick, MA.
25.
Rak
,
M.
,
Wozniak
,
A.
, and
Mayer
,
R.
,
2014
, “
Review of Interpolation Methods for Point Cloud Modelling in Coordinate Metrology
,”
XIth International Scientific Conference on Coordinate Measuring Techniques
, Bielsko-Biała, Poland, Apr. 2–4, pp. 172–176.https://www.researchgate.net/publication/264547751_REVIEW_OF_INTERPOLATION_METHODS_FOR_POINT_CLOUD_MODELLING_IN_COORDINATE_METROLOGY
26.
ISO
,
2007
, “
Geometrical Product Specifications (GPS)—Dimensional and Geometrical Tolerances for Moulded Parts—Part 3: General Dimensional and Geometrical Tolerances and Machining Allowances for Castings
,” International Organization for Standardization, Geneva, Switzerland, Standard No.
8062-3:2007
.https://global.ihs.com/doc_detail.cfm?&rid=TIA&input_search_filter=UNI&input_doc_number=&input_doc_title=&item_s_key=00452459&item_key_date=901116&origin=DSSC
27.
ASTM
,
2015
, “
Standard Practice for Steel Castings, Surface Acceptance Standards, Visual Examination
,” ASTM International, West Conshohocken, PA, Standard No.
ASTM A802
.https://www.astm.org/Standards/A802.htm
28.
AFS
,
1977
,
Cleaning Castings
,
American Foundry Society
, Schaumburg, IL.