ASM Metals HandBook Vol. 14 - Forming and Forging
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Statistical Analysis of Forming Processes
Stuart Keeler, The Budd Company Technical Center
Introduction
STATISTICS are becoming important tools in the operation of press shops, providing numerical process analysis
capabilities that far exceed the more traditional recording of simple breakage rates. The most common use of statistics in
the press shop is the area of statistical process control (SPC). Though utilized in many formats, SPC is simply the use of
statistical techniques such as control charts to analyze a process or its output and thus enable appropriate actions to be
taken to achieve and maintain a state of statistical control. The use of statistical process control instead of traditional
quality control methods such as inspection/sorting is beneficial in a number of ways. Statistical process control:
• Decreases scrap, rework, and inspection costs by controlling the process
• Decreases operating costs by optimizing the frequency of tool adjustments and tool changes
• Maximizes productivity by identifying and eliminating the causes of out-of-control conditions
• Allows the establishment of a predictable and consistent level of quality
•
Eliminates or reduces the need for receiving inspection by the purchaser because it produces a more reliable,
trouble-free product, resulting in increased customer satisfaction
The use of statistics in analysis of the forming process, however, goes well beyond SPC. The whole area of design of
experiments (DOE) is becoming important as the interactions within the forming process are detailed and studied. This
article will discuss the role of statistics in sheet metal forming operations both in terms of different statistical process
control techniques and design of experiments. Information on the statistical analysis of mechanical testing is available in
the Section "Statistics and Data Analysis" in Mechanical Testing, Volume 8 of ASM Handbook, formerly 9th Edition
Metals Handbook.
Statistical Analysis of Forming Processes
Stuart Keeler, The Budd Company Technical Center
The Forming Process
A wide range of forming processes are currently in use. Although the details of these processes differ significantly, most
forming processes share certain characteristics. Each forming process, however simple, can be viewed as a system. For
sheet metal forming, one common breakdown of the system consists of the following components:
• Material
• Lubricant
• Tooling
• Press
Each of these major components can be further broken down into subcomponents.
The components of forming systems are highly interactive. A change in one component can produce significant changes
in the effects of other components. Not only are the changes within a single component difficult to trace and understand,
but the interaction of the components makes the task even more difficult. Small changes made in one or more components
of the system can cause very large changes in the output of the system (the finished part). These synergistic changes may
not be predictable or even possible to anticipate.
Ideally, the forming system should be a continuous process. For many processes, the system appears to be continuous.
The tools are inserted into the designated press and remain there for the production life cycle of the part, which often
spans several years. Changes made during the production life cycle may in fact create major disruptions in the continuous
nature of the process. These changes can include engineering modifications, tooling replacement, routine maintenance,
process improvements, and other seemingly minor modifications to the process.
Many forming processes are conducted on a batch basis, typically with large volumes. Tooling is inserted into a press, a
specific number of pieces are made, and the tooling is removed from the press. This type of process is often considered to
be an interrupted or segmented form of a continuous process. In reality, however, a new forming system is created each
time the tooling is inserted into the press. This is evidenced by the extended period of trial-and-error adjustments
necessary to the tooling before the production of satisfactory parts can begin.
Statistical Analysis of Forming Processes
Stuart Keeler, The Budd Company Technical Center
The Statistical Approach
Statistical process control programs are becoming commonplace in industry. An entire science has been developed to deal
with the problem of defining, analyzing, correcting, and controlling production processes (Ref 1, 2, 3, 4, 5). By providing
data on the capabilities and output of a process, statistical methods provide a rational, rather than an emotional, basis for
problem solving and decision making. Other benefits of statistical process control have been listed in the introduction to
this article.
As a system, the forming process is amenable to system analysis and the techniques of system control. Various statistical
techniques, many of which have their origins in quality control practices, can be applied to the forming process. In this
article, these statistical techniques are divided into two broad categories: historical tracking and statistical deformation
control (process design).
References cited in this section
1.
Statistical Quality Control Handbook, Western Electric Company, 1977
2.
J.M. Juran, F.M. Gryna, Jr., and R.S. Bingham, Jr., Quality Control Handbook, McGraw-Hill, 1979
3.
E.L. Grant and R. S. Leavenworth, Statistical Quality Control, 5th ed., Mc-Graw-Hill, 1980
4.
A.L. Strongrich, G.E. Herbert, an
d T.J. Jacoby, "Statistical Process Control: A Quality Improvement Tool," Paper
83099, Society of Automotive Engineers, 1983
5.
General Motors Statistical Process Control Manual, Document 1893, General Motors Corporation, 1984
Statistical Analysis of Forming Processes
Stuart Keeler, The Budd Company Technical Center
Historical Tracking
Historical tracking is a long-term process of measuring, recording, and analyzing one or more specific characteristics of a
process. This record then becomes the basis upon which the current state of the process can be assessed and the future
state of the process predicted. Numerous statistical techniques are applicable to historical tracking (Ref 1, 2, 3, 4, 5); one
is the control chart and another is statistical deformation control.
Control Charting
The heart of many SPC systems is the control chart. The control chart is a method of monitoring process output through
the measurement of a selected characteristic and the analysis of its performance over time. Because the output from one
process is often the input to the next process, the physical location of the measurement can be at either end of the transfer
link. For example, the output from a blanking press--the blanks--becomes the input to the next stage, which is the press
itself.
A control chart can be a very powerful statistical tool. Information from the control chart can be used to inform the
operator when to adjust the process and, perhaps more important, when not to adjust the process. This places the operator
in control of the process, based on statistically valid numbers instead of trial and error.
For example, the operator is given a machine capable of producing the required parts and is then given the means to
measure the characteristics of output (the finished parts) in real time. Thus, the operator knows the quality of the part
coming off the machine on a real time basis. In addition, the operator has control limits for the process. These control
limits tell the operator when to adjust the process and when not to adjust the process, which permits the operator to
prevent rather than detect defects. Such a system for the control of steel sheet thickness is described in the following
example.
Example 1: Constructing a Control Chart for Steel Thickness Measurements.
Uniformity of blank thickness is often stated to be important for high productivity in sheet metal forming operations,
although published information on this subject is limited (Ref 6, 7). Once the tooling is set for a specific sheet thickness,
adjustments to the tooling cannot be readily made. A control chart can be constructed to statistically monitor variations in
the incoming steel.
For each coil of steel received, five blanks are sampled at specific locations along the length of the coil, such as the head,
quarter, center, quarter, and tail locations. Examples of such measurements are given below.
The values of (the average thickness) and R (the range of thicknesses) are plotted on the respective graphs. After
sufficient measurements are made, the -value and the upper and lower control limits (UCL and LCL) can be calculated
and plotted on the same diagram.
The control chart shown in Fig. 1 indicates that the thickness of the steel being processed is stable. A process is said to be
in a state of statistical control if it is operating without special causes of variation (Ref 4). It will exhibit random variation
within calculated control limits and will have predictability; that is, measurements taken in the future are expected to be
within the same control limits. However, no prediction can be made about where any individual measurement will lie
within these control limits.
Coil number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Test No.
1
0.97
0.79
0.76
0.76
0.81
0.84
0.84
0.84
0.84
0.76
0.89
0.91
0.76
0.91
0.81
0.71
0.84
0.76
0.89
0.84
2
0.89
0.79
0.76
0.84
0.86
0.96
0.86
0.84
0.91
0.89
0.94
0.97
0.81
0.89
0.89
0.79
0.81
0.79
0.94
0.89
3
0.86
0.86
0.81
0.84
0.94
0.79
0.97
0.91
0.89
0.94
0.89
0.99
0.94
1.02
0.84
0.89
0.86
0.89
0.71
0.89
4
0.84
0.79
0.76
0.81
0.94
0.84
0.76
0.89
0.86
0.81
0.89
0.86
0.76
0.86
0.86
0.79
0.84
0.76
0.69
0.96
5
0.76
0.79
0.81
0.94
0.89
0.84
0.76
0.91
0.79
0.74
0.94
0.76
0.79
0.76
0.89
0.84
0.84
0.76
0.81
0.94
Total 4.30
4.02
3.90
4.19
4.44
4.27
4.19
4.39
4.29
4.14
4.55
4.49
4.06
4.44
4.29
4.02
4.19
3.96
4.04
4.52
Average,
X
0.86
0.80
0.78
0.84
0.89
0.85
0.84
0.88
0.86
0.83
0.91
0.90
0.81
0.89
0.86
0.80
0.84
0.79
0.81
0.90
Range, R 0.21
0.07
0.05
0.18
0.13
0.17
0.21
0.07
0.12
0.20
0.05
0.23
0.18
0.26
0.05
0.18
0.05
0.13
0.25
0.12
Fig. 1 Raw data (in millimeters; 1 in. = 25.4 mm) obtained from steel thickness measurements and the resulting
X
-R
control charts. Upper and lower
control limits can be calculated and the mean determined when sufficient data have been collected.
Unfortunately, the control limits shown in Fig. 1 are rather wide and would require frequent tooling adjustments. This
means that a normal distribution of thicknesses within the control chart would be expected. However, this expected range
is too large for the tooling and would necessitate tooling adjustments to accommodate changes in thickness between the
extremes of the range. Therefore, it is necessary to work with the steel supplier to reduce the range of the control limits to
an engineering specification window acceptable to the tooling.
Control limits are important in statistical process control because they define the amount of variation in a process due
solely to chance causes. If the process is operating within these limits (Fig. 2a), it is considered to be stable. If the process
is operating outside these limits (Fig. 2b), it is unstable.
Fig. 2
Distribution curves (histograms; left) and control charts illustrating processes that are in control (within
control limits) (a) and out of control (ou
tside of control limits) (b). Variation outside of assigned control limits is
always the result of some assignable cause, as shown in (b).
The control chart represents the best that the operator of a given process can do with the process as it exists. If this is
unacceptable, then the basic process must be changed. Engineering and management, not the operator, are required to
implement these process changes because this may require new equipment, new tools, new processing sequences,
additional stages, or even a new part design.
If the process is operating within its control limits (statistical control), then the capability of the system to meet
specifications can be assessed. If the system is out of control, then changes to the process must be made to make the
process stable before the capabilities can be assessed.
Control charts are most effective when monitored over an extended period of time. Thus, changes in the process can be
detected, often before rejects begin to occur. Two general types of changes in the process might be encountered. One is
the central sample tendency
X
, which is monitored to detect a shift in the location of the distribution (Fig. 3). A location
change would imply that the normal distribution remains the same but that the average is displaced. An example in
forming might be the angle of a bend. The variation from bend to bend would remain acceptable, but the average angle of
all bends would have changed. Some factors that may affect the
X
-value are gradual deterioration of the equipment,
worker fatigue, accumulation of waste products (such as excess lubricant or flaked metallic coatings), and environment.
Fig. 3 Shifting of a control chart (upper and lower control limits a
nd mean) due to a change in processing.
Values of R remain the some. See also Fig. 4.
Another type of process change is a change in the sample range or the variation from one sample to another (Fig. 4). This
range change is observed as a change in the width of the normal curve for a given area under the curve. This means
increased variability. For the bending example shown in Fig. 3, the average bend angle would remain the same, but large
differences would be detected among samples from the same lot or even consecutive samples. Some factors that may
affect the R chart are changes in operator skill, worker fatigue, change in the mix of components feeding an assembly line,
and gradual change in quality of the incoming material.
Fig. 4 Increase in the range of values within a subset (increase in R). Values of
X
remain the same. See
Fig.
3.
The two key concepts that emerge from control charts are control and capability. The term control defines the stability of
the process, which in turn means that the process is predictable. It does not necessarily mean that the process is acceptable
with regard to the specification. This is in contrast to the term capable; this term means that the process has the capability
to meet specifications.
Example 2: Solving a Problem of Fender Blank Size Variation.
Two fender blanks were generated with each stroke of a blanking punch (Fig. 5a). Measurements of the critical dimension
y-y on each blank showed large variations in R-values, but
X
-values were quite constant (Fig. 5b). Further analysis
revealed that plots of only the right-side blanks and only the left-side blanks had different characteristics (Fig. 6). These
data showed a reduced variation in R but a larger variation in the
X
-values. Interestingly, the
X
-values of the right- and
left-side blanks changed simultaneously but in opposite directions.
Fig. 5 (a) Schematic showing nesting of blanks for an automobile fender. Dimension y-y
was monitored for the
SPC study reported in Example 2. (b)
X
-R
control charts for both right side and left side fender blanks taken
as a single population. See also Fig. 6.