Chapter 12: STANDARD DATA AND FORMULASPrepared by: LARA CINDY AVENIDO BSIE III IE 322 : METHODS ENGINEERING1

Introductiony Standard time data are elemental times obtained from time

studies that have been stored for later use. y The principle of applying standard data was established many years ago by FrederickW.Taylor, who proposed that each elemental time be properly indexed so that it could be used to establish future time standards. y When we speak of standard data today, we refer to all the tabulated element standards, plots, nomograms, and tables that allow the measurement of a specific job without the use of a timing device.2

IntroductionStandard data can have several levels of refinement: Motion Element Task The more refined the standard data element, the broader its range of usage. Thus, motion standard data have the greater application, but it takes longer to develop such a standard than either element or task standard data. Element standard data are widely applicable and allow the faster development of a standard than motion data.3

Introductiony A time study formula is an alternate and, typically,

simpler presentation of standard data, especially for variable elements. y Formula construction involves the design of an algebraic expression that establishes a time standard in advance of production by substituting known values peculiar to the job for the variable elements.

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Standard Time Data Development

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Standard Time Data Developmenty To develop standard time data, analysts must distinguish constant

elements from variable elements.A constant element is one whose time remains approximately the

same, cycle after cycle. A variable element is one whose time varies within a specified range of work. Thus, the element start machine would be a constant, while the element drill 3/8-inch diameter hole would vary with the depth of the hole, the feed, and the speed of the drill.6

Standard Time Data Developmenty Standard data are indexed and filed as they are developed. Also, setup

elements are kept separate from elements incorporated into each piece time, and constant elements are separated from variable elements. y Typical standard data for machine operation would be tabulated as follows: 1) Setup a) Constants b) Variables 2) Each piece a) Constants b) Variables.7

Standard Time Data Developmenty Standard data are compiled from different elements in

time studies of a given process over a period of time. y In tabulating standard data, the analyst must be careful to define the endpoints clearly. Otherwise, there may be a time overlap in the recorded data. y For example, in the element out stock to stop on the bar feed No. 3 Warner & Swasey turret lathe, the element could include reaching for the feed lever, grasping the lever, feeding the bar stock through the collet to a stock stop located in the hex turret, closing the collet, and reaching for the turret handle.8

Standard Time Data Developmenty Then again, this element may involve only the feeding of bar

stock through the collet to a stock stop. Since standard data elements are compiled from a great number of studies taken by different time study observers, the limits or end points of each element should be carefully defined. y Figure 12-1 illustrates a form for summarizing data taken from an individual time study to develop standard data on die-casting machines.

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Tabular Datay For example, when developing standard data

times for machine elements, the analyst may need to tabulate horsepower requirements for various materials in relation to depth of cut, cutting speeds, and feeds. y To avoid overloading existing equipment, the analyst should have information on the workload being assigned to each machine for the conditions under which the material is being removed.12

Tabular Datay For example, in the machining of high-alloy steel forgings on a

lathe capable of a developed horsepower of 10, it would not be feasible to take a 3/8-inch depth of cut while operating at a feed of 0.011 inch per revolution and a speed of 200 surface feet per minute. Tabular data, either from the machine tool manufacturer or from empirical studies indicate a horsepower requirements are found conditions. Consequently, the work would need to be planned for a feed of 0.009 inch at a speed of 200 surface feet; this would only require a horsepower rating of 8.7. such tabular data are best stored, retrieved, and accumulated into a final standard time using commercially available spreadsheet programs (e.g., Microsoft Excel).13

Tabular Data

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Using Nomograms and Plotsy Because of space limitations, tabularizing values for

variable elements is not always convenient. By plotting a curve or a system of curves in the form of an alignment chart, the analyst can express considerable standard data graphically on one page. y For example, if the problem is to determine the production in pieces per hour to turn 5 linear inches of a 4-inch diameter shaft of medium carbon steel on a machine utilizing 0.015-inch feed per revolution and having a cutting time of 55 percent of the cycle time, the answer could be readily determined graphically.15

Using Nomograms and Plots

Figure 12-2 illustrates a nomogram for determining turning and facing time.

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Figure 12-3 illustrates a plot of forming time in hours per hundred pieces for a certain gage stock over a range of sizes expressed in square inches.

Each of the 12 points in this plot represents a separate time study. The plotted points indicate a straight-line relationship, which can be expressed as a formula: Standard time = 50.088 + 0.00038 size17

Using Nomograms and Plots Disadvantages of Using Nomograms and Plots

First, it is easy to introduce an error in reading from the plot, because of the amount of interpolation usually required. Second, there is the chance of outright error through incorrect reading or misalignment of the intersections on the various scales.18

Formula Construction from Empirical DataSteps in Formula Construction are: Identify Variables Analyze Elements and Collect Data Plot Data and Compute Variable Expressions Check for Accuracy and Finalize

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Identify Variablesy The first and most basic step in formula construction is

identifying the critical variables.

This process includes separating those that are independent from those that are dependent and also determining the range of each variable.

y For example, a formula might be developed for curing bonded

rubber parts between 2 and 8 ounces in weight. The independent variable is the weight of the rubber, while the dependent variable is the time to cure. The range for the dependent variable would be 2 to 8 ounces, while the dependent variable of time would have to be quantified from studies.20

Analyze Elements and Collect Data After the initial identification is finished, the next step is

collecting data for the formula. This step involves gathering previous studies with standardized

work elements that are applicable to the desired formula, as well as taking new studies, to obtain a sufficiently large sample to cover the range of work for the formula. Note: It is important that like elements in the different studies have consistent endpoints.21

Analyze Elements and Collect Datay The number of studies needed to construct a formula is influenced by

the range of work for which the formula is to be used, the relative consistency of like constant elements in the various studies, and the number of factors that influence the time required to perform the variable elements. y At least 10 studies should be available before a formula is constructed. If fewer than 10 are used, the accuracy of the formula may be impaired through poor model fits. y The more studies used, the more data will be available, and the more normal will be the conditions reflected. y In summary, the analyst should take note of the maxim garbage in garbage out. The formula will only be as accurate as the data used to construct it.22

Plot Data and Compute Variable Expressionsy Next, the data are posted to a spreadsheet for analysis of the

constants and variables. The constants are identified and combined and the variables analyzed so as to have the factors influencing time expressed in an algebraic form. By plotting a curve of time versus the independent variable, the analyst may reduce potential algebraic relationships. y For example, plotted data may take a number of forms: a straight line, nonlinear increasing trend, a nonlinear decreasing trend. Or no obviously regular geometric form.23

Plot Data and Compute Variable Expressionsy If a straight line, then the relationship is quite straightforward:

y=a+bxwith the constants a and b determined from least-squares regression analysis. If the plot shows a nonlinear increasing trend, then power relationships of the form x2, x3, xn, or ex should be attempted. y For nonlinear decreasing trends, negative power or negative exponentials should be attempted. For asymptotic trends, log relationships or negative exponentials of the form:

y = 1 e-xshould be attempted.24

Plot Data and Compute Variable Expressionsy Note that adding additional terms to the model will always

produce a better model with a higher percentage of the variance in the data explained. y However, the model may not be statistically significantly better, that is, statistically there is no difference in the quality of the predicted value between the two models. y Furthermore, the simpler the formula, the better it can be understood and applied. y The range of each variable should be specifically identified. The limitations of the formula must be noted by describing its applicable range in detail.25

Plot Data and Compute Variable Expressionsy There is a formalized procedure for computing the best model,

termed the general linear test. y It computes the decrease in unexplained variance between the simpler model, termed the reduced model, and the more complex model, termed the full model. y The decrease in variance is tested statistically and, only if the decrease is significant, the more complex model is used (see Example 12-2).

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Check for Accuracy and Finalizey The easiest and fastest way to check the formula is to use it to

check existing time studies. Any marked differences (roughly 5 percent) between the formula value the expected validity, the analyst should accumulate additional data by taking more stopwatch and/or standard data studies. y The final step in the formula development process is to write the formula report. The analyst should consolidate all data, calculations, derivations, and applications of the formula and present this information in a complete report prior to putting the formula into use.30

Analytical Formulas

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Analytical Formulasy Standard times can be calculated using analytical-formulas

found in technical handbooks or from information provided by machine tool manufacturers. By finding the appropriate feeds and speeds for different types and thicknesses of materials, analysts can calculate cutting times for different machining operations. Drill Press Work Lathe Work Milling Machine Work

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Drill Press Worky A drill is a fluted end-

cutting tool used to originate or enlarge a hole in solid material.

In drilling operations on a flat surface, the axis of the drill is at 90 degrees to the surface being drilled

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Drill Press Worky Since the commercialy To illustrate, calculate the lead of

standard for the included angle of drill points is 118 degrees, the lead of the drill may be readily found through the following expression:

a general-purpose drill 1-inch in diameter:

where:l = Lead of drill. r = Radius of drill. tan A = Tangent of the included angle of the drill.34

l = 0.3 inch lead y After determining the total length that the drill must move, we divide this distance by the feed of the drill in inches per minute, to find the drill cutting time in minutes.

Drill Press Work

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Drill Press Worky Drill speed is expressed in feet per minute

(fpm), and feed in thousandths of an inch per y For example, to determine the feed in inches per minute of a revolution. To change the feed into inches per minute when the feed per revolution and 1-inch drill running at a the speed in feet per minute is known, the surface speed of 100 feet per following equation can be used: minute and a feed of 0.013

inch per revolution, we have:where: Fm f Sf d36

= Feed in inches per minute. = Feed in inches per revolution. = Surface feet per minute. = Diameter of drill in inches.

= 4.97 inches per minute

Drill Press Worky To determine how long it would take for this 1-inch drill

running at the same speed and feed to drill through 2 inches of a malleable iron casting, we use the equation: where: T = Cutting time in minutes. L = Total length drill must move. Fm = Feed in inches per minute. which should yield:= 0.464 minutes cutting time

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Drill Press Worky The cutting time thus calculated does y

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Not all speeds may be not include an allowance, which must available on the machine being be added to determine the standard used. time. y For example, the The allowance should include time for recommended spindle speed variations in material thickness and for a given job might be 1,550 for tolerance in setting the stops, both of which affect the cycle cutting time. rpm, but the machine may be capable of running only 1,200 Personal and unavoidable delay rpm. In that case, 1,200 rpm allowances should also be added to should be used as the basis for arrive at an equitable standard time. computing standard times.

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Lathe Worky Many variations of machiney All of these lathes are used primarily

tools are classified as lathes. These include Engine lathe Turret lathe Automatic lathe

with stationary tools or with tools that translate over the surface to remove material from the revolving work, which includes Forgings Castings, or Bar Stock

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Lathe WorkFactors that alter speeds and feeds:

the condition and design of the machine tool the material being cut the condition and design of the cutting tool the coolant used for cutting the method of holding work, and the method of mounting the cutting tool.

As in drill press work, feeds are expressed in thousandths of an inch per revolution, and speeds in surface feet per minute.40

Lathe Worky To determine the cutting time for L inches of cut, the length of

cut in inches is divided by the feed in inches per minute, or:where: T = Cutting time in minutes. L = Total length of cut Fm = Feed in inches per min. and where: f = Feed in inches per rev. Sf = Speed in surface feet per min. d = Diameter of work in inches.

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Milling Machine Worky Milling refers to the removal of

y In milling work, as in drill press and material with a rotating lathe work, the speed of the cutter is multiple-toothed cutter. expressed in surface feet per minute. y While the cutter rotates, the work is fed past the cutter. This Feeds or table travel are usually expressed in thousandths of an inch differs from a drill press for per tooth. which the work is usually stationary.

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Milling Machine Worky To determine the cutter speed in y To determine the feed of the work

revolutions per minute from the surface feet per minute and the diameter of the cutter, use the following expression: where:Nr = Cutter speed in rev. per min. Sf = Cutter speed in ft. per min. d = Outside diameter of cutter in mins.43

in inches per minute into the cutter, use the expression:

Fm = fnt Nrwhere:Fm = Feed of the work into the cutter in inches per minute. f = Feed of cutter in inches per tooth. nt = Number of cutter teeth. Nr = Cutter speed in revolutions per minute.

Milling Machine Worky The number of cutter teeth

suitable for a particular application may be expressed as: where: Ft = Chip thickness nt = Number of cutter teeth Fm = Feed of the work into the cutter in inches per minute44

To compute the cutting time on milling operations, the analyst must take into consideration the lead of the milling cutter when figuring the total length of cut under power feed. This can be determined by triangulation, as illustrated in Figure 12-6, which shows the slab-milling of a pad.

Milling Machine Worky In this case, to arrive at they In preceding example, suppose we

total length of the work (8 inches). By knowing the diameter of the cutter, you can determine AC as being the cutter radius, and you can then calculate the height of the right triangle ABC by subtracting the depth of cut BE from the cutter radius AE, as follows:

assume that the cutter diameter is 4 inches and that it has 22 teeth. The teeth per tooth is 0.008 inch, and the cutting speed is 60 feet per minute. We can compute the cutting time by using the equation: where: T = Cutting time in minutes. L = Total length drill must move. Fm = Feed in inches per minute.

BC = AC2 AB245

Milling Machine Worky Then, L would be equal to (8 inches 1 BC) and

BC = 4-3.06 = 0.975 Therefore, L = 8.975 Fm = fnt Nr Fm = (0.008) (22) Nr or Then Fm and46

= (0.008)(22)(57.3) = 10.1 inches per minute

Standard Data Usage

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Standard Data UsageFor easy reference, constant standard data elements should be tabulated and filed under

the machine or the process. variable data can either be tabulated or expressed as a curve or equation, and then filed under the facility or operation class.

In some instances, for which standard data are broken down to cover a given machine and class of operation, it may be desirable to combine constants with variables and tabularize the summary. This quick-reference data express the time allowed to perform a given operation completely.48

Standard Data UsageFigure 12 7 illustrates welding data in which the constants change electrode and arc are combined with the variables weld cleaning and welding. The result is the workhours required to weld 1 inch for various sizes of welds.

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Table 12-2 illustrates standard data for a given facility and operation class for which elements have been combined.

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Standard Data Usage

Table 12-3 illustrates standard setup data for No.5 Warner & Swasey turret lathes at a specific plant

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Standard Data UsageThe allowed setup time would equal B+C+D+F+G+H+I = 8.70 minutes Element A is not included in the setup time because of the simplicity of the job. Element E is not included in the setup since, in this case, first-piece inspection is not performed by the inspector.

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Standard Data Usage

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Standard Data Usagey After investigating the design of the drill jig to be used and

making an analytical motion study of the job to determine the elements required to perform the operation, the analyst compiles an element summary, as shown below.

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Standard Data Usagey The actual drilling time to drill the two holes must be added to

this 0.278-minute time. As previously outlined, this can be readily determined. For a -inch diameter drill used for drilling cast iron, a surface speed of 100 feet per minute and a feed of 0.008 inch per revolution would be used. y One hundred surface feet per minute would equal 764 revolutions per minute. where:

Sf = Surface feet per minute. d = Diameter of drill in inches.55

Standard Data Usagey However, investigation of the drill press for which this work has been

routed reveals that 600 rpm or 900 rpm are the closest speeds available to the recommended 764 rpm. The analyst proposes to use the slower speed, due to the condition of the machine, and determines the drilling time as follows:

Fm = (600)(0.008) = 0.48 inches per minute

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The EndThank you and God bless.

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