# Integrating Spreadsheet Templates and Data Analysis into Fluid Power Instruction

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1 Volume 16, Number 4 - August 2000 to October 2000 Integrating Spreadsheet Templates and Data Analysis into Fluid Power Instruction By Dr. Bruce Marsh KEYWORD SEARCH Curriculum Fluid Power Teaching Methods Reviewed Article The Official Electronic Publication of the National Association of Industrial Technology

3 analyses and incorporates proper cell referencing and input data structuring, the usefulness of the template can be significantly increased. One of the principal advantages of the what if analysis structure is the overall time savings it provides; tedious and repetitive manual calculations are not required. Most templates that are designed and constructed for integration in fluid power instruction will automatically possess this capability to varying degrees and can be modified to further enhance this capability. Two examples that demonstrate the use and application of spreadsheet templates in fluid power instruction can be seen in Problem-Solving Templates 1 and 2. Although both of these templates have given values in their problem statements and questions, the structure of the templates permit the entry of any value into the givens cells as well as the automatic recalculation of new solution values using new given, provided cell formulas and references are entered correctly. Another aspect of these templates that should be noted is their step-by-step solution approach (single formula calculations). This approach was used solely for instructional purposes. In reality, most experienced template designers would combine multiple solution steps into a singlestep formula expression. Regression Analysis of Fluid Power Data Simple and multiple regression (macro-based) is an important aspect of analysis and is available in Excel through the Data Analysis option under the Tools menu or through the Add-ins option under the Tools menu, if Data Analysis is not listed as a Tools option. Simple regression analysis is also available using the Trendline option in Excel. This option, sometimes referred to as trend forecasting, is a graphicsbased approach for conducting simple regression analyses. The usefulness of the trendline analysis lies in the ability of users to know when and how to incorporate and utilize the different regression analyses. Figures 1 and 2 indicate, respectively, the trendline types and display options available within Excel. As mentioned previously, it is important for users to develop an understanding of the ways in which each of the trendline types can be used. For example, a comparison of R- squared values of four trendline types (linear, power, logarithmic, and exponential) can be performed to determine the regression method that yields the maximum accountability of variability (the greater the accountability, the greater the validity of the regression equation). To begin the trendline analysis process, an XY scatterplot of the data is needed. The scatterplot is not only a necessary first step in the trendline analysis process but it can also be used to determine if a regression analysis data is actually warranted. An added advantage of the trendline analysis is that the regression equation and R-squared value can be incorporated on the chart of the plotted 3

4 data and will automatically update if there is a change in the data set. An example that demonstrates the effectiveness of the trendline analysis and R-squared comparison technique can be seen in an attempt to simplify the relationship between pressure, force, and area (PFA). As indicated in published textbooks, Industrial Hydraulics Manual (1992) and Esposito (1998), the PFA relationship is characterized through the following equation: Pressure (P) = Force (F) / Area (A). This formula is used extensively to determine system pressure requirements given a particular cylinder/piston diameter and output force requirement; variations of the formula are also used to conduct reverse order calculations. Regardless of the formula variation used, one aspect of all PFA calculations is the need to convert cylinder/piston diameter to an area. Since this conversion aspect adds an additional calculation to the entire process [ Area (A) = * Diameter 2 ], a simplified, single-step formula expression would be desirable. To determine the feasibility of establishing a simplified, singlestep expression incorporating pressure, force, and diameter (PFD) variables, the following four-step analysis was conducted. Step 1A: Establishing Primary Variables and Data. To begin the analysis process, four columns of data were generated. Diameter data was selected in increments of 0.25 inches starting with one inch and ending at six inches. Area data was calculated from the diameter data and used, along with the test force value of 500 lbs, to calculate theoretical pressure values. Diameter and Theoretical Pressure data were labeled as X and Y variables, respectively, for use in the Step 1B regression analysis. Step 1B: Conducting Regression Analysis of Diameter (X) and Pressure Force = 500 lbs. The basis for this analysis was to determine the extent of the relationship between the identified X and Y variables as well as a valid regression approach and equation. It should be noted that any regression equation derived from this data set would only be valid with a force of 500 lbs. The results of this analysis, Figures 3A to 3D, indicated that the Power regression yielded the maximum accountability of variability (R-squared = 1.0) and thus, the most valid regression equation. This equation, Equation (1), was: y 1 = x 1, where y 1 = pressure (psi) and x 1 = diameter (in). Step 2A: Establishing Secondary Variables and Data. It was noted that the slope coefficient in the Power regression equation changed whenever the Test Force was varied. Consequently, it was deemed that an equation could be developed to replace the Equation (1) slope coefficient (636.62) to overcome the force limiting factor of the equation. Using the what if capability of Excel, the following table of Test Force (X) and Slope Coefficient (Y) data was generated by varying the Test Force in the Data Table of Primary Variables and recording the slope 4

5 coefficient change in the associated Power regression equation (Figure 3B): Step 2B: Conducting Regression Analysis of Test Force (X) and Slope Coefficient (Y). The basis for this analysis was to determine the extent of the relationship between the X and Y variables in Table 2 as well as a valid regression approach and equation. The results of this analysis indicated that three regression analyses, linear, power, and polynomial, yielded R-squared values of 1.0 and any one of these three could be used. The Power regression equation detailed in Figure 4, was selected due to its simplicity. This equation, y 2 = x 2 where y 2 = forced-based coefficient and x 2 = force (lbs), was labeled Equation (2). The regression equations of the linear and polynomial regression analyses that were not selected for use were, respectively, y 2 = 1.273x and y 2 = - 9.0E-10x x Step 3: Pressure, Force, Diameter (PFD) Equation Development. As mentioned previously, the development of Equation (2) permitted the replacement of the slope coefficient in Equation (1) and enabled the determination of pressure at any applied force and diameter. Algebraically, the conversion was as follows: Figure 1. Trendline Type. To access the trendline type dialog box, create an XY scatter chart, double click the chart to enter the edit mode, single click on a plotted point, and select Trendline under the Insert pulldown. Adapted from Microsoft Excel. Figure 2. Trendline Options. The trendline options dialog box is accessible by selecting the Options tab whenever the trendline dialog box is displayed. If the trendline has already been created but needs to be edited, double click the chart to enter edit mode and double click the regression line. Adapted from Microsoft Excel. Equation (1) y 1 = x 1 where, y 1 = Pressure (psi) x 1 = Diameter (in) Equation (2) y 2 = x 2 where, y 2 = Forced-Based Coefficient x 2 = Force (lbs.) Equation (3A) y 1 = y 2 * x 1 where, Equation (1) coefficient (636.62) replaced with y 2 equation Equation (3B) y 1 = (1.273 x 2 ) * x 1 Equation (3C-1) Pressure = * Force * Diameter 2 Table 1. Data Table of Primary Variables 5

6 Equation (3C) Force = Pressure / (1.273 * Diameter 2 ) Equation (3C-3) Diameter = [ Pressure / (1.273 * Force) ] 0.5 Step 4: Pressure, Force, Diameter (PFD) Equation Validation. Equation validation is an important aspect, especially one that incorporates two regression equations. To validate the PFD equation, the traditional, two-step PFA equation was used to calculate the theoretical pressure that would be required to lift a force of 500 lbs using a cylinder with a 2.5 inch diameter piston. The results of this calculation were as follows: Traditional PAF Equation: Pressure = Force / Area = 500 lbs / 4.91 in 2 = psi Area = * (Diameter) 2 = * (2.5 in) 2 = 4.91 in 2 The tradition approach indicated that a system pressure of approximately 102 psi would be required. Using the single-step Equation (3C-1), the theoretical pressure was calculated using the same force and diameter values, 500 lbs and 2.5 inch, respectively. The results of this calculation were as follows: PFD Equation (3C-1): Pressure= * Force * Diameter 2 = * 500 lbs * (2.5 in) = * 0.16 = psi The PFD equation indicated that a theoretical system pressure of approximately 102 psi would also be required to lift a force of 500 lbs using a cylinder with a 2.5 inch diameter piston; formula validation was successful and can be used in fluid power calculations. Summary This paper is intended to aid professionals in the field into the ways 6

7 and means upon which a spreadsheet templates can be integrated into a Fluid Power instruction. The inherent flexibility and adaptability of spreadsheet templates in data and formuladriven classes make it a useful instructional tool. If spreadsheet integration is successful, student learning of Fluid Power concepts can be enhanced; thereby, strengthening students problem solving skills, facilitating better and faster decision-making, and increasing the their marketability as Industrial Technologist. It should also be noted that the experiences provided through spreadsheet-based instruction can provide students with valuable insight for the utilization of this software in other classes or on-the-job before and after graduation. References Esposito, A. (1998). Fluid power with applications (3rd ed.). New Jersey: Prentice Hall. Microsoft excel user s guide (version 5.0). (1994). Microsoft Corporation Middleton, M. (1997). Data analysis using microsoft excel. Belmont, California: Wadsworth Publishing Co. Vickers Incorporated (1992). Industrial hydraulics manual. Rochester Hills, Michigan: Vickers Incorporated Training Center. Table 2. Data Table of Secondary Variables 7

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