Paper ID #34697

Teaching GD&T Fundamentals in the Course Design of Machine Elements

Dr. Xiaobin Le P.E., Wentworth Institute of Technology

Professor, Ph.D., PE., Mechanical Engineering Program, School of Engineering, Wentworth Institute ofTechnology, Boston, MA 02115, Phone: 617-989-4223, Email: Lex@wit.edu, Specialization in Computer-Aided Design, Mechanical Design, Finite Element Analysis, Fatigue Design, Solid Mechanics and Engi-neering Reliability

Prof. Anthony William Duva P.E., Wentworth Institute of Technology

Anthony W. Duva An Associate Professor in the Mechanical Engineering and Technology Departmentat Wentworth Institute of Technology since 2001 with 14 years of prior full time industrial experience.He has worked in the design of various technologies from advanced underwater and ultrahigh altitudepropulsion systems to automated manufacturing equipment. His interests include advanced thermal andmechanical system design for green power generation.

Prof. Richard L. Roberts, Wentworth Institute of Technology

Associate Professor Mechanical Engineering Program College of Engineering Wentworth Institute ofTechnology, 550 Huntington Ave., Boston, MA 02115

c©American Society for Engineering Education, 2021

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Teaching GD&T Fundamentals in the Course Design of Machine Elements

Abstract: Geometric Dimensioning and Tolerancing (GD&T) is an extremely important skill for mechanical engineering students who will mainly design mechanical devices and components. However, a GD&T course is typically not included in an undergraduate mechanical engineering curriculum. In our mechanical engineering curriculum, bits of basic concepts of GD&T are briefly mentioned or discussed in several different courses. It has been observed in the last several years that some students in their senior capstone project designs still didn’t know how to properly define assembly dimension tolerances or component dimension tolerances. In the last two years, the authors used one and a half weeks out of a total of a fifteen-week semester to teach GD&T fundamentals in the course Design of Machine Elements. Homework assignments and quizzes were used to check or to reinforce their understanding of GD&T fundamentals. Also, students were requested to implement what they had learned about GD&T fundamentals in two design projects. This paper will present the approach of teaching GD&T fundamentals and present the results from a class survey. The results indicated that our teaching GD&T fundamentals did facilitate students to develop a better understanding of the GD&T fundamentals and to determine dimension tolerances of free dimensions and mating dimensions. Keywords: Mechanical Engineering, Mechanical Design, Geometric Dimensioning and Tolerance (GD&T), Free Dimension, Mating Dimension, Types of Fits, Free Dimension Tolerance, Mating Dimension Tolerance 1. Introduction For mass production, to guarantee interchangeability of the same components in a product, dimension tolerances of the components must be properly specified using geometric dimensioning and tolerancing (GD&T). GD&T permits mechanical engineers and manufacturing staff to communicate efficiently and effectively geometric features and allowable variations that each feature may contain. Therefore, utilizing GD&T is an essential tool and skill for mechanical engineers who will mainly design mechanical devices or components which has been recognized as an increasingly integral part of engineering design practice[1,2,3,4,5]. For several reasons, GD&T is not commonly offered as a required course and is typically only briefly mentioned or discussed in undergraduate mechanical engineering programs [6,7,8,9]. One reason is that GD&T is often considered part of on-the-job or technical training. A second reason might be that GD&T can be a particularly tricky topic to teach due to its complexity, breadth of information, and required spatial reasoning. A third reason might be that GD&T concepts can be difficult for students to learn because of the 3D nature of geometric tolerance zones. A fourth reason might be the cap of credits of a mechanical engineering curriculum. For example, the total credits of the mechanical engineering program at our university can not exceed 136. With the help of some advanced techniques such as 3D printers, 3D parametric models, and a coordinate measuring machine (CMM), there is an increasing number of publications explored regarding how to teach GD&T for undergraduate engineering students [6,8,10,11].

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In our mechanical engineering program, bits of basic concepts of GD&T were briefly mentioned or discussed in several different courses. Students didn’t have a chance to get a basic understanding of GD&T fundamentals. It was observed in the last several years that some students in their senior capstone design projects still didn’t know how to properly define assembly tolerances and component tolerances. In the required course Design of Machine Elements, most of the students could explain the dimension tolerance of a part such as a hole with dimension tolerance ∅1.2000.001

0.005, but few students could explain the assembly dimension tolerance. For example, a shaft is assembled into a hole with an assembly tolerance ∅1.2000.001

0.005. Few students could properly interpret this assembly tolerance ∅1.2000.001

0.005. Also, some students only had limited knowledge about the various types of fits. In other words, many students lacked a basic understanding of GD&T fundamentals. GD&T is a very complicated topic and our university does not offer a course dedicated to GD&T in our mechanical engineering program. However, since GD&T is an essential tool and skill for mechanical engineering students, we proposed an approach for teaching GD&T fundamentals so that students could have a better understanding of GD&T fundamentals. This paper will present these activities and some feedback from the interactions with students and a class survey. The results indicated that our teaching GD&T fundamentals did facilitate students to develop a better understanding of GD&T fundamentals and the ability to determine dimension tolerances of free dimensions and mating dimensions. 2. Teach GD&T fundamentals in the course Design of Machine Elements Background Our mechanical engineering program doesn’t offer a GD&T course, only basic concepts of GD&T were mentioned or briefly explained in different courses. In their Freshmen year, students were introduced to the concept of dimension variations, a basic concept of the GD&T first time in the course ENG1600-Introduction to CAD/CAM, which is a one-credit course with one two-hour lab per week. When they created a drawing, they were told that a dimension should have some variation, that is, dimension tolerance. When they manufactured a simple part, they realized that they could not reach an exact expected dimension. They began to understand that an exact dimension could not be achieved and that a dimension should be specified with a variation or tolerance. In their Sophomore year, students learned a little more about GD&T in MECH2300-Engineering Graphics. This course is a three-credit course with a one-hour lecture and two two-hour labs per week. In this course, the dimension tolerances were discussed for dimensioning in a mechanical drawing along with a brief introduction to the various types of fits. The concept of default dimension tolerances was also discussed when a sheet format of a mechanical drawing was explained. Also in their Sophomore year, students realized that a dimension did have dimension tolerances in the course MEH2500-Mechanics of Materials, which is a four-credit course with two one-and-a-half-hour lectures and one two-hour lab per week. In this course, there were several physical material strength test labs. Before each material strength test, students were asked to measure the dimensions of bars or side lengths of rectangular shapes. they found that the measured dimensions such as the diameter of the bars or the side lengths were different even though the nominal dimensions were the same. In their junior year, they had a course MECH3000-Design of Machine Elements. Some basic concepts

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such as dimension tolerance and types of fits were discussed, typically in one two-hour lecture. Different definitions of types of fits were briefly explained. This was the second time that the concepts of types of fits were discussed in a course. In their senior year, there was a two-part capstone design course sequence: MECH5000-Mechanical Capstone Analysis and MECH5500-Mechanical Capstone Project. MECH5000 Mechanical Capstone Analysis is a three-credit course with one one-hour lecture and two two-hour labs per week. MECH5500-Mechanical Capstone Project is a four-credit course with a one-hour lecture and three two-hour labs. MECH5000 -Mechanical Capstone analysis is a paper design of the capstone project. MECH5500-Mechanical Capstone project is to manufacture and test the paper design which has been completed in MECH5000. These are the courses students need to implement GD&T in their design. Since these courses were student-driven, only some basic concepts of GD&T were discussed during lectures. Most of the issues related to GD&T were solved during team meetings with capstone project advisors. From the activities mentioned above, bits of basic concepts of GD&T were briefly discussed or mentioned in different courses. It was obvious that students lacked a detailed understanding of GD&T fundemtals[6,8,9] The objectives of teaching GD&T fundamentals Over the last several years, the authors have been thinking about how to tackle this issue that our mechanical engineering students lacked a basic understanding of GD&T. As mentioned, GD&T is not offered as a single technical course not only because the GD&T is a difficult topic to teach [6,7,8,9], but also because there are some constraints of the typical mechanical engineering curriculum such as the cap on total credits. Due to the limited time for covering GD&T, we proposed an approach for teaching GD&T fundamentals in an existing course, in which we will focus on dimension tolerances and types of fits. Because of the complexity of geometric tolerance, we will only explain basic definitions of geometric tolerances and then explain GD&T’s Rule 1, which describes the relationship between dimension tolerances and geometric tolerancing. We chose the course MECH3000-Design of Machine Elements to implement this approach because students can directly utilize GD&T fundamentals in their design projects. The objectives or the key topics of teaching the GD&T fundamentals in this approach are: • Have a basic understanding of the definitions of geometric tolerancing and Rule 1 in GD&T • Have a solid understanding of a free dimension and a mating dimension • Be able to determine the dimension tolerance of a free dimension • Have a solid understanding of types of fits • Be able to determine the dimension tolerances of mating dimensions when the assembly

tolerances based on the design intent are specified. • Be able to run simple dimension tolerance analysis of a chain of dimensions The concise descriptions of teaching GD&T fundamentals In the last two years, the authors used one and a half weeks out of a total of fifteen-week-semester to teach GD&T fundamentals in the course MECH3000-Design of Machine Elements. The following are concise descriptions of the delivered topics, which are based on literature [12,

13, 14].

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Topic one: Some basic definitions and Rule 1 of GD&T Some basic concepts and definitions of GD&T are easy to be explained and readily accepted by students such as: What is GD&T?; What are the benefits of GD&T? What is dimension tolerance? What is MMC (Maximum material condition)? What is LMC (the least material condition)? For example, a dimension tolerance such as the diameter ∅1.25" −0.005

+0.005 of a cylindrical bar is easily explained and understood by most mechanical engineering students. It is commonly accepted that geometric tolerancing when coupled with different datums and geometric modifiers is typically complicated to explain and very hard for students to grasp in a short lecture without many visualized examples or labs [6,7,8,9]. For teaching GD&T fundamentals in our approach, we focused on explaining the four geometric features: size, location, orientation, and form as shown in Figure 1[13]. The variation of these features will be specified by geometric tolerancing.

Figure 1: Schematics used for explaining four geometric features

When employing geometric tolerancing, the 14 geometric characteristics [12,13] such as concentricity, cylindricity, parallelism, straightness, flatness, etc. were simply displayed by their definitions and explained with some schematic pictures as shown in Figure 2. The basic concepts of geometric characteristics were explained with schematic pictures and the use of visualization along with the definitions to be easily understood by students. We did not however expect they would have a full understanding of geometric characteristics and could apply geometric tolerancing in their design. The overall objective was to ensure students were aware of these 14 geometric characteristics and had some basic understanding of them. We informed students that they needed to take additional training for geometric tolerancing in the future.

Figure 2: Schematics used for explaining geometric characteristics

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The main focus for teaching GD&T fundamentals was regarding dimension tolerances. The Y14.5 standard specifies a default tolerance zone for features of size through what is referred to as Rule 1, also known as the envelope principle [13] when there are only dimension tolerances without geometric tolerancing. This rule states that when only a tolerance of size is specified for a feature of size, the limits of size prescribe the extent of allowed variation in its geometric form. Specifically, the envelope principle (Rule 1) states that the surface of a feature of size may not extend beyond an envelope of perfect form at MMC (Maximum Material Condition)[13]. In this way, Rule 1 of GD&T shows the relationship between dimension tolerance and geometric tolerancing. We used some schematic pictures to explain the envelope principle such as examples shown in Figure 3.

Figure 3: Schematics used for explaining the envelope principle

Topic two: Types of dimensions For any component, there are two types of dimensions: a free dimension and a mating (assembling) dimension.

A free dimension is defined as the dimension the variation of which will not affect or interfere with other parts for the required functions in the assembly.

A mating (assembly) dimension is defined as the dimension the variation of which will affect other parts and the required functions in the assembly.

Let us assume that the design intent in this assembly shown in Figure 4 is that part 2 can freely slide along the slot of part 1. In this case, the width of the slot of part 1 and the width of part 2 are mating dimensions as shown in Figure 4. All other dimensions, in this case, will be free dimensions as shown in Figure 4.

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. Figure 4: Schematic used for explaining types of dimensions

Topic three: Dimension tolerance of a free dimension For a mechanical part, generally, the maximum possible variation of the dimension could be 1/16”, that is, 0.063”. When the variation of a dimension is over 1/16” and this variation does not affect the function of the assembly, it is a free dimension. Since the tolerance of a free dimension will not affect other parts and assembly functions, its dimension tolerance will be determined by a manufacturing process with the least manufacturing cost. This is typically the default tolerances of a company. In other words, the dimension tolerance of a free dimension is solely determined by the manufacturing process. Tables 1 and 2 from the Machinery’s handbook [14] were presented to guide students in determining the dimension tolerance of a free dimension. Table 1 shows the tolerance grade capability of some typical machining processes. Table 2 gives the ANSI standard tolerance at corresponding tolerance grades. After the manufacturing process has been determined for a component, students could use these two Tables to determine the dimension tolerance of a free dimension.

Table 1 Relation of Machining Processes to Tolerance Grades [14]

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Table 2 ANSI Standard Tolerance ANSI B4.1-1967(R1987)[14]

Topic four: Types of fits and ANSI standard fits For a mating dimension, two components will be assembled or mated together through the design interface of mating dimensions. Let us use a generic hole to be an empty shape of geometry and a generic shaft to be a solid shape of geometry as shown in Figure 5.

Figure 5 A generic hole and a generic shaft

Let us use 𝑑𝑑ℎ𝐿𝐿

ℎ𝑈𝑈and 𝑑𝑑𝑠𝑠𝐿𝐿𝑠𝑠𝑈𝑈 to represent the generic hole and the generic shaft dimension tolerances.

𝑑𝑑 is the nominal dimension of the mating dimension. ℎ represents a hole and 𝑠𝑠 a shaft. The subscript 𝑈𝑈 represents the upper limit of the dimension tolerance and the subscript 𝐿𝐿 the lower limit of the dimension tolerance. For example, a generic hole has a diameter of 1.500” with a dimension tolerance of ±0.004" will be 𝑑𝑑ℎ𝐿𝐿

ℎ𝑈𝑈 = ∅1.500" −0.004+0.004. Let us use 𝑑𝑑𝑎𝑎𝐿𝐿

𝑎𝑎𝑈𝑈 to represent the assembly tolerances. 𝑎𝑎 represents assembly tolerance. Then, the governing equations for assembly tolerance of mating dimensions are:

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𝑎𝑎𝑈𝑈 = ℎ𝑈𝑈 − 𝑠𝑠𝐿𝐿 = �> 0 Maximum clearance < 0 Minimum interference (1)

𝑎𝑎𝐿𝐿 = ℎ𝐿𝐿 − 𝑠𝑠𝑈𝑈 = �> 0 Minimum clearance < 0 Maximum interference (2)

Based on the values of 𝑎𝑎𝑈𝑈 and 𝑎𝑎𝐿𝐿 for mating dimensions, there are three possible types of fits: Clearance fit, Interference fit, and Transition fit. When both 𝑎𝑎𝑈𝑈 and 𝑎𝑎𝐿𝐿 are positive, it is a clearance fit, where there is always a gap between the shaft and the hole. The dimension of the hole is always larger than the dimension of the shaft for a clearance fit. When both 𝑎𝑎𝑈𝑈 and 𝑎𝑎𝐿𝐿 are negative, it is an interference fit, where there is always some interference between the shaft and the hole. The dimension of the shaft is always larger than the dimension of the hole for an interference fit. When 𝑎𝑎𝑈𝑈 is positive and 𝑎𝑎𝐿𝐿 is negative, it will be a transition fit, where there might have a gap or might have interference between the shaft and the hole. In this case, sometimes the dimension of the hole is larger than the dimension of the shaft, but sometimes, the dimension of the shaft is larger than the dimension of the hole. In our approach, we used several examples to explain and demonstrate the governing equations to facilitate students developing a solid understanding of types of fits and the meaning of assembly tolerances. For example, as shown in Figure 6, per the governing equations (1) and (2), we have:

𝑎𝑎𝑈𝑈 = ℎ𝑈𝑈 − 𝑠𝑠𝐿𝐿 = 0.002" − (−0.005") = 0.007" 𝑎𝑎𝐿𝐿 = ℎ𝐿𝐿 − 𝑠𝑠𝑈𝑈 = 0 − (−0.002)=0.002"

So, the assembly tolerance in this example will be 𝑑𝑑𝑎𝑎𝐿𝐿𝑎𝑎𝑈𝑈 = ∅0.500" 0.002

0.007. The assembly tolerance ∅0.500" 0.002

0.007 will be read as a clearance fit with a possible maximum clearance of 0.007” and a possible minimum clearance of 0.002”.

Figure 6: An example of a clearance fit

After the governing equations were fully explained, we introduced the ANSI standard fits (ANSIB4.1-1967(R2009))[14]. We provided the book link of the ANSI standard fits for students so that students could access the full tables of the ANSI standard fits. We fully explained the proper use of the tables of ANSI standard fits with several examples to make sure that students can obtain proper dimension tolerances of a hole and a shaft when the assembly tolerance was specified. The various types of ANSI standard fits are listed in Table 3. One example of the ANSI standard fit table is provided in Table 4.

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Table 3 ANSI Standard fits Type of fits Class Features RC RC1-9 Running or sliding clearance fit LC LC1-11 Clearance locational fit LT LT1-6 Transition locational fit LN LN1-3 Interference locational fit FN FN1-5 Force and shrink fit

Table 4 Partial table of ANSI running and Sliding fits ANSI B4.1-1967(R2009) [14]

Topic five: Dimension tolerances of mating dimensions Unlike free dimensions, a mating dimension tolerance can not be determined by a manufacturing process and must satisfy the required assembly tolerance, which is specified per required functions. One of the key objectives of teaching GD&T fundamentals is to teach students how to determine dimension tolerances of mating dimensions. When mating dimensions are one generic hole with one generic shaft, we discussed three approaches to determine dimension tolerances of mating dimensions. Approach one-Use the ANSI standard fit table: When the assembly tolerance such as type of fits and corresponding class level is specified per required function, we could directly use the ANSI standard fits[14] such as Table 4 to obtain corresponding dimension tolerances of the hole and shaft dimension. After the assembly tolerance per required functions is specified, there are four unknowns ℎ𝑈𝑈, ℎ𝐿𝐿, 𝑠𝑠𝑈𝑈 and 𝑠𝑠𝐿𝐿 in the two governing equations (1) and (2). Therefore, we can preselect dimension tolerances of either the hole or a shaft first and then use the two governing equations to calculate the rest of the unknowns. When we predetermine the dimension tolerance of a hole or a shaft,

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we need to be aware of the embedded relationship between the assembly tolerance, the shaft tolerance, and the hole tolerance in the governing equations. If we use Equation (1) and subtract Equation (2), we have:

𝑎𝑎𝑈𝑈 − 𝑎𝑎𝐿𝐿 = (ℎ𝑈𝑈 − ℎ𝐿𝐿) + (𝑠𝑠𝑈𝑈 − 𝑠𝑠𝐿𝐿) (3)

This equation shows that the variation of assembly tolerance is equal to the sum of the variations of the hole dimension tolerance and the shaft tolerance. Based on which method we choose, the hole or the shaft, we can have the following two different approaches. Approach two- Basic hole system: After the assembly tolerance per required functions is specified and if the hole dimension tolerance 𝑑𝑑ℎ𝐿𝐿

ℎ𝑈𝑈 is predetermined, the dimension tolerance of the shaft can be calculated through the following two equations.

𝑠𝑠𝐿𝐿 = ℎ𝑈𝑈 − 𝑎𝑎𝑈𝑈 (4) 𝑠𝑠𝑈𝑈 = ℎ𝐿𝐿 − 𝑎𝑎𝐿𝐿 (5)

Approach three- Basic shaft system: After the assembly tolerance per required functions is specified and if the shaft dimension tolerance 𝑑𝑑𝑠𝑠𝐿𝐿

𝑠𝑠𝑈𝑈 is predetermined, the dimension tolerance of the hole can be calculated through the following two equations.

ℎ𝑈𝑈 = 𝑠𝑠𝐿𝐿 + 𝑎𝑎𝑈𝑈 (6) ℎ𝐿𝐿 = 𝑠𝑠𝑈𝑈 + 𝑎𝑎𝐿𝐿 (7)

We used several examples to fully explain how to determine dimension tolerances of mating dimensions by using the above three approaches. Topic six: Dimension tolerance analysis of a chain of dimensions When an assembly tolerance is involved as part of a chain of dimension tolerances as shown in Figure 7[13], the biggest dimension can be treated as a generic hole and the sum of all other chain dimensions can be treated as a generic shaft dimension. In this case, we only discussed how to run an assembly tolerance analysis to see what type of fits would be present. Let us use 𝐿𝐿 𝑡𝑡𝐿𝐿

𝑡𝑡𝑈𝑈 to represent the biggest open dimension in a chain of dimensions, which is treated as a generic hole’s dimension 𝐿𝐿. 𝑡𝑡𝑈𝑈 and 𝑡𝑡𝐿𝐿 are the upper limit and the lower limit of the biggest open dimension 𝐿𝐿. Let us use 𝐿𝐿𝑖𝑖 𝑡𝑡𝐿𝐿𝐿𝐿

𝑡𝑡𝑈𝑈𝐿𝐿 to represent the dimension tolerance of the ith chain dimension 𝐿𝐿𝑖𝑖. 𝑡𝑡𝑈𝑈𝑖𝑖 and 𝑡𝑡𝐿𝐿𝑖𝑖 are the upper limit and lower limit of the ith chain dimension 𝐿𝐿𝑖𝑖. The sum ∑𝐿𝐿𝑖𝑖 will be treated as a generic shaft. Then, the governing equations for a chain of dimensions are:

𝑤𝑤𝑚𝑚𝑎𝑎𝑚𝑚 = (𝐿𝐿 + 𝑡𝑡𝑈𝑈) − ∑(𝐿𝐿𝑖𝑖 + 𝑡𝑡𝐿𝐿𝑖𝑖) (8)

𝑤𝑤𝑚𝑚𝑖𝑖𝑚𝑚 = (𝐿𝐿 + 𝑡𝑡𝐿𝐿) −�(𝐿𝐿𝑖𝑖 + 𝑡𝑡𝑈𝑈𝑖𝑖) (9) Where, 𝑤𝑤𝑚𝑚𝑖𝑖𝑚𝑚 and 𝑤𝑤𝑚𝑚𝑎𝑎𝑚𝑚 are the lower and upper limits of the assembly tolerance. A positive value means a gap, and a negative value is an interference.

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Figure 7: Schematic of a chain dimension

3. Implementations

In the last two years, we used one and a half weeks out of a total of fifteen-week-semester to teach the GD&T fundamentals in the course MECH3000-Design of Machine Elements. We then asked students to practice GD&T fundamentals in one homework assignment. We also used one one-hour quiz to test their knowledge of GD&T fundamentals. There were two class design projects for our MECH3000-Design of Machine Elements. The first project was the evaluation of a toggle clamp and the second class project was to design a single-stage gearbox. Students were required to implement GD&T fundamentals in these two projects and to determine the dimension tolerance of free dimensions along with mating dimensions. For example, the pivot pins and the holes in the evaluation of a toggle clamp mating dimensions were analyzed. The bearing between the shaft and housing in the single-stage gearbox project were also examples of mating dimensions analyzed. 4. Class survey and data analysis At the end of the course, we asked students to participate in a class survey to obtain feedback from students. We received 20 responses out of a total of 24 students with an 83.3 percent response. The class survey contained nine questions. The survey results for questions 1 to 5 are listed in Table 5. From Table 5, we have the following survey results: • 100 percent of students strongly agreed or agreed that the lecturing of GD&T fundamentals

facilitated them to have a better understanding of GD&T. • 95% percent of students strongly agreed or agreed that they knew the difference between a

free dimension and a mating dimension. • 90% percent of students strongly agreed or agreed that they had a better understanding that

the dimension tolerance for a free dimension will typically be determined by the company’s least-cost manufacturing process.

• 85% percent of students strongly agreed or agreed that they had a better understanding of the envelope principle. But 15% of students still didn’t understand the envelope principle. This means that more effort should be devoted to explaining the envelope principle in the future.

• 95% percent of students strongly agreed or agreed that they had a better understanding of the types of fits and knew how to choose mating dimension tolerances from the ANSI standard fits tables.

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Table 5 The survey results for the survey questions 1 to 5 Question 1: The lecturings in this class facilitated me to have a better understanding of the geometric dimensioning and tolerances Choice Strongly agree Agree No opinion disagree Strongly disagree Results 9 11 0 0 0 Percentage 45% 55% 0% 0% 0% Question 2: I had a better understanding of the definitions of and differences between a free dimension and a mating dimension. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 10 9 1 0 0 Percentage 50% 45% 5% 0% 0% Question 3: I had a better understanding that the dimension tolerance for a free dimension will typically be the default tolerance which is determined by the company’s least-cost manufacturing process. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 13 5 2 0 0 Percentage 65% 25% 10% 0% 0% Question 4: I had a better understanding of Rule #1 of the geometric dimensioning and tolerancing that according to Rule #1, the variations of geometric shape and form are still confined by corresponding dimension tolerance even the geometric tolerance is not directly specified. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 6 11 3 0 0 Percentage 30% 55% 15% 0% 0% Question 5: I had a better understanding of the types of fits and knew how to choose mating dimension tolerances from the ANSI standard fits tables (ANSIB4.1-1967(R2009)) Choice Strongly agree Agree No opinion disagree Strongly disagree Results 10 9 1 0 0 Percentage 50% 45% 5% 0% 0%

The survey results for survey questions 6 to 9 are listed in Table 6. From Table 6, we have the following survey results: • 100% percent of students strongly agreed or agreed that they had a better understanding that

mating dimension tolerances must be accordingly determined by the required assembly dimension tolerance, which is defined by the required functions and design intents.

• 95% percent of students strongly agreed or agreed that they knew how to determine mating dimension tolerances on an interface with a general hole and a general shaft when the assembly tolerance is fully specified.

• Only 75% percent of students strongly agreed or agreed that teaching the GD&T fundamentals facilitated their ability to conduct mechanical component design with proper dimension tolerance. 25% percent of students indicated “no opinion” about this statement. This result indicated that the implementation of GD&T in mechanical design was a difficult task even with our approach.

• Only 50% percent of students strongly agreed or agreed that the mechanical program might offer one technical course about geometric dimensioning and tolerancing. 40% percent of

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students showed “no opinion” whether GD&T should be offered as one technical course. 10% of students disagreed that GD&T should be offered as one technical course.

Table 6 The survey results for the survey questions 6 to 9 Question 6: I had a better understanding that mating dimension tolerances must be accordingly determined by the required assembly dimension tolerance, which is defined by the required functions and design intents. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 12 8 0 0 0 Percentage 60% 40% 0% 0% 0% Question 7: I knew how to determine mating dimension tolerances on an interface with a general hole and a general shaft when the assembly tolerance is fully specified. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 10 9 1 0 0 Percentage 50% 45% 5% 0% 0% Question 8: The lecturing in this class really facilitated me to conduct mechanical component design with proper dimension tolerance. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 5 10 5 0 0 Percentage 25% 50% 25% 0% 0% Question 9: I believed that the mechanical program might offer one technical course about geometric dimensioning and tolerancing. Choice Strongly agree Agree No opinion disagree Strongly disagree Results 4 6 8 2 0 Percentage 20% 30% 40% 10% 0%

5. Discussion and conclusions GD&T is an essential tool and skill for mechanical engineering students. However, GD&T is not offered as one technical course in most mechanical engineering curriculum. The approach presented in this paper was to teach the GD&T fundamentals so that students had a better basic understanding of GD&T and knew how to determine dimension tolerances of a free dimension and mating dimensions. Based on the interaction with students and the feedback from students, our approach of teaching the GD&T fundamentals has reached the expected objectives: • 100 percent of students had a better understanding of geometric dimensioning and tolerance

through teaching the GD&T fundamentals; • 95% percent of students knew the difference between a free dimension and a mating

dimension. • 95% percent of students had a better understanding of the types of fits and knew how to

choose mating dimension tolerances from the ANSI standard fits tables. • 100% percent of students knew that mating dimension tolerances must be accordingly

determined by the required assembly dimension tolerance. • 95% percent of students knew how to determine mating dimension tolerances when the

assembly tolerance is fully specified.

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• 90% percent of students knew that the dimension tolerance for a free dimension would be typically determined by the company’s least-cost manufacturing process.

GD&T is indeed a difficult topic to teach and to be understood by undergraduate students, especially geometric tolerancing aspects. Based on the feedback from students, they still had some difficulty in understanding geometric tolerancing and implementing the GD&T skills in mechanical component design based on the following survey results: • Only 85% percent of students had some basic understanding of the envelope principle (Rule

1 of GD&T). 15% of students lacked a basic understanding of the envelope principle. • Only 75% percent of students strongly agreed or agreed that teaching the GD&T

fundamentals facilitated them to conduct mechanical component design with proper dimension tolerance.

• Only 50% percent of students strongly agreed or agreed that the mechanical program might offer one technical course about geometric dimensioning and tolerancing.

This unfortunately was what we expected because we only taught GD&T fundamentals for one and a half weeks in one existing technical class. Effective undergraduate education in our opinion requires repetition of topics in several courses for maximizing student understanding and retention. In summary, our teaching GD&T fundamentals did facilitate students in developing a basic understanding of GD&T fundamentals and learning to determine dimension tolerances of free dimensions and mating dimensions. They had a solid understanding of dimension tolerances, free dimensions, mating dimensions, and type of fits. They were able to demonstrate how to determine dimension tolerances of a free dimension. They also were able to demonstrate how to determine dimension tolerances of mating dimensions when the assembly tolerance is specified as well as the appropriate use of ANSI standard tolerance tables. 6. References [1]. Narang, R., Teaching Applied Measuring Methods Using GD&T, The ASEE 2008 Annual

Conference & Exposition, June 22-25, 2008, Pittsburgh, Pennsylvania. [2]. Wiebe, E. N., & Branoff, T., Supporting GD&T Practices Through 3 D Modeling Activities,

The ASEE 1999 Annual Conference & Exposition, June 20-23, Charlotte, North Carolina. [3]. Leduc, A., 3 D Modeling/ Gd&T Cornerstones For Manufacturing Education, The ASEE

2002 Annual Conference, June 16-19, 2002, Montreal, Canada. [4]. Branoff, T. J., Evaluating Concepts Presented in a Geometric Dimensioning and Tolerancing

Course, The 2018 ASEE Annual Conference & Exposition, June 24-27, 2018, Salt Lake City, Utah.

[5]. Sun, W., & Gao, Y., Teaching Geometric Dimensioning and Tolerancing by Using an Algorithm to Implement the Datum-based Model, The 2020 ASEE Virtual Annual Conference, June 21-24, 2020, Virtual Online Conference.

[6]. Hewerdine, K. P., & Leake, J. M., & Hall, W. B., Linking CAD and Metrology to Explain, Demonstrate, and Teach GD&T, The 2011 ASEE Annual Conference & Exposition, June 26-29, 2011, Vancouver, BC.

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[7]. Rios, O., An Example of Teaching Geometric Dimensioning and Tolerancing (GD&T) Concepts using 3D Printed Parts, The 2018 Gulf Southwest Section Conference, AT&T Executive Education, and Conference Center, April 4-6, 2018, Austin, TX 78705.

[8]. Waldorf, D. J., & Georgeou, T. M., Geometric Dimensioning and Tolerancing (GD&T) Integration throughout a Manufacturing Engineering Curriculum, The 2016 ASEE Annual Conference & Exposition, June 26-29, 2016, New Orleans, Louisiana.

[9]. Oppenheim, T., Board 93: MAKER: Improving the Quality of Mechanical Engineering Senior Capstone Designs by Incorporating Geometric Dimensioning and Tolerancing During the Concept Design Phase, The 2019 ASEE Annual Conference & Exposition, June 16-19, 2019, Tampa, Florida.

[10]. Paige, M. A., & Fu, K., Spatial Demonstration Tools for Teaching Geometric Dimensioning and Tolerancing (GD&T) to First-Year Undergraduate Engineering Students, The 2017 ASEE Annual Conference & Exposition, June 25-28, 2017, Columbus, Ohio.

[11]. Yip-Hoi, D. M., & Gill, D., Use of model-based definition to support the learning of GD&T in manufacturing engineering curriculum. The ASEE 2017Annual Conference, June 25-28, 2017, Columbus, Ohio

[12]. The American Society of Mechanical Engineers, Dimensioning and Tolerancing Standard ASME Y14.5M -1994

[13]. Richard G. Budynas, and J. Keith Nisbett, Shrigley’s Mechanical Engineering Design, Tenth Edition, McGraw-Hill Education, New York, NY, 2015

[14]. Erik Oberg, Franklin D. Jones, Holbrook Horton, Henry Ryffel and Christopher McCauley, Machinery’s Handbook 30th edition, Industrial Press, Inc, 2016