Summer 2015

CAD/CAM EML 4535 Final Project Report

MODEL AND SIMULATION OF LOCKING PLIERS

SEAN TREIBER

SE638676

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Figure 1. Skil “Ratch N Lock” Locking Pliers

Figure 2. Link. Figure 3. Locking Nob. Figure 4. Sliding Block

Figure 6. Handle Figure 5. Jaw Figure 7. Jaw Handle

1. Project Goals

A pair of Skil “Ratch N Lock” pliers were created using NX 8.5 by Siemens, a comprehensive parametric

computer aided design program with built in finite element analysis (FEA) capabilities. The objective of

this study was to develop a solid model of the essential parts that are necessary for the functionality of

the locking pliers. This was done by first using the modeling module of NX to establish the geometry for

the individual components and then assembling these individual parts in the assembly module.

Once the geometry is established and the assembly compiled, the finished CAD model was utilized in a

subsequent FEA study to explore the model’s behavior under specific load cases. This FEA study was

performed using the simulation module, in conjunction with the FEM module, within NX 8.5. In the finite

element module of NX 8.5, 1D, 2D, and 3D elements were added with respect to the already established

CAD model geometry. In the simulation constraints and loads were added. The results of such simulation

was verified through hand calculation of key parameters.

2. Background and Description

The “Ratch N Lock” locking and ratcheting pliers manufactured by Skil features parallel jaws and a dual

pivot design. This allows for better griping capability. The locking mechanism works using a ratcheting

system that, when the Locking Nob is engaged, allows for uni-directional motion; the jaws of the pliers

can close but not open. The Locking Nob has teeth that can only slide along one direction of the Locking

block. The teeth of the Locking Nob and the grooves of the Locking Block cease motion when the rotation

is reversed. These locking and ratcheting pliers, shown below in Figure 1, contain 7 main parts, all of which

were modeled to create the finish CAD model. These 7 parts are the Link, the Locking Block, the Locking

Nob, the Sliding Block, Jaw, Handle, and Jaw Handle. The photographed parts can be seen in Figures 2-7,

all of which were provided by the T.A.

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Figure A1. Sketch for Step A1. Figure A2. Extrude for Step A1.

3. Solid Model

3.2 Link

Step A1:

The link was created by first doing a sketch on the X-Y plane and then using the Region Boundary Curves

option, it was extruded 1/16th of an inch symmetrically about the mid-plane. This yielded the main part

thickness of 1/8th of an inch. The both the sketch and the extrusion can be seen in the Figures A1 and A2

below.

Step A2:

The next step involved extruding the retaining pins for the link. This was done using the Regions Boundary

Curves option and the ring was extruded symmetrically 1/8th of an inch creating a total thickness for this

feature equal to 1/4th of an inch. And the pin was extruded negative 5/32th of an inch and positive 3/16th

of an inch from the mid-plane. The extrusions for the ring and the retaining pin portion of the Link can be

seen in Figures A3 and A4 respectively. The final part can be seen below the extrusion figures, in Figure

A5.

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Figure A3. Extrude 1 for Step A2. Figure A4. Sketch for Step A2.

Figure A5. The Final Part: The Link

3.2 Locking Block

Step B1:

The locking block was created by a single sketch followed with two extrudes and an edge blend. The sketch

was made on the X-Y plane. The 2-D sketch can be seen below in Figure B1.This sketch was extruded 1/8th

inches symmetrically producing a total thickness of 1/4th inches. This was done using the Region Boundary

Curves option in the extrude settings. The Extrude can be seen in Figure B2 below.

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Figure B2. Extrude for Step B1.

Figure B1. Sketch for Step B1

Figure B3. Extrude of Step B2. Figure B4. Final Part: Locking Block.

Figure C1. Sketch for Step C1. Figure C2. Extrude for Step C1. Figure C3. Final Part: Sliding Block.

.

Step B2:

The inner circle created in the sketch was extruded positive 3/16th inches from the mid-plane and negative

5/32th inches, seen in Figure B3 below. An edge blend with a radius of 0.02 inches was done to achieve

the desired curvature along the top corners, and the final part can be seen in Figure B4 below.

3.3 Sliding Block

Step C1:

The sliding block was created by a single sketch followed with a single extrude. The sketch was made on

the X-Y plane. The 2-D sketch is shown in Figure C1. To finish the sliding block the 2-d sketch was extruded

using the symmetric value option in the extrude settings. It was extruded 1/8th of an inch. Figure C2 below

shows the extruded sketch and the final part can be viewed in Figure C3.

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Figure D1. Sketch for Step D1. Figure D2. Extrude for Step D1.

Figure D3. Sketch for Step D2. Figure D4. Subtract Extrude 1 for Step D2. Figure D5. Subtract Extrude 2 for Step D2.

3.4 Locking Nob

Step D1:

The Locking Nob was created by a several sketches followed with four unite extrudes and 2 subtract

extrudes. The initial sketch was made on the X-Y plane and can be seen in Figure D1 below. This sketch

was unite extruded symmetrically 3/16ths of an inch about the X-Y plane. The extrusion can be seen below

in the Figure D2.

Step D2:

A second sketch was made on the X-Y plane and this was followed by two subtract extrusions each offset

from the X-Y plane by 3/32nds of an inch and performed to a depth of ½ of an inch from the X-Y plane. The

sketch, subtract extrudes 1 and 2 are displayed in Figures D3, D4 and D5 respectively.

Step D3:

A third sketch was created on the X-Y Plane of two concentric circles. This sketch was followed by two

unite extrudes. The 2-D sketch can be seen below in Figure D6. The first unite extrude was done

symmetrically about the X-Y plane to a value of 1/8th of an inch. This extrude can be seen in the left figure

below the sketch figure. The second unite extrude was done from a starting value of positive 5/32nds of

inch from the X-Y plane to and distance of negative 3/8ths of an inch. These extrudes can be viewed below

in Figures D7 and D8.

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Figure D6. Sketch for Step D3. Figure D7. Extrude 1 for Step D3. Figure D8.Extrude 2 for Step D3.

Figure D9. Chamfer 1 for Step D4. Figure D10. Chamfer 2 for Step D4. Figure D11. Chamfer 3 for Step D4.

Figure D12. Sketch for Step D5. Figure D13. Subtract Extrude for Step D5.

Step D4:

Next, chamfers were added to the appropriate edges of the solid model. All chamfers add were done with

the cross section setting of symmetric, which dictates a 45o inclination. The first chamfer added was

around the upper and lower edges of the first extrude in Step D3. This was done with a distance of 1/64th

of an inch and can be seen in Figure D9 below. The second chamfer was added along the inner upper and

lower edge of the subtraction extrudes from Step D2. The second chamfer was done using a distance of

3/64ths of an inch and can be seen in Figure D10 below. The third chamfer was done to a distance of 1/64th

of an inch and was displayed in Figure D11 below.

Step D5:

A circular hole was then made in the part by first creating a 2-d sketch on the X-Z plane, then using a

subtraction extrude to a distance along the Z direction equal to negative 1/3rd of an inch. The circle sketch

can be seen below in Figure D12 and Figure D13 depicts the subtraction extrude.

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Figure D14. Sketch for Step D6. Figure D15.Subtract Extrude for Step D6.

Figure D16. Feature Pattern 1 for Step D6.

Figure D17. Feature Pattern 2 for Step D6. Figure D18.Final Part: Locking Nob

Step D6:

The teeth were created by first creating a sketch on the X-Y plane, subtraction extruding that sketch

symmetrically 1 inch. The sketch can be seen below in Figure D14. The subtraction extrude can be found

in Figure D15. Then the subtraction extrude was feature patterned using a circular path. The direction was

reversed and the feature pattern was repeated to create the final Locking Nob part. The patterns can be

found in Figures D16 and D17. The final part is shown below as well in Figure D18.

3.5 Jaw

Step E1:

Most of the solid 3D model for the jaw part was created from one sketch on the X-Y plane followed with

two extrudes. The two extrudes were performed with the Boolean option “none” to allow ease of

modeling the taper (Step E3, below) at the end of the jaw part. The two extrudes were done symmetrically

about the X-Y plane the first to a distance of 9/32nds of an inch and the second being done to a distance of

3/8ths of an inch. The sketch figure can be seen below followed by the first and second extrudes, Figures

E1, E2, and E3 respectively. Next, the edge blend tool was utilized to create the required radii on the 3D

solid. Two edges were converted to radii the first with a radius of 1/16th of an inch and the second with a

radius of 1/4th of an inch. These features can be seen below in Figures E4 and E5.

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Figure E1. Sketch for Step E1. Figure E2. Extrude 1 for Step E1. Figure E3. Extrude 2 for Step E1.

Figure E4. Edge Blend 1 for Step E1. Figure E5. Edge Blend 2 for Step E1.

Figure E6. Datum Plane and Sketch for Step E2.

Figure E7. Subtract Extrude 1 for Step E2. Figure E8. Subtract Extrude or Step E2.

Step E2:

The tapered nature of the head of the jaw part was created by first making a datum plane normal to the

reference line made in the sketch of Step E1. A sketch was created on this datum plane of two parallel

lines at an angle of negative 6 with respect to the X axis, the two sketches were closed with 6 more lines.

The result was two closed regions from which subtraction extrusions were done. The sketch figure with

the newly created datum plane and both the extrusions can be seen in the subsequent figures below. The

two extrusions were then mirrored about the X-Y plane using the features mirror tool. The extrusions

performed in Step E1, that yielded two un-united solids, were combined using the unite tool.

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Figure E9. Feature Mirror for Step E2. Figure E10. Unite Bodies for Step E2.

Figure E11. Sketch for Step E3. Figure E12. Subtract Extrude for Step E3

Figure E13. Chamfer for Step E3. Figure E14. Final Part: Jaw.

Step E3:

In order to create the hole necessary to connect the jaw part to the rest of the plier assembly, a sketch on

the X-Y plane was created. This was then subtraction extruded symmetrically about the X-Y plane to a

distance of 1/8th of an inch. The sketch and the subtraction extrusion can be viewed below in the figures.

To finish the jaw part a chamfer with a distance of 0.05 inches was made to top edge of the part. This

chamfer was done using the symmetric cross section setting which created the chamfer with the desired

45o inclination. The chamfer and the final Jaw part can be seen in the figures below.

3.6 Handle

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Figure F1. Datum Planes from Step F1. Figure F2. Sketches on each created datum plane from Step F1.

Figure F3. Guide Curve Sketches from Step F1 Figure F4. Sweep with Cubic Interpolation from Step F1

Step F1:

Datum Planes were created using the on curve option in the datum plane settings menu. Sketches were

created on each of the 4 new datum planes to act as cross sectional curves for the sweep. The datum

planes and the respective sketches are shown below in Figures F1 and F2. The guide curves for the sweep

were then sketched on the X-Y plane. The sweep with cubic interpolation was then performed. The Guide

curve sketch can be viewed below in Figure F3, followed by the sweep depicted in Figure F4.

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Figure F5. Edge blend 1 from Step F2.

Figure F7 Subtraction Extrude from Step F2. Figure F8. Unite Tool from Step F2 and Final Part: Handle.

Figure F6. Edge blend 2 from Step F2.

Step F2:

Two edge blends were then performed, one along the top edge of the handle the second along the bottom

edge. Both edge blends can be viewed below in Figures F5 and F6 respectively. This was followed by a

subtraction extrude of the sketch used to create the metal body of the Handle. This subtraction extrude

was done symmetrically about the X-Y plane to distance of 3/16th of an inches which resulted in a hollow

grip that perfectly matches the thickness and X-Y geometry of the metal body of the Handle. This

subtraction extrude can be seen in Figure F7. The final part, which was finished with the use of the unite

tool between the grip and the metal portion, can be seen in Figure F8.

3.7 Jaw Handle

Step G1:

The creation of a 2D sketch on the X-Y plane was followed with two extrudes with the Boolean function

of “none” resulting in two separate extruded regions. This was done to make the tapering of the head of

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Figure G1. Sketch from Step G1 Figure G2. Extrude 1 from Step G1 Figure G3. Extrude 2 from Step G1

Figure G4. Sketch from Step G2 Figure G5. Extrude 1 from Step G2

Figure G7. Mirror Feature from Step G2. Figure G6. Extrude 2 from Step G2

the Jaw Handle easier. The sketch, the two extrudes can be viewed below in Figures G1, G2, and G3

respectively.

Step G2:

The tapered nature of the head of the jaw handle part was created by first making a datum plane normal

to the reference line made in the sketch of Step G1. A sketch was created on this datum plane. The

sketches were used in subtraction extrudes, one from each of the separate regions created in Step G1.The

sketch figure with the newly created datum plane and both the extrusions can be seen in Figures G4, G5,

and G6. The two extrusions were then mirrored about the X-Y plane using the features mirror tool. This

can be seen in Figure G6.

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Figure G8. Datum Planes from Step G3. Figure G9. Cross Sectional and Guide Curve Sketches from Step G3.

Figure G10. Sweep with Cubic Interpolation from Step G3.

Figure G11. Edge Blend from Step G4. Figure G12. Extrude 1 from Step G4. Figure G13. Extrude 2 from Step G4.

Figure G14. Final Part: Jaw Handle.

Step G3:

To create the grip on the Jaw Handle, first four datum planes were created “on curve” normal to the

sketch provided by the TA in the solid body of the starting part for the Jaw Handle. Then cross sectional

sketches were created on each of these new datum planes, resulting in four sketches. Also the guide curve

was sketched on the X-Y plane connecting all four of the cross-sectional sketches. The “sweep” command

was then used with cubic interpolation to achieve the desired grip geometry. The created datum planes,

cross-sectional and guide curve sketches, as well as the swept body can be viewed below in Figures G8,

G9, and G10 respectively.

Step G4:

Edge blends were made to the top edge as well as the bottom edge of the grip to a radius of 0.075 inches.

These can be seen in Figure G11. A slot was then subtraction extruded from the grip utilizing the sketch

region provided by the TA in the base starting part. This can be viewed in Figure G12. The metal body was

then subtraction extruded from the solid grip using the second sketch region provided. This can be seen

in Figure G13. The final part was finished with a unite command between the jaw head, the metal base

part and finally the metal base part and the grip. The final part can be seen in Figure G14.

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Figure 8. Jaw Handle inserted, positioned, and fixed in assembly.

Figure 9. Touch-Align constraint in Step 4.2. Figure 10. 2-2 Center constraint in Step 4.2.

4. Assembly and Drafting

Component Assembly

The finalized parts were then constrained together using the assembly module NX 8.5. The steps that

were taken to do so can be found below.

Step 4.1: Jaw Handle

First the assembly module of NX 8.5 was opened and the Jaw Handle was inserted into the window using

the “Add Components” command. The positioning was set to “Absolute Origin” and the part was fixed to

the origin. This constraint can be seen in Figure 8 below.

Step 4.2: Jaw

Next the Jaw part was added to assembly using “Absolute Origin” as the initial positioning setting. The

part was then rotated 180o and translated using the dynamic motion setting in the “Move Components”

command. The Jaw was then constrained to the Jaw Handle part using the touch-align constraint with the

“preferred touch” option. To finish constraining the Jaw to the Jaw Handle, a 2-2 center constraint was

added between the outer faces of the Jaw Handle’s neck and the inner faces of the Jaw’s slot. These two

constraints can be seen below in Figures 9 and 10 respectively.

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Figure 11. Touch-Align constraint (Center Axis alignment) in Step 4.3.

Figure 12. 2-2 Center constraint in Step 4.3.

Step 4.3: Handle

The Handle was added to the assembly using the “absolute origin” positioning option, and rotated 180o

using the dynamic motion setting in the “Move Component” command. The handle was first constrained

to the Jaw part using the touch-align constraint to constrict the center axis of the pin hole for the Handle

and the corresponding hole in the Jaw. This can be seen in Figure 11. The 2-2 center constraint was then

utilized by selecting the outer surfaces of the teethed head of the Handle, and the inner surfaces of the

slot in the Jaw. This constrains the Handle fully to the Jaw and Jaw Handle parts. The center constrain can

be seen below in Figure 12.

Step 4.4: Link

Next the Link, the Locking Nob and the Locking Block were all added to the assembly using the same

procedure described in Step 4.1 (positioning set to absolute origin). These parts were all rotated 180o,

this was necessary due to their lack of symmetry. The Handle, and Jaw Handle were made 75% translucent

using the model display options in the assembly navigator; this was done to make it easier to position and

constrain the parts that govern locking internal mechanism. The Link was first constrained to the Handle

using the touch-align constrain to align the center axis’s of the retaining pin of the Link and the

corresponding hole in the Handle. Next the surface of the handle was touch-aligned to the surface of the

retaining extrusion of the Link part. This ensured a flush surface at his intersection. Next, the touch-align

constraint was utilized to create the sliding mechanism between the Link and the Jaw Handle. These touch

aligns can be viewed below in Figures 13, 14, 15, and 16. Distance constraints were added between the

center axis of the sliding extrusion on the Link and the center axis’s of the upper and lower arc lengths on

the Jaw Handle. These distance constraints can also be seen below in Figures 17, and 18. These distances

were added to ensure link part cannot translate within the retaining slot. With these touch align and

distance constraints the Link is fully constrained with respect to both the Handle and the Jaw Handle as

well as the rest of the assembly.

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Figure 13. Locking Nob, Locking Block and Link added to assembly.

Figure 14. Touch Align 1 between Link and Handle in Step 4.4. (Center Axis Alignment)

Figure 15. Touch Align between Link and Handle Surfaces in Step 4.4.

Figure 16. Touch Align between Link cylinder and Jaw Handle Slot Surfaces in Step 4.4.

Figure 17. Distance constraint between Link center axis and upper Jaw Handle arc length center axis in Step 4.4.

Figure 18. Distance constraint between Link center axis and lower Jaw Handle arc length center axis in Step 4.4.

Figure 19. Touch Align between Locking Nob cylinder and Handle retaining hole center axis’s in Step 4.5.

Figure 20. Touch Align between Locking Nob cylinder top and Handle outer surfaces in Step 4.5.

Step 4.5: Locking Nob

The Locking Nob added in Step 4.4 was constrained to the Handle using the touch align constraint to align

the center axis’s of the Locking nob’s retaining extrusion and the Handle’s corresponding retaining pin

hole. To finish constraining the Locking Nob to the overall assembly, the touch-align command was used

to align the top surfaces and the Handle and the Locking Nob’s retaining extrusion. Both the center axis

touch alignment and the surface touch align can be viewed in Figures 19 and 20 below.

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Figure 21. Touch Align between Locking Block and Handle retaining hole center axis’s in Step 4.6.

Figure 22. Touch Align between Locking Block top and Handle outer surfaces in Step 4.6

Figure 23. Touch Align between Sliding Block and Jaw Handle in Step 4.7.

Figure 24. 2-2 Center between Sliding Block outer surfaces and Jaw Handle neck’s outer surfaces in Step 4.7.

Step 4.6: Locking Block

The Locking Block, added in Step 4.4, was constrained to the Handle by first utilizing the touch align

constrain with the orientation setting set to “Prefer Touch.” This aligned the center axes of the retaining

extrusion of the Locking Block and the corresponding hole on the Handle. The part was constrained further

by using the touch align command to align the top surface of the retaining extrusion of the Locking Block

and the outer surface of the Handle. These constraints and settings can be seen below in Figures 21 and

22.

Step 4.7: Sliding Block

The Sliding Block was added to the assembly utilizing the same procedure in delineated in Step 4.1. The

component was rotated and translated to a position relatively close in proximity and orientation to the

fully constrained position. The first constraint added to the Sliding block was a touch align between the

non-grooved surface of the sliding block and the neck of the Jaw Handle. The second constraint added

was a 2-2 center constraint added between the outer surfaces of the sliding block and the outer surfaces

of the Jaw Handle neck. This constraint makes the center axis between two surfaces coincident with the

center axis of two other surfaces, affectively centering the parts with respect to each other. The third

constraint used to define the Sliding Block with respect to the rest of the assembly was a touch align

between the groove surface of the Sliding block and the geared surface of the head of the Handle. The

touch align constraint between the neck of the Jaw Handle and the Sliding block can be seen below in

Figure 23. The 2-2 center constraint is then shown in Figure 24 and Figure 25 depicts the touch align

between the grooves of the sliding block and the gear teeth of the Handle.

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Figure 25. Touch Align between Sliding Block and Handle in Step 4.7.

Figure 26. Fully Assembled Locking Pliers Model

Figure 27. Skil “Ratch N Lock” Pliers

Full Assembly and Comparison

The finished locking plier’s assembly, yielded from the exact steps delineated and expounded upon above

in steps 4.1 through 4.7, can be seen below in Figure 26. For comparison the photograph of the Skil “Ratch

N Lock” Pliers can be seen in Figure 27.

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Part Drafting

Using NX 8.5’s drafting module and view orientation wizard command the following draft was made. The

part chosen for drafting was the Jaw. The view wizard command allowed for the ease of inserting and

grouping the isometric, top and front views seen in the draft at the top left, top right and bottom right

respectively. The coordinate system for each of the views was shown, whereas datum planes and sketches

were hid. The sketch parameters from Sketch 1 of Step E1, the step outlined above in which the Jaw part

was modeled, were imported into the draft and attributed to the front view which is the view normal to

the plane in which the sketch was done. Utilizing the dimensions style menu, select dimensions were

chosen to be displayed as fractions. This was done to improve the legibility of the complex sketch. A

section A-A was created to demonstrate the geometry within the part. The background of the section

view was unchecked in the style menu for the section view. The trimetric view can be seen in the bottom

left and was rendered using the fully shaded option.

5. FEM

5.1 FEM Overview

Utilizing the previously created CAD Model, a Finite Element model was developed. This was done in order

to use the Simulation module in NX 8.5 to solve for the deflected shape of the model under a specific

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Figure 27. The Completed FE Model with all 2D and 3D meshes and 1D elements

Figure 28. The Plot of the Magnitude of Nodal Displacements.

loading case. This was also done to solve for the bending stress developed in the Jaw Handle under the

same loading conditions. In order to create the FE Model, seen in Figure 27 below, 2D shell elements and

3D solid elements were mapped to appropriate parts of the CAD model. These generated meshes were

then assembled using 1D connection elements in conjunction with CBUSH elements to provide stiffness

along DOFs necessary to simulate either a pin joint or a ball joint. The process of generating the meshes

and assembling the FE Model is described below in Sections 5.2-5.4. The simulated deflected shape can

be seen in Figure 28. This was solved for after applying Surface to Surface Gluing and Surface Contacts as

well as the external loading and the constraints. The process of adding these simulation features can be

seen in Sections 6.1 and 6.2, below. The results of this simulation were then verified using equilibrium

equations and bending stress theory. This is seen in Section 7, below.

5.2 Idealized Part:

The first step in the completion of the FEM model was to create an idealized part, using the create

Idealized part option in the FEM menu. This idealized part is an exact copy of the master CAD, allowing

for simplification or modifications to be made to this copy and not affect the original Master CAD model.

The process for creating the master CAD can be view above in the CAD Model section. Next the idealized

part was accessed and the Promote Bodies command was used on the Jaw Handle, Connecting Link and

the Upper Jaw. This was done so that these parts could be further modified. This Promote Bodies can be

view below in Figure 5.2-1.The Mid-Surface command was then used on the Jaw Handle and the

Connecting Link. This was followed by the Split Bodies command being utilized on both the Upper Jaw and

the Jaw Handle. The Split Bodies command on the Jaw Handle was done using a plane normal to its arc

whereas the command was used with respect to the X-Y Plane for the Upper Jaw. The splitting on the Jaw

Handle was done to allow for the use of both 2D QUAD4 element meshing on the lower portion of the

part and 3D TETRA4 element meshing on the upper portion. The splitting on the Upper Jaw was done to

allow for meshing of half the part and reflecting that mesh to accommodate the entire part. The Mid-

Surface command on the connecting link and the Jaw Handle can be seen in Figure 5.2-2, followed by the

split bodies commands depicted in Figures 5.2-3 and 5.2-4.

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Figure 5.2-1 . Promote Bodies Command in Idealized Part File.

Figure 5.2-2 . Mid-Surface Command on the Jaw Handle and the Connecting Link.

Figure 5.2-3. Split Bodies command on Upper Jaw. Figure 5.2-4. Split Bodies command on Jaw Handle.

5.3 FE Model:

The next step to the completion the FE Model was to use the FEM module in NX 8.5. In this module, the

modified idealized part was imported. The 3D meshing was the first elements added to the Idealized part.

This was followed by the 2D and finally the 1D elements.

Step 1: 3D Element Meshing

CTETRA4 Elements were utilized to mesh the Handle, the upper split portion of the Jaw Handle and the

entire Lower Jaw. The element size for all of these part was set to 0.075 inches and the option to attempt

free meshing was selected. For the Upper Jaw, the split portion above the X-Y plane was meshed also

using CTETRA4 Elements with an element size of 0.075 inches. This mesh was then reflected about the X-

Y plane using the Copy and Reflect command. Once this was done both portions created from the Split

Bodies command in the Idealized part were meshed. Next the duplicate nodes command was utilized to

identify coincident nodes in the Upper Jaw that were created as a result of the Copy and Reflect command.

Within the Duplicate Nodes command the “Merge Nodes” option was used to merge duplicate and

coincident nodes, effectively joining the two portions of the upper Jaw into one part with respect to the

FE analysis detailed below. Figure 5.3-1 shows the meshing of the Handle, the Lower Jaw and upper

portion of the Jaw Handle. In Figures 5.3-2, 5.3-3, and 5.3-4, respectively, the meshing of the Upper Jaw,

the Copy and Reflect of that mesh about the X-Y plane and the merging of the resultant duplicate nodes

are depicted. CTETRA4 Elements were utilized for these parts because small deformations are expected

for these parts relative to the deformation of the Jaw Handle. Linear tetrahedral elements were chosen

over parabolic tetrahedral elements to lower computation intensity. After these 3D meshes were created,

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Figure 5.3-4. Merging Duplicate nodes resulting from Copy and Reflect Command.

Figure5.3-3 .Copy and reflect of the Tetra Mesh of the Upper Jaw about the X-Y Plane.

Figure 5.3-2.Tetra4 Meshing of the upper portion of the split Upper Jaw.

Figure 5.3-1.Tetra4 Meshing of the upper portion of the split Jaw Handle, the Handle and the Lower Jaw.

they were all given the material Steel, in accordance with the governing Power Point presentation

provided by the T.A. these properties can be seen in Table 1 below. 3D CTETRA Elements were utilized for

these parts due to their complex geometry along all three primary directions; these parts have subtract

extrudes and tapers that cannot be simulated accurately with 2D shell mesh elements.

Table 1. Properties Table for 3D Meshes.

Part Material

Lower Jaw Steel

Upper Jaw Handle Steel

Handle Steel

Upper Jaw Steel

Sliding Block Steel

Step 2: 2D Element Meshing

Utilizing the Mid-Surfaces of the lower portion of the Jaw Handle and the Connecting Link, created by

modifying the idealized part, the 2D Element meshing was done. The 2D QUAD4 Elements were utilized

in meshing both the Mid-Surface of the Jaw handle and the Connecting Link. The element size for the

connecting Link was made to be 0.05 inches whereas the element size for the Jaw handle was 0.075

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Figure 5.3-5. 2D Quad4 Mesh of the Connecting Link.

Figure 5.3-8. Mesh Extrusion 2 in Step 2 of Section 5.3. Figure 5.3-7. Mesh Extrusion 1 in Step 2 of Section 5.3.

Figure 5.3-6. 2D Quad4 Mesh of lower portion of the Jaw Handle.

inches. This was done because a finer mesh quality is necessary when modeling the Connecting Link due

to its relatively smaller size with respect to the rest of the parts in this model. The creation of these meshes

After these surfaces were meshed, the next step in establishing the 2D meshing for this FE Model was to

create an interfacing surface between the upper and lower portions of the split Jaw handle; the upper

portion meshed with 3D TETRA4 Elements whereas the lower portion meshed with 2D QUAD4 Elements.

This interface meshed surface was created by using the extrude mesh command twice along the edge

connecting the two portions of the Jaw Handle. The mesh extrusion was done with per copy distances of

0.0625 inches and the number of copies was set to 3. These parameters were set to these values so that

the total dimensions of the extrusion matched the cross sectional dimensions of the upper portion of the

Jaw Handle. The extrusion in the negative Z direction can be seen in Figure 5.3-7, and the extrusion in the

positive Z direction is depicted in Figure 5.3-8. After these 2D meshes were created they were given

materials and thicknesses equal to those provided in the governing Power Point presentation. These

properties were tabulated and can be seen below in Table 2. 2D Meshing Elements were utilized to mesh

these parts because these two parts have a constant thickness in the Z direction and the dimensions on

planes parallel to the X-Y plane are significantly larger than the Z dimension.

Table 2. Properties Table for 2D Meshes.

Location Material Thickness(in)

Lower Jaw Handle Steel 0.375

Lower Jaw Handle to Upper Jaw Handle Steel 0.375

Connecting Link Steel 0.125

24

Figure 5.3-9. Node creation in Step 3 of Section 5.3. Figure 5.3-10. CBAR creation in Step 3 of Section 5.3.

Step 3: 1D Element Meshing

The 1D CBAR Element was created in order to provide an object for the upper and lower Jaw to apply an

axial loading. In order to create this 1D Element, the Create Node between Nodes command was utilized

to make a node equidistant to both the center node of the front of the Upper and Lower Jaws. This is

depicted in Figure 5.3-9 below. Next the Create Element command was utilized to make the CBAR Element

between each of the nodes. The “Add to Existing” option was chosen when the CBAR Element between

the middle node and the center-front node of the Lower Jaw. This was crucial to ensuring that the CBAR

elements would be treated as a single part; grouped in a single mesh. The Create Element command can

be seen below in Figure 5.3-10. After the elements were established they were given properties that

include the Fore Section (Rod), and Material. 1D CBAR because it simplifies the modeling of a part in

which the cross section of the desired mesh does not change along its axis.

Table 3. Property Table for 1D CBAR Element.

5.4 FE Assembly

Step 1. Pin Joint between Connecting Link and Lower Jaw Handle

In order to create a Pin Joint between the Connecting Link and the Lower Jaw Handle, two

coincident nodes were created at the center point of the lower pin hole of the Connecting Link.

These nodes were created using the Inferred Point option to specify the point, selecting the edge

of the pinhole. Next, using the 1D Connector command, an RBE2 Element was created between

one of the newly created central nodes and the nodes lining the edge of the pinhole in the

connecting link. This is shown below in Figure 5.4-1. A second RBE2 Element was inserted in a

similar fashion between the other central node and 8 of the nodes lining the slot in the 2D mesh

of the lower portion of the Jaw Handle. This is shown in Figure 5.4-2 .Then the two RBE2 Elements

were joined with a 1D CBUSH Element. The CBUSH was created between the two coincident

central nodes of each of the RBE2 elements. The CBUSH Element acts like spring with definable

stiffness’s along all 6 DOFs. These can be used to selectively kill DOFs to simulate different joints.

For a Pin Joint, such as this, the stiffness’s along all translational are set to 10e08 lbs. /in,

Location Material Fore Section (Radius)(in)

Between the Upper and Lower Jaws Nylon 0.0625

25

Figure 5.4-1. RBE2 creation on the Connecting Link.

Figure 5.4-3. CBUSH Creation joining the 2 RBE2 elements in Step 1 of Section 5.4.

Figure 5.4-2. RBE2 creation on lower portion of the Jaw Handle.

effectively killing translation. Also for this pin joint, stiffness’s along DOFs 4 and 5 are also set to

10e08 lbs. /in and stiffness along DOF 6 is set to 0 lbs. /in. This simulates a pin by killing all

translation and all rotation except about the axis of the pin.

Step 2. Pin Joint between Connecting Link and Handle

In order to create a pin between the 3D solid mesh of the Handle and the 2D shell of the Connecting Link,

was to create an RBE2 Element connecting the nodes along the edge of the larger pin hole of the

Connecting Link to a node at the center of the circular edge. A second node was created at this location

in order to place a CBUSH here. This step is shown in Figure 5.4-4. Next an RBE2 element was created on

the upper and lower surfaces of the Handle. These connect the nodes along the edge of the hole to a

central node. This is shown in Figures 5.4-5, and 5.4-6. A CBAR element was then used to connect the

central nodes of these two RBE2 elements to a middle node coincident with the central node of the RBE2

element of the Connecting Link. This CBAR creation is shown in Figure 5.4-7. Finally a CBUSH was inserted

between the two coincident nodes. Because this connection is to simulate a pin joint, this CBUSH was put

in the same collector as the pin between the Jaw Handle and the Connecting Link. The stiffness’s and

reasoning is outlined in Step 1 above. The CBUSH creation can be seen below in Figure 5.4-8.

26

Figure 5.4-4.RBE2 on the Connecting Link in Step 2 of Section 5.4.

Figure 5.4-7.CBAR creation in Step 2 of Section 5.4.

Figure 5.4-5. RBE2 on the lower surface of the Handle in Step 2 of Section 5.4.

Figure 5.4-6. RBE2 on the upper surface of the Handle in Step 2 of Section 5.4.

Figure 5.4-8.CBUSH creation in Step 2 of Section 5.4.

Step 3. Pin Joint between Handle and Lower Jaw

The first part of creating the connection between the Lower Jaw and the Handle was to create 4 nodes,

two of which are coincident at the mid-plane of the Handle at the center of the pinhole, the other two are

at the centers of the pinholes in the Lower Jaw. Then an RBE2 element was inserted between one of the

mid-plane nodes and the nodes along the inner surface of the pinhole of the Handle. These nodes were

selected using the Feature Angle Nodes method. This can be viewed in Figure 5.4-9 below. Next an RBE2

element was created connecting the central nodes of the upper and lower edges of the pinhole in the

Lower Jaw and the nodes along those edges. This can be seen in Figures 5.4-10. To finish a the pin joint

between these 3D meshes a CBAR was created between the central nodes of the RBE2 elements of the

Lower Jaw and the coincidental at the mid-plane of the Handle and then a CBUSH was created between

27

Figure 5.4-13. CBUSH creation in Step 3 of Section 5.4.

Figure 5.4-12.CBAR creation in Step 3 of Section 5.4. Figure 5.4-11. RBE2 on circular edge of pinhole on lower surface of Lower Jaw in Step 3 of Section 5.4.

Figure 5.4-10. RBE2 on circular edge of pinhole on upper surface of Lower Jaw in Step 3 of Section 5.4.

Figure 5.4-9. RBE2 in center of cylindrical surface of the Handle in Step 3 of Section 5.4.

the two coincidental nodes. These steps are shown in Figures 5.4-11, 5.4-12, and 5.4-13. This CBUSH was

also placed in the same collector as the other pin joint CBUSH elements.

Step 4. Ball Joint between Handle and Sliding Block

The first step in the creation of the Ball joint between the Handle and the Sliding block was to create 2

coincidental nodes between the toothed surface of the Sliding block and the geared surface of the Handle.

An RBE2 element was created between one of the central nodes and the 4 corner nodes on the bottom

gear tooth of the Handle. Next an RBE2 element was created between the other central node and the 20

closest nodes on the Sliding Block. These nodes were selected using the Feature Angle Node method with

a tolerance of 5 degrees. Finally a CBUSH element was created between the two coincidental nodes. These

steps are shown in Figures 5.4-14, 5.4-15, and 5.4-16 respectively. The CBUSH for this connection was

28

Figure 5.4-14.RBE2 between central node and corner nodes of lower tooth of the Handle.

Figure 5.4-15. RBE2 between central node and nodes on inner surface of the Sliding Block.

Figure 5.4-16. CBUSH creation in Step 4 of Section 5.4. Figure 5.4-17. CSYS Override to Absolute CSYS for all CBUSH Elements.

placed in a separate collector then the pin joint CBUSH elements. The stiffness’s for this collector were

equal to 10e08 lbs./in for DOFs 1, 2, and 3, effectively killing translation along any of the major axis’ and

equal to 0 lbs./in for DOFs 4, 5, and 6,not impeding any rotational motion. These stiffness’s simulated a

ball joint’s ability to allow rotation but not translational motion. To finish the FEM Assembly a CSYS

override was performed for all CBUSH elements (Pin and Ball Joint CBUSH elements), this step can be

viewed in Figure 5.4-17, below.

Table 4. CBUSH Element Stiffness’s and CSYS.

Location X Translation

Y Translation

Z Translation

X Rotation

Y Rotation

Z Rotation

CSYS

Connecting Link to Jaw Handle

10e08 10e08 10e08 10e08 10e08 0 Absolute

Connecting Link to Handle

10e08 10e08 10e08 10e08 10e08 0 Absolute

Handle to Lower Jaw

10e08 10e08 10e08 10e08 10e08 0 Absolute

5.5 FE Model Check

Step 1. Element Edge Check

29

Figure 5.5-1. Element Edge Check.

Figure 5.5-2. Pin Connection: Show Adjacent check Progression 1 (RBE2 isolated).

Figure 5.5-3. Pin Connection: Show Adjacent check Progression 2 (Connections to RBE2).

Figure 5.5-4. Pin Connection: Show Adjacent check Progression 3 (Connections to

Figure 5.5-5. Pin Connection: Show Adjacent check Progression 4

First to check the FE Model an element Edge check was performed for the Upper Jaw to ensure the Merge

Duplicate Nodes command was used correctly. As shown in Figure 5.5-1, below, the nodes were merged

and an edge does not appear on the mid-plane of the Upper Jaw.

Step 2. Show Adjacent Check

Show Adjacent command was utilized to check the connections of the CBUSH elements to ensure the pin

and ball joint connections are properly simulated. In Figures 5.5-2, 5.5-3, 5.5-4 and 5.5-5, the progression

of Show Adjacent commands are shown for the Pin Joint between the Handle and the Connecting Link. IN

Figures 5.5-6, 5.5-7, and 5.5-8 the progression of Show Adjacent commands are shown for the Ball Joint

between the Handle and the Sliding Block.

30

Figure 5.5-8. Ball Connection: Show Adjacent check Progression 3 (Connections to CBUSH)

Figure 5.5-6. Ball Connection: Show Adjacent check Progression 1 (RBE2 isolated).

Figure 5.5-7. Ball Connection: Show Adjacent check Progression 2 (Connections to RBE2).

Figure 5.5-9.Element Normals check

Step 3. 2D Element Normals Check

By performing two separate 2D Mesh Extrusions in Step 2 of the FE Model section, a check of the normal

vectors of the resulting 2D elements is required. The normal vectors must be in the direction pointing

outwards toward the 3D solid Upper Jaw Handle. This is necessary for the Surface Gluing command

detailed in the Simulation portion below. The Reverse Normals option was utilized achieve the desired

direction for all of these normal vectors. Figure 5.5-9 below shows this check.

6. Sim

6.1 Gluing and Contact

Step 1. Defining Gluing and Contact Regions

Using the Create new region option under the Sim navigation tab, 8 regions in total were

spawned in order to facilitate the 4 Contacting Surfaces and 4 Gluing Surfaces necessary for the

completion of this Sim. In order to select the nodes of each face, to establish the individual region,

the Method was set to “Feature Angle Nodes” which allows the selection of all elements on a

face or planar object by checking the angle (limiting angle set to 5o for all regions) between

adjacent elements. If the angle between the selected elements is greater than the limiting angle

31

Figure 6.1-1. The necessary Regions created in Step 1 of the Section 6.1.

Figure 6.1-2. Face Gluing 2 in Step 2 of section 6.1 Figure 6.1-3. Face Gluing 2 in Step 2 of section 6.1

the nodes of the adjacent element are not selected. In the figure below all the necessary Regions

are shown.

Step 2. Face Gluing

The next step in setting up the Sim in NX 8.5 was to glue surfaces that were meshed separately

but comprise a single part. This includes the bonded connection between the Upper Jaw and the

upper portion of the Jaw Handle and as well as the connection between the 2D mesh of the lower

portion of the Jaw Handle and the 3D solid mesh of the upper portion of the Jaw Handle. The

four regions used to complete this Face Gluing Command were created in Step 1 of Section 6.1.

The 2 Gluing commands were executed with respect to the lower planar face of the Upper Jaw

and the upper planar face of the upper portion of the Jaw Handle and then between the 2D mesh

extrusion of the lower portion of the Jaw Handle and the lower planar face of the 3D solid mesh

of the lower portion of the Jaw Handle. These 2 command can be seen in Figure 6.1-2 and 6.1-3

respectively.

32

Figure 6.1-5. Surface to Surface Contact 2 in Step 3 of section 6.1

Figure 6.1-4. Surface to Surface Contact 1 in Step 3 of section 6.1

Step 3. Contact Surfaces

Contacting surfaces were established in the sim by using the Surface to Surface Contact

Command and the contacting regions created in Step 1 of Section 6.1. This establishes a non-

linear behavior in the solution of these regions. The contact was made between the Sliding Block

and the Jaw Handle, and between the Lower Jaw and the Jaw Handle. These two commands can

be viewed in Figures 6.1-4 and 6.1-5 below.

6.2 Loading and Support

Step 1. Defining the Loading Case

In order to create the loading case for this FE model, the Create Force command was utilized

twice. Each force was created utilizing the point to point method to establish the vector’s

direction. The magnitude of each force was set to 10 lbs. Nodes on the X-Y plane, which acts as

the symmetric plane for the FE Model, on the bottom curved surface of the Handle and the

bottom of the 2D mesh of the lower portion of the Jaw Handle were used as the points for the

point to point method. This is shown in Figures 6.2-1 and 6.2-2 below.

Figure 6.2-1. Force Creation 1. Figure 6.2-2. Force Creation 2.

33

Step 2. Support/Constraints

The first constraint placed on the FE model was the fixed constraint applied to the center node

of the Nylon bar between the Upper and Lower Jaws. This was done to the middle node because

the compressive nature of the Upper and Lower Jaws creates an axial load that is relatively large

in magnitude. Due this load being concentrated along the axis of the bar the middle node stays

relatively non-displaced. This constraint is not adequate enough to fully constrain the FE Model

because the 3D solid elements and the 2D shell elements would still have a translational degree

of freedom along the Z direction of the absolute coordinate system of the simulation. This is

constrained by adding a User Defined Constraint that fixes DOF 3 while leaving DOF 1, 2, 4, 5, and

6, free. This User Defined constraint is applied to a non-linearized grouping of nodes on the

Handle, the 2D Shell of the Jaw Handle and the Sliding Block. These two constraints, jointly, fully

constraint the FE Model within the Simulation. The fixed constraint as applied to the center node

of the Nylon bar is shown below in Figure 6.2-3 and the User Defined Constraint and applied non-

linearized grouping of nodes is shown in Figure 6.2-4.

7. Results and Verification

7.1 Displacement Solution Plot

The solve function in the Sim was run after fully establishing the FE model: defining the materials

and dimensions of the meshes as described in Sections 5.2 and 5.2 above, assembling the FE

model as delineated in Sections and adding bonds and contacts as well as loads, constraints as

outlined in Sections 6.1 and 6.2. The resulting plot, Figure 29 below, was created and the name

was added to the header by utilizing the Customize option in the Legend Tab of the Post View in

the Simulation Results Navigator. The maximum deflection was found to occur at the bottom of

the Handle under this loading case. The value for the maximum deflection as found through this

FE Analysis was 0.0254 inches which has a percent error of 3.1496% when compared to results

of the T.A. This is well within a reasonable margin of error considering the complexity of this

model and the non-linear behavior of the surface contacting.

Figure 6.2-3. Fixed constraint applied to the center node of the Nylon Bar.

Figure 6.2-4. User Defined Constraint applied to non-linearized groupings of nodes on the Jaw Handle, the Handle and the Sliding Block.

34

7.2 Stress Plot for 2D Shell Mesh of Lower Jaw Handle

Figure 30, below, displays the plot of the Elemental-Nodal Maximum Principal Stress for the 2D

shell mesh of the lower portion of the Jaw Handle. The header was changed according to the

procedures followed above in Section 7.1. Figure 31 was generated using the Identify command

in the Sim module to interrogate the plot and display the maximum principal stress at node

12577, which is a node on the edge of the 2D mesh, and belongs to an element 3 rows below the

slot in the lower portion of the Jaw Handle. This node was chosen in order to provide a bending

stress value, from the Simulation solution, for which the bending stress solution derived from

Hand Calculation can be compared. This node, according to the Simulation Solution, experiences

a maximum principal stress of 1729.86 lbs./in2.

Figure 29. Deformed Displacement Plot. (Magnitude: inches).

Figure 30. Maximum Principal Stress (Magnitude: PSI).

35

7.3 FO6 File Output

Figure 7.3-1, below shows a screen shot of the .fo6 file and includes the printout of the SPC forces,

the forces in the nylon bar as well as the forces in the custom output group consisting of the

CBUSH Elements used to simulate both pin and ball joint connections.

Figure 31. Maximum Principal Stress at node 12577 (Magnitude: PSI).

Figure 7.3-1. Fo6 file Output.

36

As shown in the .fo6 screen shot above, the SPC forces along T3 are of the magnitude e0 which

is one order of magnitude less than that of the external loading on the bottom of the Jaw Handle

and Handle. T3 is translational DOF out of plane of symmetry for this symmetric loading and

therefore any forces developed in the constraints along T3 should be close to 0. This is not the

case and therefore the simulation results should be further validated. The reasons for this

discrepancy can be viewed in the results and discussion, Section 7.6, below.

7.4 Hand Calculation for Verification of Simulation Solution of Bending Stress

Step 1. Distance and Angle Measurements

First in order to calculate principal stress at node 12577 several measurements in the FE Model

was required. The first of these measurements was to measure the length of the moment arm

perpendicular to the external 10 lbs. loading acting on the bottom most node of the lower portion

of the Jaw Handle. This distance extends from the node on which the load is acting to the

coincidental central nodes of the RBE2 elements connected to the Connecting Link, and the Jaw

handle respectively. This measurement was completed using the Measure Distance command

with the method being set to “Projected Distance.” This is displayed in Figure 7.3-1, below. The

length was found to be 2.418 inches. The next measurement required to calculate the stress in

node 12577 by hand was to measure the angle between the vector along which the external 10

lbs. loading is acting and the axis along which the first measurement (length of the moment arm)

was taken. This was completed using the Measure Angle command with “By Objects” as the type

and the two reference types set to “Vector.” The measurement of the angle is shown in Figure

7.3-2. The angle was found to be 87.0186o with is within a reason margin of difference when

compared to an ideal 90o between the force vector and moment arm length when calculating

moment generate by that force about a particular point. The final measurement taken, to be able

calculate the stress at node 12577, was the distance across the planar face of the Jaw Handle.

This was done by first creating a local CSYS in which the Z axis is aligned with the Z axis of the

global absolute CSYS and the Y axis was specified using a point to point vector from the node in

which the external force is acting to the central node of the one of the RBE2 elements simulating

a pin connection between the Connecting Link and the Jaw Handle. Then the measure distance

command with “Projected Distance” option selected was used along the X axis of this local CSYS.

This measurement resulted in a length of 0.416968 inches. The creation of the local CSYS is

shown in Figure 7.4-3 and the Measure Distance is shown in Figure 7.4-4 below.

37

Step 2. Calculation of Bending Stress

Utilizing the distances and angle measured in Step 1 of Section 7.4 and bending stress theory, the

bending stress for Node 12577 was calculated by hand in order to provide a basis for comparison

with the results of the Simulation. This calculation was done in MathCad and the results can be

seen in the screenshot depicted in Figure ### in the Appendix. The resulting moment was found

to be 24.151 lbs.*in. The bending stress was found to be 2223 PSI. Table 5, below, compares the

hand calculated value of the bending stress and the NX simulated value at Node 12577.

7.5 Hand Calculation for X (Resultant Axial Load in Nylon Bar) and N (normal force between

Lower Jaw and Jaw Handle)

In order to calculate these two unknowns, two linearly independent equations were required.

These two equations were found by utilizing static equilibrium equations. The first can be found

by taking the sum of moments about Point E in the overall FBD pictured in Figure 32, below. Then

the second equation can be found by taking the sum of moments about Point I in Figure 32.

Figure 7.4-1. Measure Distance for moment arm of external Force

Figure 7.4-2. Measure Angle between moment arm axis and force vector direction.

Figure 7.4-3. Creation of Local CSYS as described in Section 7.3 Step 1.

Figure 7.4-4.Measure Distance for Moment of Area calculation.

38

Step 1. Sum of Moments about Point E

The first step in calculating the axial load in the nylon bar and the contact force between the

Lower Jaw and the Jaw Handle was to create a Free Body diagram of the Lower Jaw. This Free

Body Diagram can be seen in Figure 7.5-1 below. In this FBD, the pin joint between the Lower

Jaw and the Handle has been removed and the resulting support forces are included at Point E,

which acts at the center of the pin joint. The other external forces on the Lower Jaw in this FBD

include the axial force of the nylon bar (X) and the contact force normal to the inner curved

surface of the Lower Jaw due to contact between the Lower Jaw and the Jaw Handle (N1). This

normal contact force acts at the apex of the curved surface. These force vectors can be viewed

in the FBD below. The first equation required to solve for the two unknown forces was found

from using static equilibrium of moments about the Point E. This resulted in equation 1 in Figure

7.5-3. The full derivation process for the following FBD and equilibrium equation can be seen in

the Appendix.

Figure 32. Overall FBD for Locking Pliers System.

39

Step 2. Sum of Moments about Point I

The second equilibrium equation used to find the forces X and N1, was found by taking the sum

of moments about the Point I of Figure 7.5-2. Point I is the intersection point between the contact

force between the Sliding Block and the Handle (G) and the force developed in the Connecting

Link (C). The Connecting Link, which is linked to the rest of the assembly by two pin connections,

acts as a two force member and thusly all forces that acts on it, are along its axis. A local CSYS

was developed in which the axis of the Connecting Link was aligned with the local Y axis. Point I

is the intersection between this Local Y axis and the force vector of G. Taking a moment about

Point I effectively neglects these forces (G and C) and thus the equilibrium equation becomes an

equation of two unknowns: X and N1, and one known: moment due to external force of 10 lbs.

applied to the bottom of the Jaw Handle. This provides the second linearly independent equation

necessary to solve for forces X and N1

Figure 7.5-1. Free Body Diagram of Lower Jaw used to find first equilibrium equation to solve for N1 and X.

40

Step 3. Calculation of X and N1

Utilizing the equations developed from the above procedure, X and N1 were found. Equation 1

and Equation 2 can be seen below in Figure 7.5-3. X was found to be 21.314 lbs. and the normal

contact force N1 was found to be 243.353 lbs. The process for solving for these values was done

in MathCad and the screenshot can be found in the Appendix, Figure 34.

Figure 7.5-2. Free Body Diagram of Jaw Handle, Connecting Link and Sliding Block used to find the second equilibrium equation to solve for N1 and X.

Figure 7.5-3. Equations 1 and 2 found from sum of moments about Point E and Point I, respectively.

41

7.6 Results and Discussion

Table 5 displays a summary of the above results of both the Hand Calculation and NX Simulation

of the bending stress, the axial load in the nylon bar, and the normal contact force between the

Lower Jaw and the Jaw Handle. As shown in the table, the percent error between the values of

the bending stress was the highest and the percent error between the values of the axial loading

and between the values of the normal contact force are under 10% which indicate they are within

loose agreement standards for this type of problem.

Table 5. Summary Table for Results of Simulation and Hand Calculation

X (lbs.) N1 (lbs.) σ (PSI)

Hand Calculation 21.314 234.353 2223

NX Simulation 22.58 213.1603 1779.868

Percent Error (%) 5.939758 9.04305 19.93396

The reason for these differences can be seen in the fo6 file discussed in Section 7.3, above. The

SPC forces along T3 are relatively high considering they should be equal to 0 for this symmetric

load case. This is due to the fact that the meshing on the Lower Jaw is not perfectly symmetric

coupled with the mesh element density was not high enough to accurately simulate line contact

between the curved surface of the Lower Jaw and the planar surface of the Jaw Handle. This

asymmetry and unrefined mesh led to out of plane loading, as displayed in the T3 forces of the

SPC section of the .fo6 file. These out of plane forces can be minimized by adding a CBUSH

element between the apex node of the curved surface of the Lower Jaw and the closest node on

the Jaw Handle. This CBUSH would need to have its CSYS overridden to a Local CSYS defined by

the local X axis being normal to the planar face of the Jaw Handle and the local Y and Z axes being

along that plane. This CBUSH’s stiffness’s would also be set to 10e8 along DOFs 1 and 3,

effectively killing translational motion along the local X and Z axes. Also improving mesh density

on these two parts would significantly improve the results of this simulation.

8. Summary

A solid model of the “Skil Ratch N Lock” were successfully created using the parametric computer aided

design program NX 8.5 by Siemens. The procedures for making each individual component was delineated

above in Section 3. The dimensions in each of the sketches and extrudes were taken directly from drafts

provided by the T.A. The process for the assembly of these components to a full solid model was

meticulously outlined above in Section 4. This solid model served as a base for the FEA study utilizing NX

8.5’s simulation and FEM modules described in Sections 5, and 6. Then verification of these results was

performed and described in Section 7. Overall this simulation was within reasonable margins of error and

therefore can be considered successful.

42

Figure 33. MathCad Screenshot for calculating Bending Stress

9. Appendix

The model and simulation created in this report contain dimensions and procedures given by the TA and

the professor. These instructions were provided in a combination, of both PowerPoint presentations and

YouTube tutorial videos. The following section provides links to all the presentations and video tutorials

used, as well as all figures required for the hand calculation of the bending stress and the axial load in the

nylon bar.

Hand Calculation for Bending Stress:

43

Figure 34. MathCad Screenshot for calculating Bending Stress

Hand Calculation for Axial Loading in Nylon Bar:

PowerPoint Presentations:

https://webcourses.ucf.edu/files/45287654/download?download_frd=1

https://webcourses.ucf.edu/files/45368643/download?download_frd=1

https://webcourses.ucf.edu/files/45542958/download?download_frd=1

https://webcourses.ucf.edu/files/45744748/download?download_frd=1

https://webcourses.ucf.edu/files/46089783/download?download_frd=1

https://webcourses.ucf.edu/files/46162670/download?download_frd=1

https://webcourses.ucf.edu/files/46308168/download?download_frd=1

44

YouTube Tutorials:

https://www.youtube.com/watch?v=qbQvHvXd8us&feature=youtu.be&list=PLQPYjyAxkS8hMSZgBti89E

6qs52y65jyP

https://www.youtube.com/watch?v=RSINc9Rs_3A&index=3&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65j

yP

https://www.youtube.com/watch?v=VBHkpem8ozQ&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65jyP&inde

x=4

https://www.youtube.com/watch?v=qAkt0QucBys&index=5&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65j

yP

https://www.youtube.com/watch?v=-

mKbbBUzYvk&index=6&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65jyP

https://www.youtube.com/watch?v=IieGBiwYS6U&index=7&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65jy

P

https://www.youtube.com/watch?v=_oUfKHxvu2M&index=8&list=PLQPYjyAxkS8hMSZgBti89E6qs52y65

jyP

https://www.youtube.com/watch?v=zjH3TSk2A8c

https://www.youtube.com/watch?v=ieCi8QGkOLQ

https://www.youtube.com/watch?v=LdtVKi0U8PY

Full procedure for Developing Hand Calculation of Axial Loading in Nylon Bar:

The following pages were created by the professor, Dr. Zarda, to help with the hand calculation and fully

outline the steps required to create the FBDs used above to solve for axial force in the Nylon Bar and the

normal force developed due to the contact between the curved surface of the Lower Jaw and the planar

surface of the Jaw Handle.