DESIGN OF MACHINE ELEMENTS

MECH3000 Minor Project: Analysis of a Toggle Clamp

GROUP:

Jack Connolly Dylan Ryan

Emily Seslar

Professor Le

Section 05

Fall 2018

Department of Mechanical Engineering

College of Engineering and Computer Science

Wentworth Institute of Technology

550 Huntington Ave, Boston, MA02115

1

Executive Summary

This project entailed the scenario of the company hypothetically employing us deciding to purchase another

company’s intellectual property of a toggle clamp. It was up to us to utilize analyzing technology to develop a

detailed simulation of the toggle clamp. After this we adapted the prototype to be both functionally and structurally

superior over other products on the market. We first went through the reverse engineering effort for the prototype

with a performance simulation of the clamp lock mechanism and understanding the interface design requirements.

We examined the loading analysis and gathered up a great amount of information to come to a diagnostic

conclusion. Afterwards we compared the overall performance to the required design specifications. The design

specifications and conditions for the toggle clamp include the rated clamp loading to be at 150 lb. The factor of

safety must reach a 2.0. Furthermore, the clamp must be capable of functioning from 0 inches to 0.25 inches over

the height between the selected touch flat surface of the part and the flat ground. When it comes to how the device

locks into place, there is no physical clicking-into-place lock, however there are force manipulating factors at stake

here. The main components that aid in the locking motion are the two red bars in the center of the device. When

these two bars are pushed into the horizontal position, they become a two-force member. There are only horizontal

forces that exist at this point, meaning that the only way that the device can come unlocked, is with an outside y

direction force. For example, your hand applying a force to the handle that has any portion in the y -direction. We

initially investigated the clearance and interference interfaces of various components. Clearance fit is when

equipment is designed so that parts have either a gap between them, so they can move separately from each other or

they are firmly in contact and do not move relative to each other. The gap or lack of it between the hole and shaft is

called the clearance. Clearance is determined by the size difference between the parts. Fits and tolerances are used to

specify the size range of parts. All of the tolerances are bilateral for this design. This goes for rotation and no

rotation. The pin tolerances tended to be the tightest. Without a tolerance that falls within the restraints, the device

will not work correctly. Due to this utter significance, it is vital that the tolerances are properly found and

communicated to the manufacturers. We also did the hand calculations that analyzed the inner forces of the device.

For the main beam, it was found that By = 0 pounds, Ay = -150 pounds Ax = -645.2 pounds Bx = 645.2 pounds, and

Cx = 645.2 lb. We found these inner forces by using equilibrium principles like summing up forces and having them

equal zero. We did this for the rest of the components, including the pins, bars, handle, and base. Finally, we ran

FEA simulations on all of the individual components, which displayed a visual illustration of the intensity o f

strength that the part can handle. It displays the minimum, maximum, and the yield strength. We ran the simulations

in the worst possibly case with the clamp being the farthest away from the base. From this project we gain an

outlook on the analysis process in the real work world. With these Finite Element Analysis technologies, engineers

can companies can optimize devices with ease.

(Figure 1)

2

Table of Contents

Executive Summary .........................................................................................................................1

Table of Contents .............................................................................................................................2

List of Figures ..................................................................................................................................3

List of Tables ...................................................................................................................................3

Case Study Introduction...................................................................................................................4

Analysis............................................................................................................................................4

Design Interface Analysis ................................................................................................................4

Loading Analysis .............................................................................................................................6

FEA Simulation ...............................................................................................................................9

FEA Simulation on the Clamp Bottom Arm........................................................................9

FEA Simulation on the Clamp Upper Arm........................................................................10

FEA Simulation on the Base ..............................................................................................10

FEA Simulation on the Link Strap.....................................................................................11

Design Check (Factor of Safety Calculations) ..............................................................................11

Design Check on Each Pin.................................................................................................11

Design Check on the Link Strap ........................................................................................14

Design Check on the Clamp Upper Arm ...........................................................................16

Design Check on the Clamp Bottom Arm .........................................................................16

Design Check on the Base .................................................................................................17

Detail Drawings of All Parts ..........................................................................................................18

Exploded Assembly Drawing ........................................................................................................23

Findings, Discussion, and Conclusion ...........................................................................................24

References ......................................................................................................................................24

3

List of Figures

1. Interface Schematic ................................................................................................................ 4

2. Calculating Reaction Forces Within the System ....................................................................... 6

3. Free Body Diagram for Each Pin ............................................................................................ 7

4. Free Body Diagram for The Link Strap ................................................................................... 8

5. Free Body Diagram for The Clamp Upper Arm ....................................................................... 8

6. Free Body Diagram for The Clamp Bottom Arm ..................................................................... 8

7. Free Body Diagram for The Base ............................................................................................ 9

8. FEA Simulation on The Clamp Bottom Arm ........................................................................... 9

9. FEA Simulation on The Clamp Upper Arm ........................................................................... 10

10. FEA Simulation on The Base ................................................................................................ 10

11. FEA Simulation on The Link Strap ....................................................................................... 11

12. FEA Based Design Check (Link Strap) ................................................................................. 15

13. Design Check on The Clamp Upper Arm .............................................................................. 16

14. Design Check on The Clamp Bottom Arm ............................................................................. 16

15. Design Check on The Base ................................................................................................... 17

16. Drawings

a. Base ........................................................................................................................ 18

b. Bottom Arm ............................................................................................................ 19

c. Link Strap ............................................................................................................... 20

d. Upper Arm .............................................................................................................. 21

e. Spindle ................................................................................................................... 22

f. Exploded View ........................................................................................................ 23

List of Tables

1. Clearance Interfaces................................................................................................................ 5

2. Interference Interfaces............................................................................................................. 5

3. Design Check for Pin A ....................................................................................................... 11

4. Design Check for Pin B......................................................................................................... 12

5. Design Check for Pin C......................................................................................................... 13

6. Design Check for Pin D ........................................................................................................ 13

7. Design Check for the Link Strap (Theoretical) ....................................................................... 14

4

Case Study Introduction

The problem statement of this investigation is that a devised company approached us as

mechanical engineers and they need to perform a case study on a device that they want to purchase the

rights to. The device is a toggle clamp that can lock into place on its own. A toggle clamp is a device that

has a single clamping plate that can hold a workpiece down on a work surface, for example: a bench top.

The clamp is fixed, as it is hypothetically bolted to the work surface. The fact that the clamp only has one

clamping plate is interesting because it means that it is used in combination with the table surface to hold a

workpiece in a secure fashion. The plate on the clamp pushes on the workpiece, therefore holding it steady

between the plate and the work surface. Our job as engineers is most of the time to continuously improve

the current way of doing things. By running simulations on the components to the toggle clamp, we could

see where the failures occurred and how to improve the design so that the failure occurs with more outside

force being applied next time. We were provided with the design specifications and circumstances for the

toggle clamp including the rated clamp loading to be 150 lb. The factor of safety can be defined as how

much stronger a system is than it needs to be for an intended load. Additionally, the clamp must be capable

of performing from 0-0.25 inches over the height between the selected touch flat surface of the part and the

flat ground. The device must be capable of locking into place when holding something down onto a work

table. There is no actual tab or locking mechanism, however the inner forces cause the tool to be functional.

The two main components that support the locking motion are the red bars in the middle of the device.

They become a two-force member when they are moved into the horizontal position. In this case, there are

only horizontal forces that exist, meaning that the only way that the device can come unlocked is with an

outside y-direction force. For example, it could be your hand applying a force that has any portion in the y -

direction. With this vision of attempting to achieve as close to perfect efficiency as possible, we must

utilize FEA technology to achieve these results that exist beyond human perception.

Analysis

Design Interface Analysis

We assigned the interface points as shown below for calculations.

(Figure 1)

5

The assembly of the device was designed such that the pins would be fixed to one component and

would have clearance in another. This means that some components will rotate with respect to the pins,

while others are fixed. The relations written below describe each interface. The pins are press fit into the

clamp’s lower and upper bars, thus requiring higher precision tolerancing. The next table describes the

clearance fits which allow the pins to slide inside of the components (the link bars and base).

CLEARANCE INTERFACES (ROTATION PERMITTED) (Table 1)

Interface Assembly

Tolerance Pin Dimension

Interfaced

Component (P/N)

Component Hole

Dimension

A ∅ 0.10000.00500.0150 in ∅ 0.10000.0001

0.0003 in Base (1, 2) ∅ 0.10000.00530.0151 in

B ∅ 0.10000.0050.015 in ∅ 0.10000.0001

0.0003 in Link Strap (1, 2) ∅ 0.10000.00530.0151 in

C ∅ 0.10000.0050.015 in ∅ 0.10000.0001

0.0003 in Link Strap (1, 2) ∅ 0.10000.00530.0151 in

D ∅ 0.10000.0050.015 in ∅ 0.10000.0001

0.0003 in Base (1, 2) ∅ 0.10000.00530.0151 in

INTERFERANCE INTERFACES (NO ROTATION PERMITTED) (Table 2)

Interface Assembly

Tolerance Pin Dimension

Interfaced

Component (P/N)

Component Hole

Dimension

A ∅ 0.1000−0.0050−0.0030 in ∅ 0.10000.0001

0.0003 in Clamp Lower Bar ∅ 0.1000−0.0047−0.0029 in

B ∅ 0.1000−0.0050−0.0030 in ∅ 0.10000.0001

0.0003 in Clamp Lower Bar ∅ 0.1000−0.0047−0.0029 in

C ∅ 0.1000−0.0050−0.0030 in ∅ 0.10000.0001

0.0003 in Clamp Upper Bar ∅ 0.1000−0.0047−0.0029 in

D ∅ 0.1000−0.0050−0.0030 in ∅ 0.10000.0001

0.0003 in Clamp Upper Bar ∅ 0.1000−0.0047−0.0029 in

6

Loading Analysis

CALCULATING REACTION FORCES WITHIN THE SYSTEM (Figure 2)

7

FREE BODY DIAGRAM FOR EACH PIN (Figure 3)

8

FREE BODY DIAGRAM FOR THE LINK STRAP (Figure 4)

FREE BODY DIAGRAM FOR THE CLAMP UPPER ARM (Figure 5)

FREE BODY DIAGRAM FOR THE CLAMP BOTTOM ARM (Figure 6)

9

FREE BODY DIAGRAM FOR THE BASE (Figure 7)

FEA Simulations

FEA SIMULATION ON THE CLAMP BOTTOM ARM (Figure 8)

Maximum Stress: 218800 psi

Minimum Stress: 175.3 psi

10

FEA SIMULATION ON THE CLAMP UPPER ARM (Figure 9)

Maximum Stress: 69250 psi

Minimum Stress: 0 psi

FEA SIMULATION ON THE BASE (Figure 10)

Maximum Stress: 6.7 psi

Minimum Stress: 108900 psi

11

FEA SIMULATION ON THE LINK STRAP (Figure 11)

Maximum Stress: 49900 psi (18.0% error from theoretical calculation)

Minimum Stress: 1.3 psi

Design Check (Factor of Safety Calculations)

Design Check on Each Pin

PIN A (Table 3)

Calculating Shear Force:

𝐹𝑛𝑒𝑡 −𝐴 = √(𝐹𝑥)2 + (𝐹𝑦 )

2

𝐹𝑥 = 645.2 lb, 𝐹𝑦 = 150 lb

𝐹𝑛 𝑒𝑡 −𝐴 = √(645 .2)2 + (150)2

𝐹𝑛𝑒𝑡 −𝐴 = 662.8 lb

12

Calculating Shear Stress (applying double shear equation):

𝜏𝐴 =𝐹

2𝐴=

𝐹

2 ∗𝜋4

𝑑 2=

2𝐹

𝜋𝑑 2

𝐹 = 662.8 lb, 𝑑 = 0.1001 in

𝜏𝐴 =2 ∗ 662.8

𝜋(0.1001) 2

𝜏𝐴 = 42,111 psi

Applying Shear Stress to Design Equation:

𝑛 =𝑆𝑦

𝜏𝐴

𝜏𝐴 = 42,111 psi, 𝑆𝑦 = 50,800 psi

𝑛 =50800

42111

𝑛 = 1.206

This means the pin will not shear but it does not meet the design criteria (𝑛 = 2).

PIN B (Table 4)

Calculating Shear Stress (applying double shear equation):

𝜏𝐴 =𝐹

2𝐴=

𝐹

2 ∗𝜋4

𝑑 2=

2𝐹

𝜋𝑑 2

𝐹 = 645.2 lb, 𝑑 = 0.1001 in

𝜏𝐴 =2 ∗ 645.2

𝜋(0.1001) 2

𝜏𝐴 = 40,993 psi

Applying Shear Stress to Design Equation:

𝑛 =𝑆𝑦

𝜏𝐴

𝜏𝐴 = 40,993 psi, 𝑆𝑦 = 50,800 psi

13

𝑛 =50800

40993

𝑛 = 1.239

This means the pin will not shear but it does not meet the design criteria (𝑛 = 2).

PIN C (Table 5)

Calculating Shear Stress (applying double shear equation):

𝜏𝐴 =𝐹

2𝐴=

𝐹

2 ∗𝜋4

𝑑 2=

2𝐹

𝜋𝑑 2

𝐹 = 645.2 lb, 𝑑 = 0.1001 in

𝜏𝐴 =2 ∗ 645.2

𝜋(0.1001) 2

𝜏𝐴 = 40,993 psi

Applying Shear Stress to Design Equation:

𝑛 =𝑆𝑦

𝜏𝐴

𝜏𝐴 = 40,993 psi, 𝑆𝑦 = 50,800 psi

𝑛 =50800

40993

𝑛 = 1.239

This means the pin will not shear but it does not meet the design criteria (𝑛 = 2).

PIN D (Table 6)

Calculating Shear Stress (applying double shear equation):

𝜏𝐴 =𝐹

2𝐴=

𝐹

2 ∗𝜋4

𝑑 2=

2𝐹

𝜋𝑑 2

𝐹 = 645.2 lb, 𝑑 = 0.1001 in

𝜏𝐴 =2 ∗ 645.2

𝜋(0.1001) 2

𝜏𝐴 = 40,993 psi

14

Applying Shear Stress to Design Equation:

𝑛 =𝑆𝑦

𝜏𝐴

𝜏𝐴 = 40,993 psi, 𝑆𝑦 = 50,800 psi

𝑛 =50800

40993

𝑛 = 1.239

This means the pin will not shear but it does not meet the design criteria (𝑛 = 2).

DESIGN CHECK ON THE LINK STRAP

THEORETICAL CALCULATION (Table 7) Calculating Nominal Normal Stress:

𝜎𝑛𝑜𝑚 =𝐹

𝐴𝐶𝑆

𝐴𝐶𝑆 = (𝑤 − 𝑑) ∗ 𝑡

Where. . .

𝑤 = width = 0.324 in

𝑑 = hole diameter = 0.1151 in

𝑡 = thickness = 0.078 in

𝜎𝑛𝑜𝑚 =322.6

(0.324 − 0.1151 ) ∗ 0.078

𝜎𝑛𝑜𝑚 = 19,798 psi

Stress Concentration due to Pin Hole (using eFatigue):

15

𝑘𝑡 = 2.29

𝜎𝑚𝑎𝑥 = 𝑘𝑡 ∗ 𝜎𝑛𝑜𝑚

𝜎𝑚𝑎𝑥 = 2.29 ∗ 19798

𝜎𝑚𝑎𝑥 = 45,338 psi

Applying Shear Stress to Design Equation:

𝑛 =𝑆𝑦

𝜎𝑚𝑎𝑥

𝜎𝑚𝑎𝑥 = 45,338 psi, 𝑆𝑦 = 50,800 psi

𝑛 =50800

45338

𝑛 = 1.120

This means the link strap will not fracture but it does not meet the design criteria (𝑛 = 2).

The following plots show where the components reach below a factor of safety of 2, meaning

they do not meet the required specification.

LEGEND

𝑛 > 2

𝑛 < 2

FEA BASED DESIGN CHECK (Figure 12)

Minimum Factor of Safety: 1.02

16

DESIGN CHECK ON THE CLAMP UPPER ARM (Figure 13)

Minimum Factor of Safety: 0.74

DESIGN CHECK ON THE CLAMP BOTTOM ARM (Figure 14)

Minimum Factor of Safety: 0.22

17

DESIGN CHECK ON THE BASE (Figure 15)

Minimum Factor of Safety: 0.47

18

Detail Drawings of All Parts

19

20

21

22

Exploded Assembly Drawing

23

24

Findings, Discussion, and Conclusion

When the toggle clamp secures an object with a 150 pound clamping force, the reactionary forces

would cause the clamp to fail in certain locations. After analyzing the FEA’s from all major pieces, there

are multiple areas from the FEA that have a stress greater than that of the materials yield strength. The bas e

and both upper and lower arms failed with a clamping force of 150 pounds. To improve the clamp to ensure

that it can withstand that force, there are multiple options that could be used. A different material could be

used in the parts that failed. The right material can ensure that the clamp doesn’t fail with a 150 pound

force applied to it. The design of the parts could also be changed to reduce the amount of stress on the

parts. The thickness of the parts can be increased, or the shape of the part could be changed. The best way

to choose which method to improve the part would be the cheapest method.

References

[1] “Toggle Clamps”. Elesa, www.elesa.com/static/sfogliabili/files/SpeedyBlock_ENG_USA_WEB.pdf

[2] “Fatigue Analysis on the Web.” EFatigue Analysis on the Web, www.efatigue.com/.

[3] “Alloy Steel Pins.” McMaster-Carr, www.mcmaster.com/standard-dowel-pins.

[4] “AISI 1020 Steel, cold rolled” MatWeb: Material Property Data , www.matweb.com/.