City College of New York School of Engineering

Mechanical Engineering Department

Spring-2014

Mechanical Engineering I 6500: Computer-Aided Design Instructor : Prof. Gary Benenson

Student : Mehmet Bariskan

Final Project : Design and FEM Analysis of

Scissor Jack

2

1. Overview:

A jack is a mechanical device used as a lifting device to lift heavy loads or apply great forces.

Jacks employ a screw thread or hydraulic cylinder to apply linear forces. Car jacks use

mechanical advantage to allow us to lift a vehicle by manual force alone. More powerful

jacks use hydraulic power to provide more lift over greater distance. A scissor jack is a

device constructed with a cross-hatch mechanism, much like a scissor. A commercially

available scissor jack is shown in Figure 1.

Figure 1: Scissor Jack

A scissor jack is operated by turning a lead screw. It is commonly used as car-jacks. In the

case of a scissor jack, a small force applied in the horizontal plane is used to raise or lower

large load. A scissor jack’s compressive force is obtained through the tension force applied

by its lead screw. An acme thread is most often used, as this thread is very strong and can

resist the large loads imposed on most jacks while not being dramatically weakened by

wear over many rotations. An inherent advantage is that, if the tapered sides of the screw

wear, the mating nut automatically comes into closer engagement, instead of allowing

backlash to develop (Rajput, 2007). These types are self-locking, which makes them

intrinsically safer than other jack technologies like hydraulic actuators which require

continual pressure to remain in a locked position.

The completed solidworks design of the scissor jack and its members shown in Figure 2.

Most scissor jacks are similar in design, consists of four lifting arms, a base plate, a carrier

plate, two connection members, eight connection pins, a power screw and a crank. This

crank is usually “Z” shaped. When this crank is turned, the screw turns, and this raises the

3

jack. The screw acts like a gear mechanism. It has teeth (the screw thread), which turn and

move the four arms, producing work. The four arms are all connected at the corners with a

bolt that allows the corners to swivel.

Figure 2: Solidworks design of Scissor Jack and its members

The lifting members are made from c-shapes. The web of the lifting member is cut out near

the pin connections to allow proper serviceability of the scissor jack at its maximum and

minimum heights. Members 3 and 4 have ideal connections to balance the load between

the left and right side.

The connecting pins are designed with cylindrical shapes and they are subjected to tension

instead of compression. The bending moment from the screw shaft creates tension on

these members.

Other pins are used as fasteners at the various joints of the members. The existence of the

jack will depend on the ability of the pin not to fail under sudden shear, tensional and

compressive forces.

4

1.1 Force and Stress Analysis

The force analysis is based on the assumption that the scissor jack is loaded vertically

symmetrical.

Figure 3: Forces in Scissor Jack members

The maximum capacity for the scissor jack is the 600 kg.

Maximum Load = 600 kg, F= 600 kg * 9.81 𝑚

𝑠2 = 5886 N

L= 145 mm, the length of the arms (From hole center to hole center)

e = 180 mm, the length from base to top center of holes (At Minimum raising height of

the jack)

𝑐𝑜𝑠𝛼 =𝑒

2⁄

𝐿=

1802⁄

145= 0.62 𝑎𝑛𝑑,

𝛼 = 51,6°

5

Assuming that I can simplify the mechanism at the joint of the top section that is shown

in Figure 4.

Figure 4: Free Body Diagram of the top section

∑ 𝐹𝑥 = 0

𝐹1 ∙ 𝑠𝑖𝑛𝛼 − 𝐹2 ∙ 𝑠𝑖𝑛𝛼 = 0 , 𝐹1 ∙ 𝑠𝑖𝑛𝛼 = 𝐹2 ∙ 𝑠𝑖𝑛𝛼

𝐹1 = 𝐹2

∑ 𝐹𝑦 = 0

𝐹1 ∙ 𝑐𝑜𝑠𝛼 + 𝐹2 ∙ 𝑐𝑜𝑠𝛼 − 𝐹 = 0

2 ∙ 𝐹1 ∙ 𝑐𝑜𝑠𝛼 = 𝐹

𝐹1 =𝐹

2∙𝑐𝑜𝑠𝛼 𝐹1 =

5886

2∙cos (51.6)

𝐹1 = 𝐹2 = 4738 𝑁

The angle is decreasing at maximum raising height of the jack. Consequently, the

maximum force is decreased. Since the maximum loading force will act at the minimum

raising height of the jack, the design stresses will be analyzed at that point.

α α

F1 F2

F

6

Figure 5: Free Body Diagram of the joint of the shaft and arms

Focusing the point of the components at the joint of the screw shaft and arms. We can say at

this point;

∑ 𝐹𝑦 = 0

𝐹1 ∙ 𝑐𝑜𝑠𝛼 − 𝐹3 ∙ 𝑐𝑜𝑠𝛼 = 0

𝐹1 ∙ 𝑐𝑜𝑠𝛼 = 𝐹3 ∙ 𝑐𝑜𝑠𝛼

𝐹1 = 𝐹3

∑ 𝐹𝑥 = 0

𝐹1 ∙ 𝑠𝑖𝑛𝛼 + 𝐹3 ∙ 𝑠𝑖𝑛𝛼 − 𝐹𝑆 = 0

𝐹𝑆 = 2 ∙ 𝐹1 ∙ 𝑠𝑖𝑛𝛼

𝐹𝑆 = 2 ∙ 4738 ∙ sin(51.6)

𝐹𝑆 = 7426 𝑁

Because of the symmetry we can write the following equation

|𝐹1| = |𝐹2| = |𝐹3| = |𝐹4| = |𝐹1′| = |𝐹2

′| = |𝐹3′| = |𝐹4

′|

α

α

Fs F1

F3

7

2. Procedure

The first target is to predict the maximum displacement and maximum stress of the

scissor jack. Since the force is applied to the carrier member, I can predict that the

maximum displacement will happen at the top side of this member which is shown in

Figure 2 (labeled with number 6). Since the maximum force occurs on the screw shaft

which is calculated in the force and stress analysis. The maximum stress should be

occur joint of the screw and connecting pins.

2.1 Design and Analysis for the Individual Parts

Solidworks had been used to create and analyze the geometry under various boundary

conditions (restarints) and loading condition (force). The scissor jack had been analyzed

for stress and displacement.

I have followed the following steps:

I- I have started to design with the carrier member which is shown in Figure 6

and its technical drawing is shown in the drawing section.

Figure 6: Carrier Member

The top surface of the model was loaded with a compressive force of 5886 N, and the

holes were fixed as shown in Figure 6.

8

The material is carbon steel (Ck 45) according to manufacturer website. If we don’t

know the material we can measure the hardness to estimate it’s tensile and yield

strength. The Ck45 graded steel has the following properties.

Applied Material Ck45, AISI 1045 Steel

Elastic Modulus 201 GPa

Tensile Strength 625 MPa

Yield Strength 530 MPa

Table 1: Properties of Ck45 Steel

Several studies were performed for creating the mesh. Then, I ran the model for stress

and displacement analysis.

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-1

166.68 51 1699 3614 10194 5 N/A 1

Study-2 176.85 51 2897 5786 16710 4 N/A 1

Study-3 174.76 53 5941 10936 32160 3 N/A 1

Study-4 175.11 54 15994 27605 81375 2 N/A 2

Study-5 179.41 54 35041 57818 171294 1.5 N/A 3

Study-6 187.47 54 101542 159455 474117 1 N/A 9

Study-7 202.43 54 243096 366597 1092015 0.75 N/A 23

Study-8 233.07 54 786449 1141860 3410388 0.5 N/A 85

Table 2: The Results of the Mesh Studies for the carrier member

The study shows us the maximum displacement occurs at the middle section of the

member’s longitudinal axis with approximately 54 µm. The maximum stress occurs at

the same place in the first four studies. The study 5 and 6 show that the maximum

stress occurs at the upside of the holes. The study 7 and 8 show that more refinement

is giving the rising stress at the upside of the holes that is showing also the boundary

conditions are not really pairing with the real life conditions or using the solidworks is

9

useless if you cannot define the appropriate boundary conditions. I am going to focus

that problem in the assembly study.

Figure 7: The maximum stress figure (left) and, the maximum displacement figure (right)

for the carrier member

II- I have completed the second analysis with the lifting arms which are labeled

in the figure 2. I have labeled them in the figure 2 with the number of 3 and 4.

The forces change with respect to its angular position. Firstly, I have applied the

compressive force that is calculated in force and stress analysis section. The arm must

be able to withstand an axial force of 4738 N for compression that is shown in Figure 8.

Figure 8: Lifting Arm

10

Several studies were performed to creating the mesh. Then, I ran the model for stress

and displacement analysis.

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-9

93.50 82 5611 11389 33843 5 N/A 3

Study-10 92.70 83 7276 14689 43743 4 N/A 4

Study-11 95.73 82 10754 21644 64500 3 N/A 5

Study-12 101.37 82 29066 53163 158769 2 N/A 12

Study-13 101.38 82 64975 110234 329514 1.5 N/A 29

Study-14 103.32 82 195905 312378 935082 1 N/A 88

Study-15 104.59 82 418984 647022 1937466 0.75 N/A 231

Study-16 103.54 82 1352434 1999109 5989299 0.5 N/A 889

Table 3: The Results of the Mesh Studies for the Lifting Arm

The study shows us the maximum displacement occurs at the top section of the lifting

arm with approximately 83 µm. Displacement occurs to the latitudinal direction because

of the arm shape causing the bending effect which is shown in Figure 9. The maximum

stress occurs in the pin holes that is shown in Figure 9. In this study, I only did

compressive study to lifting arm’s longitudinal axis. When I change the fixed place to top

holes and loaded place to bottom holes, I have the similar results for the stress and

displacement causing by the action and reaction forces.

11

Figure 9: The maximum stress figure (left) and, the maximum displacement figure (right)

for the lifting arms.

III- I have completed the third analysis with the shaft screw which is labeled in

the figure 2. I have labeled it in the figure 2 with the number of 16.

I have applied a tensile force that is calculated in force and stress analysis section.

The shaft must be able to withstand an axial force of 7426 N for tension that is

shown in Figure 7.

Figure 10: Shaft Screw

12

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-17

93.81 89 1864 3842 11286 5 N/A 1

Study-18 93.69 90 4583 8344 24645 4 N/A 1

Study-19 94.01 90 7015 12348 36504 3 N/A 2

Study-20 94.27 90 23755 38472 114186 2 N/A 4

Study-21 94.35 90 53650 82739 246444 1.5 N/A 13

Study-22 94.57 90 248545 364679 1088640 0.9 N/A 55

Study-23 94.59 90 389636 565694 1689549 0.75 N/A 81

Study-24 95.35 90 1102266 1572182 4699632 0.5 N/A 532

Table 4: The Results of the Mesh Studies for the shaft screw (tensile)

The study shows us the maximum displacement occurs at the place where the force

applied of the shaft screw with approximately 90 µm. Displacement occurs to the

longitudinal direction. The maximum stress occurs at the same face with the

displacement and its magnitude approximately 95 MPa. The both pattern are shown in

Figure 11. The technical drawing of the shaft is attached in the drawing section.

Figure 11: The maximum stress figure (left) and, the maximum displacement figure

(right) for the shaft screw.

13

IV- I have completed the fourth analysis with the shaft screw again. In this study,

I will focus the torsional stress in the shaft screw.

Firstly, I need to find out that what is the maximum torque that a human can apply to the

crank shaft? The crank shaft is labeled with number 9 in the figure 2.

The maximum force we could produce with a down push is (m * g) where m is our

mass. Considering the turning the shaft is not just a down push, I have made several

searches. I went to a gym and there are different type of people that they can pull and

push between 30 kg to 50 kg. I am going to apply the maximum force with 50 Kg, since

the load could apply from the stronger person to the jack.

F= 50 kg. * 9.81 𝑚

𝑠2 = 490.5 N

When I consider the head of the shaft screw that has a diameter of 23 mm. The torque

that we may create:

490.5 N * 0.023

2 m = 5.64 Nm

We could apply the torque to the head of the outer face of the shaft directly that is

shown in Figure 12. The fixed surface has chosen in the joint of the shaft screw and the

middle pin. Also, the fixed hinge restraint has applied to the between the middle pin and

the head of the shaft which is shown in the Figure 12.

Figure 12: Boundary conditions of the shaft screw #1 (torque)

14

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-25

54.95 251 2030 4109 11949 5 N/A 2

Study-26 56.36 253 4655 8435 24783 4 N/A 3

Study-27 59.28 253 6679 11946 35052 3 N/A 5

Study-28 65.28 253 24270 39109 115383 2 N/A 16

Study-29 70.78 253 67293 102722 302505 1.5 N/A 46

Study-30

80.67 253 277011 404403 1199013 0.9 N/A 279

Study-31 86.20 253 388592 564211 1679241 0.75 N/A 386

Study-32 110 253 1118962 1594211 4752015 0.5 N/A 1410

Table 5: The Results of the Mesh Studies #1 for the shaft screw (torque)

The results are not converging. I have decided to change the boundary conditions.

Since there is a movement between the teeth’s, I have decided to change the fixed

place to the shaft face that is shown in Figure 13.

Figure 13: Boundary conditions of the shaft screw #2 (torque)

15

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-33

54.95 303 2030 4109 12243 5 N/A 1

Study-34 56.35 305 4655 8435 25221 4 N/A 3

Study-35 56.16 305 6679 11946 35673 3 N/A 5

Study-36 57.85 305 24270 39109 116958 2 N/A 19

Study-37 57.13 305 67293 102722 305691 1.5 N/A 56

Study-38

57.10 305 189352 282335 834324 1 N/A 418

Study-39 57.45 305 388592 564211 1690752 0.75 N/A 514

Study-40 58.11 305 1118962 1594211 4778511 0.5 N/A 2024

Table 6: The Results of the Mesh Studies #2 for the shaft screw (torque)

Figure 14: The maximum Stress of the shaft screw (torque)

16

Figure 15: The maximum Displacement of the shaft screw (torque)

The study shows us the maximum displacement occurs at the head section of the shaft

screw with approximately 305 µm. Displacement occurs to the circular direction. The

maximum stress occurs between the shaft and head of the screw which is sown in

Figure 15 with approximately 58 MPa.

V- I have completed the fifth analysis with the base plate that is labeled with

number 1 in the Figure 2. In this study, I will focus the compressive load by

causing of the lower lifting arms that is 4738 N. I have created the new planes

with 51.6 degree towards to lifting arms that is shown in Figure 16. The fixed

surface has chosen the bottom surface of the base plate. The left arms and

the right arms cause the force of 4738 N separately that were applied to the

base channel. After the studies, I have found the maximum displacement

approximately 3 µm around at the four holes and the maximum stress were

found approximately 114 MPa in the four holes. Both patterns are showing in

Figure 17 and Figure 18 respectively.

17

Figure 16: Base Channel

Mesh Density

& Quality

(Standard

Mesh)

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Location(s)

Local

Refinemen

t

Running

Time

(second)

Study-41 99.34 3 4146 8758 22671 5 N/A 1

Study-42 111.59 3 5896 12272 31653 4 N/A 1

Study-43 113.85 3 10008 20328 52035 3 N/A 2

Study-44 113.59 3 33095 59249 158874 2 N/A 3

Study-45 113.30 3 72743 123194 336435 1.5 N/A 7

Study-46 115.96 3 213035 341571 950610 1 N/A 20

Study-47 113.76 3 504062 774165 219506 0.75 N/A 48

Study-48 114.57 3 1588087 2342876 6736581 0.5 N/A 347

Table 7: The Results of the Mesh Studies for the base plate

18

Figure 17: The maximum stress of the base plate

Figure 18: The maximum displacement of the base plate

19

2.2 Assembly Analysis

I- Assembly

After, I have created the parts for the scissor jack. I have combined them in a solidworks

assembly file. We need to use the mate command properly to attach the parts each

other’s. I have started with the carrier member, right lifting arm and left lifting arm. There

is a hinge command in the mechanical mates section. I have selected that command to

create a hinge connection between the hole of the carrier member and the hole of the

left arm, chosen concentric and coincident selections are shown in Figure 19.

Figure 19: The Hinge (Mechanical Mates) Selections for upside connections

I have completed the remaining three holes with the same method. Then, I have used

the same command for the joint of the upper and bottom lifting arms. In this step,

selection of the concentric and coincident selections are shown in Figure 20. Following

step was to connect the lifting arms to the base plate which is shown in Figure 21. The

operation was applied to the all pin connection holes as described above.

20

Figure 20: The Hinge (Mechanical Mates) Selections for arm connections

21

Figure 21: The Hinge Mate (Mechanical Mates) Selections for bottom side connections

The screw mate that, I have applied between the shaft screw and middle pin. The outer

face of the shaft screw and the inner face of the hole in the middle pin were chosen as

mate faces. The screw mate command with distance / revolution option was applied that

is shown in Figure 22. I have applied a concentric mate to the same faces. The

concentric mate also was applied between the remaining middle pin and outer face of

the shaft screw.

Figure 22: The Screw Mate (Mechanical Mates) Selections

The coincident mate was applied to two panel that are shown in in Figure 23. Then, the

hinge mate was applied between outer face of the middle pin’s bearing and inner face of

the holes of the arms at the connection places. A tangent mate was applied between

the one face of the shaft’s head and the outer face of the middle pin to prevent

movement between two components that is shown in Figure 24.

22

Figure 23: Coincident mate selections

Figure 24: Tangent mate selections

II – FE Analysis

I have followed the following steps to perform static studies in Solidworks program.

23

Firstly, I have applied the material to the all component that is described in Table 1.

Secondly, I have applied a fixture to fix the bottom face of the scissor jack. I have

applied an external load of 5886 N to upside of the carrier member. The both boundary

conditions are shown in Figure 25.

Figure 25: The boundary conditions for the assembly

The third step was to apply the connectors to the pin holes. I have chosen pin type of

connector and apply to the inner face of the holes with the connection type of the “With

retaining ring (No translation)” option. I have applied the pin connectors to the 12

connections with the 24 inner face off the holes which are shown in Figure 26.

The fourth step was to define contact sets. We have to specify the contact sets to

program otherwise all parts has considered as a single part. I have defined total of 30

contact sets between the faces of the components. We need to focus to movement of

the scissor jack and inspect the faces working towards. The outer flank faces of the

upper lifting arms and inner flank faces of the lower lifting arms can be examples of the

contact sets have to be considered. After two faces are chosen in the program, we need

to choose also the type of the contact sets. I have completed all the contact sets with

the “No Penetration” option.

The fifth step was to mesh the assembly and run the study. The results are shown in

Table 8.

24

Figure 26: The pin connections

Mesh Density

& Quality

Maximum

Stress

(MPa)

Maximum

Displacement

(µm)

Total

# of

Element

Total

# of

Nodes

Total

# of

DOF

Global

Element

Size

(mm)

Running

Time

(second)

Study-49

Curvature 211.61 417 71805 139476 416247 10 2194

Study-50 218.38 409 161672 297903 889521 5 4612

Study-51 222.20 438 264319 468019 1397634 3.5 7316

Study-52 2

Study-53 1.5

Study-54 1

Study-55 0.75

Table 8: The Results of the Mesh Studies for the assembly

25

Figure 27: von-Misses stress contour of the scissor jack at 5886 N load

Figure 28: Displacement contour of the scissor jack at 5886 N load

26

3. Results

The convergence studies were completed for the individual parts with eight studies. The

tabulated data for von Mises stress and displacement are gathered in Table 9 and 10.

Maximum

Stress

(MPa)

Part # 6 Carrier

Member

Part #

2,3,4,5

Arms

Part # 16

Shaft Screw

Tension

Part # 16

Shaft Screw

Torque

Part # 1 Base

Study 166.68 93.50 93.81 54.95 99.34

Study 176.85 92.70 93.69 56.35 111.59

Study 174.76 95.73 94.01 56.16 113.85

Study 175.11 101.37 94.27 57.85 113.59

Study 179.41 101.38 94.35 57.13 113.30

Study 187.47 103.32 94.57 57.10 115.96

Study 202.43 104.59 94.59 57.45 113.76

Study 233.07 103.54 95.35 58.11 114.57

Table 9: von Mises Stresses for the individual parts

Maximum Displacement (µm)

Part # 6 Carrier

Member

Part #

2,3,4,5

Arms

Part # 16

Shaft Screw

Tension

Part # 16

Shaft Screw

Torque

Part # 1 Base

Study 51 82 251 303 3

Study 51 83 253 305 3

Study 53 82 253 305 3

Study 54 82 253 305 3

Study 54 82 253 305 3

Study 54 82 253 305 3

Study 54 82 253 305 3

Study 54 82 253 305 3

Table 10: Displacement results for the individual parts

27

4. Discussion

All the studies that I have completed in this project are showing us the maximum stress

occurs at the carrier member. The study for that individual part has converged at 5 point

within 5 % error and it occurs top surface of the member. But, when I made the study

using the smaller element size. I have found the maximum stress bigger than the

acceptable window for the convergence study but the place of the maximum stress has

change its place from top surface of the part to edge of the pin holes. I have skipped

that part after I couldn’t converging the number even I have added the fillets to sharp

edges and trying the different boundary conditions for the holes. In the assembly study,

I have reached the maximum stress of 222 MPa. I am not trusting this number also

since, I couldn’t complete the studies as I have targeted. If, I can trust my first study

solution with 5 points in the safe window for the carrier member. The maximum stress is

187.47 MPa according to from study 2 to study 8. When I consider the material

mechanical properties of the tensile stress which is 625 MPa.

If (𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ

𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑆𝑡𝑟𝑒𝑠𝑠) ≥ 2 (2 is taken as a constant for Factor of Safety)

625 𝑀𝑃𝑎

187.47 𝑀𝑃𝑎 = 3.3

We can say that design is acceptable for the carrier member.

The lifting arm was studied under the tensile load of 4738 N from the two holes towards

to another two holes while these holes fixed. The maximum stress is approximately 104

MPa that is shown in Figure 9 and the convergence study is in the Table 3. Even that

design is acceptable for this study, there are different stresses could be cause the lifting

arm to fail. Focusing the teeth section in the real jack there is a contact between them

while jack works. If that teethes loaded in the operation, we should consider the bending

effect as well.

The shaft screw and the base member also in the acceptable stresses when we

compare with the material tensile strength.

In this project, I have learned that the procedure of the FE Analysis for the assembly

projects. I have spent most of the project time while trying to find accurate boundary

conditions for the scissor jack. I am still not sure that the applied boundary conditions

are pairing with the real object or not. Because of the project time not enough for me to

finish the assembly study. I am going to continue to work on this project to understand if

solidworks can give an accurate answer or its just targeting us to some information.

28

5. Drawings

Figure 29: Technical Drawing of the Carrier Member

29

Figure 4: Technical Drawing of the Lifting Arm

30

Figure 4: Technical Drawing of the Screw Shaft

31

Figure 4: Technical Drawing of the Base Plate

32