1. Faculty of Process and System Engineering
Master Thesis Presentation
Influence of plate thickness on contact time at elastic, elastic-plastic, plastic
impact of brass sphere on thin glass plates
presented by
Tausif Patel
Matriculation # (206098)
Supervisors:-
Dr.Ing. Peter Mueller
M.Sc. Farhad Jebelisinaki Date:- 30. 09 .2016 Magdeburg
1
3. INTRODUCTION
What is contact deformation ?
Contact deformation :-
Three ranges of deformation behavior
can be identified elastic, elastic-plastic,
and fully plastic
Normal impact :-
The center of mass of colliding bodies is on the common normal line passing through the impact point.
3
4. INTRODUCTION (CONTD.)
What is coefficient of restitution ?
Ratio of relative velocity after the impact to relative velocity before the impact
𝜺 =
𝒗 𝟏,𝑹
𝒗 𝟏
𝜺 =
𝑾 𝒌𝒊𝒏,𝑹
𝑾 𝒌𝒊𝒏
ε = 1 (elastic)
ε = 0 (plastic)
0 < ε < 1 (elastic – plastic)
4
5. OBJECTIVES AND TASK DESCRIPTION
To investigate how the impact plate thickness influence the contact time at elastic, elastic-plastic and
plastic impact of brass spheres on thin glass plates.
Brass spheres of (d = 3 to 8.731 mm).
Coated and noncoated glass plates (H = 2, 4, 8, 12 mm).
Fall heights (h = 50 to 150 mm) – to study the effect of impact velocities.
40 single experiments per each adjustment.
Comparison of experimental results with theoretical models from Hertz and Zener .
Force-displacement curves using compression tests. 5
7. EXPERIMENTAL SETUP AND METHODOLOGY
7
The experimental setup has divided into two
steps
Measurement of coefficient of restitution
Measurement of contact time
Measurement of coefficient of restitution
Method used in experiment to compute the
coefficient of restitution
𝑣 =
𝑔. ∆𝑡
2
𝜀 =
𝑡 𝑛 + 1
𝑡 𝑛
8. EXPERIMENTAL SETUP AND METHODOLOGY
Measurement of contact time
Experimental setup has been modified for formation of electric current to measure contact time
For measurement of contact time only the first impact was considered.
8
9. EXPERIMENTAL SETUP AND METHODOLOGY
9
Compression test
Material behavior has been studied using
single granule uniaxial compression tests until
primary fracture at a constant loading velocity
𝑣 𝐵 = 0.01 mm/min.
Test were repeated 10 times per series of
samples
10. RESULTS AND DISCUSSION
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Coefficientofrestitutionε
Impact velocity v (m/s)
6.350
3
6.350
3
Measurements
d = [mm]
Zener d = [mm]
CoR vs. impact velocity (glass plate, H = 2 mm) and theoretical curves according to the Zener model
11. RESULTS AND DISCUSSION
11
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Coefficientofrestitutionε
Impact velocity v (m/s)
3 6.35
8 8.731
3 6.35
8 8.731
Measurements
d = [mm]
Zener d = [mm]
CoR vs. impact velocity (glass plate, H = 4 mm) and theoretical curves according to the Zener model
12. RESULTS AND DISCUSSION
12
CoR vs. plate thickness on glass plate (𝑣 = 0.85 m/s) CoR vs. plate thickness on coated plate (𝑣 = 0.85 m/s)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14
Coefficientofrestitutionε
Plate thickness H mm
3 6.350
8 8.731
3 6.350
8 8.731
Zener d = [mm]
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 2 4 6 8 10 12 14
Coefficientofrestitutionε
Plate thickness H mm
3 6.35
8 8.731
3 6.35
8 8.731
Measurements
d = [mm]
Zener d = [mm]
Measurements
d = [mm]
13. RESULTS AND DISCUSSION
13
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Coefficientofrestitutionε
Sphere diameter/plate thickness (d/H)
0.55
0.9
1.25
0.55
0.9
1.25
Measurements
v = [m/s]
Zener v= [m/s]
CoR vs. ratio of sphere diameter to plate thickness (d / H) and the theoretical curves according to the Zener
model
15. RESULTS AND DISCUSSION
15
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14
Contacttimeµs
Plate thickness H mm
3 6.350
8 8.731
3 6.350
8 8.731
Measurements d =[mm]
Zener d =[mm]
Contact time vs. plate thickness (𝑣 = 0.98 m/s) theoretical curves according to Zener model
16. RESULTS AND DISCUSSION
16
30
40
50
60
70
80
90
100
0.45 0.65 0.85 1.05 1.25 1.45 1.65 1.85
Contacttimeµs
Impact velocity v (m/s)
2 4
8 12
2 4
8 12
Contact time vs. Impact velocity at (d = 8 mm) the theoretical curves according to the Zener model
Measurements
H=[mm]
Zener H= [mm]
17. RESULTS AND DISCUSSION
17
10
15
20
25
30
35
40
45
50
55
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Contacttimeµs
Impact velocity v (m/s)
3 6.35
8 8.731
3 6.35
8 8.731
Contact time vs. Impact velocity (H = 4 mm) and the theoretical curves as per Zener’s model
Measurements
d =[mm]
Measurements d =[mm]
Zener d =[mm]
18. RESULTS AND DISCUSSION
18
Contact time vs. sphere diameter at (H= 4 mm) an VA= 0.98, 1.65 and
theoretical curves as per Hertz & Zener model
Contact time vs. sphere diameter at (H= 12 mm) and VA= 0.98, 1.65
and theoretical curves as per Hertz & Zener model
0
10
20
30
40
50
60
0 2 4 6 8 10
Contacttimeμs
Sphere diameter d (mm)
Measurement VA = 0.98 (m/s)
Measurements VA=1.65 (m/s)
Zener VA = 0.98 (m/s)
Herz VA = 0.98 (m/s)
Zener VA= 1.65 (m/s)
Hertz VA =1.65 (m/s)
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10
Contacttimeμs
Sphere diameter d (mm)
measurement VA=0.98
Measurements VA=1.65 (m/s)
Zener VA=0.98
Hertz VA=0.98
Zener VA=1.65 (m/s)
Hertz VA= 1.65 (m/s)
19. RESULTS AND DISCUSSION
19
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
0.0000 0.0100 0.0200 0.0300 0.0400 0.0500
Force(N)
Displacement (mm)
Experimental force N linear fit
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0.0000 0.0100 0.0200 0.0300 0.0400 0.0500
Force(N) Displacement (mm)
Experimental force N linear fit
Force vs displacement behavior of (d= 3 mm) and (d = 6.350 mm) and approach
for linear relation in plastic regime
20. SUMARRY AND OUTLOOK
Coefficient of restitution is inversely proportional to impact velocity & sphere
diameter where as it is directly proportional to plate thickness
The Experimental values are lesser than values derived from Zener’s model
The measured values of the contact time on a plate of 2 mm thickness showed a
notable deviation from the theoretical model of Zener
Contact time increases with increasing the sphere diameter where as it decreases with
increasing the plate thickness & impact velocities
Experimental contact time values are slightly higher than values derived from Zener’s
model 20
22. 22
λ 0 0.5 1 1.5
ε 1 0.44 0.18 0.067
Intermediate values of CoR vs inelastic parameter
CoR vs the inelasticity parameter according to Zener’s model
