A cylindrical accumulator
(
p
r
e
s
s
u
r
i
z
e
d
reservoir
)
for the
5
0
0
0
psi hydraulics system
o
n
a large front
-
end loader mining vehicle
i
s
sealed using a gasketed bolted joint

Question

A cylindrical accumulator 
(
p
r
e
s
s
u
r
i
z
e
d
 ﻿reservoir
)
 ﻿for the 
5
0
0
0
psi hydraulics system 
o
n
 ﻿a large front
-
end loader mining vehicle 
i
s
 ﻿sealed using a gasketed bolted joint 
s
o
 ﻿that the internal bore 
(
i
n
n
e
r
 ﻿diameter
)
 
o
f
 ﻿the accumulator can 
b
y
 ﻿inspected 
a
s
 ﻿part 
o
f
 ﻿scheduled maintenance. The inner diameter 
o
f
 ﻿the accumulator 
i
s
 
1
2
0
m
m
 ﻿and the bolted joint 
i
s
 ﻿made 
o
n
 ﻿a 
P
C
D
 
o
f
 
1
8
0
m
m
 ﻿using fine
-
series 
1
0
m
m
 ﻿bolts, washers and nuts. The stiffness 
o
f
 ﻿the bolt and the members 
i
s
 
2
1
7
.
3
k
N
m
m
 ﻿and 
4
3
0
.
5
k
N
m
m
 ﻿respectively.
Calculate the joint separation force acting 
o
n
 ﻿the end plate. Present answer 
i
n
 
[
k
N
]

VIPSolutions · Accepted Answer

# Joint Separation Force Calculation

Given data:

- **System pressure** ($P$): 500 psi  
  ($1~\mathrm{psi} = 6.895~\mathrm{kPa}$)
- **Inner diameter of accumulator** ($d_\text{in}$): 120 mm
- **Pitch Circle Diameter (PCD)**: 180 mm *(used for bolt layout, not directly for force)*
- **Bolt size**: 10 mm (not directly needed for this calculation)
- **Stiffness of bolt** ($k_b$): 217.3 kN/mm
- **Stiffness of members** ($k_m$): 430.5 kN/mm

We are to calculate the **joint separation force** acting on the end plate in **kN**.

---

## Step 1: Convert Pressure to SI Units

$$
P = 500~\text{psi} \times 6.895~\frac{\text{kPa}}{\text{psi}} = 34,475~\text{kPa} = 34,475,000~\text{N/m}^2
$$

---

## Step 2: Calculate Area Acted Upon

The force acts on the **internal bore area**:

$$
A = \pi \left(\frac{d_\text{in}}{2}\right)^2
$$
$$
d_\text{in} = 120~\text{mm} = .12~\text{m}
$$
$$
A = \pi \left(\frac{.12}{2}\right)^2 = \pi \times (.06)^2 = \pi \times .0036 = .01131~\text{m}^2
$$

---

## Step 3: Calculate Separation Force

$$
F = P \cdot A
$$
$$
F = 34,475,000~\text{N/m}^2 \times .01131~\text{m}^2 = 389,818~\text{N}
$$
$$
F = 389.8~\text{kN}
$$

---

## Step 4: Final Answer

### **Joint Separation Force**

$$
\boxed{389.8~\text{kN}}
$$

---

#### **Summary Table**

| Parameter           | Value       |
|---------------------|------------|
| Pressure            | 500 psi (34,475 kPa) |
| Inner Diameter      | 120 mm     |
| Area                | .01131 m² |
| Separation Force    | **389.8 kN** |

---

**Note:**  
- This value is the total force attempting to separate the end plate from the accumulator due to internal pressure.  
- Member and bolt stiffnesses are not required for this direct pressure-area force calculation. They are relevant for more detailed joint separation and preload calculations.

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