Acoustical optimization of mufflers hybridized with spiral perforated tubes using finite element method,Artificial Neural Network,and Genetic Algorithm

Abstract

Because venting noise emitted from high pressure valve often occurred in industry and is huge, the noise abatement of the venting noise to protect human’s hearing health is necessary. In order to depress the high speed noise, a muffler internally equipped with spiral perforated tube is presented. To mitigate this noise, a dissipative muffler with perforated spiral tube installed on the pipeline is proposed. To evaluate the acoustical performance, a finite element method using COMSOL software is adopted. Also, the sensitivity analyses of Transmission Loss (TL) of the proposed muffler with respect to (1) diameter of the spiral and perforated tube (D), (2) pitch of the spiral tube (L), (3) acoustical impedance of the dissipative acoustic material (R), and (4) perforation rate of a perforated tube (σ) has been carried out. For the optimization studies, both Artificial Neural Network (ANN) and Genetic Algorithm (GA) to optimize the muffler parameters L and D are applied. Here, two high target frequencies (2000 and 3500 Hz) to optimize the proposed muffler are exemplified. Consequently, the hybrid design of perforated spiral tube optimized using ANN and GA will mitigate the high pressure valve noise efficiently.

Keywords

Spiral perforated FEM muffler Genetic Algorithm Artificial Neural Network

Introduction

Research of mufflers used in reducing venting noise has been thoroughly examined. Munjal¹ established a four-pole transfer matrix to predict the noise reduction on the basis of fluid dynamic theory. Sullivan and Crocker^2,3 established coupled equations for a perforated muffler at outer and inner tubes. However, the research mentioned above neglected the acoustical effect of a high order wave.

For the research of sound absorbing wool, Delany and Bazley,⁴ initiated the estimation of sound absorption coefficient for sound absorbing material. Johnson⁵ took acoustical flow resistance, porosity, curvature, and viscous characteristics length to calculate the sound absorption coefficient. Later, Champoux and Allard⁶ analyzed sound absorbing property using a thermal characteristics length. Lafarge et al.,⁷ predicted the sound absorbing coefficient using a Johnson-Champoux-Allard model. Yet, those researches focused on the investigation of sound absorbing effect for the sound absorbing material. There was no acoustical investigation of duct system inserted to be discussed.

For the research of acoustical duct together with sound absorbing material, Cummings,⁸ analyzed the acoustical performance of various sections of ducts (curved rectangular and circular) internally inserted with acoustical splitters. Rostafinski⁹ presented a prediction model used in evaluating sound propagation inside a curved duct. Fuller and Bies,^10,11 analyzed the influence of acoustical performance by tuning both the duct shape (straight duct and curved duct) and section area. Selamet et al.¹² investigated the transmission loss of a Hershel-Quinckee tube. Kim and Ih¹³ evaluated the sound transmission loss of a curved and expansion chamber using a four-pole transfer matrix method. These researches developed a series of mathematical model to predict the acoustical performance of the ducts which were internally inserted with dissipative material. Results revealed that both the curved tube and dissipative material played essential roles in reducing the sound wave.

However, there were no discussions of muffler optimization in above researches. In practical world, most of mufflers (in existed factory) have been confined within a limited space. The shape optimization of mufflers is compulsory. Therefore, Chiu proposed an optimal assessment on multi-chamber mufflers equipped with perforated intruding inlets and resonated tube.¹⁴ Subsequently, Chiu^15,16 assessed the optimization of reverse-flow mufflers and multi-chamber mufflers internally hybridized with plug-inlet tube on a venting process. Also, considering the back pressure constraints, a series of muffler optimizations used in eliminating venting noise elimination have been explored.^17
–19

Nevertheless, the above researches dedicated on the reactive muffler which is effective for low and medium frequencies but not sufficient for high frequency. Concerning about the broadband noise often occurred in venting system, a thinking of muffler design using spiral curve embedded inside a chamber (filled with dissipative material) is rising. For the broadband sound wave analysis, several researches of broadband noise using FEM (finite element method)^20
–22 have been lectured; but, they needed a great amount of calculation time in the muffler modeling. In addition, there are difficulties to drive the FEM software for muffler optimization. In order to overcome the drawback, a simplified mathematical model established by using Artificial Neural Networks (ANNs) and FEM to build a TL (Transmission Loss) function will be in a polynomial form. Using the polynomial function as an objective function, the muffler optimization in conjunction with optimizer can then be achieved.^23
–26

To efficiently depress the venting noise, an exploration of a muffler that is internally inserted with a spiral curved and perforated tube which is embedded within a dissipative material is presented. An acoustical simulation and optimization using the FEM (run on COMSOL), the Artificial Neural Networks, and the optimizer will be adopted in this research. Here, Genetic Algorithm, a robust algorithm used in searching for global optimum, is also adopted as the optimizer during the muffler optimization. Because the acoustical effect of frequencies from 2k to 4k Hz is very sensitive for human hearing, both the 2000 Hz (Case I) and 3500 Hz (Case II) are then selected as the targeted frequencies for noise elimination during muffler optimization.

Finite element model

As indicated in Figure 1, a muffler hybridized with spiral and perforated tube has been introduced. The acoustical model (COMSOL) at a solid boundary is

n \cdot {\frac{1}{ρ_{c}} (\nabla p_{t} - q)} = 0

(1)

where q (dipole sound source), c (sound speed), and $ρ$ (air density) are set at zero, 343 (m/s), and 1.293 ( $k g / m^{3}$ ), respectively.

The acoustical model (COMSOL) at a solid boundary of the perforated tube is

n . {\frac{1}{ρ_{c}} (\nabla p_{t} - q)} = - (p_{t 1} - p_{t 2}) \frac{i ω}{Z_{i}}

(2)

Z_{i} = ρ_{c} c_{c} [\frac{1}{σ} \sqrt{\frac{8 μ k}{ρ_{c} c_{c}}} (1 + \frac{t_{p}}{d_{h}}) + θ_{f} + i \frac{k}{σ} (t_{p} + δ_{h})]

(3)

Using the Johnson-Champoux-Allard model to simulate the acoustical behavior of porous material yields

ρ_{e f f} = \frac{α_{\infty} ρ_{0}}{φ} (1 + \frac{σ_{0} φ}{j ρ_{0} ω α_{\infty}} G_{J} (ω))

(4)

G_{J} (ω) = {(1 + \frac{4 j α_{\infty}^{2} η ρ_{0} ω}{σ_{0}^{2} \land^{2} φ^{2}})}^{\frac{1}{2}}

(5)

where $α_{\infty}$ , $η$ , and $φ$ are the curvature level, the shearing viscosity ( $= 1.84 \times 10^{- 5} k g / m s$ ), and the porosity of the dissipative material. In addition, $σ_{0}$ (the flowing impedance) is

σ_{0} = \frac{μ}{α} = \frac{150 μ {(1 - φ)}^{2}}{D_{p}^{2} φ^{3}}

(6)

The bulk factor ( $K_{e f f}$ ) is related to the curvature ( $α_{\infty}$ ) and is expressed as

K_{e f f} = \frac{γ P_{0}}{φ \cdot [γ - (γ - 1) {[1 + \frac{8 η}{j {Λ^{'}}^{2} B^{2} ω ρ_{o}} {(1 + j ρ_{0} \frac{ω B^{2} {Λ^{'}}^{2}}{16 η})}^{\frac{1}{2}}]}^{- 1}]}

(7)

Both the viscous character length (∧) and thermal character length ( $\land^{/}$ ) are in the form of

\land = \frac{1}{c} {(\frac{8 α_{\infty} η}{σ_{0} φ})}^{\frac{1}{2}}

(8)

\land^{/} = \frac{1}{c^{/}} {(\frac{8 α_{\infty} η}{σ_{0} φ})}^{\frac{1}{2}}

(9)

The governing equation of the sound wave propagating into the muffler is

\nabla \cdot - \frac{1}{ρ_{c}} (\nabla p_{t} - q) - \frac{k_{e q}^{2} p_{t}}{ρ_{c}} = Q

(10a)

where

p_{t} = p + p_{b}; k_{e q}^{2} = {(\frac{ω}{c_{c}})}^{2}; c_{c} = c; ρ_{c} = ρ

(10b)

The Sound Transmission Loss (TL) is

T L = 10 \log \frac{W_{i n}}{W_{o u t}}

(11)

To verify the accuracy of FEM model run on COMSOL, a muffler internally inserted with a straight perforated tube is exemplified in Figure 2. As indicated in Figure 2, the TL curve of a muffler internally equipped with a straight perforated tube verified by an experimental data²⁷ reveals that they are in agreement. In addition, the COMSOL’s simulated result is also in agreement with both the SYSNOISE’s simulated result and theoretical result from Sullivan and Crocker.²⁷ Therefore, the accuracy of COMSOL is available and can be used in the muffler simulation in the following section.

Artificial Neural Network model

With the hidden layers inside the structure of ANN (Artificial Neural Network), the mathematical function is implicit and will lead to the inconvenience during the calculation process. Therefore, an explicit form of a polynomial neural network is necessary. According to Ivakhnenko’s research,²⁸ the interconnections between the layers of neurons can be simplified and the automatic algorithm used for the structure design and weight adjustment can also be established when using the polynomial neural network. Hence, the coefficients of the polynomial transfer functions can be assessed by using a regression process. The polynomial neural network having an input layer, a hidden layer, Σ (summation), and an output layer (product) is shown in Figure 3.

Considering h’s unit number of hidden layer, the total output of the neural network yields

y_{k} = \prod_{j = 1}^{h} \sum_{i = 0}^{n} W_{i j} X_{i j}

(12)

Developing equation (12) yields

y_{k} = B_{0} + \sum_{i = 1}^{n} B_{i} x_{i} + \sum_{i = 1}^{n} \sum_{j = 1}^{n} B_{i j} x_{i} x_{j} + \sum_{i = 1}^{n} \sum_{j = 1}^{n} \sum_{k = 1}^{n} B_{i j k} x_{i} x_{j} x_{k} + \dots \dots \dots \dots \dots

(13)

where y_k is the output value, x_i, x_j, x_k are the input data, and B₀, B_i, B_ij, and B_ijk are the coefficients of the node function.

A trained ANN model can be achieved by inputting the training data bank of muffler’s design parameters and theoretical TL (simulated by the COMSOL) and doing the polynomial calculation along with the PSE standard. The PSE, a deviation of mean square, is expressed as

PSE = \frac{1}{N N} \sum_{i = 1}^{N N} {(\hat{y_{i}} - y_{i})}^{2} + CPM \frac{2 σ p^{2} Q Q}{N N}

(14)

where CPM, $σ p^{2}$ , and QQ are the product of the penalty function, the error variation, and the number of the network coefficients. And, NN, $\hat{y_{i}}$ , and y_i are the number of training data, the required data, and the predicted data for the ANN model. The muffler’s TL can be predicted by inputting arbitrary design data into the ANN model (a trained and simplified OBJ function). Using the simplified OBJ function (the ANN model) and the Genetic Algorithm, the muffler can be optimally shaped.

Genetic Algorithm

On the basis of Darwinian natural selection, Holland²⁹ initiated the Genetic Algorithms (GA). Later, Jone³⁰ extended the theory in practical application. In previous studies,^17,31,32 the GA has been adopted in solving the engineering problem. Six kinds of GA’s control parameters used in the study include gene population (pop), a length of chromosome (bit), a selection strategy (elitism), a mutation ratio (pm), a crossover ratio (pc), and a maximum iteration (iter_max). Using GA control parameters in muffler’s geometrical parameter set, each candidate parent will be chosen via the coding/decoding transformation and the simplified objective function. The precision (MM) of the parameter set’s search yields

MM = \frac{P_{m a x} - P_{m i n}}{N_{p} - 1}

(15)

where P_max and P_min are the maximum and minimum ranges of the parameter, m is the number of the design parameters, and N_p is in the form of 2^m. The uniform crossover is adopted in the GA optimization. The related GA optimization process is depicted in Figure 4. As illustrated in Figure 4, the optimization process will be finished when the number of generations reaches to a specified value of iter_max.

Sensitivity analysis

In order to efficiently depress a broadband venting noise, muffler A (spiral curved and perforated tube) and muffler B (straight perforated tube) with/without dissipative material are investigated. Before an appropriate muffler is chosen, the comparison of TL between muffler A and muffler B shown in Figure 5 has been performed. Here, muffler A has the geometrical data of σ = 5 (%), L = 140 (mm), D = 50 (mm), and the perforated hole’s diameter of 5 mm. The TL simulation of muffler A and muffler B at the circumstance of σ = 5 (%) and R = 0 (kg/m³ s) (without adding the dissipative material) is performed and shown in Figure 6. As illustrated in Figure 6, the TL of muffler A at the frequency beyond 2000 Hz is superior to that of muffler B. Considering the dissipative material internally inserted inside mufflers A and B with R = 500 (kg/m³ s), the simulated TL has been calculated and plotted in Figure 7. As illustrated in Figure 7, the TL curve of muffler A is much better than that of muffler B. Moreover, the TL of muffler A will obviously increase after adding a dissipative material with R = 500 (kg/m³ s) to the muffler. Moreover, an investigation of muffler’s acoustical effect by adding a higher value of R (acoustical flowing resistance with 1000 (kg/m³ s)) is performed. The simulated TL of mufflers A and B is plotted and shown in Figure 8. As depicted in Figure 8, the acoustical performance of muffler A is still superior to that of the muffler B. In addition, it is obvious that the TL of muffler A and B will increase when the value of R increases. As can be seen in Figures 6 to 8, the acoustical performance of muffler A is much better than that of the muffler B. Muffler A hybridized with a spiral and perforated tube is then chosen as the silencing device in the following analysis.

Subsequently, a sensitivity of TL with respect to its geometric parameter is initiated as following. As indicated in Figure 9, D (diameter of spiral and perforated tube) is selected as the parameter. The influence of TL with respect to various D without adding dissipative material is shown in Figure 10. Result in Figure 10 reveals that the TL will increase if the D decreases. Similarly, under the circumstance of adding dissipative material (with R = 500 (kg/m³ s)) in the muffler, the TL shown in Figure 11 is inversely proportional to the value of D. And, the TL curve will be prompted up when the dissipative material is added. As indicated in Figure 12, L (the pitch of the spiral and perforated tube) is selected for the sensitivity analysis. Considering the situation of no dissipative material being added, the influence of TL with respect to various L is simulated and plotted in Figure 13. Figure 13 indicates that the TL will change when the value of L varies. Similarly, considering the effect of adding dissipative material (R = 500 (kg/m³ s)) to the muffler, the influence of TL with respect to various L shown in Figure 14 is obvious when frequency is beyond 1700 Hz. As indicated in Figure 15, σ (the perforation rate of a spiral and perforated tube) is chosen for sensitivity analysis. The influence of TL with respect to various D without adding dissipative material is shown in Figure 16. Result in Figure 16 indicates that the TL variation due to the perforation rate of a spiral and perforated tube is obvious when frequency is beyond 500 Hz. Also, as depicted in Figure 17, the R (acoustical flowing resistance of dissipative material) is selected for sensitivity analysis. The influence of TL with respect to various R is shown in Figure 18. Result in Figure 18 reveals that the TL cure will be prompted up when the R increases.

Case study

In order to improve the acoustical performance of muffler used in reducing venting noise, a muffler internally inserted with a spiral and perforated tube and embedded with dissipative material has been introduced. As mentioned in above section, lots of geometric parameters are sensitive to the TL value. Before the optimization of muffler A is performed, a sensitivity analysis of the mufflers A has been carried out. Result in the sensitivity analysis reveals that the geometry of the spiral perforated tube A has huge influence to the TL value. To simplify the optimization process, two kinds of muffler’s design parameters (L: the pitch of a spiral tube, and D: the diameter of a spiral tube) shown in Figure 19 have been chosen as the design parameter in the optimization process. To explore the optimal design of mufflers A at two targeted frequencies (2000 and 3500 Hz), two cases (Case I and Case II) have been introduced and assessed individually by using the trained ANN model linked with the GA method.

Results and discussion

Results

Using the trained ANN model linked with the GA method, the design parameters of L and D at target frequencies of 2000 and 3500 Hz has been optimized. The range and schedule levels of the parameters are illustrated in Table 1. The TL with respect to sixteen data sets used for ANN training is depicted in Table 2. Using L and D as the input data and the resulting TL as the output data in the ANN model and inputting a series of training data into the ANN model, the resulting simplified objective functions (a polynomial OBJ function built by the ANN model in Figure 3) with respect to Case I (the targeted frequencies of 2000 Hz) and Case II (the targeted frequencies of 3500 Hz) are shown below.

Table 1.

The relationship between L (the pitch of a spiral tube) and D (the diameter of a spiral tube) in muffler A.

Parameter	Min (mm)	Max (mm)	4 level (mm)
L (mm)	125	140	125	130	135	140
D (mm)	20	35	20	25	30	35

Table 2.

The selected level and related parameter set used for ANN training purpose.

No. of exp.	D (mm)	L (mm)
1	20	125
2	20	130
3	20	135
4	20	140
5	25	125
6	25	130
7	25	135
8	25	140
9	30	125
10	30	130
11	30	135
12	30	140
13	35	125
14	35	130
15	35	135
16	35	140

Case I: target frequency—2000 Hz

{N 1}_{2000} = - 4.76314 + 0.0173205 \times L

(16a)

{N 2}_{2000} = - 22.9497 + 0.2732055 \times D

(16b)

{N 4}_{2000} = 0.327817 - 0.349672 \times {N 2}_{2}^{2000}

(16c)

\begin{array}{l} {N 5}_{2000} = - 0.852212 + 1 x N 4_{2000} + 0.532488 x N 1_{2000} + 0.192716 x N 2_{2000} \\ + 12.391 x N 4_{2000}^{2} - 0.672747 x N 1_{2000} x N 2_{2000} \\ - 4.6311 x N 4_{2000} x N 1_{2000} x N 2_{2000} - 0.15668 x N 1_{2000}^{3} \end{array}

(16d)

{TL}_{2000} = 19.2478 + 5.73656 x N 5_{2000}

(16e)

Case II: target frequency—3500 Hz

{N 1}_{35000} = - 4.76314 + 0.173205 \times D

(17a)

{N 2}_{3500} = - 22.9497 + 0.173205 \times L

(17b)

\begin{array}{l} N 4_{5000} = - 0.611433 - 0.470873 x N 1_{3500} - 1.30568 x N 2_{3500} \\ - 0.389863 x N 1_{3500} - 0.262333 x N 2_{3500}^{2} + 0.388473 x N 2_{3500}^{3} \end{array}

(17c)

{N 5}_{3500} = - 0.370852 x N 2_{3500} x N 4_{3500} + 0.816377 x N 4_{3}^{3500}

(17d)

{TL}_{3500} = 8.39248 + 3.60903 x N 4_{3500}

(17e)

Subsequently, the above polynomial OBJ functions in equations (16) and (17) will be served as the objective functions during the optimization processing. Before the muffler’s optimization is executed, the GA control parameters used in the study are preset and shown in Table 3. As illustrated in Tables 4 and 5, the optimal design data sets optimized with respect to Case I (target frequencies of 2000 Hz) and Case II (target frequencies of 3500 Hz) are obtained and compared to the original design data. And, as depicted in Tables 6 and 7, the accuracy of the ANN model (a simplified objective function) has been checked by plugging the optimal design data into the simplified objective function and the COMSOL. The result in Tables 6 and 7 reveals that the accuracies of ANN model with respect to Case I (2000 Hz) and Case II (3500 Hz) are 6.42% and 7.66%.

Table 3.

The genetic algorithm’s control parameter set using in the GA optimization process.

GA control parameter	Value or strategy
Population	Generated random
Crossover	Uniform crossover
Elitism	Open
Selection strategy	Elitism
Iter_max	1000
Bit	20
Pop	100
Pc	0.7
Pm	0.6

Table 4.

The comparison of related design parameters before and after optimization at 2000 Hz is performed (Case I).

Design parameter (mm)	L	D
Before optimization	140	25
After optimization (at 2000 Hz)	129.3	22.4

Table 5.

The comparison of related design parameters before and after optimization at 3500 Hz is performed (Case II).

Design parameter (mm)	L	D
Before optimization	140	25
After optimization (at 3500 Hz)	124.9	23.4

Table 6.

Accuracy check between the NNM model and COMSOL (Case I: optimal design set at 2000 Hz).

	TL (dB)	Error (%)
STL (optimal design parameter set at 2000 Hz) obtained by ANN’s objective function in conjunction with GA	13.22	6.42
STL (optimal design parameter set at 2000 Hz) calculated by COMSOL	12.37	6.42

Table 7.

Accuracy check between the NNM model and COMSOL (Case II: optimal design set at 3500Hz).

	TL (dB)	Error (%)
STL (optimal design parameter set at 3500 Hz) obtained by ANN’s objective function in conjunction with GA	18.66	7.66
STL (optimal design parameter set at 3500 Hz) calculated by COMSOL	20.09	7.66

Bring the original data and the optimal design data into COMSOL, the theoretical TLs profiles before and after optimization being performed are shown in Figures 20 and 21. As illustrated in Figure 20, the TLs at the targeted frequency of 2000 Hz (Case I) before and after the optimization is performed are 5.1 and 12.3 dB, respectively. In addition, as depicted in Figure 21, the TLs at the targeted frequency of 3500 Hz (Case II) before and after optimization is executed are 5.7 and 20.0 dB, respectively.

Discussion

As can be seen in the section of sensitivity analysis, the influence of the TL with respect to the geometric data of a spiral and perforated tube is huge. Therefore, both the pitch (L) and diameter (D) of the spiral tube have been selected as the design parameters during the muffler optimization. The numerical assessment of muffler A using ANN’s simplified objective function in conjunction with the GA method has been performed. The simulated results are obtained and shown in Tables 4 to 7 and Figures 20 and 21. Results reveal that the noise abatement of muffler A at the target tones of 2000 and 3500 Hz can be individually improved by 7.2 and 14.3 dB. Moreover, the accuracy verification of the ANN model by using the COMSOL shown in Tables 6 and 7 is between 6.42% and 7.66%.

Conclusion

In order to efficiently depress the gas venting noise, a muffler A (one-chamber hybridized with a spiral curved and perforated tube) has been introduced. Before the optimization of muffler is performed, the comparison of acoustical performance between muffle A and muffler B (one-chamber hybridized with a straight perforated tube) has been investigated. The simulated result reveals that the acoustical effect of spiral perforated tube is better than that of the straight perforated tube. In addition, the sensitivity analysis of muffler A’s geometrical parameters has been explored. The sensitivity result indicates that both L (spiral tube’s pitch) and D (diameter of spiral tube) have higher influence. Selecting two design parameters and putting into the muffler optimization via a simplified objective function (built by ANN and COMSOL’s simulation data) in conjunction with a GA optimizer, the muffler optimization can be efficiently achieved. Considering no dissipative material effect, the optimized TLs at the target tones of 2000 Hz (Case I) and 3500 Hz (Case II) can be individually improved by 7.2 and 14.3 dB.

Footnotes

Notation

This paper is constructed on the basis of the following notations:

bit: bit length of chromosome

B₀, B_i, B_ij, B_ijk: coefficient of the node function in the ANN

CPM: product of the penalty function

D: diameter of the spiral and perforated tube (m)

$i t e r_{\max}$ : maximum iteration during GA optimization

L: pitch of spiral tube (m)

m: number of the design parameters

MM: precision of the parameter search

NN: number of training data

N_p: total possible searching number (=2^m)

pc: crossover ratio

pm: mutation ratio

P_max: maximum range of the parameter

P_min: minimum range of the parameter.

pop: number of population

R: acoustical impedance of dissipative material (kg/m³ s)

x_i, x_j, x_k: input data in the ANN

y_k: output value in the ANN

${\hat{y}}_{i}$ : required data in the ANN

y_i: predicted data for the ANN

TL: transmission loss (dB)

σ: perforation rate of a perforated tube (%)

$σ p^{2}$ : error variation in the ANN

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Min-Chie Chiu

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Shape optimization of multi-chamber side inlet/outlet mufflers hybridized with multiple perforated intruding tubes using genetic algorithm. J Mar Sci Technol 2013; 21(3): 238–249.

No. of exp.	D (mm)	L (mm)
1	20	125
2	20	130
3	20	135
4	20	140
5	25	125
6	25	130
7	25	135
8	25	140
9	30	125
10	30	130
11	30	135
12	30	140
13	35	125
14	35	130
15	35	135
16	35	140

No. of exp.	D (mm)	L (mm)
1	20	125
2	20	130
3	20	135
4	20	140
5	25	125
6	25	130
7	25	135
8	25	140
9	30	125
10	30	130
11	30	135
12	30	140
13	35	125
14	35	130
15	35	135
16	35	140

No. of exp.	D (mm)	L (mm)
1	20	125
2	20	130
3	20	135
4	20	140
5	25	125
6	25	130
7	25	135
8	25	140
9	30	125
10	30	130
11	30	135
12	30	140
13	35	125
14	35	130
15	35	135
16	35	140