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Computer-aided design of an artillery system
Pergamon
0045-7949(94)E0202-D
TECHNICAL
COMPUTER-AIDED
DESIGN
Computers & Strurrures Vol. 53. No. 4. pp. 1023-1031. 1994 Copyright (i> 1994 Elsevier Science Ltd Printedin Gml Britain. All rights reserved 0045-7949/w s7.00 + 0.00
NOTE
OF AN ARTILLERY
SYSTEM
L. K. Seah and K. T. Ooi Department of Mechanical and Production Engineering, Nanyang Technological University, Singapore 2263, Republic of Singapore (Received I November 1993)
Abstract-This paper discusses the design approaches of an artillery system and the developments of a computer-aided design analysis that automates the laborious and complicated design calculations for a complete howitzer artillery system. From the initial input of a gun configuration at zero elevation and traversing angle, the analysis is capable of recalculating the change in active dimensions, positions and internal reaction forces of all the major sub-assemblies at any given new elevation and traversing angle. This greatly reduces the time taken to re-analyse the gun design for various gun configurations, with any design modifications. The analysis also provides a better understanding of the design and characteristics of the gun as a whole because with these analysis tools the designer is able to examine the effects of any modified components on other parts of the gun assembly with minimum time and effort.
NOTATION
ALPHA THETA RECOIL_F PFORM_F
BEARING_HF BEARING_MOMENT RTRAI L_VF RTRAICHF
RTRAIL_ZF
elevation angle (degree) traversing angle (degree) recoil force (kN) vertical reacting force at the point where the firing platform is set on the ground (kN) horizontal force component acting on the chassis (kN) moment acting on the chassis (kN m) vertical reaction force component at the right-hand side trial leg (kN) horizontal reaction force component at the right-hand side trail leg (kN) reaction force component in Z-axis direction at the right-hand side trail leg (kN) INTRODUCTION
Designers are always trying to achieve an optimum design with minimum effort. In designing complicated structures, it is very often that a designer adopts a modular design approach which could substantially reduce the complexity of the problem. However, one of the main disadvantages of the modular design approach is that any alterations done on a particular module might yield adverse effects on other modules of the structure. These adverse effects most properly would only be realized after the testing of the assembled structure. On the other hand, while the integrated design approach minimizes this disadvantage, it also provides a better understanding of the design and characteristics of the whole structure, the latter is important for any future modifications and improvements. Figure 1 shows a schematic diagram of a typical howitzer artillery system. During the firing operation, the firing chamber is loaded with explosive charge together with the
projectile through the breech mechanism. As the charge is being ignited, combustion of the charge causes the pressure and temperature in the chamber to rise. The combustion rate is accelerated by the rising pressure and temperature in the chamber. The whole combustion process typically took less than 20 msec and the maximum pressure generated is in the region of 3000 bar. It is this pressure that forces the projectile to accelerate toward the barrel exit. The typical projectile exit velocity is about 900 m/set. This resulted in a very high reaction force on the gun barrel. The reaction force is partly reduced by the muzzle break located at the barrel exit and the remainder is absorbed by the recoil mechanism. The energy absorbed by the recoil mechanism is transmitted to the rest of the structural components. The whole firing operation includes the recoiling and counter-recoiling processes. The recoiling process attempts to resist the large reaction force as mentioned above. This is accomplished by a sophisticated hydraulic system which involves the compression of the virtually incompressible hydraulic oil and the displacement of a huge lump of mass (about 3000 kg). Part of the energy absorbed during the recoiling process is stored and used to return the displaced components back to the initial position during the counterrecoiling process. For a typical howitzer artillery system the recoiling process took about 2OOmsec and 3sec for counter recoiling. This paper attempts to illustrate the advantages of an integrated design approach in designing an artillery gun system. Although only the linear elastic structural analysis was considered, detailed analysis of a complete artillery system in 3-D space is rather complicated. This is further complicated by the fact that it has numerous design parameters as well as various operating parameters, i.e., elevating angle, traversing angle and charges. The integrated design analysis was carried out in such a way that it allows future modifications and improvements of the gun design to be accomplished with comparative ease, and with the aid of a computer it minimizes the time and the effort to re-analyse the artillery system for any future design exercises.
1023
1024
Technical Note
larrel
Fig. 1. Side view of a howitzer artillery system.
/
\
Elevating mechanism \
/---
c
/ Traversing
Fig. 2. Sub-assemblies of an artillery system.
mechanism
Technical Note
1025
Equilibrator
Fig. 3. Sub-assemblies of an artillery system.
DESIGN APPROACH
In order to improve the performance of an artillery gun in terms of firing range, reliability and manoeuvrability, the whole structural assembly of the gun has to be modified to withstand higher loads, and at the same time to be optimized for the highest strength to weight ratio. The major sub-assemblies of a general artillery system, as shown in Figs 2-4, are as follows: recoil mechanism, barrel and breech mechanism, equilibrators, cradles, saddle, chassis, trail legs, firing platform, elevating and traversing mechanism. When in operation, every component in the howitzer artillery system is subject to highly transient loadings. This is due to the variations in the pressure force generated in the firing chamber and the reactions of the recoiling mechanisms, the loading on each component for a whole firing
process is rather difficult to analyse. The situation is complicated by the fact that the recoiling process during the whole firing period involved a rapid displacement of several huge components of several tons mass. The whole process occurred in a very short period of time typically in the order of less than 200 msec. Apart from the above complications, a typical howitzer artillery system is generally designed to operate under various elevation angles, and an ability to perform at various traversing angles with a wide range of charges. Hence, a design analysis must be capable of predicting the performance of the structural system under all these conditions. Any structural optimizations or design modifications necessitate that the loadings on each structural component at 3-D space be re-analysed. The use of the finite element technique alone might not be appropriate for the analysis and the optimization of an artillery structural system. This is due to the level of complexity involved in the finite element modelling of the whole gun assembly. In addition, the transient nature of the loadings on the system hinders the use of the FEM efficiently. Although the complexity of the finite element modelling can be simplified by disintegrating the whole system into various sub-assemblies, however, the
1026
Technical Note
Firing platform
Trail legs Fig. 4. Sub-,-assemblies of an artillery system.
Fig, 5. Co-ordinate system+
1027
Technical Note 150 -
167.2
po
-
147.4
J105
-
127.6
5
go-
107.8
k _
75-
88.0
kI
60-
68.2
K ='
45-
48.4
135
6 3 : 4 & o i 8 %
30 15 -
0
30
: :
: :
:
60
90
120
; cc
28.6
_:__L_-_
_J_-:-_f_+-
6
:
8.8
150
180
210
240
270
300
TIME, ms
Fig. 6. Recoil displacement and pressure versus time (charge 11).
disadvantage of this design approach is that modifications performed on a certain sub-assembly could have adverse effects on other sub-assemblies. If each sub-assembly is analysed separately, such adverse effects would probably only be realized after the field firing test. Furthermore, reliable finite element results could only be obtained if the boundary and loading conditions in each sub-assembly had been accurately modelled.
interconnecting joints of each sub-assembly as shown in Figs 24 have been expressed in the form of co-ordinates (x, y, z). All the positions, lengths, moment arms and angles required in the analysis for any gun configuration are re-calculated based on a set of input co-ordinates at zero elevation and traversing angles. A generalized force analysis of all the major gun sub-assemblies is implemented in ternis of these calculated positions, lengths, moment arms and’angles. In this way, the analysis of the whole gun would stil! be valid with any modifications as long as the modified gun assembly can still be modelled based on the same co-ordinate system. Field firing test results indicated that the recoil pressure and barrel displacement vary with time once the firing is initiated, as shown in Fig. 6. Hence, the forces acting on various parts of the gun assemblies are transient. The analysis integrated all the parameters, dimensional
THE INTEGRATEDMODEL The modelling of the integrated gun assembly is based on a co-ordinate system as shown in Fig. 5. The origin of the x and y axes is at the midpoint between the two trunion bearings (Fig. 3), and the origin of the z-axis is at the point where the firing platform is set on the ground (Fig. 4). The
.'.. RECOIL-F -PFORM_F
THETA=0
230 210 190 170
50 ‘.
30 10
‘. .
_...:
-10 0
20
40
60
80
100
TIME (ms)
Fig. 7.
120
140
160
180
200
1028
Technical Note ALPHA=0 .“. ALPHA=1 ..-. ALPHA=70
THETA=0
cd 1
7
70 50 30 10 -7 0
I. 0
I 20
*
t
,
40
I 60
v
I 80
*
I 700
/
I. 120
*a 140
f 160
/
I 180
I
t 200
TIME (ms)
Fig. 8. - ALPHA=0 .“.ALPHA=l
160 - THETA=0 140
-
120
-
100
-
7
80 60
-
40
-
20
-
O-20
r
-40
-
-60
-
-801”“““““““““’ 0
20
40
60
80
120
100
140
160
180
200
TIME (ms)
Fig. 9.
,
0
- THETA=0 --- THETA=30
ALPHA=0
-
0
I
20
40
I1
*
60
I.
1
80
100
11,
TIME (ms)
Fig. 10.
120
ti
140
I
L
160
‘
1
180
*
1
200
1029
Technical Note ALPHA-O - THETA=0 ... THETA=30
90 80
-
70
-
60
-
50
-
40
-
30
-
20
-
10
-
O-I”
20
0
40
60
100
80
120
140
160
180
200
TIME (ms)
Fig. 11.
ables, input loadings, gun geometrical configurations and at any instant of time it is assumed that:
loading conditions for more detailed stress analysis using the FEM, if needed. An integrated design analysis for a typical howitzer artillery system has been completed. However, because of security reasons, it is not possible to include the whole lengthy analysis in this paper.
(1) the material behaves elastically, (2) the stress-strain relationship is the same as in the case of static loading. From the initial input of gun configuration at zero elevation and traversing angle, the analysis is capable of recalculating the change in active dimensions, positions and internal reaction forces of all the major sub-assemblies at any given new elevation angle, traversing angle and charge, with any design modifications. The results obtained from the analysis give a better understanding of the design and characteristics of the gun as a whole which is important for any future modifications and improvements in the gun design. Additionally, the results obtained from the analysis could be used as input
RESULTS
A computer program for the integrated design analysis of a typical howitzer artillery system has been developed. The computer program needs 88 input variables and is capable of predicting transient loadings at all major components. Figures 7-13 show some of the typical results output from the computer program. These results simulate a typical howitzer artillery system firing at 0”. 17” and 70” elevation angles (i.e., ALPHA) with 0” and 30” traversing angles (i.e.,
ALPHA=0 THETA=0 ... THETA=30
-
50 -
-10
’ 0
’
’ 20
’
’ 40
’
’ 60
’
’ 80
’
’ 100
a
TIME (ms)
Fig. 12.
’ 120
s
’ 140
’ 160
’ 180
’
’ 200
1030
Technical Note
Fig. 13. Forces acting on the chassis. THETA).
The transient inputs of recoil force and barrel displacement are based on the field firine; test results shown in Pig. 6. Figure 7 shows the variation of recoil force (i.e., RECO I L-F) in the recoil cylinder and the ground reaction force
(i.e., PFORM_VF) at the point where the firing platform is set. These figures show that PFORM_VF decreases as the recoil force increases when the gun is at 0” and 17” elevating angles, however, when the elevating angle is 70” PFORM_VF increases as the recoil force increases. This is because RTrail_ZF
i
Fig. 14. Plan view of an artillery system.
Technical Note the magnitude of the upward tilting moment induced when the gun was fired is decreasing when the elevation angle is increasing. Figures 8 and 9 show the variation of the horizontal force (i.e.,-BEARING_HF) and moment (i.e., BEARING-MOMENT) acting on the bearing of the chassis. The notation of the forces iHas shown in Fig. 13, in this case the traversing angle, ‘THETA’ is equal to zero. These figures show that when the elevating angle increases, the moment will increase but the horizontal force will decrease. Figures 10-12 show the variation of the components of the ground reaction (as in Fig. 14) at the end of one of the trail legs (i.e., trail leg at right hand side). The vertical force component (i.e., RTRAILYF) as in Fig. 10, acting in the direction of the Y-axis, varies proportionally with the recoil force and decreases as the traversing angle (i.e., THETA) increases. The horizontal force component (i.e., RTRAICHF) as in Fig. 11, acting in the direction of the X-axis, also varies proportionally with the recoil force at a much higher magnitude than the vertical component. This horizontal force component (i.e., RTRAlL_HF) also decreases as the traversing angle increases. The force component in the Z-axis direction (i.e., RTRAIL_ZF), as shown in Fig. 12, is zero when the traversing angle is zero as expected and increases proportionally with the recoil force when the traversing angle is not zero.
1031
Without the present analysis, the points discussed above might not be realized until field firing tests were carried out. Calculations of stresses based on the forces determined in some parts of the gun had been performed, and good agreement was obtained compared to the strain gauge results obtained from field firing tests.
CONCLUSIONS The paper describes the advantages of an integrated design approach in designing an artillery system. This integrated design approach combined with the power of digital computer, greatly minimizes the time and effort to analyse and re-analyse the structural response of an artillery system for any future improvement and modifications on the gun structures. The analysis tools also enable the designer to examine the effects of any modified components on other parts of the gun assembly with retative ease.
REFERENCES J. M. Biggs, Introduction to Structural Dynamics. McGrawHill, New York (1964). C. H. Norris et al., St~~~r~ Design& Dynamics Loads McGraw-Hill, New York (1959).
0045-7949(94)E0202-D
TECHNICAL
COMPUTER-AIDED
DESIGN
Computers & Strurrures Vol. 53. No. 4. pp. 1023-1031. 1994 Copyright (i> 1994 Elsevier Science Ltd Printedin Gml Britain. All rights reserved 0045-7949/w s7.00 + 0.00
NOTE
OF AN ARTILLERY
SYSTEM
L. K. Seah and K. T. Ooi Department of Mechanical and Production Engineering, Nanyang Technological University, Singapore 2263, Republic of Singapore (Received I November 1993)
Abstract-This paper discusses the design approaches of an artillery system and the developments of a computer-aided design analysis that automates the laborious and complicated design calculations for a complete howitzer artillery system. From the initial input of a gun configuration at zero elevation and traversing angle, the analysis is capable of recalculating the change in active dimensions, positions and internal reaction forces of all the major sub-assemblies at any given new elevation and traversing angle. This greatly reduces the time taken to re-analyse the gun design for various gun configurations, with any design modifications. The analysis also provides a better understanding of the design and characteristics of the gun as a whole because with these analysis tools the designer is able to examine the effects of any modified components on other parts of the gun assembly with minimum time and effort.
NOTATION
ALPHA THETA RECOIL_F PFORM_F
BEARING_HF BEARING_MOMENT RTRAI L_VF RTRAICHF
RTRAIL_ZF
elevation angle (degree) traversing angle (degree) recoil force (kN) vertical reacting force at the point where the firing platform is set on the ground (kN) horizontal force component acting on the chassis (kN) moment acting on the chassis (kN m) vertical reaction force component at the right-hand side trial leg (kN) horizontal reaction force component at the right-hand side trail leg (kN) reaction force component in Z-axis direction at the right-hand side trail leg (kN) INTRODUCTION
Designers are always trying to achieve an optimum design with minimum effort. In designing complicated structures, it is very often that a designer adopts a modular design approach which could substantially reduce the complexity of the problem. However, one of the main disadvantages of the modular design approach is that any alterations done on a particular module might yield adverse effects on other modules of the structure. These adverse effects most properly would only be realized after the testing of the assembled structure. On the other hand, while the integrated design approach minimizes this disadvantage, it also provides a better understanding of the design and characteristics of the whole structure, the latter is important for any future modifications and improvements. Figure 1 shows a schematic diagram of a typical howitzer artillery system. During the firing operation, the firing chamber is loaded with explosive charge together with the
projectile through the breech mechanism. As the charge is being ignited, combustion of the charge causes the pressure and temperature in the chamber to rise. The combustion rate is accelerated by the rising pressure and temperature in the chamber. The whole combustion process typically took less than 20 msec and the maximum pressure generated is in the region of 3000 bar. It is this pressure that forces the projectile to accelerate toward the barrel exit. The typical projectile exit velocity is about 900 m/set. This resulted in a very high reaction force on the gun barrel. The reaction force is partly reduced by the muzzle break located at the barrel exit and the remainder is absorbed by the recoil mechanism. The energy absorbed by the recoil mechanism is transmitted to the rest of the structural components. The whole firing operation includes the recoiling and counter-recoiling processes. The recoiling process attempts to resist the large reaction force as mentioned above. This is accomplished by a sophisticated hydraulic system which involves the compression of the virtually incompressible hydraulic oil and the displacement of a huge lump of mass (about 3000 kg). Part of the energy absorbed during the recoiling process is stored and used to return the displaced components back to the initial position during the counterrecoiling process. For a typical howitzer artillery system the recoiling process took about 2OOmsec and 3sec for counter recoiling. This paper attempts to illustrate the advantages of an integrated design approach in designing an artillery gun system. Although only the linear elastic structural analysis was considered, detailed analysis of a complete artillery system in 3-D space is rather complicated. This is further complicated by the fact that it has numerous design parameters as well as various operating parameters, i.e., elevating angle, traversing angle and charges. The integrated design analysis was carried out in such a way that it allows future modifications and improvements of the gun design to be accomplished with comparative ease, and with the aid of a computer it minimizes the time and the effort to re-analyse the artillery system for any future design exercises.
1023
1024
Technical Note
larrel
Fig. 1. Side view of a howitzer artillery system.
/
\
Elevating mechanism \
/---
c
/ Traversing
Fig. 2. Sub-assemblies of an artillery system.
mechanism
Technical Note
1025
Equilibrator
Fig. 3. Sub-assemblies of an artillery system.
DESIGN APPROACH
In order to improve the performance of an artillery gun in terms of firing range, reliability and manoeuvrability, the whole structural assembly of the gun has to be modified to withstand higher loads, and at the same time to be optimized for the highest strength to weight ratio. The major sub-assemblies of a general artillery system, as shown in Figs 2-4, are as follows: recoil mechanism, barrel and breech mechanism, equilibrators, cradles, saddle, chassis, trail legs, firing platform, elevating and traversing mechanism. When in operation, every component in the howitzer artillery system is subject to highly transient loadings. This is due to the variations in the pressure force generated in the firing chamber and the reactions of the recoiling mechanisms, the loading on each component for a whole firing
process is rather difficult to analyse. The situation is complicated by the fact that the recoiling process during the whole firing period involved a rapid displacement of several huge components of several tons mass. The whole process occurred in a very short period of time typically in the order of less than 200 msec. Apart from the above complications, a typical howitzer artillery system is generally designed to operate under various elevation angles, and an ability to perform at various traversing angles with a wide range of charges. Hence, a design analysis must be capable of predicting the performance of the structural system under all these conditions. Any structural optimizations or design modifications necessitate that the loadings on each structural component at 3-D space be re-analysed. The use of the finite element technique alone might not be appropriate for the analysis and the optimization of an artillery structural system. This is due to the level of complexity involved in the finite element modelling of the whole gun assembly. In addition, the transient nature of the loadings on the system hinders the use of the FEM efficiently. Although the complexity of the finite element modelling can be simplified by disintegrating the whole system into various sub-assemblies, however, the
1026
Technical Note
Firing platform
Trail legs Fig. 4. Sub-,-assemblies of an artillery system.
Fig, 5. Co-ordinate system+
1027
Technical Note 150 -
167.2
po
-
147.4
J105
-
127.6
5
go-
107.8
k _
75-
88.0
kI
60-
68.2
K ='
45-
48.4
135
6 3 : 4 & o i 8 %
30 15 -
0
30
: :
: :
:
60
90
120
; cc
28.6
_:__L_-_
_J_-:-_f_+-
6
:
8.8
150
180
210
240
270
300
TIME, ms
Fig. 6. Recoil displacement and pressure versus time (charge 11).
disadvantage of this design approach is that modifications performed on a certain sub-assembly could have adverse effects on other sub-assemblies. If each sub-assembly is analysed separately, such adverse effects would probably only be realized after the field firing test. Furthermore, reliable finite element results could only be obtained if the boundary and loading conditions in each sub-assembly had been accurately modelled.
interconnecting joints of each sub-assembly as shown in Figs 24 have been expressed in the form of co-ordinates (x, y, z). All the positions, lengths, moment arms and angles required in the analysis for any gun configuration are re-calculated based on a set of input co-ordinates at zero elevation and traversing angles. A generalized force analysis of all the major gun sub-assemblies is implemented in ternis of these calculated positions, lengths, moment arms and’angles. In this way, the analysis of the whole gun would stil! be valid with any modifications as long as the modified gun assembly can still be modelled based on the same co-ordinate system. Field firing test results indicated that the recoil pressure and barrel displacement vary with time once the firing is initiated, as shown in Fig. 6. Hence, the forces acting on various parts of the gun assemblies are transient. The analysis integrated all the parameters, dimensional
THE INTEGRATEDMODEL The modelling of the integrated gun assembly is based on a co-ordinate system as shown in Fig. 5. The origin of the x and y axes is at the midpoint between the two trunion bearings (Fig. 3), and the origin of the z-axis is at the point where the firing platform is set on the ground (Fig. 4). The
.'.. RECOIL-F -PFORM_F
THETA=0
230 210 190 170
50 ‘.
30 10
‘. .
_...:
-10 0
20
40
60
80
100
TIME (ms)
Fig. 7.
120
140
160
180
200
1028
Technical Note ALPHA=0 .“. ALPHA=1 ..-. ALPHA=70
THETA=0
cd 1
7
70 50 30 10 -7 0
I. 0
I 20
*
t
,
40
I 60
v
I 80
*
I 700
/
I. 120
*a 140
f 160
/
I 180
I
t 200
TIME (ms)
Fig. 8. - ALPHA=0 .“.ALPHA=l
160 - THETA=0 140
-
120
-
100
-
7
80 60
-
40
-
20
-
O-20
r
-40
-
-60
-
-801”“““““““““’ 0
20
40
60
80
120
100
140
160
180
200
TIME (ms)
Fig. 9.
,
0
- THETA=0 --- THETA=30
ALPHA=0
-
0
I
20
40
I1
*
60
I.
1
80
100
11,
TIME (ms)
Fig. 10.
120
ti
140
I
L
160
‘
1
180
*
1
200
1029
Technical Note ALPHA-O - THETA=0 ... THETA=30
90 80
-
70
-
60
-
50
-
40
-
30
-
20
-
10
-
O-I”
20
0
40
60
100
80
120
140
160
180
200
TIME (ms)
Fig. 11.
ables, input loadings, gun geometrical configurations and at any instant of time it is assumed that:
loading conditions for more detailed stress analysis using the FEM, if needed. An integrated design analysis for a typical howitzer artillery system has been completed. However, because of security reasons, it is not possible to include the whole lengthy analysis in this paper.
(1) the material behaves elastically, (2) the stress-strain relationship is the same as in the case of static loading. From the initial input of gun configuration at zero elevation and traversing angle, the analysis is capable of recalculating the change in active dimensions, positions and internal reaction forces of all the major sub-assemblies at any given new elevation angle, traversing angle and charge, with any design modifications. The results obtained from the analysis give a better understanding of the design and characteristics of the gun as a whole which is important for any future modifications and improvements in the gun design. Additionally, the results obtained from the analysis could be used as input
RESULTS
A computer program for the integrated design analysis of a typical howitzer artillery system has been developed. The computer program needs 88 input variables and is capable of predicting transient loadings at all major components. Figures 7-13 show some of the typical results output from the computer program. These results simulate a typical howitzer artillery system firing at 0”. 17” and 70” elevation angles (i.e., ALPHA) with 0” and 30” traversing angles (i.e.,
ALPHA=0 THETA=0 ... THETA=30
-
50 -
-10
’ 0
’
’ 20
’
’ 40
’
’ 60
’
’ 80
’
’ 100
a
TIME (ms)
Fig. 12.
’ 120
s
’ 140
’ 160
’ 180
’
’ 200
1030
Technical Note
Fig. 13. Forces acting on the chassis. THETA).
The transient inputs of recoil force and barrel displacement are based on the field firine; test results shown in Pig. 6. Figure 7 shows the variation of recoil force (i.e., RECO I L-F) in the recoil cylinder and the ground reaction force
(i.e., PFORM_VF) at the point where the firing platform is set. These figures show that PFORM_VF decreases as the recoil force increases when the gun is at 0” and 17” elevating angles, however, when the elevating angle is 70” PFORM_VF increases as the recoil force increases. This is because RTrail_ZF
i
Fig. 14. Plan view of an artillery system.
Technical Note the magnitude of the upward tilting moment induced when the gun was fired is decreasing when the elevation angle is increasing. Figures 8 and 9 show the variation of the horizontal force (i.e.,-BEARING_HF) and moment (i.e., BEARING-MOMENT) acting on the bearing of the chassis. The notation of the forces iHas shown in Fig. 13, in this case the traversing angle, ‘THETA’ is equal to zero. These figures show that when the elevating angle increases, the moment will increase but the horizontal force will decrease. Figures 10-12 show the variation of the components of the ground reaction (as in Fig. 14) at the end of one of the trail legs (i.e., trail leg at right hand side). The vertical force component (i.e., RTRAILYF) as in Fig. 10, acting in the direction of the Y-axis, varies proportionally with the recoil force and decreases as the traversing angle (i.e., THETA) increases. The horizontal force component (i.e., RTRAICHF) as in Fig. 11, acting in the direction of the X-axis, also varies proportionally with the recoil force at a much higher magnitude than the vertical component. This horizontal force component (i.e., RTRAlL_HF) also decreases as the traversing angle increases. The force component in the Z-axis direction (i.e., RTRAIL_ZF), as shown in Fig. 12, is zero when the traversing angle is zero as expected and increases proportionally with the recoil force when the traversing angle is not zero.
1031
Without the present analysis, the points discussed above might not be realized until field firing tests were carried out. Calculations of stresses based on the forces determined in some parts of the gun had been performed, and good agreement was obtained compared to the strain gauge results obtained from field firing tests.
CONCLUSIONS The paper describes the advantages of an integrated design approach in designing an artillery system. This integrated design approach combined with the power of digital computer, greatly minimizes the time and effort to analyse and re-analyse the structural response of an artillery system for any future improvement and modifications on the gun structures. The analysis tools also enable the designer to examine the effects of any modified components on other parts of the gun assembly with retative ease.
REFERENCES J. M. Biggs, Introduction to Structural Dynamics. McGrawHill, New York (1964). C. H. Norris et al., St~~~r~ Design& Dynamics Loads McGraw-Hill, New York (1959).