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Prediction of linear noise-load relationship for impact forming machines
Int J Mach Tool Des Rcs Vol 22. No I. pp. I 6. 1982. Printed in Greal Britain
0020 73',7 82 0100tJI 06 $ 0 3 0 0 0 Pergamon Pre,,,. l i d
PREDICTION OF LINEAR N O I S E - L O A D RELATIONSHIP FOR IMPACT F O R M I N G MACHINES S. VAJPAYEE, M. M. SADEK* and S. A. Tom~,s
(Received 18 June 1981 INTRODUCTION NOlSE emitted during hot forming on a high-energy-rate-forming (HERF) machine bears a linear relationship with the magnitude of the forming load [ 1]. The existence of this linear correlation has been confirmed for a drop hammer [2] : though the slope and the intercept of the noise-load line differed from the H E R F case. It appears that for every hammer this noise-load relationship can be expected to be unique and independent of the process variables, i.e. input energy, billet size and properties, etc. A linear noise emission vs forming load variation, independent of the process variables, with a unique gradient and intercept for each hammer, could be used as a measure of the overall acoustic quality of the hammer structure. Such a criterion might prove in certain cases to be more meaningful than the conventional "sound power" criterion, especially when the prime concern is the avoidance of the operator's hearing damage. Furthermore, such a criterion would be easier to apply than that of the sound power. The present paper contains a theoretical analysis furnishing an explanation of the observed linear noise-load variation. THEORETICAL ANALYSIS With impact forming machines, the most significant contribution to the acoustic energy emitted is made by the ringing of the machine structure. The intensity of structural ringing depends on the severity of the blow, i.e. the magnitude and duration of the forming load pulse. During billet deformation, a part of the input kinetic energy of the tup is transferred to the hammer structure, and part of this is ultimately radiated as sound emission. It can therefore be expected that for a given input energy, a reduction of the energy lost will result in a corresponding abatement of the noise emitted, i.e. an improvement in the forming efficiency will reduce the noise emitted. This indirect approach to noise control through efficiency improvement has been investigated recently 1-3] by studying the effects of process and machine structure parameters on the forming efficiency. In the present paper the analysis is carried further by considering the impact forming operation as a dynamical model excited by a force simulating the forming process. Two different models are considered. In the first the acoustic energy prediction is based on the energy lost in causing the machine structure to vibrate. The second model is based on the prediction of the resulting surface velocity of each of the main components of the structure.
First order approximation--equivalent spring model The forming efficiency can be expressed by the following expression [4]: r/ = 1 -- (F,,,/Fcl2
(1)
where Fm and F c are the peak forming load and the clash load. respectively. The clash load Fc is related to the input energy Ei by
F, = x~2 K,. E~
(2)
* Department of Mechanical Engineering, University of Birmingham. P.O. Box 363, B~rminehar~ ~. B!5 2TT. [ ' K 1
2
S. VmPAYELM. M. S~OEKand S. A. TOBIAS
where K,, is the stiffness of an "equivalent" spring which simulates the machine structure. The forming load F= can be considered to be a process parameter whereas the equivalent stiffness K= is a structural parameter. The clash load F c is experimentally determined by die clashing. The forming efficiency rl, being the ratio of the useful energy Ef to the input energy E i, can also be expressed in terms of energy lost to the structure E t as = E f / E i = (E~ - E t ) / E , = I - E d E ,.
(3)
Combining equations (1) and (3), and writing for F c from equation (2), one gets (4)
F,, 2 = 2 K = E t.
The energy E~ lost to the hammer structure will eventually be dissipated through damping and radiated as noise. Let 6 denote the proportion of E t which is radiated as acoustic energy E,~, i.e. (5)
E ~ = 3Et.
Assuming that the hammer can be considered to be a point source radiating in half space, the acoustic energy Eac, related to the square of the sound pressure p sensed by the microphone positioned at a distance r from the " ' a c o u s t i c " centre of the hammer, will be given for a unit time by (6)
E=c = 2 n r 2 I
where, I is the sound intensity p 2 / p c (p and c are respectively the air density and the speed of sound waves in the medium). Thus the sound pressure p can be expressed in the following form : 1 pc~E=~ P=rX/ "
(7)
Substitution for E=¢, obtained by combining equations (4) and (5), in the above equation results in the following expression for the relation between the sound pressure p and the forming load F~
This shows that the sound pressure p varies linearly with the forming load Fro. The slope of
COLUMNS
ANVIL M2
3
FIG. 1. Lumped-massmodel of the hammer.
Prediction of Linear Noise-Load Relationship
3
this linear relationship will be a function of p, c, 6 and the structural parameter K,~ as well as the measuring distance r. It can thus be concluded that noise generated per unit forming load will be of a lower level when forming on a stiff machine structure as compared to when forming on a flexible structure. Second order approximation--lumped
mass model
The previous analysis is based on the assumption that the forming load varies linearly with deformation. The actual load stroke history can take any of a variety of forms, depending on the process variables such as billet material, dimensions etc. In the present model, the forcing function is implicitly defined in terms of the process variables and takes into account the effect of strain rate and friction at the die-billet interfaces. The hammer structure is represented by a damped five degrees-of-freedom system shown in Fig. 1. The tup M~ is free, though connected to the hammer through the damper of coefficient Ct which accounts for the friction between the tup and the guideways of the columns, represented by M 4. The hammer foundation M3 is supported on a soft spring K 3The parameters K4, C4 and Ks, C 5 represent the stiffness and the damping of rubber mats, respectively, which are commonly used at the anvil-column and column-headgear interfaces. The mass M5 represents the headgear housing the mechanism to lift and/or drop the tup to impact on the billet placed on the anvil M E. T h i s impact sets the system into motion with a resulting force acting between the tup and the anvil during the period of billet deformation. The equations of motion during the period of billet deformation are M1~:1 + CllXl - -x4) : M2"~'2 + g 4 t x 2 - x4) + C4(-~2 - -~4) + K2(x2 - x3) + C2()c2 - "~3) : M3x'3 - K 2 t X 2 - x3) -- C 2 ( x 2 - x 3 ) "4- K 3 X 3 + C 3 X 3 = Ma-x'a - K 4 ( x 2 - x 4 ) - C4(-~2 - -~4) + Ks(x4 - xs) + Cs(x,, - x s ) = M55~'5 - K s ( x , , - x s ) - Cs(~,, - xs) =
- Fi Fi 0
(9}
0 0.
From the instant of impact (t = 0), initially the force F i varies according to the elastic stressstrain relationship of the billet material. This is followed by the plastic deformation of the billet for which [5]. Fi = f A i
(
1 + 3Hi, /
(101
where f is the flow stress of the billet material,/z is the coefficient of friction at die-billet interfaces and D,, H i, A i are the instantaneous diameter, height and the cross-section area of the billet. As plastic deformation of the billet progresses, the instantaneous force F~ varies with time since the billet dimensions A~, H i and D i change. Ai can be related to the motion of the tup and anvil by V Ai - Hi -Hb
V _ hi -
V H b - (x l-x2)
i
where V is the billet volume, H b its initial height and h i the instantaneous deformation of the billet. Since the force F~ is a function of Ai which in turn depends on the instantaneous values of the tup and anvil displacements x~i and x2, the set of differential equations (9) are coupled and hence cumbersome to solve. A computer program was written to achieve the solution numerically. The end of deformation (at t = T) is characterised by ~ r -- ~2r = 0; the corresponding relative displacement between the tup and the anvil being equal to the net billet deformation. The useful energy Ey is obtained by working out the area under F i and (x ~ - x2) i curve which when divided by the input energy Ei yields the forming efficiency ,7. Beyond T, the system undergoes free vibration. The radiated sound pressure is estimated from the surface velocities of the various masses both during and after the billet deformation--by treating them as
4
S. VMPAYEF_, M. M. SM)EK and S. A. TOBIAS TABLE I M l M 3 M4 M~
= = = =
500 k g 20 t o n n e s 5 tonnes 2 tones
Ct C2 Ca C4 CS
= = = = =
5 kN/(m/s) 1 MN/(m/s) 1 MN/(m/s) 400 kN/(m/s) 20 kN/(m/s)
Ei = 3 k J p = 1.21 k g / m 3 C = 343 m / s r=l.5m
H V f /1
kt k3 k4 ks
= = = =
= = = ---
5 GN/m 30 M N / m 2 GN/rn 100 M N / m
50 mm 98 c m 3 625 M N / m 2 0.5
dipoles. Any ringing of a hammer part beyond a 60 dB reduction in its surface velocity will be insignificant and was therefore ignored. RESULTS
AND
DISCUSSIONS
The equivalent parameters of a particular machine and process are presented in Table 1. These were used for the prediction of the emitted sound pressure for three different anvils of mass 5, 10 and 15 tonnes, the result being presented in Fig. 2. The noise-load relationship was linear for all the three anvils. The slope of each line varies with the mass of the anvil ; a heavier anvil will generate less noise than a lighter one. This is plausible since the energy lost to the structure in the former case will be less than in the latter because of the improved forming efficiency associated with heavy anvil [3-1. Furthermore, the divergence of the lines implies that the effect ofany change in anvil weight will be more pronounced at higher forming loads, as observed [2] for a drop hammer. The effect of anvil weight on the sound pressure level is illustrated in Fig. 3, for a forming load of 5 MN. Note that an increase in the anvil weight improves the acoustic quality of the hammer. However, the curve gets flatter with increasing anvil inertia and this means that a further increase in the weight of an already heavy anvil will be only marginally beneficial from a noise viewpoint. In practice the mass ratio (tup weight/anvil weight) is usually 1/20. Increasing the anvil weight four-fold (mass ratio = 1/80) will reduce the noise by 2 dB as shown in Fig. 3. A reduction in the anvil weight to 1/4 will, however, increase the noise level by more than 3 dB. Though the prime objective of the computer-aided analysis presented was to provide theoretical support to the experimentally observed noise-load linear relationship, the 20---
+
.15
z
/,
I 2
~
6
LOAO, M N FIG. 2. Predicted noise-load variation for three ~ I
masses.
Prediction of Linear Noise-Load Relationship
5
~12S
S 120
iic
~
J I1C
0
20 t.0 ANVIL MASS, Xl03kg
60
FIG. 3. Effectof anvil mass on noise level. developed computer program can also predict various outputs, such as net billet deformation, its duration, forming efficiency, load-time history, etc. of an impact forming process. As an example, the predicted load-time and load-deformation histories arising when forming in a two-stepped die-cavity, are shown in Figs. 4(a) and (b). It may be noticed that the forming load displays sudden jumps corresponding to the filling of the two steps in the die-cavity. Elsewhere the variation in load is non-linear. An interactive version of the computer package allowing the user to talk to the computer for handling a variety of different forming configurations in either a drop hammer or a power hammer is also available. CONCLUSIONS The analysis presented has shown that the noise emitted by an impact forming machine will increase linearly with the magnitude of the forming load. This conclusion provides analytical support to the previously observed experimental results on two different hammers. It was also shown that the gradient of the noise level line is a function of anvil weight, being less for a heavier anvil. Increasing the weight of an already heavy anvil is only marginally beneficial, as far as reduction in noise emission is concerned. However, a reduction of anvil weight may cause a disproportionate increase in the emitted noise level. The computer package developed during the course of present investigation can also predict other forming outputs.
Acknowledgement--Thanks are due to the Drop Forging Research Association for allowing the use of their test facilities. L.
.
.
.
.
.
,
~3
a~
.3
<
S z 2
°2
1
°o
1
'
•
~,
'
•
8
TIME, MS
(a)
i
i
~2
0
-
~
~
3
DEFORMATION, MM
(b)
FIG. 4. Predicted forming load variation with (a) time and (b) deformation.
6
S. VAJPAYEE,M. M. SADEK and S. A. TOSIAS REFERENCES
S.V.~GPAYEEand M. M. SADEK~Statistical analysis of the influence of process variables on noise generation in impact hot forming, ASME Paper No. 79, DET-29, Design Engng. Tech. Conf. St. Louis, (Sop. 1979). [2] S. VAJPAYEE,A. C. HOBDELLand M. M. S.~Eg, The influence of machine suspension and process parameters on hammer noise, to be presented at the Winter Annual Meeting of the ASME (1981). [3] S. VAJP^VV.E, M M. SADEK and S. A. TOBI~S, Int. J. Mach. Tool Des. Res. 19, 237 (1979). [4] M.K. D^s and S. A. Tosl,~s, The efficiency of energy transfer and the determination of the clash load in impact forming machines, 4th Int. Conf. of the Centrefor High Energy Forming, Denver, (Jul. 1973). [5] W. JOHNSON, Impact Strength of Materials. Edward Arnold, London (1972). [1]
0020 73',7 82 0100tJI 06 $ 0 3 0 0 0 Pergamon Pre,,,. l i d
PREDICTION OF LINEAR N O I S E - L O A D RELATIONSHIP FOR IMPACT F O R M I N G MACHINES S. VAJPAYEE, M. M. SADEK* and S. A. Tom~,s
(Received 18 June 1981 INTRODUCTION NOlSE emitted during hot forming on a high-energy-rate-forming (HERF) machine bears a linear relationship with the magnitude of the forming load [ 1]. The existence of this linear correlation has been confirmed for a drop hammer [2] : though the slope and the intercept of the noise-load line differed from the H E R F case. It appears that for every hammer this noise-load relationship can be expected to be unique and independent of the process variables, i.e. input energy, billet size and properties, etc. A linear noise emission vs forming load variation, independent of the process variables, with a unique gradient and intercept for each hammer, could be used as a measure of the overall acoustic quality of the hammer structure. Such a criterion might prove in certain cases to be more meaningful than the conventional "sound power" criterion, especially when the prime concern is the avoidance of the operator's hearing damage. Furthermore, such a criterion would be easier to apply than that of the sound power. The present paper contains a theoretical analysis furnishing an explanation of the observed linear noise-load variation. THEORETICAL ANALYSIS With impact forming machines, the most significant contribution to the acoustic energy emitted is made by the ringing of the machine structure. The intensity of structural ringing depends on the severity of the blow, i.e. the magnitude and duration of the forming load pulse. During billet deformation, a part of the input kinetic energy of the tup is transferred to the hammer structure, and part of this is ultimately radiated as sound emission. It can therefore be expected that for a given input energy, a reduction of the energy lost will result in a corresponding abatement of the noise emitted, i.e. an improvement in the forming efficiency will reduce the noise emitted. This indirect approach to noise control through efficiency improvement has been investigated recently 1-3] by studying the effects of process and machine structure parameters on the forming efficiency. In the present paper the analysis is carried further by considering the impact forming operation as a dynamical model excited by a force simulating the forming process. Two different models are considered. In the first the acoustic energy prediction is based on the energy lost in causing the machine structure to vibrate. The second model is based on the prediction of the resulting surface velocity of each of the main components of the structure.
First order approximation--equivalent spring model The forming efficiency can be expressed by the following expression [4]: r/ = 1 -- (F,,,/Fcl2
(1)
where Fm and F c are the peak forming load and the clash load. respectively. The clash load Fc is related to the input energy Ei by
F, = x~2 K,. E~
(2)
* Department of Mechanical Engineering, University of Birmingham. P.O. Box 363, B~rminehar~ ~. B!5 2TT. [ ' K 1
2
S. VmPAYELM. M. S~OEKand S. A. TOBIAS
where K,, is the stiffness of an "equivalent" spring which simulates the machine structure. The forming load F= can be considered to be a process parameter whereas the equivalent stiffness K= is a structural parameter. The clash load F c is experimentally determined by die clashing. The forming efficiency rl, being the ratio of the useful energy Ef to the input energy E i, can also be expressed in terms of energy lost to the structure E t as = E f / E i = (E~ - E t ) / E , = I - E d E ,.
(3)
Combining equations (1) and (3), and writing for F c from equation (2), one gets (4)
F,, 2 = 2 K = E t.
The energy E~ lost to the hammer structure will eventually be dissipated through damping and radiated as noise. Let 6 denote the proportion of E t which is radiated as acoustic energy E,~, i.e. (5)
E ~ = 3Et.
Assuming that the hammer can be considered to be a point source radiating in half space, the acoustic energy Eac, related to the square of the sound pressure p sensed by the microphone positioned at a distance r from the " ' a c o u s t i c " centre of the hammer, will be given for a unit time by (6)
E=c = 2 n r 2 I
where, I is the sound intensity p 2 / p c (p and c are respectively the air density and the speed of sound waves in the medium). Thus the sound pressure p can be expressed in the following form : 1 pc~E=~ P=rX/ "
(7)
Substitution for E=¢, obtained by combining equations (4) and (5), in the above equation results in the following expression for the relation between the sound pressure p and the forming load F~
This shows that the sound pressure p varies linearly with the forming load Fro. The slope of
COLUMNS
ANVIL M2
3
FIG. 1. Lumped-massmodel of the hammer.
Prediction of Linear Noise-Load Relationship
3
this linear relationship will be a function of p, c, 6 and the structural parameter K,~ as well as the measuring distance r. It can thus be concluded that noise generated per unit forming load will be of a lower level when forming on a stiff machine structure as compared to when forming on a flexible structure. Second order approximation--lumped
mass model
The previous analysis is based on the assumption that the forming load varies linearly with deformation. The actual load stroke history can take any of a variety of forms, depending on the process variables such as billet material, dimensions etc. In the present model, the forcing function is implicitly defined in terms of the process variables and takes into account the effect of strain rate and friction at the die-billet interfaces. The hammer structure is represented by a damped five degrees-of-freedom system shown in Fig. 1. The tup M~ is free, though connected to the hammer through the damper of coefficient Ct which accounts for the friction between the tup and the guideways of the columns, represented by M 4. The hammer foundation M3 is supported on a soft spring K 3The parameters K4, C4 and Ks, C 5 represent the stiffness and the damping of rubber mats, respectively, which are commonly used at the anvil-column and column-headgear interfaces. The mass M5 represents the headgear housing the mechanism to lift and/or drop the tup to impact on the billet placed on the anvil M E. T h i s impact sets the system into motion with a resulting force acting between the tup and the anvil during the period of billet deformation. The equations of motion during the period of billet deformation are M1~:1 + CllXl - -x4) : M2"~'2 + g 4 t x 2 - x4) + C4(-~2 - -~4) + K2(x2 - x3) + C2()c2 - "~3) : M3x'3 - K 2 t X 2 - x3) -- C 2 ( x 2 - x 3 ) "4- K 3 X 3 + C 3 X 3 = Ma-x'a - K 4 ( x 2 - x 4 ) - C4(-~2 - -~4) + Ks(x4 - xs) + Cs(x,, - x s ) = M55~'5 - K s ( x , , - x s ) - Cs(~,, - xs) =
- Fi Fi 0
(9}
0 0.
From the instant of impact (t = 0), initially the force F i varies according to the elastic stressstrain relationship of the billet material. This is followed by the plastic deformation of the billet for which [5]. Fi = f A i
(
1 + 3Hi, /
(101
where f is the flow stress of the billet material,/z is the coefficient of friction at die-billet interfaces and D,, H i, A i are the instantaneous diameter, height and the cross-section area of the billet. As plastic deformation of the billet progresses, the instantaneous force F~ varies with time since the billet dimensions A~, H i and D i change. Ai can be related to the motion of the tup and anvil by V Ai - Hi -Hb
V _ hi -
V H b - (x l-x2)
i
where V is the billet volume, H b its initial height and h i the instantaneous deformation of the billet. Since the force F~ is a function of Ai which in turn depends on the instantaneous values of the tup and anvil displacements x~i and x2, the set of differential equations (9) are coupled and hence cumbersome to solve. A computer program was written to achieve the solution numerically. The end of deformation (at t = T) is characterised by ~ r -- ~2r = 0; the corresponding relative displacement between the tup and the anvil being equal to the net billet deformation. The useful energy Ey is obtained by working out the area under F i and (x ~ - x2) i curve which when divided by the input energy Ei yields the forming efficiency ,7. Beyond T, the system undergoes free vibration. The radiated sound pressure is estimated from the surface velocities of the various masses both during and after the billet deformation--by treating them as
4
S. VMPAYEF_, M. M. SM)EK and S. A. TOBIAS TABLE I M l M 3 M4 M~
= = = =
500 k g 20 t o n n e s 5 tonnes 2 tones
Ct C2 Ca C4 CS
= = = = =
5 kN/(m/s) 1 MN/(m/s) 1 MN/(m/s) 400 kN/(m/s) 20 kN/(m/s)
Ei = 3 k J p = 1.21 k g / m 3 C = 343 m / s r=l.5m
H V f /1
kt k3 k4 ks
= = = =
= = = ---
5 GN/m 30 M N / m 2 GN/rn 100 M N / m
50 mm 98 c m 3 625 M N / m 2 0.5
dipoles. Any ringing of a hammer part beyond a 60 dB reduction in its surface velocity will be insignificant and was therefore ignored. RESULTS
AND
DISCUSSIONS
The equivalent parameters of a particular machine and process are presented in Table 1. These were used for the prediction of the emitted sound pressure for three different anvils of mass 5, 10 and 15 tonnes, the result being presented in Fig. 2. The noise-load relationship was linear for all the three anvils. The slope of each line varies with the mass of the anvil ; a heavier anvil will generate less noise than a lighter one. This is plausible since the energy lost to the structure in the former case will be less than in the latter because of the improved forming efficiency associated with heavy anvil [3-1. Furthermore, the divergence of the lines implies that the effect ofany change in anvil weight will be more pronounced at higher forming loads, as observed [2] for a drop hammer. The effect of anvil weight on the sound pressure level is illustrated in Fig. 3, for a forming load of 5 MN. Note that an increase in the anvil weight improves the acoustic quality of the hammer. However, the curve gets flatter with increasing anvil inertia and this means that a further increase in the weight of an already heavy anvil will be only marginally beneficial from a noise viewpoint. In practice the mass ratio (tup weight/anvil weight) is usually 1/20. Increasing the anvil weight four-fold (mass ratio = 1/80) will reduce the noise by 2 dB as shown in Fig. 3. A reduction in the anvil weight to 1/4 will, however, increase the noise level by more than 3 dB. Though the prime objective of the computer-aided analysis presented was to provide theoretical support to the experimentally observed noise-load linear relationship, the 20---
+
.15
z
/,
I 2
~
6
LOAO, M N FIG. 2. Predicted noise-load variation for three ~ I
masses.
Prediction of Linear Noise-Load Relationship
5
~12S
S 120
iic
~
J I1C
0
20 t.0 ANVIL MASS, Xl03kg
60
FIG. 3. Effectof anvil mass on noise level. developed computer program can also predict various outputs, such as net billet deformation, its duration, forming efficiency, load-time history, etc. of an impact forming process. As an example, the predicted load-time and load-deformation histories arising when forming in a two-stepped die-cavity, are shown in Figs. 4(a) and (b). It may be noticed that the forming load displays sudden jumps corresponding to the filling of the two steps in the die-cavity. Elsewhere the variation in load is non-linear. An interactive version of the computer package allowing the user to talk to the computer for handling a variety of different forming configurations in either a drop hammer or a power hammer is also available. CONCLUSIONS The analysis presented has shown that the noise emitted by an impact forming machine will increase linearly with the magnitude of the forming load. This conclusion provides analytical support to the previously observed experimental results on two different hammers. It was also shown that the gradient of the noise level line is a function of anvil weight, being less for a heavier anvil. Increasing the weight of an already heavy anvil is only marginally beneficial, as far as reduction in noise emission is concerned. However, a reduction of anvil weight may cause a disproportionate increase in the emitted noise level. The computer package developed during the course of present investigation can also predict other forming outputs.
Acknowledgement--Thanks are due to the Drop Forging Research Association for allowing the use of their test facilities. L.
.
.
.
.
.
,
~3
a~
.3
<
S z 2
°2
1
°o
1
'
•
~,
'
•
8
TIME, MS
(a)
i
i
~2
0
-
~
~
3
DEFORMATION, MM
(b)
FIG. 4. Predicted forming load variation with (a) time and (b) deformation.
6
S. VAJPAYEE,M. M. SADEK and S. A. TOSIAS REFERENCES
S.V.~GPAYEEand M. M. SADEK~Statistical analysis of the influence of process variables on noise generation in impact hot forming, ASME Paper No. 79, DET-29, Design Engng. Tech. Conf. St. Louis, (Sop. 1979). [2] S. VAJPAYEE,A. C. HOBDELLand M. M. S.~Eg, The influence of machine suspension and process parameters on hammer noise, to be presented at the Winter Annual Meeting of the ASME (1981). [3] S. VAJP^VV.E, M M. SADEK and S. A. TOBI~S, Int. J. Mach. Tool Des. Res. 19, 237 (1979). [4] M.K. D^s and S. A. Tosl,~s, The efficiency of energy transfer and the determination of the clash load in impact forming machines, 4th Int. Conf. of the Centrefor High Energy Forming, Denver, (Jul. 1973). [5] W. JOHNSON, Impact Strength of Materials. Edward Arnold, London (1972). [1]