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Development and evaluation of ferrocement legs for a lathe
Int. J. Mach. Tools Manufact. Vol. 30. No. 4, pp. 629...636. 1990. Printed in Great Britain
DEVELOPMENT
0890-.6955/9053.00 + .00 Pergamon Press plc
AND EVALUATION OF FERROCEMENT LEGS FOR A LATHE M. RArIMAN* and M. A. MANSURt
(Received 25 September 1989; in final form 20 February 1990) Abs~--The feasibility of using ferrocement as a replacement material for cast iron in the fabrication of supporting legs (columns) for a centre lathe has been investigated in this project. These machine tool structures were designed with the aid of a finite element package so as to have static stiffncsses at least equal to those of the corresponding cast iron legs. Tests were carried out to evaluate the performance of the ferrocement legs with reference to the traditional cast iron legs. The highly improved dynamic performance as exhibited by the ferrocement legs indicates that this new construction material has a great potential in the machine tool industry.
INTRODUCTION
IT HAS been a common consensus that the desired technical properties for a machine tool structure are high static stiffness against bending and torsion, good dynamic characteristics (high natural frequency and high damping ratio), good long-term dimensional stability, and a reasonably low coefficient of expansion. Also, the amount of materials required and the resulting weight of the structure, its production process and overall cost are some of the important factors commonly considered while assessing the suitability of a material [1-3].Cast iron, a traditional material used in the manufacture of structural components of a machine tool possesses these characteristics to an acceptable level. But its inherent disadvantages like, high cost, poor torsional rigidity due to thin walls, difficulty in producing the finished product, etc. have led researchers to look for alternative materials either to supplement or to completely replace east iron for the fabrication of machine tool structures. Attempts have already been made to use mild steel weldments, synthetic granite, hydraulic cement concrete and polymer concrete with some success [4--6]. The authors in a recent study [7] have also investigated the possibility of using "ferrocement", a relatively new material, in the construction of machine tool structures. Ferrocement may be defined as a type of thin-walled reinforced concrete commonly constructed of hydraulic cement mortar reinforced with closely spaced layers of continuous and relatively small diameter mesh. Two prototype ferrocement beds for a typical centre lathe were designed and fabricated and their performances were evaluated by considering the parent cast iron bed as the basis. Dramatic improvements in the static and dynamic performances exhibited by the ferrocement beds have encouraged the authors to pursue the work further. The study reported in this paper, therefore, represents a continuation of the earlier work [7]. In this study, the supporting legs of the same bed have been designed and fabricated using ferrocement as the material, and appropriate tests are conducted to enable a comparative performance evaluation. DESIGN CONSIDERATIONS
The centre lathe for which a ferrocement bed was previously designed and fabricated [7] was chosen in the present study. The supporting legs, both at the head and tail ends of the bed, have been duplicated using ferrocement as a construction material. The *Department of Mechanical and Production Engineering National University of Singapore, Singapore. tDepartment of Civil Engineering, National University of Singapore, Singapore. ~rs 3o:4-a
629
630
M. RAaMANand M. A. MANSUR
geometrical configuration selected conformed very closely to the existing cast iron legs so as to accommodate all the prevailing auxiliaries. Based on the manufacturer's design data and the computations made in the earlier studies [7,8] the legs were designed to withstand the worst loading conditions. Since the legs experience different loadings due to various cutting forces depending on the location of the carriage and tailstock, calculations were made for two extreme cases: fight extreme--when the tailstock and carriage are at the extreme right end of the bedmand the left extreme--when the tailstock and carriage are at the extreme left end of the bed. The forces acting on the supporting legs were calculated as follows: (a) the forces exerted by the tool on the workpiece were first determined; (b) the corresponding forces exerted on the headstock, carriage, tailstock and the bed were then evaluated; and (c) with the forces in step (b) and including the self weight of various components, the resulting forces exerted on the leg were finally determined. ANALYSIS FOR OPTIMAL THICKNESS
The new ferrocement prototype has been designed to have a static stiffness greater, than or at least equal, to the original prototype. As the actual profile of the legs is rather complex, analysis was carried out with the help of a computer using a finite element package, PAFEC 75. A total of 42 two-dimensional elements were used to model each leg structure. The material properties used were obtained from previous experiments [7]. With the aid of a computer, deflection properties were obtained for the legs o f two different materials. A favourable ferrocement wall thickness was obtained to give the same or slightly less static deflections at all locations as compared to those of the respective cast iron type. For the tail-end support, a ferrocement thickness of 50 ram, 5 times the thickness of the original cast iron leg, was found to satisfy the above condition. For the head-end, a design thickness of 4 times the original thickness was sufficient. Analyses indicated that the natural frequencies for the ferrocement legs selected as above were significantly higher than those for the corresponding cast iron legs at these design thicknesses. FABRICATION
The fine wire mesh used in the fabrication of reinforcement cages for ferrocement was of welded type with 12.7 mm square grids and 1.2 mm wire diameter, the yield strength of mesh reinforcement being 410 MPa. Mild steel bars of 6 mm in diameter with a yield strength of 371 MPa were first bent to the correct dimensions and were tack-welded to get the skeleton for the leg structure. Three layers of fine wire mesh were used in each fib (Fig. 1). The various metal inserts for bed-mounting platform were placed at the correct places and tack-welded to the skeletal cage. The mould was then made to contain the reinforcing cage. No internal mould was necessary as the legs were cast one side at a time, the top face being the last one. If they were cast with an internal mould at one casting, the internal mould would be difficult to remove thus obstructing the access to the interior of the supports. Natural sand passing through BS sieve No. 8 was used for the mortar. The cement-sand ratio was 1:2, and the water-cement ratio was 0.45. An admixture, Rapidard, was used at 4.73 l per 100 kg of cement to accelerate the gain in strength. The legs were cast on a vibrating table using a precisely constructed plywood mould (Fig. 2). Finishing was done on the inside face after initial setting of the mortar. When all the four sides were cast in sequence, the supports were erected to cast the base. The threadings at the anchorage points were sealed to prevent mortar penetration and, thus preventing blockage of the screw threads. For the head-end support, the motor mounting-plate was cast by tilting the legs so that the inclined plate was horizontal. The
Ferrocement Legs for a Lathe
FIG. 1. Reinforcing cage for ferrocement legs.
FIc. 2. Plywood mould.
631
632
M. RAHMAN and M. A. MANSUR
top faces were then properly secured and the bed-mounting platforms were adjusted to the correct position. Extra care was needed while casting the top surface for each leg as this surface requires a slope to drain out coolant into the collecting trays. Smooth finishing was done by finger tips after hand pressing the mortar. Completed ferrocement legs along with the cast iron legs are shown in Figs 3 and 4. TEST P R O G R A M M E
As part of a detailed investigation on the performance of ferrocement legs, both static and dynamic tests were carried out to determine the static stiffness, natural frequency, damping factors and mode shapes. The static loading tests (Fig. 5) were conducted on both cast iron and ferrocement legs using a 20 tonnes screw-jack under rigidly supported condition. Force measurements were taken using a calibrated load
Fro. 3. Ferrocement and cast iron head-end legs.
Fro. 4. Ferrocement and cast iron tail-end legs.
Ferrocement Legs for a Lathe
633
FIG. 5. Experimental set-up for static test.
cell connected to the end of the screw-jack. Deflections were measured by a transducer connected to a strain meter. Force was applied only in the longitudinal direction as this is the most likely bending direction. Dynamic evaluation of the leg supports was carried out using modal analysis technique. Frequency response function (FRF) method was employed to measure the modal parameters like natural frequency, damping factor and mode shapes. The transient excitation method was employed in this experiment. A Fast Fourier Transform (FFT) analyser (ONO SOKKI Model-CF-910), an impact hammer (PCB Model 480B), an accelerometer (B & K Model 263A), a desk top computer (HP 216 Series 2000) and the modal analysis software ( M O D A L 3.0 by Structural Measurement System Inc.) were used in this experiment. The leg structures were hung by a portable crane using a flexible cable so as to obtain a free-body situation in the direction perpendicular to the hanging. RESULTS AND DISCUSSION
The overall weights of the ferrocement and cast iron legs are shown in Table 1. It could be seen that the weights of the ferrocement leg supports were comparable to that of the cast iron type. As the density of cast iron is approximately 4 times that of ferrocement, and with a thickness ratio of 4:1 (ferrocement to cast iron), these results were as expected. The minor differences were due to the addition of metal inserts and dimensional inaccuracies during casting. The results of static deflection tests are shown in Figs 6 and 7. A lateral load of up to 15 kN was applied. It can be seen that the load-deflection relationships are quite linear. The inverse of the slopes of these lines for the ferrocement head-end and tailend legs were 0.040 mm/kN and 0.058 mm/kN, respectively. The corresponding values TABLE 1. OVERALL WEIGHTS OF THE LEGS Type Ferrocement legs Cast-iron legs
Head-end
Tail-end
180 kg 164 kg
167 kg 152 kg
M. RA~MAN and M. A. MANSUR
634
1J, 12
tO
O.L,
0.8
1.2
1.6
211
2.L,
2.8
3~2
3.6
DEFLECTION,MI4 FIG. 6. Static deflection for head-end leg,. 16
:i
y"
..,f-.-
°'i 6
I, /
0 ~ 09
II" ,o~
.
.,,.f"
O.t,
.
0.0
j+""
.
~- CAST IRON
1.2
.
.
1.6
.
2.0
.
Z/,
.
2.8
3.2
3.6
OEFLECTION,MM FIG. 7. Static deflection for tail-end leg.
for the cast iron legs were 0.20 mm/kN and 0.21 mm/kN, respectively. These slopes indicate that the ferrocement legs have stiffness considerably larger than the cast iron legs. The loading conditions shown were solely for experimental purposes. In actual working conditions, the legs are not subjected to such a high load at all. The actual loading conditions are a combination of loads acting in various directions. The most severe loadings on the legs were the compressive loads. The deflections produced by service loading will not be significantly large enougli to have any drastic effects on machining accuracy. Many factors like Young's Modulus, second moment of area and geometrical configurations affected the stiffness of the structure. All these factors contributed to the higher static stiffness of the ferrocement legs. Natural frequencies and damping ratios of legs are shown in Tables 2 and 3, respectively. Comparison of frequencies and damping ratios was done at the same mode shapes as seen from the animated plots of Modal 3.0. The plots were also used to distinguish the torsional modes from the rest of the mode shapes. For the tail-end, the torsional mode of cast iron structure was at the first resonance frequency. However, the corresponding torsional mode for ferrocement structure was at the third resonance frequency. The other modes were also at different order of resonance. This could be due to the geometrical configuration of the two tailrend legs. In the case of cast iron, the base was open. However the base for the ferrocement was partly closed. Thus, an earlier torsional mode was detected for the cast iron tail-end legs. As the geometrical configuration for the head-end was quite similar, no such observations were made. Generally, the head- and tail-end ferrocement legs exhibited a higher range of natural frequencies. They also have much higher corresponding frequencies than the cast iron
Ferrocement Legs for a Lathe
635
TABLE 2 NATURAL FREQUENCIES AND DAMPING RATIOS OF CAST IRON AND FERROCEMENT LEGS COMPARED WITH THEORETICAL RESULTS (HEAD-END: FREE BODY CONDITION)
Mode shape
1st Mode
2nd Mode
Torsional
3rd Mode
Cast iron
R. f . expt theor 8
1 146 219 0.82
2 258 262 0.44
3 277 277 0.47
4 321 290 0.34
Ferrocement
Rn fn expt theor 8
1 303 357 3.54
2 585 524 1.97
3 693 672 2.19
4 938 910 1.20
R n = Resonance
No.
f . = Natural frequency (Hz). 8 = damping ratio (%). TABLE 3. NATURAL FREQUENCIES AND DAMPING RATIOS OF CAST IRON AND FERROCEMENT LEGS COMPARED WITH THEORETICAL RESULTS (TAIL-END" FREE BODY CONDITION)
Mode shape
Torsional
1st Mode
2nd Mode
3rd Mode
Cast iron
R. f . expt theor 8
1 109 229 0.92
2 338 246 0.36
3 402 300 0.29
4 478 491 0.29
Ferrocement
R. f . expt theor 8
3 816 865 1.15
1 708 510 1.17
2 755 858 2.18
4 897 907 0.73
legs. Experimental results were quite consistent with those obtained by finite element analysis. The inherent damping characteristics of ferrocement were clearly illustrated from the damping ratios obtained as shown in Tables 2 and 3. Damping ratios for ferrocement structures were significantly higher than those of cast iron structures at the corresponding modes of vibration. Although free-body condition is not applicable to actual working situation, it serves as a good basis for comparison of the various modal parameters. Experimentally, the free-body condition is easily achieved than any other conditions. It approaches the ideal free-body condition state quite closely. Due to the above reasons, the results obtained were reliable. Thus experimental data based on this condition can be used to validate and verify other experimental data obtained for other conditions.
CONCLUSIONS
In this project, both the head-and the tail-end legs of a lathe were designed and fabricated. Ferrocement legs of about 4-5 times the original cast "iron thickness are found to be sufficient to achieve the desired condition. Static as well as dynamic tests were carried out to evaluate their performance in relation to parent cast iron legs. Test results indicate that the ferrocement legs have adequate stiffness to replace the cast iron legs. They also possess highly improved dynamic properties in terms of natural frequency and damping ratio to further justify their use in the machine tool industry.
Acknowledgements--The authors
express their sincere thanks to LeBlond Makino Asia Pte Ltd for its collaboration in this research project.
636
M. RAHMANand M. A. MANSUR REFERENCES
[1] [2] [3] [4] [5] [6] [7] [8]
F. KOENIGSBERGERand J. TLUSTY,Machine Tool Structures, Vol. I. Pergamon Press, New York (1970). N. ACHEXKAN,Machine Tool Design, Voi. 1. Mir, Moscow (1968). F. Kova~msBrdmm, Design Principles of Metal Cutting Machine Tools. Pergamon Press, New York. G. H. MORGAN,P. A. i c K r ~ w N and H. J. RENKER,Materials for machine tool structures, 20th Int. Mach. Tool Des. Res. Conf pp. 429--434. Macmillan Press, New York (1980). S. E. OVlAWE,T. TA¥ and A. A. SHUMSHERUDDIN,Development of a machine tool structure using composite synthetic granite, 23rd IMTDR Conf. pp. 31-37. Macmillan Press, New York (1983). H. H~TMANN and V. VENKATARAMAN,Investigations on the use of prestressed and reinforced concrete as a material for machine tool structure, Proc. 4th All India Conf. on Machine Tools Design and Research, IIT Madras, India, pp. 287-299. M. RAHMAN, M. A. MANSUR, W. D. AMBROSEand K. H. CHUA, Design, fabrication and performance of a ferrocement machine tool bed, Int. J. Mach. Tools Manufact. 27, 431-442 (1987). M. A. MANSURand M. RAHMAN, Ferrocement as a machine tool bed, J. Ferrocement 19, 19-28 (1989).
DEVELOPMENT
0890-.6955/9053.00 + .00 Pergamon Press plc
AND EVALUATION OF FERROCEMENT LEGS FOR A LATHE M. RArIMAN* and M. A. MANSURt
(Received 25 September 1989; in final form 20 February 1990) Abs~--The feasibility of using ferrocement as a replacement material for cast iron in the fabrication of supporting legs (columns) for a centre lathe has been investigated in this project. These machine tool structures were designed with the aid of a finite element package so as to have static stiffncsses at least equal to those of the corresponding cast iron legs. Tests were carried out to evaluate the performance of the ferrocement legs with reference to the traditional cast iron legs. The highly improved dynamic performance as exhibited by the ferrocement legs indicates that this new construction material has a great potential in the machine tool industry.
INTRODUCTION
IT HAS been a common consensus that the desired technical properties for a machine tool structure are high static stiffness against bending and torsion, good dynamic characteristics (high natural frequency and high damping ratio), good long-term dimensional stability, and a reasonably low coefficient of expansion. Also, the amount of materials required and the resulting weight of the structure, its production process and overall cost are some of the important factors commonly considered while assessing the suitability of a material [1-3].Cast iron, a traditional material used in the manufacture of structural components of a machine tool possesses these characteristics to an acceptable level. But its inherent disadvantages like, high cost, poor torsional rigidity due to thin walls, difficulty in producing the finished product, etc. have led researchers to look for alternative materials either to supplement or to completely replace east iron for the fabrication of machine tool structures. Attempts have already been made to use mild steel weldments, synthetic granite, hydraulic cement concrete and polymer concrete with some success [4--6]. The authors in a recent study [7] have also investigated the possibility of using "ferrocement", a relatively new material, in the construction of machine tool structures. Ferrocement may be defined as a type of thin-walled reinforced concrete commonly constructed of hydraulic cement mortar reinforced with closely spaced layers of continuous and relatively small diameter mesh. Two prototype ferrocement beds for a typical centre lathe were designed and fabricated and their performances were evaluated by considering the parent cast iron bed as the basis. Dramatic improvements in the static and dynamic performances exhibited by the ferrocement beds have encouraged the authors to pursue the work further. The study reported in this paper, therefore, represents a continuation of the earlier work [7]. In this study, the supporting legs of the same bed have been designed and fabricated using ferrocement as the material, and appropriate tests are conducted to enable a comparative performance evaluation. DESIGN CONSIDERATIONS
The centre lathe for which a ferrocement bed was previously designed and fabricated [7] was chosen in the present study. The supporting legs, both at the head and tail ends of the bed, have been duplicated using ferrocement as a construction material. The *Department of Mechanical and Production Engineering National University of Singapore, Singapore. tDepartment of Civil Engineering, National University of Singapore, Singapore. ~rs 3o:4-a
629
630
M. RAaMANand M. A. MANSUR
geometrical configuration selected conformed very closely to the existing cast iron legs so as to accommodate all the prevailing auxiliaries. Based on the manufacturer's design data and the computations made in the earlier studies [7,8] the legs were designed to withstand the worst loading conditions. Since the legs experience different loadings due to various cutting forces depending on the location of the carriage and tailstock, calculations were made for two extreme cases: fight extreme--when the tailstock and carriage are at the extreme right end of the bedmand the left extreme--when the tailstock and carriage are at the extreme left end of the bed. The forces acting on the supporting legs were calculated as follows: (a) the forces exerted by the tool on the workpiece were first determined; (b) the corresponding forces exerted on the headstock, carriage, tailstock and the bed were then evaluated; and (c) with the forces in step (b) and including the self weight of various components, the resulting forces exerted on the leg were finally determined. ANALYSIS FOR OPTIMAL THICKNESS
The new ferrocement prototype has been designed to have a static stiffness greater, than or at least equal, to the original prototype. As the actual profile of the legs is rather complex, analysis was carried out with the help of a computer using a finite element package, PAFEC 75. A total of 42 two-dimensional elements were used to model each leg structure. The material properties used were obtained from previous experiments [7]. With the aid of a computer, deflection properties were obtained for the legs o f two different materials. A favourable ferrocement wall thickness was obtained to give the same or slightly less static deflections at all locations as compared to those of the respective cast iron type. For the tail-end support, a ferrocement thickness of 50 ram, 5 times the thickness of the original cast iron leg, was found to satisfy the above condition. For the head-end, a design thickness of 4 times the original thickness was sufficient. Analyses indicated that the natural frequencies for the ferrocement legs selected as above were significantly higher than those for the corresponding cast iron legs at these design thicknesses. FABRICATION
The fine wire mesh used in the fabrication of reinforcement cages for ferrocement was of welded type with 12.7 mm square grids and 1.2 mm wire diameter, the yield strength of mesh reinforcement being 410 MPa. Mild steel bars of 6 mm in diameter with a yield strength of 371 MPa were first bent to the correct dimensions and were tack-welded to get the skeleton for the leg structure. Three layers of fine wire mesh were used in each fib (Fig. 1). The various metal inserts for bed-mounting platform were placed at the correct places and tack-welded to the skeletal cage. The mould was then made to contain the reinforcing cage. No internal mould was necessary as the legs were cast one side at a time, the top face being the last one. If they were cast with an internal mould at one casting, the internal mould would be difficult to remove thus obstructing the access to the interior of the supports. Natural sand passing through BS sieve No. 8 was used for the mortar. The cement-sand ratio was 1:2, and the water-cement ratio was 0.45. An admixture, Rapidard, was used at 4.73 l per 100 kg of cement to accelerate the gain in strength. The legs were cast on a vibrating table using a precisely constructed plywood mould (Fig. 2). Finishing was done on the inside face after initial setting of the mortar. When all the four sides were cast in sequence, the supports were erected to cast the base. The threadings at the anchorage points were sealed to prevent mortar penetration and, thus preventing blockage of the screw threads. For the head-end support, the motor mounting-plate was cast by tilting the legs so that the inclined plate was horizontal. The
Ferrocement Legs for a Lathe
FIG. 1. Reinforcing cage for ferrocement legs.
FIc. 2. Plywood mould.
631
632
M. RAHMAN and M. A. MANSUR
top faces were then properly secured and the bed-mounting platforms were adjusted to the correct position. Extra care was needed while casting the top surface for each leg as this surface requires a slope to drain out coolant into the collecting trays. Smooth finishing was done by finger tips after hand pressing the mortar. Completed ferrocement legs along with the cast iron legs are shown in Figs 3 and 4. TEST P R O G R A M M E
As part of a detailed investigation on the performance of ferrocement legs, both static and dynamic tests were carried out to determine the static stiffness, natural frequency, damping factors and mode shapes. The static loading tests (Fig. 5) were conducted on both cast iron and ferrocement legs using a 20 tonnes screw-jack under rigidly supported condition. Force measurements were taken using a calibrated load
Fro. 3. Ferrocement and cast iron head-end legs.
Fro. 4. Ferrocement and cast iron tail-end legs.
Ferrocement Legs for a Lathe
633
FIG. 5. Experimental set-up for static test.
cell connected to the end of the screw-jack. Deflections were measured by a transducer connected to a strain meter. Force was applied only in the longitudinal direction as this is the most likely bending direction. Dynamic evaluation of the leg supports was carried out using modal analysis technique. Frequency response function (FRF) method was employed to measure the modal parameters like natural frequency, damping factor and mode shapes. The transient excitation method was employed in this experiment. A Fast Fourier Transform (FFT) analyser (ONO SOKKI Model-CF-910), an impact hammer (PCB Model 480B), an accelerometer (B & K Model 263A), a desk top computer (HP 216 Series 2000) and the modal analysis software ( M O D A L 3.0 by Structural Measurement System Inc.) were used in this experiment. The leg structures were hung by a portable crane using a flexible cable so as to obtain a free-body situation in the direction perpendicular to the hanging. RESULTS AND DISCUSSION
The overall weights of the ferrocement and cast iron legs are shown in Table 1. It could be seen that the weights of the ferrocement leg supports were comparable to that of the cast iron type. As the density of cast iron is approximately 4 times that of ferrocement, and with a thickness ratio of 4:1 (ferrocement to cast iron), these results were as expected. The minor differences were due to the addition of metal inserts and dimensional inaccuracies during casting. The results of static deflection tests are shown in Figs 6 and 7. A lateral load of up to 15 kN was applied. It can be seen that the load-deflection relationships are quite linear. The inverse of the slopes of these lines for the ferrocement head-end and tailend legs were 0.040 mm/kN and 0.058 mm/kN, respectively. The corresponding values TABLE 1. OVERALL WEIGHTS OF THE LEGS Type Ferrocement legs Cast-iron legs
Head-end
Tail-end
180 kg 164 kg
167 kg 152 kg
M. RA~MAN and M. A. MANSUR
634
1J, 12
tO
O.L,
0.8
1.2
1.6
211
2.L,
2.8
3~2
3.6
DEFLECTION,MI4 FIG. 6. Static deflection for head-end leg,. 16
:i
y"
..,f-.-
°'i 6
I, /
0 ~ 09
II" ,o~
.
.,,.f"
O.t,
.
0.0
j+""
.
~- CAST IRON
1.2
.
.
1.6
.
2.0
.
Z/,
.
2.8
3.2
3.6
OEFLECTION,MM FIG. 7. Static deflection for tail-end leg.
for the cast iron legs were 0.20 mm/kN and 0.21 mm/kN, respectively. These slopes indicate that the ferrocement legs have stiffness considerably larger than the cast iron legs. The loading conditions shown were solely for experimental purposes. In actual working conditions, the legs are not subjected to such a high load at all. The actual loading conditions are a combination of loads acting in various directions. The most severe loadings on the legs were the compressive loads. The deflections produced by service loading will not be significantly large enougli to have any drastic effects on machining accuracy. Many factors like Young's Modulus, second moment of area and geometrical configurations affected the stiffness of the structure. All these factors contributed to the higher static stiffness of the ferrocement legs. Natural frequencies and damping ratios of legs are shown in Tables 2 and 3, respectively. Comparison of frequencies and damping ratios was done at the same mode shapes as seen from the animated plots of Modal 3.0. The plots were also used to distinguish the torsional modes from the rest of the mode shapes. For the tail-end, the torsional mode of cast iron structure was at the first resonance frequency. However, the corresponding torsional mode for ferrocement structure was at the third resonance frequency. The other modes were also at different order of resonance. This could be due to the geometrical configuration of the two tailrend legs. In the case of cast iron, the base was open. However the base for the ferrocement was partly closed. Thus, an earlier torsional mode was detected for the cast iron tail-end legs. As the geometrical configuration for the head-end was quite similar, no such observations were made. Generally, the head- and tail-end ferrocement legs exhibited a higher range of natural frequencies. They also have much higher corresponding frequencies than the cast iron
Ferrocement Legs for a Lathe
635
TABLE 2 NATURAL FREQUENCIES AND DAMPING RATIOS OF CAST IRON AND FERROCEMENT LEGS COMPARED WITH THEORETICAL RESULTS (HEAD-END: FREE BODY CONDITION)
Mode shape
1st Mode
2nd Mode
Torsional
3rd Mode
Cast iron
R. f . expt theor 8
1 146 219 0.82
2 258 262 0.44
3 277 277 0.47
4 321 290 0.34
Ferrocement
Rn fn expt theor 8
1 303 357 3.54
2 585 524 1.97
3 693 672 2.19
4 938 910 1.20
R n = Resonance
No.
f . = Natural frequency (Hz). 8 = damping ratio (%). TABLE 3. NATURAL FREQUENCIES AND DAMPING RATIOS OF CAST IRON AND FERROCEMENT LEGS COMPARED WITH THEORETICAL RESULTS (TAIL-END" FREE BODY CONDITION)
Mode shape
Torsional
1st Mode
2nd Mode
3rd Mode
Cast iron
R. f . expt theor 8
1 109 229 0.92
2 338 246 0.36
3 402 300 0.29
4 478 491 0.29
Ferrocement
R. f . expt theor 8
3 816 865 1.15
1 708 510 1.17
2 755 858 2.18
4 897 907 0.73
legs. Experimental results were quite consistent with those obtained by finite element analysis. The inherent damping characteristics of ferrocement were clearly illustrated from the damping ratios obtained as shown in Tables 2 and 3. Damping ratios for ferrocement structures were significantly higher than those of cast iron structures at the corresponding modes of vibration. Although free-body condition is not applicable to actual working situation, it serves as a good basis for comparison of the various modal parameters. Experimentally, the free-body condition is easily achieved than any other conditions. It approaches the ideal free-body condition state quite closely. Due to the above reasons, the results obtained were reliable. Thus experimental data based on this condition can be used to validate and verify other experimental data obtained for other conditions.
CONCLUSIONS
In this project, both the head-and the tail-end legs of a lathe were designed and fabricated. Ferrocement legs of about 4-5 times the original cast "iron thickness are found to be sufficient to achieve the desired condition. Static as well as dynamic tests were carried out to evaluate their performance in relation to parent cast iron legs. Test results indicate that the ferrocement legs have adequate stiffness to replace the cast iron legs. They also possess highly improved dynamic properties in terms of natural frequency and damping ratio to further justify their use in the machine tool industry.
Acknowledgements--The authors
express their sincere thanks to LeBlond Makino Asia Pte Ltd for its collaboration in this research project.
636
M. RAHMANand M. A. MANSUR REFERENCES
[1] [2] [3] [4] [5] [6] [7] [8]
F. KOENIGSBERGERand J. TLUSTY,Machine Tool Structures, Vol. I. Pergamon Press, New York (1970). N. ACHEXKAN,Machine Tool Design, Voi. 1. Mir, Moscow (1968). F. Kova~msBrdmm, Design Principles of Metal Cutting Machine Tools. Pergamon Press, New York. G. H. MORGAN,P. A. i c K r ~ w N and H. J. RENKER,Materials for machine tool structures, 20th Int. Mach. Tool Des. Res. Conf pp. 429--434. Macmillan Press, New York (1980). S. E. OVlAWE,T. TA¥ and A. A. SHUMSHERUDDIN,Development of a machine tool structure using composite synthetic granite, 23rd IMTDR Conf. pp. 31-37. Macmillan Press, New York (1983). H. H~TMANN and V. VENKATARAMAN,Investigations on the use of prestressed and reinforced concrete as a material for machine tool structure, Proc. 4th All India Conf. on Machine Tools Design and Research, IIT Madras, India, pp. 287-299. M. RAHMAN, M. A. MANSUR, W. D. AMBROSEand K. H. CHUA, Design, fabrication and performance of a ferrocement machine tool bed, Int. J. Mach. Tools Manufact. 27, 431-442 (1987). M. A. MANSURand M. RAHMAN, Ferrocement as a machine tool bed, J. Ferrocement 19, 19-28 (1989).