Bed is the main element of a machine tool and acts as base for rest of the units.
The main requirement of a lathe bed is to provide a guide for continued accurate longitudinal movement of the carriage and tailstock. It has one or more slide ways cast as an integral part.
The above requirement can be met by following:
(1) Ability of the structure of the bed to resist distortion effectively due to static and dynamic loads.
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(2) Stability of the motion of the carriage under load.
(3) Wear resistance of guides.
(4) Freedom from residual stresses.
(5) Levelling.
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(6) Resistance to vibrations.
(7) Freedom from slip-stick.
Distortion due to Static and Dynamic Loads:
Fig. 11.8 shows the forces acting on a turning tool resolved in three mutually perpendicular directions. These forces are eventually transmitted to the bed in addition to the forces due to the weight of the parts on the bed and due to feed motion. The disposition of these forces with respect to the guide ways introduces forces and couples in three directions as shown in Fig. 11.9.
They cause stresses in the bed structure which are difficult to evaluate analytically because of the intricate shape of the bed. However, they can be evaluated experimentally be experimental stress analysis techniques leading to a sound design of any complicated structure.
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As can be seen from Fig. 11.9, Mx. is the couple which is mainly responsible for the torsion produced in the bed. Various forms of bed are known to resist torsion effectively. It may be pointed out that as far as torsion is concerned the circular cross-section is the best while the I-section resists bending most effectively.
As far as rigidity in bending and torsion is concerned a section in the form of a hollow rectangle is the most rational. Since design considerations also favour this form of cross- section, it is the basis of all bed designs.
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For wall thickness ‘t’ the following values have been found to be satisfactory in service:
(a) Light machine tools 12 to 15 mm.; Medium machine tools 18 to 20 mm;
Heavy machine tools 23 to 35 mm.
(b) Thickness of the ribs can be from 0.6 to 0.8 times t.
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The strength and especially the rigidity of hollow machine frames is increased by ribs and partitions.
The effectiveness of partitions and ribs largely depends on their arrangements. The ribs can be arranged parallel or crosswise. The parallel ribbing though lighter and better with respect to swarf clearance, is not as stiff as the diagonal construction. The cross-section of the ribs is generally made in the form of an I-section to resist bending effectively.
The considerations noted above are satisfied to a large extent in the design shown in Fig. 11.10. Here a double-walled section (to conform to a closed rectangle) with diagonal ribbing is adopted. The second point to note here is that no portion of the guide way projects out of the structure thereby minimising chances of distortion.
Stability of Motion of the Carriage:
To get an accurate longitudinal movement the carriage should have both static and dynamic stability.
Static stability of a sliding pair can be increased by observing the following points:
(i) By reducing the effect of forces which cause displacement.
The forces and couples acting on the saddle try to displace the saddle on the sideways deviating it from the required path.
Counter balancing of these forces and couples should be such as to keep the saddle in its required path. This can be effected by arranging all forces to act in the guiding planes or as near them as possible.
(ii) By proper selection of dimensions of guides with respect to the length of the sliding member.
This introduces the principle of narrow guides. Guides of machine tools are invariably narrow guides which are guides whose sliding member (sometimes fixed member) has a length several times the diameter or width of the guide. Usually a value of five to six times is satisfactory.
Narrow guides ensure:
(a) Movement free from cross locking.
(b) Sliding motion is much more efficient and easy to control.
(c) Undue length of sliding member can be avoided by controlling the width or diameter of guides.
(iii) By proper selection of forms of guides.
(iv) By having broad based supports.
Static stability is increased by having a broad based support. Fig. 11.11 shows an example of this kind of bed.
(v) By employing Hydrostatic guides.
The cutting forces on a machine tool vary widely due to varying cutting conditions. In order to obtain dynamic stability under all cutting conditions, resort is made to Hydrostatic guides.
In this system, lubricant films are formed between the bearing faces of the slide ways by an external oil supply system as shown in Fig. 11.12. Two constant displacement pumps deliver a constant volume of liquid at a fixed pressure and the liquid finds its way through the gaps hA and hB. Initially the runner remains in the central position.
If due to a disturbing force the runner is displaced towards A, the gap hA is diminished while the gap hB widens. Since the same quantity of liquid has to pass on either side, the pressure on the left hand side increases while the pressure on the right hand diminishes which causes the runner to shoot back to its original position.
Wear Resistance of Guides:
One of the most important factors which determines the period over which machine tool maintains its original accuracy is the wear resistance of its guides. Wear resistance is a function of following factors.
(I) Material and Its Hardness:
i. Cast Iron:
For effective wear resistance it should be free from large particles of free ferrite and cementite. Cast iron with a pearlitic structure is wear resistant besides shaving good mechanical properties. Also it avoids blow holes.
ii. Steel Guides:
Since only the guides have to be wear resistant, it is not necessary that the entire bed should be made of a wear resistant material. Inserted steel guides hardened to Rc 63 are being widely used.
iii. Plastic Guides:
Recently plastic guides have been introduced. Plastic plates of phenolic resin bonded fibre are inserted into one of the sliding surfaces, glued, screwed down and scraped.
iv. Plastic Guides:
a. Reduce friction and slip stick.
b. Reduce danger of seizure when lubricant is inadequate,
c. Minimise vibrations.
(II) Surface Finish:
Surface finish and form of micro irregularities have a profound influence on the wear resistance because of their capacity to generate hydro- dynamic films. Experiments have shown that a combination of a periphery and cup wheel ground surfaces is highly wear resistant.
(III) Mean Surface Pressure and Sliding Velocities:
To reduce wear of the guide ways, the pressure over them must be uniformly distributed. The designed areas have to be such that the mean surface pressure does not exceed values established by experience. For uniform bearing the number of bearing points should not be less than 2 to 3 per square cm.
The angles selected should be such that the major forces are taken by large areas, thereby keeping wear uniform on either side of the guide. This is easier to achieve with a flat guide than with a Vee guide.
The areas of the guide faces can be determined by dividing the reactions by the allowable maximum surface pressure.
The values of maximum allowable surface pressure are:
i. For smaller sliding speeds of majority of feed rates (e.g., lathes, milling machines etc.) 25 to 30 kg/cm2.
ii. For high sliding speeds of majority of feed rates (planning machines etc.) 8 kg/cm2.
iii. For guide ways of grinding machines 0.7 kg/cm2.
The above values can be used provided the surface pressure is uniform across and along the guides. As this is not the case half the values of the maximum pressure mentioned above can be assumed to give a satisfactory bearing area for slides. For example in the case of lathes a value of 13 to 15 kg/cm2 may be assumed as maximum pressure and used in the calculations.
(IV) Friction, Lubricant and Lubricating Conditions:
Friction and hence wear can be reduced by:
i. Lubrication of sliding surfaces.
ii. By ball and roller guides.
iii. By creating hydrodynamic or hydrostatic oil films.
iv. Protection of guides.
Ball and Roller guides. Introduction of balls and rollers between sliding surfaces converts high sliding friction into low rolling friction.
Ball and roller guides are generally used when:
(a) there is no tendency of the moving member to lift;
(b) weight of the latter is sufficient to resist such tendency.
Hydrostatic Guide Ways:
As it is difficult to obtain hydrodynamic films at low speeds, hydrostatic guide ways have been developed. In this system, as already mentioned, the lubricant separates the bearing surfaces giving low friction and no mechanical wear. Frictional resistance is provided only by the low forces of viscous shear in the lubricant films.
In particular, static friction may be made negligible—a very important property for slow moving slides. Because of this, hydrostatic guide ways find wide application, where freedom from slip-stick is of utmost importance.
Protection of Guides:
This prevents dust and other abrasive particles from entering between the sliding surfaces.
Residual Stresses:
Besides other factors precision of a machine tool depends on the dimensional stability of castings.
This depends on the following:
1. Nature of the cast material.
2. Design of casting.
3. Foundry techniques.
4. Heat treatment.
5. Machining operations.
Mechanite-castings are known to maintain dimensional stability. However it is important that the correct grade of Mechanite be used depending on application.
Different section thicknesses within the casting should be avoided or evened out gradually. Uneven sections cause uneven cooling rates which in turn lead to stress concentration. Generally machine tool slide ways have thicker cross-sections than the rest of the structure. In this case even cooling rates have been obtained by the use of silicon carbide blocks. Due to higher thermal conductivity they absorb heat quickly without affecting the machinability of the casting.
To ensure maximum stability, the casting should be left in the mould until completely cooled to room temperature. Artificial stress relieving in a furnace must be done carefully under the guidance of a metallurgist as otherwise the castings may come out in a more stressed condition.
There should be a time lag of at least a few days between rough and finish machining. Drilling of holes after finish machining should be avoided.
Levelling:
To obtain an accurate feed motion proper leveling is important. The bed should be level in both longitudinal and transverse directions within the limits prescribed by relevant standards and it should be installed on firm foundation.
Vibrations:
In order to obtain a high surface finish the machine should be free from vibrations. Besides other factors, the design of the bed influences the vibration characteristics of the machine. Vibrations can be minimised by controlling the following factors with regard to the design of the machine tool structure.
1. The designer should attempt to arrange machine tool structure to have natural frequencies that do not coincide with those of the cutting action.
2. As the natural frequency ωn is proportional to the square root of static stiffness ‘C’, the static stiffness of the structure should be as high as possible.
ωn = K√C,
where C = P/λ, P = straining force, λ = deformation in mm.
This can be achieved by a judicious selection of ribs and partitions.
3. The natural frequency ωn = K / √m,
where m = the mass of the vibrating system.
For obtaining high frequencies an attempt should be made to reduce the mass to minimum.
4. The material of the structure should be capable of damping vibrations effectively. Spheroidal graphite iron is good in this respect while flake graphite iron is better. Concrete is a good vibration damping material and it can be used to fill up the hollow spaces in the structure wherever possible.
Slip-Stick Phenomenon:
In the production of a fine surface finish the slip stick characteristics of a slide way system is as important as its vibration characteristics.
Slip-Stick:
Sliding of one body over another is normally intermittent in character, because the coefficient of kinetic friction is smaller than the coefficient of static friction and because the bodies involved deform when pressures are applied to them. Fig. 11.13 (a) shows an upper block which is assumed to be moving at constant speed by a force Q. The ability of the lower body to deform is represented by the spring of stiffness K. Here K is the ratio of force Q to the deformation Δ.
i.e., K = Q/Δ.
The deflection of the spring permits the lower body to move with the upper body (no sliding) until the spring force reaches the value at which sliding occurs. This portion of the motion is represented by CB in Fig. 11.13 (6) and is called stick. When sliding occurs the coefficient of friction drops to kinetic value from static value and the deflection of the spring drops also.
This portion of the motion is represented by BC in Fig. 11.3 (b) and is called slip. The constant speed motion of the upper body is represented by the line MM in the Fig. 11.13 (b). This process of intermittent sliding is called slip-stick.
Slip-stick is essentially a slow speed phenomenon.
It can be minimised or eliminated by controlling the following design values:
1. Material.
2. Coefficient of static friction.
Material:
Cast iron with a phosphorous content of 0.6 to 0.9% is a suitable material from the point of view of slip- stick.
Static Friction:
A reduction in the difference between the values of coefficients of static and kinetic friction can minimise slip-stick.
This can be done by selecting:
1. A high viscosity lubricant which ensures increase in friction with increase in speed.
2. By ball and roller guides.
3. By hydrostatic guides.
Hydrostatic guides can altogether eliminate slip-stick.