MACHINE TOOL STRUCTURES
Machine tool parts such as beds, bases, columns, box-type housings, carriages, tables, etc., are known as machine tool structures.
Requirements of machine tool structures
1. ACCURACY
All important mating surfaces of the structures should be machined with a high degree of accuracy to provide the desired geometrical and dimensional accuracy.
The initial geometrical accuracy of the structures should be maintained during the whole service life of the machine tool.
2. RIGIDITY & STIFFNESS
It refers to the ability of machine tool structure to resist the deformation in terms of twist or deflection during operation.
The rigidity and stiffness are used in place of one another with reference to the machine tools.
Rigidity refers to the ability of machine tool structure to resist the twist caused due to the applied torque.
Mathematically, it is defined as the ratio of applied torque(T) to the angle of twist (ϴ) of the bed.
where, G- Modulus of rigidity
J – Polar moment of inertia L – length of the structure
Stiffness refers to the ability of machine tool structure to resist the deflection(δ) caused due to the applied bending load.
Mathematically, it is defined as the ratio of applied load(P) to the deflection (δ) of the bed.
Compiled by Subash Acharya,Dept Of Mech & Mfg Engg, MIT Manipal. where,
E- young’s modulus ;
k – Structure support constant; I – moment of inertia
L- length of the structure 3. STRENGTH
The shapes and sizes of the structures should not only provide safe operation and maintenance of the machine tool but also ensure that working stresses and deformations do not exceed specific limits.
It should be noted that the stresses and deformations are due to mechanical as well as thermal loading.
4. WEAR RESISTANCE
To provide wear resistance, material of the structure should be selected properly.
DESIGN CRITERIA FOR MACHINE TOOL STRUCTURES
During the operation of machine tool, the machine tool structures are subjected to compound loading consisting of torsion and bending in two planes.
Consider a simple machine tool bed with two side walls, which may be represented as a simply supported beam loaded by a concentrated force P acting at its centre .
Compiled by Subash Acharya,Dept Of Mech & Mfg Engg, MIT Manipal.
i.e.,if the failure of the beams is determined by the normal stresses under tensile loading, the volume of the steel beam required to withstand the same load is 13.07 times less than that of cast iron beam.
The variation of Vσ and V for mild steel and cast iron beams with change of l2 /h is shown in Fig. 3.2.
For identical beam length, the height of the steel section must be 48/17.14 = 2.80 times greater.
That the steel structure is lighter, deeper and thinner than a cast iron structure of equivalent strength is obvious.
However, since structures are mostly designed from stiffness considerations, the actual economy of metal consumption by using steel instead of cast iron may be much less than 13.07 times, because the steel structure must be provided with stiffening ribs.
This not only increases the weight of the steel structure but also adds to the labour cost
Compiled by Subash Acharya,Dept Of Mech & Mfg Engg, MIT Manipal.
Steel should be preferred for simple, heavily loaded structures; this is due to the fact that in lightly loaded structures the higher mechanical properties of steel cannot be fully exploited. Cast iron should be preferred for complex structures subjected to normal loading, Cast iron has self-lubricating properties due to presence of free carbon as graphite flakes and has good compressive strength.
Lately, combined welded and cast structures are becoming popular. They are generally used where steel structure is economically suitable but is difficult to manufacture owing to the complexity of some portions; these complex portions are separately cast and welded to the main structure. An example is that of cast-bearing housings that are welded into the feed box. PROFILES OF MACHINE TOOL STRUCTURES
During the operation of the machine tool, a majority of its structures are subjected to compound loading and their resultant deformation consists of torsion, bending and tension or compression. Under simple tensile or compressive loading, the strength and stiffness of an element depend only upon the area of cross section.
However, the deformation and stresses in elements subjected to torsion and bending depend, additional depend upon the shape of the cross section.
A certain volume of metal can be distributed in different ways to give different values of the moment of inertia and sectional modulus. The shape that provides the maximum moment of inertia and sectional modulus will be considered best as it will ensure minimum values of permissible stresses and deformation.
It is evident from Table 3.3 that the box-type section has the highest torsional stiffness and in the overall assessment seems best suited both in terms of strength and stiffness.(for the almost same cross-sectional area).
The additional advantage that goes in its favour is the ease of proper mating with other surfaces.
All considerations combined point towards the overwhelming superiority of the box-type profile over others for machine tool structures. In most of the cases, the machine tool bed and other structures cannot be made in the form of a closed-box profile.
There must be apertures for bearings, openings for free flow of chips and other purposes. Thus the actual profiles of machine tool structures differ from a closed-box profile. The apertures and openings in the structure have an adverse effect upon its strength and stiffness. This can be overcome by providing ribs and stiffeners. Also, stiffness can be improved by providing proper arrangement of fastening bolts.
The basic types of ribbing are Box ribbing and Diagonal ribbing: refer notes for figure
2900
2830
2950
Compiled by Subash Acharya,Dept Of Mech & Mfg Engg, MIT Manipal.
The number of ribs or stiffeners is selected from the following consideration:
In the case of diagonal ribbing, the angle between the adjacent stiffeners should lie between 60º and 100º.
In box ribbing, or vertical stiffeners, the distance between two adjacent stiffeners should be approximately equal to the width of the bed.
Static & Dynamic stiffness
Machine tool structures are mostly designed from stiffness considerations and thus should possess high static and dynamic stiffness.
Static stiffness can be calculated by examining the force displacement relationship.. Higher the static stiffness, lesser will be the relative tool workpiece displacement and higher will be the accuracy of machining.
If a dynamic force is applied to an element it experiences displacement which is time dependent. For a constant value of applied dynamic force, the displacement will vary with the change in frequency of applied force. Therefore, the ratio,
Dynamic stiffness =
Dynamic stiffness will depend on the frequency of the applied force. The ratio of dynamic deflection to static deflection is known as magnification or amplification factor. The dynamic and static stiffness are related by the expression,
Dynamic stiffness
=
The amplification factor depends on damping factor and ratio of frequency of excitation (
ω
)and natural frequency of the element ((ω
n).The natural frequency(
ω
n) of a system is given by:ω
n=√
where, k is the stiffness and m is the mass of the element.
While designing the element of the machine tools, their natural frequencies should be checked at the design stage and should be ensured as far as possible that the natural frequency should be 2.5 times greater than highest excitation frequency.
In machine tools, the excitation frequencies generally appear from rotating shaft, gears, spindles,etc. They are relatively low in most of the machine tools. Eg: If a lathe spindle rotates with a maximum speed of 1200rpm, it would produce a maximum excitation frequency of 1200/60 = 20 Hz. Correspondingly, the heaviest lathe unit should have a natural frequency of
