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The following points highlight the three elements of machine tools. The elements are: 1. Structure (Bed, Column and Frame) 2. Slides and Slideways 3. Kinematics of Machine Tool Drives.

**Element # 1. ****Structure (Bed, Column and Frame)****: **

A precision lathe is a machine tool capable of generating a true cylinder with a good surface finish. To perform the machining operation, two motions are required, the primary cutting motion and the feed motion.

In order to generate a true cylinder, the trajectory of the primary cutting motion should be true circle while the feed motion should be along a perfect straight line parallel to the axis of the primary cutting motion in the horizontal and vertical planes. If the motion is not parallel in the horizontal plane a cone will be generated, while a hyperboloid will be generated if the motion is not parallel in the vertical plane.

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The accuracy of the primary cutting motion depends mainly on the design of the main spindle, while the accuracy of the feed motion depends upon the design of the bed. Surface finish depends on the vibration characteristics of the machine and the slip stick characteristics of the slide ways. A proper design of the structure of the bed of vital importance is to minimise vibrations, and a proper design of slide ways can minimise lipstick phenomenon.

Bed, base, column and box-type housing in a machine tool are called structure and it constitutes about 70 to 90% of the total weight of the machine tool.

**The structures of the machine tools could be subdivided by various characteristics into the** **following groups: **

**(a) By purpose: **

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(i) Beds, frames, carrying bodies,

(ii) Bases, bedplates,

(iii) Housings, boxes, columns, pillars, brackets,

(iv) Castings and covers.

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**(b) By the method of manufacture: **

(i) Cast,

(ii) Welded,

(iii) Combined cast and welded.

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This element (structure) provides the stability to the machine tool, supports the various members and maintains alignment among the moving members. The operating properties of any machine tool are determined only by the degree of rigidity of individual parts which is defined as the degree of the deformation undergone by a member for an external load.

During machining operation on the machine tool, it is subjected to bending and twisting moments and if the structure does not possess high rigidity, it may undergo appreciable deformation. Thus rigidity of various parts in a machine tool is important for ensuring the adequate accuracy of the items produced on machine tools.

Lack of rigidity also causes vibrations of parts due to elastic depression of joints during machining besides the inaccuracy of manufacture. To ensure this, it is necessary to design parts as statically indeterminate systems by employing the method of equalising the displacements.

**Element # ****2. Slides and Slideways: **

A slide is a moving element providing a straight line movement to a workpiece or tool holder at a prescribed feed rate. Slideways are provided on the machine tools to withstand heavy loads encountered during cutting action. Their purpose is also to maintain the alignment of the guided parts at all respective positions.

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The slideways may be integral with structure and thus made by casting or joined separately at the top face of the structure. It is usual to provide the slide ways either in vertical or inclined plane so that falling chips do not rest over it. It contains some form of adjustment to eliminate lay between the two members on which wear takes place.

**The main requirements to be fulfilled in the design of the machine tool slide way-bearings** **are: **

(i) Adequate load carrying capacity.

(ii) To maintain alignment of guided parts under operating conditions. The required accuracy and finish of slide ways are obtained.

(iii) Selection of proper material for minimum wear and provision for compensating any wear developed after its use over some time.

(iv) Provision for effective lubrication for minimum friction.

(v) High stiffness and less deformation under the action of cutting forces.

(vi) Chip disposal should be easy and the possibility of its getting entrapped should be minimum.

(vii) Slideways should be maintained in good condition by providing protective guards for safe guard against accidental damage.

**Material of Beds and Guides: **

The requirements for selecting guideway materials are strength, damping capacity and wear resistance. Usually semi-steel with nickel and chromium is a suitable slideway material capable of resisting wear and bending stresses. Often the bed is flame hardened by heating the top surface above the critical temperature and then quenching it at a moderate rate.

The selection of the saddle material and bed material should be such that the wear in both is equal and minimum possible. It has been found experimentally that best results are exhibited by using saddle of hardened steel and bed of flame refined cast iron. (In flame refining process, the under surfaces of the bed are pre-heated before the flame heating of the surface, thus maintaining a temperature gradient instead of obtaining full quenching). Steel slides in the form of strips, either welded to steel bed or secured by screws to cast iron bed, are also used.

Now-a-days the plastic slides backed by cast iron or steel pieces are also being extensively used because of the advantages of uniform pressure, less friction, less wear, easy fabrication and less sticking effect. Its use is however limited because of the disadvantages of non-satisfactory working at speeds above 45 m/min, less strength and hardness and the bad thermal conductivity resulting in more thermal distortion.

**Roller Guides: **

**The maximum possible load (P) that can be sustained by a guide way is given by the relation, **

P = 0.133 ZVB^{3} / h^{2}

where P = Maximum possible load in kg,

Z = Absolute viscosity in kg sec/m^{2},

V = Velocity of sliding in m/sec,

B = Breadth in metre,

h = Minimum film thickness in metre,

A = Area = L x B, or L x B = P / p

where p = Permissible pressure.

**Now-a-days the trend is towards using balls and rollers as guides in machine tools slideways in order to obtain the following advantages: **

(i) Less kinematic frictional resistance,

(ii) Less wear,

(iii) High durability,

(iv) Accuracy of movement,

(v) Operation without external hydro-dynamic lubrication which is very essential in conventional guide ways in order to produce the surface contact by thin film of lubricant between them.

However the use of the balls rollers requires a highly finished and hardened guiding surface because contact is on a curved line or a point where the waviness of the surface impairs the accuracy of the motion. To combine the advantages of both the sliding guides (as regards the accuracy of guided motion) and roller guides (as regards minimisation of friction), combined rolling and sliding guideways are designed now-a-days for various machine tools.

**Hydrostatic Bearings: **

The hydrostatically lubricated bearings utilise a pressurised fluid supplied form an external source which keeps the moving slide in floating state and thus replacing the metal to metal contact by a fluid—shear type friction.

The oil flows out through the clearances and the end of the bearing. Such bearings however do not possess very high film rigidity which can be improved by either a change in the bearing gap or the rate of flow of lubricant at different bearing pressures.

Friction in the slideways can be minimised by using hydrostatically lubricated slideways, i.e., forcing oil under pressure between the mating surfaces (Fig. 11.21). The clearance between the mating surfaces is maintained between 15 to 25 microns. Air can also be used instead of oil.

**Work Table: **

Work tables in machine tools are mostly castings, and as in the case of beds, these too must be good castings free from blow holes and sufficiently balanced for strength and rigidity. Ample provision must be made for clamping any irregular job either by provisions of standard Tee slots, or by incorporation of magnetic chucks or adjustable vices, that ensure rigid gripping of maximum area.

As mostly the work tables have to advance towards stationary cutters which are either revolving at one place as in the case of milling, grinding or boring machines; or reciprocating with no rotation as in the case of shaping and planning machines, it is necessary to ensure that the guide paths are suitably mated to the bed guideways and provision made to register accurately fine movements of the table, in all the directions including angular swiveling simultaneously avoiding backlash to the maximum extent possible.

As the accuracy of the movement of the table depends upon the lead screw or rack and pinion, it is imperative that the lead screws or pinions are made of the best suitable material and accurately machined to ensure a close running fit in their nuts or worm wheels.

A minimum hardness in the lead screws or pinions and pitch error should be controlled to very fine- limits. Phosphor bronze nuts or worm wheels are preferred as phosphor bronze ensures less co-efficient of friction and throw less strain on the finer sections of the lead screw threads or pinion teeth which are costly to replace in case of wear and tear.

In modern machines, the worktables, in addition to holding the workpiece firmly, are required to do much more. In addition to primary-axis movement, tables have rotary indexing movement, turn-on and compound rotary movement so that a rough work piece at any orientation can be easily and conveniently presented to the spindle.

Rotary table incorporates the separate drive motor, reduction gearing to the table, backlash elimination, location determination, etc. This provides the fourth axis and fifth machining axis is provided by the table tilt.

**Element # ****3. Kinematics of Machine Tool Drives: **

**The kinematic functions to be performed by any machine tool are: **

(a) To transfer motion and power from the input shaft to the output spindle.

(b) To transform motion from rotation to translation or reciprocation or vice versa.

The transmission systems for cutting and feed motions are known as ‘drives’ and are obtained by a chain of higher pairs. A machine tool is basically a mechanism that produces linear motion by slides and angular motion by spindles, all accurately aligned relative to each other.

The machine tool must be capable of maintaining these alignments both under static as well as dynamic loading conditions. The machine tools are universally driven by electric motors and further transmission is obtained by belt, gears or some hydraulic or pneumatic or electrical devices.

Selection of drives depends upon production time, surface finish and accuracy required, optimum efficiency, power to weight ratio, simplicity of design with respect to maintenance, repair and control.

**Drives for Rotational Movements: **

**In machine tools, it is very essential that arrangements for the variations of speed of spindle are provided because of the following reasons: **

(a) Machining of metals should be done at right cutting speeds.

**For this purpose different speeds are required for: **

(i) Machining jobs of same material, but different diameters.

(ii) Machining jobs of different materials.

(iii) Using cutting tools of different materials, shapes and compositions.

(b) Material is removed at approximately constant power input for different cutting conditions requiring different torque at the output.

If it is assumed that power required for feeding mechanism is negligible and that losses in the machine are also negligible, then power requirement is proportional to Torque x Velocity.

**If we have to keep power input constant, then as the output demand, i.e., torque changes then the speed should be correspondingly changed such that: **

T_{1}N_{1} = T_{2}N_{2} = T_{3}N_{3} =……… = Constant (Input power)

Thus for various values of T, the corresponding values of AT should be available on the machine tool.

**For a given input power at a definite speed and torque, the drive system may deliver power** **either: **

(a) In stepped variation, i.e., at finite number of speeds at their corresponding torque,

or (b) in stepless variation, i.e., infinitely variable output speeds within a finite range.

The ideal drive for machine tool should provide adequate number of speeds and feed rates, full power available at all speeds, power loss in drive be minimum, cutting speed and feed changes be possible without interrupting machining operation, and the drive be compact.

**Typical Layout of Spindle Speeds: **

**For designing any stepped drive first of all the following factors have to be decided: **

(a) Maximum output RPM (N max.),

(b) Minimum output RPM (N min.),

(c) Number of steps of the transference (n),

(d) The number of sub-divisions of steps, and

(e) The number of stages in which the steps are to be obtained.

**In multipurpose machines the selection of speeds is very complex, as correct speed depends upon various factors, i.e., **

i. The properties of material of job;

ii. Shape of cutting tools;

iii. ‘Form Stability’ or wear resistance of tool materials: type of operation performed and the ‘process capability’ of machine.

However in single purpose machine, the selection of particular speed depends upon the machining characteristics of that process only. In the case of cylindrical work pieces, the cutting speed (V_{c}) is related to the diameter of the work and the spindle speed (N) by the relation.

From equation (1), the minimum speed (N_{min}) of spindle is dependent upon the maximum diameter of the work that can be accommodated in the machine. It is however also dependent upon the minimum speed required for other operations like screwing or tapping.

**Again from equation (1), the maximum speed (N _{max}) is dependent upon:**

(i) The greatest possible cutting speed (V_{c}), and

(ii) When diameter is minimum possible.

For design purposes, value of minimum diameter is taken = h/8 (h being the height of centre above the bed).

Further from equation (1), it is also obvious that for constant value of V_{c}, as the diameter increases, the speed N should decrease and vice versa. The output spindle speeds generally form a series which may be in arithmetical progression (A.P.), geometrical progression (G.P.), or logarithmic progression (L.P.).

It is now obvious that for constant N, the relation between V_{c} and D is a straight line. Graphically, the relation between V_{c}, D, and N is represented by ‘Ray Diagram’ shown in Fig. 11.31.

We will now study as to which of the series is most suited in all respects for machine tools. Let us assume that a bar is to be machined on a lathe and say its diameter D varies from some minimum diameter to some maximum diameter assuming V_{c} to be constant, the variation of spindle speed with change in job diameter is shown in Fig. 11.31 i.e., initially as diameter of job increases the speed change is not much but afterwards, even for small changes in diameter the spindle speed changes rapidly.

This condition is fulfilled by G.P. series: whereas A.P. series follows a straight line and cannot fulfil this requirement. Thus G.P. series is preferred as it can provide more number of ranges of speed at lower range.

**Kinematic Advantages of Geometric Progression: **

Let the various speeds in some progression in several steps be N_{1}, N_{2}, N_{3}………, N_{n-1}, N_{n}.

Let us consider that corresponding to certain diameter D, the required R.P.M. (N) for accurate cutting velocity V_{c} is not available. Say we have to select a lower speed V_{p-1} (refer Fig. 11.33). In that case loss of speed = V_{c} – V_{p-1} and percentage loss of speed

**Max. possible speed loss in between two steps N _{p} and N_{p-1} is thus given by:**

For steeples output, ɸ —> 1 and loss of velocity in that case = 0.

Thus for a G.P. the useful value of common ratio lies between 1 and 2 i.e., 1 < ɸ < 2.

**The value of ****ɸ**** is generally selected according to preferred numbers which have the following advantages: **

(i) Unnecessary variations are avoided resulting in economy to both maker and producer.

(ii) The use of standardised main dimensions of motors and shafting is possible.

(iii)The dual system can be utilised along with decimal progression. According to Renard series, the most commonly used ratios are 1.12, 1.26, 1.41, 1.56 and 2.

Sometimes ‘Androin Progression Ratio’ is also used, according to which the series in;

**Evolution on Preferred Numbers: **

Preferred numbers are nothing but a series of numbers in a geometric progression (G.P.), specially selected, to be used for standardization in preference to any other random number.

It has been established statistically and by experience that discrete increment of a particular measure, if maintained in geometric progression gives a logical, uniform and proportionate characteristic variation pattern same has also been proved in practice.

According to it if ‘a’ is basic term, after every fifth step of the series, a tenth multiple of the basic term ‘a’ should occur.

If terms be rounded off for the sake of convenience and ‘a’ is a power of 10, positive, zero or negative, (a = 10^{x}, where x = 0, positive or negative integer), then the following series for a = 10 will be obtained.

10, 16, 25, 40, 64, 100 etc., which may be continued in both directions.

From this series, designated by the symbol ‘R’ (as a tribute to Captain Renard, the first man to use preferred numbers), series R 5, R 10, R 20 and R 40, were formed, each adopted ratio being the square root of the preceding one, viz.

**Basic Series of Preferred Numbers: **

These are rounded off numbers of geometric progression R 5, R 10, R 20, R 40, and sometimes R 80. Any series can be extended infinitely upwards or downwards by multiplying or dividing repeatedly by 10.

**Derived Series of Preferred Numbers: **

These are got by selecting every pth term of the Renard series, ‘p’ being the pitch of the series. The ratio of the derived series = 10^{p/r} where r = index of the basic series (5, 10, 20, 40 or 80).

**Important Properties of Preferred Numbers: **

**General:**

1. Unlike any other progression, a geometric progression provides numbers close to each other at the lower end and as the magnitudes of the numbers increase they are more widely spaced. This is exactly identical with the requirement of a series of grading articles in practice.

2. Preferred series are simple and easily remembered.

3. They are unlimited towards the lower as well as higher numbers.

4. They include all the decimal multiples and sub- multiples of any term.

5. They provide a rational grading system.

**Mathematical: **

1. The products, quotients, powers and roots (if the root does not become less than the ratio of progression) of a preferred series are also terms of that series.

2. All the multiples and sub-multiples of the numbers 2 and 10 are included in preferred numbers.

3. Any equation of nth degree (n > 1) can be converted to one of first degree with the use of logarithms of preferred numbers and any curve can be plotted as a straight line which is always simple and reliable for calculations.

4. The number 3.15 = π, i.e., 3.1416 is found in R 10, R 20, R 40 and R 80. So the circumference and arc of circles whose diameters are preferred numbers can also be expressed in preferred numbers. This applies in particular to peripheral speeds, cutting speeds, cylindrical areas and volumes, spherical areas and volumes.

5. R 40 series includes the numbers 3000, 1500, 750 and 375 which have special importance in electricity viz., the synchronous speeds of rotating machinery for the standard frequency of 50 cycles per sec.

**Saw Diagram for Machine Tool Spindle Speeds: **

The limits of cutting velocities (V) in a machine tool are decided by the required minimum life of tool for maximum velocity (V_{max}) and lower economically justifiable velocity for minimum velocity (V_{min}).

We have V = (πdN / 1000) m/min.

where d = diameter in mm, N = R.P.M.

For a constant value of N, V ∝ d and we get a straight line graph. A particular R.P.M. “N_{1}” limits the diameter to be turned which should not be > d_{1} and also d should not be < d_{2}. If d becomes < d_{2}, then maximum and economical velocity N_{2} (where N_{2} > N_{1}) must be used.

**In general, we have **

In other words, in a range of spindle speeds which allows each diameter to be machined with a cutting velocity not more than V_{max} and not less than V_{min} the available spindle speeds must be arranged in a G.P. with the ratio ɸ = V_{max} / V_{min}.

On this basis, standardization of machine tool spindle speeds and feeds is achieved with the use of preferred series and such a standardization is valuable not only for the designer of machine tools, but it is more important for the Production Engineer as it enables him to rely on identical speeds (or feeds) being obtainable on each of the machine tools at his disposal.

**Number of Spindle Speed Steps: **

It is usual to select the number of speed steps (n) such that it is factor of 2 and 3,

i.e., n = 2^{A1} 3^{A2}

where A_{1} and A_{2} are whole numbers. While this requirement is met by the values n = 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, the frequently used values are 3, 4, 6, 8, 12, 18 and 24.

The number of spindle speed steps is obtained by cluster of gears comprising 1, 2 or 3 gears or by pulley blocks of 2, 3 or 4 pulleys.

**The number of spindle speed steps (n) is related to the ratio N _{max} / N_{min} and common ratio ɸ**

**by the following:**

The ratio N_{max}/N_{min} is called range ratio. Its value is 40—60 for lathes and boring machines, 40 for shapers, 3 for planers and slotters, 80—100 for capstan lathes, 20—30 for drilling machines, 30—50 for milling machines, and 1—10 for grinders.

Fig. 11.35 shows the relationship between speed ratio N_{max}/N_{min}, number of speed steps (n), and common ratio (ɸ) of the speed series.

The values of N_{max}/N_{min} and n depend upon factors like—Purpose of the machine tool, nature of the manufacturing process, properties of work piece material, and required degree of versatility of the machine tool.

**Kinematic Relationship in the Spindle Drive: **

Derived number of spindle speeds is usually obtained in 2, 3 or 4 steps.

This is achieved by consecutive engagement of transmission groups, the drive being through a compound gear train.

Number of spindle speeds (n) is obtained by consecutive engagements of transmission groups. The number of total spindle speeds is the product of the number of simple gear trains in each consecutive group. For example for the drive shown in Fig. 11.36.

n = 3 x 3 x 2 = 18

When consecutive gear trains of transmission are engaged, the total transmission ratio of the drive is equal to the product of the transmission ratios of the simple trains that make up the drive.

It is a common practice to limit the transmission ratio of gears in a gear box in order to avoid excessively large diameters of the driven gears. The commonly used maximum and minimum values of transmission ratio are 2 : 1 and 1: 4 for spur gears and 2.5 : 1 and 1 : 4 for helical gears.

**Basic Rules for Layout of Gear Boxes having Sliding Clusters: **

**The following rules apply for design of gear box having sliding clusters: **

(i) The transmission ratio in a gear box is limited between 2 : 1 to 1 : 4.

(ii) For stable operation the range ratio N_{max}/N_{min} of any stage is limited to 8.

(iii) One set of gears must be completely disengaged before the other set begins to come into mesh.

(iv) The axial gap between two adjacent gears must be equal to at least two gear width. Thus for a 2-step stage, the total space requirement along the axis is 4 w, where w is the width of one gear.

(v) The sum of teeth of mating gears in a given stage must be the same for same module in a clustered set.

(vi) The minimum difference between the number of teeth of adjacent gears must be 4.

(vii) The minimum number of teeth in a set of gears for spindle drives should be greater than 17.

(viii) Least number of shafts, gears and levers should be used.