Controlling a machine tool
INTRODUCTION TO CNC MACHINES
Controlling a machine tool by means of prepared program, which consists of blocks, or series of commands/numbers, is known as numerical control. Numerical Control [NC] for machine tools was introduced in 1950 by Prof. John T Parsons. The first CNC machine was built at the Massachusetts institute of technology [MIT] in 1953 by joint efforts of US Air force, MIT and the Parsons Corporation.
The CNC machine basically entails three main regions:-
- The control system
- The drives (driving elements) and
- The machine tool
CLASSIFICATION OF CNC SYSTEMS: The classification of CNC machine is shown in below tree diagram.
Three axis CNC machine:
- In 3-axis CNC vertical machine, the working table moves along x- and y-axis, and the tool along z-axis.
- In machining, tool orientation is fixed, either in vertical or horizontal direction.
- If all surfaces to be machined are accessible by the cutter in one setup, a 3-axis CNC machine is used
Five axis CNC machine:
- X-, Y-, and Z- Axis Motions and A- and B- axis Rotations (Simultaneously)
- Tool orientation can be changed simultaneously during machining.
- If some surface patches to be machined are not accessible by the cutter in one setup, a 5-axis CNC machine is used.
The below report is on Arrow series 2 VMC which is a three axis machine
Arrow Series 2 vertical machining centres
The above mentioned have been fitted with an array of productivity options by manufacturerCincinnati Machine, high-speed spindle is available on Arrows equipped with the Siemens Acramatic control. The motor-driven spindle with HSK 63 tooling provides excellent balance and vibration-free performance. Generous torque capacity ensures high performance in semi finishing hardened steels and machining aerospace materials that involve high metal-removal rates.
Specifications: Arrow 2 VMC has User-friendly interface design; customized GE Fanuc 18i-M CNC control. This control employs the latest Pentium technology to support future upgrades and enhanced with graphical simulation.
The x-y-z travel of Arrow Series 2 centres provides a work envelope as large as 3,048 x 762 x 770 mm for work pieces weighing up to 3,000 kg. Linear-scale feedback standard on the x- and y-axes maintains positioning accuracy and repeatability of ±3 µm and ±1 µm, respectively, across the entire travel range. Below is shown look of machine.
Topics covered by report:
The report covers chapters which have got all the necessary areas that give a clear understanding of CNC machine tools and their application.
Chapter one covers “resolution, repeatability and accuracy when applied to CNC machine tool topic”. Chapter two describes “the basic structural element of a machine”. Chapter threeis focused on the cutting process, cutting forces and describes the phenomenon of Chatter and BUE. Chapter four analyses Error occurring during cutting tool and workpiece and introduction for BUE. Chapter five explains need for geometric and thermal calibration of machine tools. Chapter six deals with active and passive vibration control techniques and related explanation for cause and compensation of vibrations in machine. Chapter seven describes methods of compensating geometrical errors in machine tool it covers techniques of laser interferometer, ball bar systems and related topics. Chapter eight provides explanation of CNC machine tool axis drive. With block diagram of a typical CNC Machine tool axis drive, the components of it are briefly explained. Chapter 9 explains the Interpolation technique, some part of programming and feed rate optimization method.
1. Define Resolution, Repeatability and Accuracy when applied to a CNC machine tool
Definition 1:  Defines the term resolution refers to the smallest increment or dimension that the control system can recognise and act upon, this is not the same as accuracy.
Overall resolution is that of the fine devices multiplied by its number of cycles in the complete range of motion of the slide.
Definition 2:  Defines resolution is as the error of mobility or the smallest generable movement. In servo control, it is defined as the smallest value (digital, analogue) the sensor can indicate (noise level).
Definition 3:  describes the smallest possible movement of a system. Also known as step size, resolution is determined by the feedback device and capabilities of the motion system.
Typically CNC machine tools have resolution of 0.0025nm or better
Resolution plays a prominent role in accuracy of machine tools and leading to cause major repeatability errors.
Definition 1: It is irreproducible errors in bearing or leads screws and is the limit of accuracy attainable in a particular machine.
While calculating the accuracy component will be considered correct if its dimensions lie anywhere within tolerance band. If a certain slide position is commanded many times in succession, there will be a drift, or scatter in the positions actually taken up by slides .This scatter is a measure of repeatability of system.
Definition 2: Repeatability is the ability of a motion system to reliably achieve a commanded position over many attempts. Manufacturers often specify unidirectional repeatability. This is the ability to repeat a motion increment in one direction only. This specification side-step issue of backlash and hysteresis, and therefore is less meaningful for many real world applications where reversal of motion direction is common.
Definition 3: Repeatability may be defined as value below which the absolute difference between two single test results obtained under same conditions
A typical repeatability specification for a CNC machine would be + or - 0.005mm.
Definition 1: The smallest unit of movement that a machine can consistently and repeatedly discriminate.
Absolute accuracy = on axis accuracy Abbḗ error
Definition 2: machine accuracy is the accuracy of the movement of the carriages and tables. This is influenced by:
- The geometric accuracy of the alignment of the slide ways
- The deflection of the bed and other features due to load
- Any temperature gradients existing though the machine
- The accuracy of these screw thread of any drive screws, and the amount of backlash(lost motion)
- The amount of twist (wind-up)of the shaft which will influence the measurement of rotary transducers (last motion)
- The responsiveness and accuracy of the control system
Wear of moving parts.
Definition 3: Accuracy is the absolute, steady state deviation of a control variable from a specified set point, while consistency indicates the deviation exhibited by the steady -state value after the transient process caused by disturbance variables have settled. Consistency is generally more important than accuracy.
Example: A speed is to be maintained at 200rpm. The actual speed, however, is only198 rpm. The accuracy is accordingly (198-200) rpm= -2rpm.
Describe briefly the basic structural elements of a CNC machine.
The structure of three axis vertical milling machine is shown in below diagram
From above diagram we can notice basic structural elements of CNC machine are Bed, table, column, spindle, slideways, guideways, ball screw, motor, encoder and nut (which are considered as elements of feed drive axis).
2.1 Description of basic structural elements
Let us have brief description on basic structural elements as listed above
It is the means of holding and moving the work and tool. It comes under the linking structure and generally made up of cast iron. it supports the table mounted on base guideways, this structure can be clearly understood by the diagrams shown further . It is transverse in longitudinal direction which is X axis.
It is placed upon the saddle for the purpose of holding the work piece and moving it in desired position in X axis on commanding. It is made up of cast iron.
This is vertical orientation made of cast iron, with column it is possible to move head up on down and perform the process of cutting or milling.
Rotating spindle: all work or tool carrying spindles rotating aped are subjected to deflection and thrust forces depending on nature of work being performed. To increase stability and minimize torsional strain on the spindles they are designed to be short and stiff as possible, and the final drive to the spindle is located as near to front bearing as possible. It is basically categorized into two types they are Brush type and Brushless spindles or AC spindles, Rotational movements are controlled by the spindles by circular bearings. 
It has the Y axis motion perpendicular to X axis in the CNC vertical milling machines and this saddle is mounted in between the bed and table. It is made up of solid cast iron. 
2.2 Elements of a feed drive axis.
Let us have brief description of above shown elements
A slideway is used to control the direction, or line of action, of the translational movements of the carriages or table on which the tools or work are held.
The alignment of the slideways to each other and to the axis of spindle is critical. The shape and size of the work produced depends not only on the accuracy of the amount of movement, but also on the direction of the relative movements of the tool and the work. There are different forms of slideways such as cylindrical, vee, flat and devotional. 
Linear bearings with balls, rollers or needles:
Because of the problem of metal to metal contact the relative high amount of friction is generated, which exits between the faces in contact, typically 0.15 for lubricated steel sliding on steel. A number of machines have flat roller bearings fitted to the carriages to provide a rolling motion rather than sliding motion. The rollers are in contact with the guideways machined on the bed of the machine.
To reduce the problem of machining an accurate form on the bed of the machine, hardened steel rails with special guide forms (figure....) may be bolted on the casting of the machine tool. 
Actuating mechanisms: (Screw and nut)
Of all elements of CNC machine tool, the efficiency and responsiveness of actuating mechanisms (drive unit) have the greatest influence on accuracy of the work produced.
For the efficient drive unit there are number of essential requirements:
- The drive must be stiff and responsive.
- There must be virtually no backlash in the drive
- The drive must be free running with the low temperature rise.
- There should be freedom from high frequency vibrations.
The actuating mechanisms are provided by screw and nut; rack and pinion; and ram and position.
Screw and nut: These are effective for short to medium length (100 mm to 8m) movements. There are types of screw and nut used on CNC machines which provide low wear with continued accuracy over a long life, reduced friction and smooth action, higher efficiency and better reliability. These are recirculation ball screw and hydrostatic screw.
Recirculating ball screw: For the open loop and closed loop systems, recirculation ball screw is widely used. The thread form used with these screw is shown in below figure and is known as ‘Gothic arch' the balls rotate between the screw and the nut at the same point they returned to start of the thread in the nut. There must be minimum backlash in the screw and nut. 
Motor: The motor are of two types which are servo motor or stepper motor. The servomotor is a standard DC motor which is coupled with some feedback to detect position errors; they are much cheaper compared to stepper motor. The stepper motor does not have a commutator. It is controlled by selectively turning the coils on and off. 
Encoder:itis a transducer which provides series or parallel digital value of linear or angular movement. It is used to measure the position of X, Y and Z axis. Encoders are basically of two types they are absolute encoders and pulse generators. The absolute encoder monitors table position.
Study methods for improving machine tool performance during machining process.
The need to continually improve on machining process necessitates the identification and modelling of all factors that affect product quality in the machining process. Machine tool vibration during machining has been a focused area in the manufacturing community. A typical example of vibration would be the boring machining process where the slender boring bar is susceptible to vibration. It is often that vibration is observed which is contributed by both the low rigidity of the work piece and low rigidity of the tool post structure.
There are two types of vibration which are usually associated with turning operations, forced and self-excited. Forced vibrations can be caused by many factors, including the vibration of the lathe itself at different resonance frequencies. Non-continuous circular cross sections of the work piece being machined will also result in forced vibration. Discontinuous geometry, such as holes, key ways and slots which are located on the circumference of the cutting edge and the work piece every time the tool passes over the discontinuity and starts to engage in cutting again. An example of this would be turning a square piece of the stock to make a round extension or a grooved (keyed) bar. The impact of the edges on the tool will cause vibratory motion of the tool. 
Self excited vibration, also called chatter, is usually caused by the material removal process itself. There are several factors which can influence this. An example, the cutting tool experience a phenomenon called built-up-edge, or BUE, during machining. As illustrated in below figures 1,x and 1.x, the presence of BUE may cause variation of the effective rake angle during machining. A large height of BUE introduces a large effective rake angle, leading to a low cutting force, and vice versa. Such variation if the cutting force can cause tool vibration in a self-excited mode. In cylindrical turning operations, chatter is frequently encountered during the machining of long slender bars. The deflection of bar in the thrust direction increase while the tool moves to the middle of bar and may initiate the primary or regenerative chatter, leading to self- excited vibration of the workpiece.
A non-homogeneous distribution of the micro hardness in the workpiece material can also cause chatter. Because of the difference in hardness of the microstructure, the presence of different phases of different phases in the microstructure leads to the cutting force produced during machining to vary instantaneously.
To reduce the effect of chatter, it is usually assumed that by increasing the stiffness of the cutting tool, chatter will be diminished. On the other hand, damping of the entire carriage and of the toolpost holder also reduces chatter, but at the expense of accuracy. Fundamentally, chatter is caused by a lack of adequate dynamic stiffness in the machine structure, which can be traced to lack of inherent damping in the structures.
A typical stability chart for machine tool is used by many researchers is shown in below figure three borderlines of stability can be identified which for classification purpose will be called lobed, tangent and asymptotic. The lobed borderline of stability is the exact borderlines are very difficult, and many factors complicate the usefulness of the stability charts. However, stability charts present a general picture of vibration patterns observed during machining.
Analyse the errors occurring between the cutting tool and work piece
Metal cutting is the process of removing material from a workpiece in the form of chips using single- or multi-point cutting tools with an absolute defined geometry. To some extent, the performance of a cutting tool determines the cutting behaviour and the process capability. In order to adopt a design of high performance cutting tools, it is important to understand the tool- workpiece interfaces, the mechanism of surface generation, forces generated between them and the errors occurring between cutting tool and workpiece. 
4.1 Cutting force-induced errors:
- Vibration: the transmission of the vibrations generated during the cutting action can excite some of the eigen-freqencies of the machine components. Isolation measures or component redesign can significantly reduce these parasitic shifts.
- Material instability errors: most of the no ceramics materials have the tendency to leap from an unstable to stable, including variations in geometry. Hence, it is important to use heat treated components to secure increased stability.
- Instrumentation errors: unwanted sensor errors can occur when the measurement loop is not separated from the force loop. Abbe errors would be amplified for larger Abbe offsets.
- Cantilevered loading errors: when a cantilevered load is placed on translation stage, non symmetrical moment loads are created. Shear and bending forces include deflection in the stage structural elements. In an X-Y assembly, the cantilevered load acting on the lower axis increases as the load traverses to the extremes of the upper axis. A position error in the Z direction occurs due to a combination of Y-axis deflection and X-axis roll.
- Tool deflection: one of the major causes of machining error is cutting deflection of the tool shaft due to cutting force. This error is observed especially when small diameter mill cutters are being used. This error can lead to contouring in accuracies that are negligible.
The surface roughness plays a prominent role in cutting tools; theoretically surface roughness can be achieved only if the all irregularities, such as built-up edges (BUEs), chatter and inaccuracies in the machine tool movements are eliminated completely. However, this cannot happen in practice. It is impossible to achieve the above -mentioned perfect conditions. One of the main factors contributing to actual surface roughness is the occurrence of built-up edges, which deteriorates the theoretical tool-workpiece replication. The larger the built-up edge, the rougher is the surface produced.
4.2 Built-up edges (BUEs):
Causes of formation:
In machining ductile metals like steels with long chip-tool contact length, lot of stress and temperature develops in the secondary deformation zone at the chip-tool interface. Under such high stress and temperature in between two clean surfaces of metals, strong bonding may locally take place due to adhesion similar to welding. Such bonding will be encouraged and accelerated if the chip tool materials have mutual affinity or solubility. The well-meant starts forming as an embryo at the most favourable location and thus gradually grows.
With the growth of the BUE, the force, F (shown in Fig. 5.11) also gradually increases due to wedging action of the tool tip along with the BUE formed on it. Whenever the force, F exceeds the bonding force of the BUE, the BUE is broken or sheared off and taken away by the flowing chip. Then again BUE starts forming and growing. This goes on repeatedly.
Characteristics of BUE
Built-up-edges are characterized by its shape, size and bond strength, which depend upon:
- work tool materials
- Stress and temperature, i.e., cutting velocity and feed
- cutting fluids application governing cooling and lubrication.
Effects of BUE formation:
Formation of BUE causes several harmful effects, such as:
- It unfavourably changes the rake angle at the tool tip causing increase in cutting forces and power consumption
- Repeated formation and dislodgement of the BUE causes fluctuation in cutting forces and thus induces vibration which is harmful for the tool, job and the machine tool.
- Surface finish gets deteriorated
- May reduce tool life by accelerating tool-wear at its rake surface by adhesion and flaking Occasionally, formation of thin flat type stable BUE may reduce tool wear at the rake face.
Chatter is an abnormal tool behaviour which it is one of the most critical problems in machining process and must be avoided to improve the dimensional accuracy and surface quality of the product. It causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality, it inessential to detect and prevent its occurrence.
A varied uncut chip thickness in the cutting process induces variations in the cutting force, which repeatedly induce tool vibration. This phenomenon is called the regenerative effect and is a major source of chatter
4.4 Other factors affecting the surface finish:
a) Dynamic errors in the machining variables, including cutting speed, tool feed, and depth of cut, which are mostly caused by the machine movement errors; b) cutting tool geometry errors, including initial geometrical errors and errors due to tool wear; c) work piece material heterogeneity, such as grain boundaries, impurity and existing defects etc; d) tool-work piece interface conditions, including cooling tool, and machine tool chatters, due to these factors, the actual surface roughness.
Among the above factors, the geometrical error of cutting tools has the most direct effects on surface roughness and plays an important role in determining the quality of the surface. Some geometric factors which affect achieved surface finish include nose radius, rack angle, cutting edge angle and cutting edge sharpness and evenness. To design and fabricate high quality and wear-resistance cutting tools is the first step for high quality machining.
Explain the need for geometric and thermal calibration of the machine tool
5.1 Geometric errors:
Usually these errors constitute the largest source of inaccuracy and are dominant under machine cold-start conditions. Their usual sources are
- Within the machine due to design
- Inaccuracies built-in during assembly
- Results from tolerance of components used on the machine
- Concerned with quasistatic (thermodynamic process) accuracy of the motion surface relative to each other
And their characteristics are smooth and continuous, can exhibit hysteresis and random or systematic behaviour.
5.2 Need for geometric calibration of machine:
There is clear need for some kind of “shape tolerance” to the limit the amount of geometric inaccuracy in component shape and form. Such tolerances are known as geometrical tolerances and are the subject of BS308 PART III (engineering drawing standards).
Geometrical calibration should be applied to CNC machine for all requirements which are critical to function or interchange ability. However, if the machinery and techniques used in the production of components can be relied upon to produce the required standard, then geometrical tolerance need not be specified. CNC machining applications generate curves by a series of discrete steps via circular interpolation. Geometrical tolerance may thus have particular relevance when dimensioning curved features.
5.3 Thermal errors:
The thermal error accounts for 40%-70% of the total dimensional and shape errors in precision machines. It is more effective to compensate for thermal errors rather than using expensive and high precision components for the machine construction. Thermal errors could have either quasistatic or dynamic behaviour. The possible origins are known here:
- Environmental temperature changes
- Heat from cutting action and swarf (Fine metallic filings)
- Heat from bearings
- Gears and hydraulic oil
- Drives and clutches
- Pumps and motors
- External heat sources
- Heating and cooling provided by cooling systems
- Thermal memory from previous conditions
5.4 Need for thermalcalibration:in order to come over this below mentioned errors thermal calibration is required.
- Spindle axial growth: heat induced into the spindle will cause a thermal axial expansion thus lifting the tool position in the Z-axis.
- Spindle axial drift: heat will cause a radial expansion of the spindle combined with a radial drift of the spindle axis in X-axis or Y-axis. This is a result of the complex effect of heat to the spindle bearing and structure.
- Spindle displacements holder deformation: the thermal distortion of the spindle will cause two inclination angles around the X- and Y-axis. thus two errors components of the tool tip will come up in X- and Y-axis.
- Expansion of the lead screw drive: the heat produced on the lead screw as a result of friction on the bearings and the screw nut will include thermal positional errors.
- Expansion and bending of machine column: the machine column can have several distortion modes depending upon the pattern of heat distortion in it. In general this will include a volumetric error vector.
- Expansion and bearing of machine bed: this can have a serious effect over positional, angular, squareness, parallelism, etc.., accuracy of the machine bed for 3- axis milling machine, these errors can cause large Abbe error components and must be searched along the X and Y axis drives.
- Workpiece thermal deflection: the heat generated from the cutting action can significantly deform the work piece in complex 3D modes, especially for the thin walled components or hard-cut conditions.
- Thermal parasitic errors: the heat distribution in a machine cannot be precisely predicted thus there can be some special conditions which affect drive components, thus causing unexpected parasitic errors.
Describe existing methods for passive and active vibration control.
Vibration control is the use of a sensing device to detect the level of vibration in a system and an actuation (forcing) device to apply a forcing to the system so as to counteract the effects of vibration. In some such devices, the sensing and forcing functions are implicit and integrated together. The nature of vibration may be clearly flexural or torsional or longitudinal.
Vibration control may be subdivided into the following two broad categories.
- Passive vibration control
- Active vibration control
6.1 Passive vibration control:
Passive vibration control involves modification of the stiffness, mass and damping of vibrating system to make the system less responsive to its vibratory environment, as the name passive control is specified the passive elements are used such as masses, springs, fluid dampers or damped rubbers.
6.2 Active vibration control:
Active control systems do not require external assistance they depend essentially upon a source of power to drive ‘active device' which may be electro mechanical, electro hydraulic or electro pneumatic actuator. They depend upon sensors on the structure which detects the vibration, upon computer which process signals and upon power amplifiers which receive the processed signals and drive the actuators to reduce vibration.
Generally active vibration control methods are necessarily more costly than passive methods, but some problems are so intense that active vibration alone can cure them.
6.3Methods for passive vibration control:
- There are four basically different approaches
- Vibration control by structural design
- Vibration control by localized additions
- Vibration control by added damping
- Vibration control by resilient isolation
The most commonly adopted method for passive vibration control is done by vibration absorbers and dampers let us have brief description on methods
Un damped Vibration Absorber:
It is possible to reduce the unwanted vibrations by extracting the energy that causes these vibrations. The extraction of this energy can be established by attaching to the main vibrating system a dynamic vibration absorber, which is simply a spring-mass system.
Figure 6.1: two types of application of a vibration absorber; (a) reduction of the response to forcing excitation for reducing the force transmitted to the support structure, (b) reduction of the response to support motion.
A vibration observer may be used for vibration control as shown in above figure. Here the primary system whose vibration needs to be controlled is modelled as an undamped, single-DOF- mass-spring system the objective of the observer is to reduce the vibration response of the primary system as a result of a vibration excitation f (t). But the force that is transmitted to the support structure, as a result of vibratory of the system is given by
The frequency domain equation for the system is given by
Thus if the absorber is tuned so that its natural frequency is equal to the excitation frequency, the primary system will not undergo any vibration and hence is perfectly controlled.
Hence from above we can state the following characteristics of un damped vibration absorber
- It is effective only for single excitation frequency
- for best effect, it should be “tuned” such that natural frequency is equal to the excitation frequency
- The amplitude of motion of observer is proportional to the excitation amplitude and is inversely proportional to absorber stiffness.
Now from formal analysis, considered transfer function of an undamped vibration absorber can be written as
G (ω) =
Vibration dampers are dissipative devices. They accomplish the function of vibration control through direct dissipation of vibration energy of the primary (vibrating) system. As a result, however, there will be substantial heat generation and associated thermal problems and component wear.
Consider a vibrating system that is modelled as an undamped single-DOF mass-spring system (simple oscillator). In this case the magnitude of excitation response transfer function will be a resonance with theoretically infinite magnitude hence acts as a destructive system therefore adding a simple damper as shown in below figure will correct the system. Hence equation can be written as
mӱ- bẏ+ ky-f(t)
The transfer function of system with absorber is given by
µ is absorber mass or primary system mass, ρ is absorber natural frequency or primary natural frequency, r is excitation frequency or primary system natural frequency. 
6.4 Method for Active vibration control:
A schematic diagram of an active vibration control system is shown in next page. In this process the dynamic system whose vibrations need to be controlled is monitored and its response is measured using sensors for feed back into the controller then the sensed signal is compared with desired response and error to generate proper control signal. Where as in open loop control system there is no sensor and feedback but both feedback and feed-forward schemes may be used in same control system.
During process of vibration control the actuators receives control signal and drives the system with external components for control actuation and signal conditioning will be needed to convert control signal to a form which is compatible with existing actuator. The digital signal is converted into analog signal with digital to analog converter and that analog signal is to be amplified and filtered hence power source is required to condition signal causing major difference between passive and active systems.
In feedback control systems, sensors are used to measure the response that enables the controller to determine whether it is operating properly. A sensor unit that senses the response may automatically convert (transducer) this measurement into suitable form. After conditioning the signal it is converted into analog.
Examine the types of equipments and their purpose when used for the geometric calibration of machine tools
Various equipments used for machine tools calibrations are listed below
Laser, straight edge
Laser, Talyvel and two dial gauge
Granite square artefact and dial gauge , ball Bar and laser (optical square, diagonal test)
1.1 Table: various equipments used for machine tools calibration (lecture notes Dr. c. Pislaru 2010)
7.1 Laser interferometer:
Explains Laser interferometer is the key instrument used to access a number of geometric errors in machine tools.
The purpose of the equipment is to inspect a CNC machining performance by characterizing its axes in terms of positioning, repeatability, lost motion and the affects of Abbe - offset during calibration. Main objectives that can be achieved by this laser interferometer are
- To determine the positioning accuracy performance of an axis of a CNC machine tool
- To identify possible causes of accuracy degradation.
Below is the configuration to measure the straightness
- the laser interferometer is set to take readings along x-axis of the CNC machining center with MDSI open CNC controller at a height to the table surface as shown in above figure
- target positions: 30mm equally spaced target positions are selected over a stroke of 480 mm. Five runs in each direction along the x-axis
- Positions at previous targets over the stroke are recorded for several runs with out any compensation values in the CNC controller.
- Wavelength compensation: since the wave length is dependent upon reflective index of the air, it is necessary to compensate for environmental conditions. Air temperature, pressure, and humidity are recorded to obtain wavelength compensation using Elden's equation
- Error data is obtained by plotting the specifications
- Using Talyvel electronic level, the pitch motion of x-axis at 30mm intervals is measured to evaluate possible Abee error corresponding to that axis.
7.2 Ball Bar system:
The purpose of ball bar link is to characterize circular motion provided by either a milling machine with the combination of two axes, or, in the lathe machine. It is expected to verify the eccentricity and geometric errors such as squareness and deformation errors.
The main objectives that can be achieved by ball bar system is
- To investigate the contouring characteristics of a CNC Machining Center.
- To investigate silent features of the contouring/polar results in respect of error sources of the machine.
- A 100mm kinematic ball bar system complete with calibrated setting bar is used with the quick setting sleeve from the hardware. The center of the two reference spheres coincide with each other in the center of the x-y reference plane of the machine.
- The machine is programmed to produce a 360 degree clockwise circle with a 100mm radius and a feed of 1000mm/min with a tangential approach to the start point and a tangential exit. The start and exit point was at 202 degrees in the xy plane.
- The above point is repeated
- And the 1000mm/min is changed to 4000mm/min in above step
- Measured results are displayed on pc and observed the last motion (backlash) in the x- and y- axes using the software.
Talyvel Electronic Level systems provide versatile and precise measurement for a wide variety of industrial; they combine exceptionally high accuracy, stability and repeatability with fast response and operational convenience. Used for measuring straightness, flatness or absolute level.
Some applications for which Talyvel systems have become universally accepted:
- Checking slideways for straightness and twist
- Checking columns for squareness to slideways
- Checking the surface plates for flatness
- Monitoring the settlement of large machinery
- Measuring the camber on rolls
It consists of two systems
- Level unit
- Display unit
Level unit: This unit offers stable, high accuracy measurement. Its pendulum type transducer is suspended on wires and is silicon oil damped to reduce the effects of mechanical vibration during measurements. This unit incorporates a clamp knob which, when screwed in, secures the pendulum during transport.
Display unit: This unit is powered by mains. A selector switch allows results to be displayed as angle in arc seconds or as a gradient in mm/metre or 0.001 in/in. The display also flashes to indicate an off scale condition. An analogue meter indicates the direction of tilt of the Level Unit (eg for setting Micro Alignment Telescope line of sight horizontal) and can be switched to a fine ±10 second range, which is very practical when setting to gravity. A “Low Bat” signal indicates the need to recharge the batteries. There is also a damping switch to
Smooth/average out the measurement reading. Standard 3.5m cables are supplied with
Talyvel 5; optional extension cables enable Talyvel 5 to be used at distances up to 100 metres (300 feet) from the Level Unit. This distance can be further extended to 800 metres (1/2 mile) by using cables with a built-in signal strengthening amplifier.
The front panel also incorporates an adjuster to set the display reading to zero for one Level Unit (A). The adjustment operates over approximately ±60 seconds. For absolute level indication the adjustment is set to zero.
In many systems Calibrated artefacts (an aluminium hole plate and a vertical detachable artefact), previously calibrated on a coordinate measuring machine is considered. The artefacts are measured on the machine tool and the coordinate points are transferred via serial interface, to a portable computer where software acquire and process these points, comparing them to the calibrated values.
As a result, the errors of positioning, straightness and squareness are measured, attesting the machine tool accuracy. These errors can be easily formatted to update the error compensation table and process table at the CNC, enhancing the geometric behaviour of the machine. The software also gives report of the errors, monitoring the machine accuracy condition. 
Below is figure of system in which artefacts are used to calibrate the geometric errors
Provide a block diagram of a typical CNC machine tool axis drive system with a brief description of its constituent components and their function. Postulate the parameters and physical elements that affect the static and dynamic accuracy performance
8.1 Description of its constituent components and their function:
Describes that a machine tool axis drive consists of three major blocks. CNC controller block, axis actuator, mechanical system
The components shown in block diagram of machine tool axis drive system are:
Position control summer, controller, speed summer, pre amplifier, current loop sum, amplifier, speed summer, dc motor, load model, tachometer, encoder,
Let us have a brief details about the elements and there functions
controller model: the block diagram of an analogue controller is shown below
The demand feed rate and positions are represented mathematically as a reference pulse frequency and a reference pulse stream duration respectively, the calculation block, Embedded within the controller, monitors the motion control of the machine tool using linear and circular interpolation routines. The position demand signal (X c) with the machine feed back position encoder signal (X m) .the encoder is modelled as a constant (K enc) converting motor angular velocity to a pulse frequency, the difference between two signals is called error ε and is sent to control the machine tool motion system through a digital to analogue converter simultaneously, the controller is capable of generating a velocity feed forward (VFF) output to aid response.
The error is multiplied by the gain of the position loop K v and is converted into a velocity value .this is summed algebraically with VFF and the result is transformed into a digital value in the range ±10v.
Digital to analogue (D/A) converter has the role to transform a digital dimensional signal into an analogue signal. The main advantage derived from the controller of a modern CNC machine tool being a digital computer are:
- Many loops can be controlled or compensated through time sharing
- Changes in software allow parameter alterations to be made in order to achieve the desired control response
- The controller is able to perform supervisory applications.
Pre-amplifier and amplifier models:
Below is shown the possible diagram of servo amplifier considering the connections with other components of the DC drive
The output of the D/A converter (±10 v) is compared with the output of the tachogenerator and the voltage difference is amplified by the servo amplifier. This has two components:
The pre-amplifier (PA)- consists of an operational amplifier sensitive to the difference between signal generated by the D/A converter and the tachogenerator feedback and providing voltage amplification.
The power amplifier- supplies the DC motor with the required value of armature voltage. The armature voltage will be stabilised whenever the voltage difference at the input of a PA reaches zero. This will ensure correspondence between the rotational speed of the DC motor and the reference signal generated by the D/A converter.
The two components yield good DC gain for steady -state functioning and a large bandwidth for a good transient response. The pre-amplifier works with low voltage (± 15 v) and low current (1mA) while the power amplifier needs high voltage(110 v) and high current (60A).
The below is shown the block diagram of DC motor
Figure 8.4: block diagram of DC motor
The motor used is permanent magnetic motors (PMM) which has many advantages over other types of motors like
Linear available torque-speed characteristics, high stall torque, reduced frame size and lighter motor for a given output power.
The transfer function obtained from the electrical and dynamic equations is
The load model is the output provided to reactive torque from ball screw and from the summation of the inputs of ball screw inertia provided input from angular acceleration, ball screw drag, fixed end friction torque provided input from angular velocity of ball screw pulley, slideway friction it can be clearly understood by the below block diagram
The equations for load model are:
T reaction = Tp2 + T BSd + T BSi + TSF + T friction
Where Tp2 - torque due to driven pulley inertia
T BSd - torque due to ball screw drag
T BSd =μWBS ω2
T BSi - torque due to ball screw inertia where T BSi = s JBS ω 2
TSF - torque due to slideway friction where TSF =
T friction - torque due to friction in bearings
Where M0 - load - free component, M1 - load - dependent component
A tachometer is a smaller permanent magnet dc motor mounted directly on the rear of the servomotor's shaft. The tachometer produces a voltage proportional to actual velocity of the motor shaft. It has a factory set of constant and an adjustable gain that enables tuning of the velocity feed back loop. The transfer function between the actual motor velocity and the tachometer circuit output is given as
Where is the output voltage of the tachometer, is the actual angular velocity of the motor shaft, is the tachometer constant, is the adjustable tachometer gain, and s is Laplace operator
8.2 Parameters and physical elements that affect the static and dynamic accuracy performance
The interval of time between input and output and the quality of the output signal for an axis drive from CNC machine tool are affected by disturbance such as:
- Resistant force due to friction
- Forces dependent upon acceleration and speed
- Deformation of the control elements caused by operating forces and loading conditions.
The effects of disturbance could be classified in three categories:
- Effect of noise on saturable elements
- Effect of elements tolerances
these effects the gain and time constants of the system and therefore the dynamic and static accuracy.”
These effects manifest themselves in different parts of the machine tool axis drives as is shown in below table
They affect static and dynamic accuracy of the machine tool, terms that specify the performance of this system.
Parameters effecting dynamic and static accuracy are listed below
- Velocity bandwidth
- Check overshooting
- Dead band
- Coulomb friction
- Position gain
- Resonance frequencies for different elements
- Damping coefficients
Part of motion control system
Effects of disturbance
Effects due to sampling time
Effects due to interpolation
Backlash in the driving elements and slideways
1.2 Table: the effects of distribution in different parts of CNC machine tool axis drive.
Describe the controller operation and optimisation methods related to it
Controller operation of CNC machine
The below is shown the block diagram of CNC controller for analogue feed drive
Cutting of work piece in CNC machines are done by programming G codes for interpolation techniques, below is the detail description of interpolation technique and types of interpolation
9.1 Interpolation technique:
- The interpolator is a vital part of the MCU, allowing the simultaneous movements of two or more axes
- The coordinated movement of these axes allows the machine tool to move the cutter or the workpiece in a constant tool path to generate
- Linear interpolation- Straight line and angular moves
- Circular interpolation -arc and circular moves
- Helical interpolation- thread and helical forms
- Parabolic and cubic interpolation- for complex shapes
Let us have a brief discussion on above mentioned topics
Circular interpolation: this was developed to overcome the difficulty in programming arcs and circles. It allows a programmer to make the cutting tool follow any circular path ranging from small arc segment to full 360 degrees circle for machining arcs or full circles, outside and inside radii.
There is usually an automatic selection of XY plane as the default value. There are limitations of the maximum radius by the capacity of the machine tool. However, simultaneous control for circular interpolation on two axes and linear interpolation on the third axis can be provided.
Linear interpolation: It involves moving the cutting tool from one position to another in a straight line with this type programming it is possible to program all tapers or angular surfaces; it may also be used to stimulate arcs and circles.
Helical interpolation: For the XY plane, the tool will move in a circular motion in the XY axes and linearly in Z, simultaneously. Helical interpolation is used for threading, spiral, and rough boring applications.
It is Control of a cutter path by interpolation between three fixed points, with the assumption that the intermediate points are on a parabola.
9.2 Plane selection:
The CNC controller operates the plane selection by programming G codes as listed below
G17 for xy plane
G18 for xz plane
G19 for yz plane
The below shows diagram explains the selection of plane and arc direction
Rigid tapping or synchronous feed tapping is most common in CNC machines. The rigid tapping cycle operates by synchronizing the machine spindle rotation so as to match the thread pitch. There has been difficulty in matching the machine and pitch of the specific tap used. Operation of machine and actual pitch of the tap have slight discrepancies. As tap becomes dull, the pressure required to start the tap into the whole decreases. This results into more compression stroke within the tap driver which is used before the tap begins to cut thereby causing shallower tapping depth.
As every computer existing operates on software same as with Computer in CNC is being operated by means of software.
There are three types of software used in CNC system they are listed below
Operating system software
Application software and
Machine interface software
Let us have a brief description about this software's
Operating system software:
This deal with the part program and manipulate corresponding control signal to drive machine tool axes. It is read only memory (ROM) stored in the machine control unit (MCU). This software has editor function, a control program and an executive program. Editor allows machine operator to accept inputs and edit part programs. It also allows all file management functions .The control program decodes instructions of the part program and performs calculations and interpolation.
Application system software:
Application system software controls numerical control part programs which are written for machining applications.
Machine interface software:
Machine interface software operates communication link between the machine tool and CPU. This enables CNC auxiliary function to be accomplished. Ladder logic diagrams are used in this software.
9.5 Part programming:
Part programming represents the machining sequences, or blocks, used to produce a desired component shape. Each block starts with letter N followed by the block sequence number. These blocks consist of several words. A word starts with a character followed by number that represents a specific command for machine tool.
The starting word G represents the preparatory function and the M represents the miscellaneous function in program and F, S represents the feed and spindle speeds respectively and T is the tool number. x, y, and z letters are the scalars representation of motion length in particular axis.
Part programming with CAD systems:
This system has graphical representation or displays. Each geometric statement can be made interactively by moving mouse. CAD has advantages of allowing visual inspection of the part geometry on the computer workstation. Most of CAD systems allow 3D construction.
9.6 Feed rate optimization:
A feed rate optimization technique has been developed for minimizing the cycle time in machining spline tool paths. Axis velocity, torque and jerk limits are considered throughout the motion in order to ensure smooth and linear operation of the servo drives with minimal tracking error. Feed modulation is achieved by manipulating segment durations which define the overall minimum jerk feed profile. Long tool paths are handled by applying a windowing technique. The optimized feed profile allows nonzero acceleration and jerk values at segment connections, resulting in continuous and smooth motion within the velocity, torque, and jerk limits of the drives. The cycle time reduction obtained with the proposed technique is demonstrated in high speed contouring experiments. 
CNC machines are considered to be a very important aspect in engineering design process. Its applications are very wide and it is versatile, CNC machine tool has many advantages over other conventional machining. The CNC machine has reliable features of resolution and repeatability. The CNC machine tool features high efficiency, high speed and high accuracy. Some of the errors are easily reduced during the machining process and the techniques discussed in report are useful to get error free response.