NC and CNC machine tools

Why it matters

Numerical control turned machining from a skill held in an operator's hands into a program that can be stored, checked and repeated. Almost every precision part in an Indian tool room or automotive plant now passes through a CNC lathe or machining centre. To use, buy or program one you need to know how it is built, how it knows where its axes are, and what limits its accuracy.

Key ideas

NC versus CNC. In conventional NC (1950s–70s) the program was read block by block from punched tape and executed by hard-wired logic; nothing was stored, so every part needed the tape to be read again, and editing meant punching a new tape. CNC replaces the hard-wired logic with a dedicated computer: programs are stored in memory, edited at the machine, and the control adds tool-radius and length compensation, canned cycles, subroutines, diagnostics and interpolation in software. DNC (direct, now distributed, numerical control) links many CNC machines to a central computer that downloads programs and collects shop-floor data.

Basic elements of an NC system.

• Part program — the coded instructions (G and M codes, coordinates, feeds, speeds).
• Machine control unit (MCU) — the computer, with a data-processing unit (reads and decodes the program, interpolates) and a control-loop unit (drives the axes, handles spindle, coolant and tool changes).
• Machine tool — bed, slides, spindle, ball screws, servo or stepper motors, tool changer, plus the operator panel for manual data input (MDI), jogging and overrides.

Axis convention. Z is along the spindle axis, positive away from the work; X is the longest horizontal travel; Y completes a right-handed set. Rotary axes A, B, C turn about X, Y and Z.

Motion control.

• Point-to-point — moves to positions with no cutting en route (drilling, punching).
• Straight-cut — cuts parallel to one axis at a time.
• Contouring (continuous path) — two or more axes move together under interpolation (linear, circular, helical) to cut any profile; all modern CNC mills and lathes are contouring.

Open and closed loop. An open-loop system drives a stepper motor with a counted number of pulses and assumes each pulse produces one step; it is cheap but cannot detect lost steps under heavy load. A closed-loop system uses a servo motor with a feedback device — a rotary encoder on the motor or screw, or a linear scale on the slide — and corrects any difference between commanded and actual position. Linear scales measure the slide directly and so also cancel screw pitch error and thermal growth.

Ball screws. Recirculating ball screws replace the sliding contact of a lead screw with rolling balls: friction is low, and preloading removes backlash, which is essential for climb milling and accurate contouring.

Precision terms.

• Control resolution — the smallest distance the control can command, the basic length unit (BLU).
• Accuracy — worst-case error in reaching a target; taken as half the control resolution plus the mechanical scatter.
• Repeatability — ability to return to the same point, about ±3σ of the mechanical errors.

Machining centre and turning centre. A machining centre is a CNC mill with an automatic tool changer (ATC) and often pallet changers and indexing tables; a turning centre is a CNC lathe with a turret, live tooling and sometimes a C-axis.

Formulas

N = 1000 · v / (π · D)

• N spindle speed (rev/min); v cutting speed (m/min); D workpiece or cutter diameter (mm).

F = N · f_z · z

• F table feed in milling (mm/min); f_z feed per tooth (mm/tooth); z number of teeth. In turning, F = N · f with f in mm/rev.

BLU = p / (n_s · r_g)

• p ball-screw lead (mm/rev); n_s motor steps (or encoder pulses) per revolution; r_g gear ratio = motor revolutions per screw revolution. BLU in mm.

n_p = x / BLU

• n_p pulses needed for a move of x mm.

f_p = (F · r_g · n_s) / (60 · p)

• f_p pulse frequency (Hz) for a table feed F (mm/min).

Accuracy = BLU / 2 + 3σ

• σ standard deviation of mechanical positioning errors (mm). Repeatability = ±3σ.

Worked examples

Example 1 (standard). A CNC lathe turns a 50 mm diameter bar at v = 200 m/min. A CNC mill uses a 4-tooth cutter at 1500 rev/min with f_z = 0.1 mm/tooth. Find the lathe spindle speed and the mill table feed.

1. N = 1000 · v / (π · D) = 1000 × 200 / (π × 50) = 200 000 / 157.08 = 1273 rev/min.
2. F = N · f_z · z = 1500 × 0.1 × 4 = 600 mm/min.

Example 2 (GATE level). An open-loop table is driven by a stepper motor of 200 steps/rev through a 3:1 gear reduction (motor turns 3 times per screw turn) and a ball screw of 6 mm lead. Mechanical errors have σ = 0.002 mm. Find (a) the BLU, (b) pulses for a 250 mm move, (c) the pulse frequency for 300 mm/min feed, (d) the accuracy.

1. (a) BLU = p / (n_s · r_g) = 6 / (200 × 3) = 0.01 mm.
2. (b) n_p = 250 / 0.01 = 25 000 pulses.
3. (c) Screw speed = 300/6 = 50 rev/min; motor speed = 3 × 50 = 150 rev/min; f_p = 150 × 200 / 60 = 500 Hz.
4. (d) Accuracy = 0.01/2 + 3 × 0.002 = 0.005 + 0.006 = 0.011 mm; repeatability = ±0.006 mm.

Common mistakes

• Multiplying feed per revolution by the number of teeth. Use f_z × z only when the feed is given per tooth.
• Dividing the BLU by the gear ratio the wrong way — a reduction (motor faster than screw) makes the BLU smaller.
• Forgetting the 60 when converting rev/min to pulses per second.
• Treating accuracy and repeatability as the same: a machine can repeat well around the wrong point.
• Calling every CNC system closed loop — stepper-driven open-loop CNC is common on small machines and routers.

For GATE PI

Expect numericals on BLU, pulse count and pulse frequency for open-loop stepper drives (and encoder counts for closed loop), on control resolution, accuracy and repeatability, and on spindle speed and table feed. Conceptual MCQs cover NC versus CNC versus DNC, point-to-point versus contouring, open versus closed loop, axis conventions and ball screws.

Quick check

1. What is the difference between CNC and DNC?
2. Which axis is along the spindle?
3. A 5 mm lead screw is driven by a 240-step motor through 2:1 reduction. Find the BLU.
4. For question 3, find the pulse frequency for 400 mm/min feed.
5. Why do closed-loop machines often use linear scales?

Answers: 1. CNC is one machine with its own computer; DNC links many machines to a central computer for program distribution and data collection. 2. Z. 3. 5/(240 × 2) = 0.0104 mm. 4. 400/5 × 2 × 240/60 = 640 Hz. 5. They measure slide position directly, removing screw pitch error, backlash and thermal growth from the loop.