Machine Tool Design (ME-802 (C)) - Unit 3 Short Notes

UNIT 3: MACHINE TOOL DESIGN

I. FUNDAMENTALS OF MACHINE TOOLS & KINEMATICS

A. Definition & Classification of Machine Tools

• Definition: Machine tools are power-driven, non-portable machines used to shape metal (or other materials) by removing material (machining) or deforming it (forming). They provide controlled relative motion between the tool and workpiece.

• Classification:

  • By Work Material: Metal-working, wood-working, stone-working.

  • By Operation: Turning, drilling, milling, grinding, gear cutting, boring.

  • By Degree of Automation: Manual, semi-automatic, automatic.

  • By Control: Conventional (mechanical/hydraulic), Numerical Control (NC), Computer Numerical Control (CNC).

B. Kinematical Structures of Machine Tools

• Kinematic Chain: A series of connected links (rigid bodies) and joints (kinematic pairs) that transmit motion from the input (motor) to the output (tool/workpiece). It defines all possible motions.

• Kinematic Diagram: A simplified schematic representing the kinematic chain using standard symbols for links and joints. It abstracts away physical details to show motion paths.

• Kinematical Features:

  • Degrees of Freedom (DOF): Number of independent motions possible in the system.

  • Independent Motions: Motions that can be controlled separately (e.g., spindle speed, table feed). A machine tool's complexity is often defined by its number of independent motions (e.g., 3-axis CNC has 3 independent motions).

  • Structural Analysis: Involves identifying the basic structure (main frame, supports) and kinematic structure (motion transmission elements like gears, lead screws, belts).

C. Ray Diagrams & Speed Diagrams

• Ray Diagram:

  • Definition: A graphical method to visualize and design the speed range of a machine tool spindle, typically driven by a cone pulley or gearbox.

  • Construction: Speeds are plotted on a logarithmic scale (for equal ratios). Rays originate from a common point (representing motor speed) and intersect the speed lines. Each ray represents a specific transmission ratio (e.g., a particular pulley/belt combination or gear pair).

  • Application: Ensures even distribution of speeds (geometric progression) and identifies overlapping speed ranges.

  • Formula for Geometric Progression: $$\displaystyle \phi = \sqrt[n-1]{\frac{N_{max}}{N_{min}}} $$, where $\phi$ = progression ratio, $n$ = number of speeds, $$\displaystyle N_{max/min} $$ = max/min speeds.

  \boxed{\phi = \sqrt[n-1]{\frac{N_{max}}{N_{min}}}}

• Speed Diagram:

  • Definition: A plot of spindle speed (N) vs. transmission ratio (i) for a given motor speed ($$\displaystyle N_m $$). It directly shows the speed steps achieved by each gear/pulley combination.

  • Construction: Speed $$\displaystyle N = N_m / i $$. Plotted on linear or log scales.

  • Purpose: To determine the actual speed steps and check for gaps or overlaps. Used for optimizing gear/pulley sizes.

• Distinction:

  | Feature | Ray Diagram | Speed Diagram | | :--- | :--- | :--- | | Purpose | Design & visualize speed range & distribution | Determine actual speed values for each step | | X-axis | Transmission ratio (i) | Transmission ratio (i) or Step Number | | Y-axis | Spindle Speed (N) on log scale | Spindle Speed (N) on linear or log scale | | Key Use | Ensuring geometric progression, avoiding gaps | Selecting specific gear/pulley diameters |

D. Need for Speed Variation in Machine Tools

• Rationale: Cutting speed ($$\displaystyle V_c = \pi D N / 1000 $$ m/min) must be optimized for:

  1. Tool Material & Workpiece Material: Different combinations have optimal $$\displaystyle V_c $$ (e.g., HSS vs. carbide; steel vs. aluminum).

  2. Tool Life: Taylor's Tool Life Equation: $$\displaystyle VT^n = C $$. Higher $V$ reduces tool life exponentially.

  3. Surface Finish: Optimal $$\displaystyle V_c $$ minimizes built-up edge and vibration.

  4. Operation Type: Roughing (lower $$\displaystyle V_c $$, high feed) vs. Finishing (higher $$\displaystyle V_c $$, low feed).

• Conclusion: A wide, finely divisible speed range is essential for productivity (high speed for finish) and economy (low speed for tool life in roughing).

II. DESIGN PARAMETERS: SPEED, FEED, AND POWER

A. Selection of Speed Ranges

• $$\displaystyle N_{min} $$: Determined by minimum practical cutting speed for the hardest material/operation and minimum spindle speed for safe, vibration-free operation.

• $$\displaystyle N_{max} $$: Determined by tool material limit (centrifugal force on inserts), workpiece material (safe speed for balance), and machine rigidity.

• Geometric Progression: Preferred for equal speed ratio between steps. Ensures no large gaps and simplifies design. Progression Ratio ($\phi$) is key.

• Number of Speed Steps ($n$): A compromise between cost (more gears/pulleys) and flexibility. Common values: 6, 8, 12, 16.

B. Selection of Feed Rates

• Factors: Tool geometry (nose radius), work material, machine/ workpiece rigidity, surface finish requirement, depth of cut.

• Typical Ranges (mm/rev):

  • Roughing: 0.2 - 1.5 (higher for heavy cuts)

  • Finishing: 0.05 - 0.3 (lower for better finish)

  • Drilling: 0.1 - 0.5

  • Threading: Equal to pitch.

C. Power Requirements

• Estimation: $$\displaystyle P_c = \frac{F_c \cdot V_c}{60 \times 1000} $$ kW, where $$\displaystyle F_c $$ = cutting force (N), $$\displaystyle V_c $$ = cutting speed (m/min).

• Cutting Force ($$\displaystyle F_c $$): Depends on specific cutting force ($$\displaystyle k_s $$), depth of cut ($$\displaystyle a_p $$), feed ($f$): $$\displaystyle F_c = k_s \cdot a_p \cdot f $$.

• Motor Power ($$\displaystyle P_m $$): $$\displaystyle P_m = \frac{P_c}{\eta_{total}} $$, where $$\displaystyle \eta_{total} $$ = overall efficiency (transmission, spindle bearings, etc., typically 0.7-0.85).

• Selection: Based on maximum power demand (heavy roughing) but must also handle average loads. Service factor (1.1-1.25) often applied.

D. Integrated Design

• Holistic Approach: Speed, feed, and power are interdependent via $$\displaystyle P_c \propto a_p \cdot f \cdot V_c $$.

• Balancing: For a given machine:

  • Low-speed, high-torque end must provide sufficient power at low speeds for heavy roughing.

  • High-speed end must be within tool and spindle limits.

  • Feed-drive must be powerful enough for the chosen depth/feed at any speed.

  • Design must meet requirements for the hardest material and most demanding operation the machine is intended for.

III. METAL FORMING PROCESSES & TOOL DESIGN

A. Cold Working of Metals

• Definition: Deformation of metal below its recrystallization temperature.

• Effects:

  • Strain Hardening: Dislocation density increases → increased strength & hardness, decreased ductility.

  • Residual Stresses: Non-uniform deformation → internal stresses.

  • Surface Finish: Generally good, but may have stress-corrosion cracking susceptibility.

• Common Operations: Rolling, drawing, bending, squeezing, cold forging.

B. Rolling Mills

• Types: Two-high, Three-high, Four-high, Cluster (Sendzimir).

• Detailed: Three-High Roll Mill:

  • Principle: Three rolls in a triangle. Top & bottom rolls driven, middle roll rotates by friction. Workpiece passes top→middle→bottom in one revolution.

  • Pass Arrangement: Used for reducing thickness of bars/sections in multiple passes. Can have reversing or three-stand continuous arrangements.

  • Advantages: Higher reduction per pass than two-high; no need to reverse rolls for each pass.

  • Disadvantages: Roll diameter limited by middle roll size; complex roll force balancing; not suitable for very wide plates.

C. Forging & Die Design

• Design Principles for Forging Dies:

  • Draft Angles: 3°-7° on vertical surfaces to facilitate ejection.

  • Fillets & Radii: Large fillets (≥3x stock thickness) at corners to reduce stress and improve metal flow. Radius on parting line to avoid sharp edges.

  • Parting Line: Should be single, straight, on a single plane if possible. Located on flat surface or largest cross-section to aid in flash formation and die closure.

  • Flash Design: Flash gutter (1.5-3x stock thickness) and flash land (0.5-1.5 mm). Purpose: Controls excess metal, builds pressure in die cavity, protects die edges.

  • Material: Tool Steels (e.g., H-13, H-11) for hot forging; Carbide for high-volume, abrasive materials.

D. Flow Molding (Flow Forming)

• Definition: A cold forming process where a rotating metal tube is axially compressed by rollers, causing the wall to flow and thin over a mandrel.

• Process: Tube rotates; one or more rollers (with specific profile) press against the tube, forcing it to conform to the mandrel shape. Wall thickness reduces, length increases.

• Applications: Manufacturing axisymmetric, thin-walled, high-strength components: cylinders, pressure vessels, automotive wheels, rocket motor cases.

• Tooling: Mandrel (defines inner diameter/shape), Rollers (defines outer profile). Requires precise CNC control.

IV. TOOLING: JIGS, FIXTURES, AND GAUGES

A. Jigs vs. Fixtures

• Jig:

  • Definition: A work-holding device that also guides the cutting tool to the correct location and orientation.

  • Function: Locates & Clamps workpiece + Guides tool (e.g., drill jig with bushings).

  • Use: For drilling, reaming, tapping where tool guidance is critical.

• Fixture:

  • Definition: A work-holding device that only locates and clamps the workpiece. Does not guide the tool.

  • Function: Locates & Clamps workpiece with reference to machine tool's own axes (e.g., milling fixture, welding fixture).

  • Use: For milling, turning, grinding, inspection where machine provides tool path.

• Comparison:

  | Aspect | Jig | Fixture | | :--- | :--- | :--- | | Tool Guidance | Yes (bushings) | No | | Primary Function | Locate, Clamp, Guide | Locate, Clamp | | Typical Operations | Drilling, Reaming | Milling, Turning, Grinding | | Complexity/Cost | Generally higher | Generally lower |

B. Principles of Location & Clamping in Fixtures

• Principles of Location (3-2-1 Principle):

  • Concept: A workpiece in space has 6 degrees of freedom (3 translational, 3 rotational). To fully constrain it, 6 independent locators are needed.

  • 3-2-1 Rule: Use 3 points on one plane to restrict Z-translation & X,Y-rotation. Use 2 points on a perpendicular plane to restrict Y-translation & X-rotation. Use 1 point on the third plane to restrict X-translation & Z-rotation.

  • Datum: The reference surface/feature (primary, secondary, tertiary) against which locating is done.

• Clamping:

  • Purpose: Secure workpiece against locating surfaces and cutting forces.

  • Elements: Clamps (toggle, screw, cam), Straps, Bolts, Quick-acting mechanisms.

  • Design Considerations:

    • Rigidity: Clamping force must exceed cutting forces.

    • Accessibility: No interference with tool path or chip flow.

    • Deformation: Avoid clamping on thin/soft sections.

    • Safety: Operator safety, positive locking.

    • Efficiency: Quick loading/unloading.

C. Design of Gauge - Thread Snap Gauges

• Purpose: GO/NO-GO inspection of thread pitch diameter for batch acceptance. Fast, pass/fail check.

• Design Features:

  • Type: Ring gauge for external threads (bolts), Plug gauge for internal threads (nuts).

  • GO Gauge: Must fully engage the thread with hand force. Checks minimum pitch diameter (material present).

  • NO-GO Gauge: Must not engage beyond a specified number of threads (usually 1-2). Checks maximum pitch diameter (not undersized).

  • Tolerance: Based on thread class (e.g., 6H, 6g). Gauges are made to gauge makers' tolerance (typically 10% of thread tolerance).

  • Wear Allowance: Applied to GO gauge only (made slightly smaller initially) to account for wear and maintain rejection of bad parts.

  • Construction: Hardened, ground tool steel. Threads are precision ground.

  • Calibration: Periodic checking with master ring/plug and thread micrometer.

V. ELECTRICAL DRIVES FOR MACHINE TOOLS

A. Types of Electrical Drives

• DC Motors:

  • Shunt: Constant speed, good regulation. Used for constant speed drives (e.g., pumps).

  • Series: High starting torque, speed varies with load. Used for cranes, elevators.

  • Compound: Combines characteristics. Used where moderate starting torque & better regulation needed.

• AC Motors:

  • Squirrel Cage Induction: Rugged, low cost, maintenance-free. Constant speed (slight slip). Speed control requires VFD.

  • Slip-Ring (Wound Rotor) Induction: High starting torque, speed control via external rotor resistance. Used for heavy-duty cranes, mills.

• Stepper & Servo Motors (CNC):

  • Stepper: Open-loop, precise positioning in steps. Lower torque, can lose steps.

  • Servo: Closed-loop (with encoder/resolver), high torque, high speed, precise position/velocity control. Used for axis drives in CNC.

B. Selection Criteria & Control

• Matching Characteristics:

  • Starting Torque: Must overcome static friction & initial cut (high for heavy machines).

  • Speed Range: Required $$\displaystyle N_{max}/N_{min} $$ ratio (e.g., 10:1 for lathe, 1000:1 for thread grinder).

  • Speed Regulation: How constant speed under varying load (important for finishing).

  • Overload Capacity: For intermittent heavy cuts.

• Basic Control:

  • Direction: Reversing motor terminals or using contactor arrangement.

  • Speed: For DC - armature voltage/field flux control. For AC - VFD (Variable Frequency Drive) is dominant. VFD changes frequency (f) and voltage (V) to control induction motor speed: $$\displaystyle N_s = \frac{120f}{P} $$.

• Variable Frequency Drives (VFDs): Modern standard for AC motor speed control. Provide soft starting, energy savings, and precise speed regulation. Convert AC to DC, then invert to variable-frequency AC.

[!TIP] Exam Focus: Be prepared to compare/contrast Ray vs. Speed Diagram, Jig vs. Fixture, and justify the need for speed variation using Taylor's equation. Know the 3-2-1 principle and thread gauge types (GO/NO-GO) thoroughly. For electrical drives, know which motor type suits which machine tool requirement (constant speed vs. variable torque).