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Questions and Answers

Which manufacturing process involves shaping liquid or malleable raw material using a frame?

  • Moulding (correct)
  • Extrusion
  • Turning
  • Laminating

Which process creates objects by pushing material through a die?

  • Extrusion (correct)
  • Turning
  • Stamping
  • Casting

What is the technique of manufacturing materials in multiple layers?

  • Turning
  • Milling
  • Casting
  • Laminating (correct)

Which manufacturing process involves using rotary cutters to remove material from a workpiece?

<p>Milling (D)</p>
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Which process involves rotating a workpiece and using a cutting tool?

<p>Turning (B)</p>
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What process involves pouring liquid into a mold to solidify?

<p>Casting (B)</p>
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Which process uses a press and die to shape metal?

<p>Stamping (D)</p>
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What type of manufacturing involves permanently deforming a material?

<p>Forming (B)</p>
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During injection molding, what form are the plastics when fed into the hopper?

<p>Granular form (D)</p>
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In injection molding, what happens to the molten plastic after it is injected into the mold cavity?

<p>Cooled (C)</p>
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What is being created when a heater polymer tube is inflated to take the shape of a hollow form with a thin wall.

<p>Blow molding (B)</p>
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What process involves decomposing organic materials into simpler substances?

<p>Composting (D)</p>
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What is created when materials are heated and their shape is altered?

<p>Reforms (B)</p>
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What is a jig used for during production?

<p>Guiding a tool to a specific position (D)</p>
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What is the purpose of a fixture during production?

<p>To hold the workpiece to a machine (B)</p>
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What is a pre-production prototype considered?

<p>A testing model (D)</p>
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What is the goal of tooling up a production line?

<p>Avoid faulty products (C)</p>
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What is carbon fiber primarily used for in racing bicycles?

<p>To form an incredibly strong frame (C)</p>
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What is a common use for Kevlar material?

<p>Protective clothing (A)</p>
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What is the typical size range of nanomaterials?

<p>1-100 nanometers (C)</p>
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Flashcards

Injection moulding

A production process employed during the mass production of components made from polymers. Granular form pellets are fed into a hopper, and gravity is fed into a heater where they become molten.

Jig

A jig is a device used to guide a tool to a specific position on a workpiece. Jigs help speed up the making process and can eliminate errors ensuring every operation is repeated exactly the same.

Fixture

A fixture is a tool which holds the workpiece to a machine bed, which will allow a cutting or shaping operation to occur without the need to measure, mark or move the workpiece.

Prototype

A pre-production prototype is a final version of a product or concept used for advanced testing, allowing designers, manufacturers and users evaluate its performance prior to launching full scale production.

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Modern materials

Specific modern materials are often designed for a particular purpose, or alternatively, the materials' properties are used by designers to improve products.

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Carbon fibre

Is used in the design and manufacture of racing bicycles because of its: high strength and low weight, ability to be shaped into complex forms and smooth finish.

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Kevlar

A trade name given to a modern fibre-based material which is commonly spun into sheets of fabric and used to produce protective clothing. Can be used with other materials to form a composite and is commonly used in the aerospace industry in jet engine linings.

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SMART materials

The use of SMART materials in products has had an innovating effect in a number of ways: products can often become more interactive as a result of the use of the SMART material, products do not require user input to change, the SMART material reacts automatically.

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Nanomaterials

Are between 1 and 100 nanometres (one thousand-millionth of a metre). Used in car manufacturing to produce faster, safer and more efficient cars

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Titanium

A very versatile, strong and lightweight metal usually used in alloys with other metals. for replacement joints, limbs and dental implants as part of the healthcare industry.

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Shape memory alloys (SMAs)

Can be heated and 'programmed' to a specific shape. This shape becomes the memory shape that the material returns to once heated again.

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Elasticity

A material's ability to return to its original shape once the forces deforming it are removed.

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Durability

A material's ability to withstand wear or damage.

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Tensile strength

The ability to withstand a pulling force without stretching.

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Compressive strength

The capacity to withstand compressive stress without fracturing.

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Malleability

Ability to be formed or shaped without breaking.

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Plating

Metal plating can improve durability, corrosion resistance and exterior appearance. Metal provides a corrosion resistant and durable finish.

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Heat treatments

Provide characteristics to finished metal shapes like gears.

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Stains

Are used to colour the timber; but no film or protection is involved.

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Joining or Forming

The primary difference is joining involves fusing materials together, where forming involves shaping a product.

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Study Notes

Duality in Linear Programming

  • Examines the relationship between a primal and a dual linear programming (LP) problem.

Primal Problem (Maximization)

  • The primal LP seeks to maximize $c^Tx$.
  • Subject to constraints $Ax \le b$ and $x \ge 0$.

Dual Problem (Minimization)

  • The dual LP seeks to minimize $b^Ty$.
  • Subject to constraints $A^Ty \ge c$ and $y \ge 0$.

Duality Theorems

Weak Duality Theorem

  • If $x$ is a feasible solution to the primal LP and $y$ is a feasible solution to the dual LP, the objective values satisfy $c^Tx \le b^Ty$.

Strong Duality Theorem

  • If the primal LP has an optimal solution $x^$, then the dual LP also has an optimal solution $y^$, such that their objective values are equal: $c^Tx^* = b^Ty^*$.

Complementary Slackness Theorem

  • Relates optimal primal and dual solutions.
  • At optimality, for all $i$, $y_i^* (b_i - a_i^T x^) = 0$, meaning if $y_i^ > 0$, then the $i$-th constraint in the primal problem is tight ($a_i^T x^* = b_i$), and vice versa.
  • At optimality, for all $j$, $x_j^* (a_j^T y^* - c_j) = 0$, meaning if $x_j^* > 0$, then the $j$-th constraint in the dual problem is tight ($a_j^T y^* = c_j$), and vice versa.

Economic Interpretation of the Dual Problem

  • The primal LP can represent a profit-maximization problem with limited resources.
  • $x_j$ refers to the amount of activity $j$ to perform.
  • $c_j$ is the profit per unit of activity $j$.
  • $b_i$ is the amount of resource $i$ that is available.
  • $a_{ij}$ is the amount of resource $i$ used by activity $j$.
  • The dual variable $y_i$ represents the shadow price(or imputed value) of resource $i$.
  • Key Idea: The dual minimizes imputed value of all resources s.t. imputed cost of inputs for each activity $j$ is no less than its profit $c_j$

Shadow Prices

  • Shadow price are how much the objective function value would change with a one-unit increase in the availability of the resource.

  • Illustrative Example:

    • A maximization problem with constraints:

      • $x_1 + x_2 + x_3 \le 100$
      • $2x_1 + x_2 + 3x_3 \le 55$

    • Corresponding dual variables $y_1$ and $y_2$.

  • $y_1$ could be interpreted as the increase in profit per unit increase in resource 1.

  • $y_2$ could be interpreted as the increase in profit per unit increase in resource 2.

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