# Mechanical Technology Grade 12 November 2024 NSC QP (Eng)

> Grade 12 Mechanical Technology question paper from the November 2024 NSC (English), 23 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/mechanical-technology-nov-2024-fitting-and-machining-eng/34933258-3438-4724-a8b2-133325854697
- Updated: 2026-09-27
- Subject: Mechanical Technology
- Grade: Grade 12
- Document type: Question paper
- Year: 2024
- Exam period: November 2024 NSC
- Curriculum: CAPS
- Pages: 23

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Mechanical Technology · Grade 12 · November 2024 NSC · 2024. Question paper, 23 pages. Read online or download the PDF.

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### Page 1

Confidential

                                NATIONAL
                           SENIOR CERTIFICATE

                                   GRADE 12

           MECHANICAL TECHNOLOGY: FITTING AND MACHINING

                                NOVEMBER 2024

MARKS: 200

TIME: 3 hours

        This question paper consists of 17 pages and a 6-page formula sheet.

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Mechanical Technology: Fitting and Machining   2                            DBE/November 2024
                                           NSC Confidential

 INSTRUCTIONS AND INFORMATION

 1.         Write your centre number and examination number in the spaces provided
            on the ANSWER BOOK.

 2.         Read ALL the questions carefully.

 3.         Answer ALL the questions.

 4.         Number the answers correctly according to the numbering system used in
            this question paper.

 5.         Start EACH question on a NEW page.

 6.         Show ALL calculations and units. Round off final answers to TWO decimal
            places.

 7.         Candidates may use non-programmable scientific calculators and drawing
            instruments.

 8.         The value of gravitational acceleration should be taken as 9,81 m/s2 or
            10 m/s2.

 9.         All dimensions are in millimetres, unless stated otherwise in the question.

 10.        Write neatly and legibly.

 11.        A formula sheet is attached at the end of the question paper.

 12.        Use the criteria below to assist you in managing your time.

 QUESTION                         CONTENT                         MARKS       TIME IN MINUTES
                                  GENERIC
       1         Multiple-choice Questions                            6                 6
       2         Safety                                              10                 10
       3         Materials                                           14                 14
                                  SPECIFIC
        4        Multiple-choice Questions                          14                  10
        5        Terminology (Lathe and Milling Machine)            18                  20
        6        Terminology (Indexing)                             28                  25
        7        Tools and Equipment                                13                  10
        8        Forces                                             33                  33
        9        Maintenance                                        18                  12
       10        Joining Methods                                    18                  12
       11        Systems and Control (Drive Systems)                28                  28
                                                     TOTAL          200                180

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Mechanical Technology: Fitting and Machining   3                              DBE/November 2024
                                           NSC Confidential

 QUESTION 1: MULTIPLE-CHOICE QUESTIONS (GENERIC)

 Various options are provided as possible answers to the following questions. Choose
 the answer and write only the letter (A–D) next to the question numbers
 (1.1 to 1.6) in your ANSWER BOOK, e.g. 1.7 E.         Nov

 1.1       Which statement below is CORRECT in terms of a recommendation for the
           application of first aid?

           Do NOT …

           A     remove anything that is stuck to the wound.
           B     check the pulse of the patient.
           C     give attention to the loss of blood or breathing difficulties.
           D     check the surroundings for dangerous objects.                                       (1)

 1.2       Where more than … employees are employed at a workplace, the employer
           must provide an accessible first-aid box.

           A     2
           B     3
           C     4
           D     5                                                                                   (1)

 1.3       What causes accidents when working with revolving machinery, such as
           a bench grinder?

           A     Overconfidence
           B     Correct wheel size
           C     Gap between tool rest and grinding wheel not exceeding 3 mm
           D     Correctly rated grinding wheel for the bench grinder                             (1)

 1.4       Which test does NOT damage a work piece?

           A     Spark test
           B     Sound test
           C     Bending test
           D     Machining test                                                                   (1)

 1.5       Which of the following products is case-hardened?

           A     Tin cans
           B     Machine guards
           C     Hand files
           D     Gears and cams                                                                   (1)

 1.6       Which process is the first step in the production of high-strength steel?

           A     Normalising
           B     Annealing
           C     Hardening
           D     Tempering                                                                        (1)
                                                                                                  [6]
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Mechanical Technology: Fitting and Machining   4                              DBE/November 2024
                                           NSC Confidential

 QUESTION 2: SAFETY (GENERIC)

 2.1       State TWO safety precautions that must be adhered to after the horizontal
           band saw has been switched on.                                                         (2)

 2.2       Name the THREE stages when basic first-aid treatment is given to help an
           injured person.                                                                        (3)

 2.3       Why must oil or grease NOT be in contact with the oxygen fittings when
           handling oxygen cylinders?                                                             (1)

 2.4       State TWO disadvantages of the process workshop layout.                                (2)

 2.5       State TWO advantages of the product workshop layout.                                   (2)
                                                                                                  [10]

 QUESTION 3: MATERIALS (GENERIC)

 3.1       State if the following materials are easy or hard to file during a filing test:

           3.1.1       Cast iron                                                                  (1)

           3.1.2       Cast steel                                                                 (1)

           3.1.3       Mild steel                                                                 (1)

 3.2       Explain what heat treatment is.                                                        (3)

 3.3       Explain what the effects will be if metal is heated too fast during the heat-
           treatment process.                                                                     (4)

 3.4       Name the TWO types of steel best suited for case hardening.                            (2)

 3.5       Explain the reason for tempering steel during the heat-treatment process.              (2)
                                                                                                  [14]

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Mechanical Technology: Fitting and Machining   5                          DBE/November 2024
                                           NSC Confidential

 QUESTION 4: MULTIPLE-CHOICE QUESTIONS (SPECIFIC)

 Various options are provided as possible answers to the following questions. Choose
 the answer and write only the letter (A–D) next to the question numbers
 (4.1 to 4.14) in the ANSWER BOOK, e.g. 4.15 E.

 4.1       Identify the lathe procedure shown in FIGURE 4.1 below.

                                               FIGURE 4.1

           A     Parallel boring
           B     Internal taper cutting
           C     Internal drilling
           D     Taper measuring                                                                 (1)

 4.2       Identify the CORRECT statement below regarding a safety precaution of a
           lathe machine after it has been switched on:

           A     Never lean on the lathe.
           B     Make sure all guards are in place.
           C     Remove all jewellery.
           D     Check that there is no oil or grease on the floor around the machine.           (1)

 4.3       Machining on a centre lathe that is unbalanced results in …

           A     a good finish.
           B     clatter on the gear teeth.
           C     less wear of machine parts.
           D     no vibrations.                                                               (1)

 4.4       Which of the following are basic codes used during coding of
           CNC machines?

           A     E-codes
           B     F-codes
           C     G-codes
           D     H-codes                                                                      (1)

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Mechanical Technology: Fitting and Machining   6                        DBE/November 2024
                                           NSC Confidential

 4.5       How should you take care of a moment tester?

           A     Store the equipment in a moist area.
           B     Leave all mass pieces to avoid mass pieces from being stolen.
           C     Add mass pieces very quickly.
           D     All nuts and bolts should be secured properly.                             (1)

 4.6       Identify the reading shown in FIGURE 4.6 below when a 25–50 mm
           interchangeable rod is used with the micrometer.

                                               FIGURE 4.6

           A     40,17 mm
           B     40,23 mm
           C     40,13 mm
           D     40,63 mm                                                                   (1)

 4.7       Which ONE of the following is a factor that governs the value of the safety
           factor?

           A     The value of the minimum load
           B     The consequences of success
           C     The effect of corrosion and wear
           D     The unreliability of the material                                          (1)

 4.8       What is the unit for strain?

           A     No unit
           B     Pascal
           C     Millimetres
           D     Metres                                                                     (1)

 4.9       Which type of material is used to make water pipes?

           A     Teflon
           B     PVC
           C     Vesconite
           D     Bakelite                                                                   (1)

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Mechanical Technology: Fitting and Machining   7                                DBE/November 2024
                                           NSC Confidential

 4.10      Which of the following describes coefficient of friction?

           A     It is the minimum force needed to stop an object moving on a surface,
                 divided by the forces pressing them together.
           B     It is the maximum force needed to stop an object moving on a surface,
                 divided by the forces pressing them together.
           C     It is the minimum force needed to get an object to move on a surface,
                 divided by the forces pressing them together.
           D     It is the maximum force needed to get an object to move on a surface,
                 divided by the forces pressing them together.                                         (1)

 4.11      Which statement         below     describes        metric   square   screw   thread
           CORRECTLY?

           A     Square thread is a screw thread where the width of the screw thread,
                 the depth of the screw thread and the space between the threads are
                 approximately equal.
           B     Square thread is a screw thread where the total length of the screw
                 thread, the minimum thickness of the screw thread and the space
                 between the threads are approximately equal.
           C     Square thread is a screw thread where only the width of the screw
                 thread and the minor depth of the screw thread are approximately
                 equal.
           D     Square thread is a screw thread where only the total depth of the screw
                 thread and the minimum space between the threads are approximately
                 equal.                                                                                (1)

 4.12      Where are multiple screw threads mostly used?

           A     Where greater holding strength is needed
           B     Where slow motion is needed to turn the screw
           C     Where parallel motion is needed
           D     Where quick motion is needed                                                          (1)

 4.13      Where would you find a radial piston pump?

           A     Hydraulic system
           B     Gear system
           C     Pneumatic system
           D     Pulley system                                                                     (1)

 4.14      Which ONE of the following is a function of a reservoir in a hydraulic system?

           A     Controls the flow of hydraulic pressure
           B     Prevents any heat dispersion
           C     Promotes air separation from the fluid
           D     Pumps the hydraulic fluid through the system                                       (1)
                                                                                                    [14]

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Mechanical Technology: Fitting and Machining   8                                 DBE/November 2024
                                           NSC Confidential

 QUESTION 5: TERMINOLOGY (LATHE AND MILLING MACHINE) (SPECIFIC)

 5.1       State THREE disadvantages of cutting a taper on a lathe machine using the
           compound slide method.                                                                    (3)

 5.2       FIGURE 5.2 below shows a taper with an included angle of 7° that should
           be machined between centres.

                                                        368                 60

                                    60

                     Ø85
                                                        7°
                                                                                   d

                                                 FIGURE 5.2

           5.2.1           Calculate the small diameter (d) of the taper.                            (4)

           5.2.2           Calculate the set-over of the tailstock required to cut the taper.        (3)

 5.3       Calculate the following dimensions for a parallel key suitable for a 105 mm
           diameter shaft that must be used in a gearbox:

           5.3.1           Width                                                                     (2)

           5.3.2           Thickness                                                                 (2)

           5.3.3           Length                                                                    (2)

 5.4       State TWO safety measures when working with a milling machine.                            (2)
                                                                                                     [18]

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Mechanical Technology: Fitting and Machining   9                       DBE/November 2024
                                           NSC Confidential

 QUESTION 6: TERMINOLOGY (INDEXING) (SPECIFIC)

 6.1       A spur gear with a pitch-circle diameter of 186 mm and a module of 3 must
           be cut for an engineering firm.

           Calculate the following:

           6.1.1         Circular pitch                                                    (2)

           6.1.2         Number of teeth                                                   (3)

           6.1.3         Dedendum                                                          (2)

 6.2      FIGURE 6.2 below shows an internal dovetail component.

                                                        W

                                    y
                            E                 D

                h = 32
                                        60°                           60°
                                B
                                                                                7
                                    α                                   α
                                C             A

                                    x                125 (w)            x   7
                                                      M

                                                  FIGURE 6.2

          Calculate the following:

           6.2.1         Maximum width distance (W) of the dovetail                        (6)

           6.2.2         Distance (M) over the precision rollers                           (6)

 6.3       A spur gear with 101 teeth needs to be manufactured for a client.
           The dividing head used has a ratio of 40 : 1.

           HINT: Use A = 100 divisions for the simple indexing.

          Calculate the following:

           6.3.1         Indexing that is needed                                           (4)

           6.3.2         Change gears that are required                                    (5)
                                                                                           [28]

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Mechanical Technology: Fitting and Machining 10                          DBE/November 2024
                                           NSC Confidential

 QUESTION 7: TOOLS AND EQUIPMENT (SPECIFIC)

 7.1       A Brinell hardness tester is prepared to conduct a hardness test on a
           specimen. Answer the questions that follow.

           7.1.1         Where on the hardness tester is the specimen placed to conduct
                         the test?                                                                 (1)

           7.1.2         State TWO methods to determine the Brinell Hardness Number
                         (BHN).                                                                    (2)

 7.2       FIGURE 7.2 below shows a V-screw thread micrometer. Label A–D.

                     B                                            C         D

                                                              A

                                               FIGURE 7.2                                      (4)

 7.3       What is the function of a screw-thread micrometer?                                  (2)

 7.4       Calculate the height of a M24 x 2,5 screw thread.                                   (2)

 7.5       Explain how the reading of a depth micrometer differs from the reading of a
           screw-thread micrometer.                                                            (1)

 7.6       Why are interchangeable rods used with depth micrometers?                           (1)
                                                                                               [13]

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Mechanical Technology: Fitting and Machining 11                            DBE/November 2024
                                           NSC Confidential

 QUESTION 8: FORCES (SPECIFIC)

 8.1       FIGURE 8.1 below shows a system of THREE pulling forces and ONE
           pushing force acting on the same point.

           HINT:      Draw and complete the diagram in FIGURE 8.1. Show ALL the
                      horizontal and vertical components before you do the calculation.

                                                  45 N
                                                                    80 N

                        25 N
                                            60°
                                                              45°

                                                              30°

                                                                      150 N

                                              FIGURE 8.1

          Calculate the following:

           8.1.1       Sum of the horizontal components                                           (4)

           8.1.2       Sum of the vertical components                                             (5)

           8.1.3       Magnitude of the resultant                                                 (2)

           8.1.4       Angle and direction of the equilibrant                                     (3)

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Mechanical Technology: Fitting and Machining 12                             DBE/November 2024
                                           NSC Confidential

 8.2       FIGURE 8.2 below shows a uniform beam supported by TWO vertical
           supports, A and B. Two vertical point loads and a uniformly distributed load
           (UDL) are exerted onto the beam.

                      75 N                                                  60 N
                     1m             4m                4m               1,5 m
                                               10 N/m (UDL)

                                                 12 m
               A                                                                     B

                                              FIGURE 8.2

          Calculate the following:

           8.2.1          The point load representing the UDL                                       (2)

           8.2.2          The reactions in supports A and B                                         (8)

 8.3       A pulling force of 110 kN is applied to a solid mild-steel shaft. The resistance
           area of the shaft is 7,07 x 10-4 m2. After the force has been applied to the
           shaft, the original length extends by 0,0001 m.

          Calculate the following:

           8.3.1          The stress in the material in MPa                                         (2)

           8.3.2          The diameter of the shaft in mm                                           (4)

           8.3.3          The original length of the shaft in millimetres if the strain is
                          1,64 x 10-5                                                               (3)
                                                                                                    [33]

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Mechanical Technology: Fitting and Machining 13                       DBE/November 2024
                                           NSC Confidential

 QUESTION 9: MAINTENANCE (SPECIFIC)

 9.1       Name THREE different types of mechanical drives.                               (3)

 9.2       Why is it necessary to conduct maintenance on operating systems or
           machines?                                                                      (2)

 9.3       State THREE preventative maintenance procedures to ensure that gear
           drives work properly.                                                          (3)

 9.4       State the TWO subgroups that preventative maintenance is divided into.         (2)

 9.5       Why are polyester resins used with glass fibre?                                (1)

 9.6       State THREE consequences due to a lack of preventative maintenance.            (3)

 9.7       Explain the difference between thermo-hardened and thermoplastic
           composites.                                                                        (4)
                                                                                              [18]

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Mechanical Technology: Fitting and Machining 14                         DBE/November 2024
                                           NSC Confidential

 QUESTION 10: JOINING METHODS (SPECIFIC)

 10.1      A four-start square thread needs to be manufactured. The lead of the square
           thread is 40 mm and the crest diameter is 105 mm. The clearance angle
           must be 4°.

           Calculate the following:

           10.1.1      Pitch diameter                                                       (4)

           10.1.2      Helix angle of the thread                                            (4)

           10.1.3      Leading angle                                                        (2)

           10.1.4      Following angle                                                      (2)

 10.2      FIGURE 10.2 below shows a square thread. Label A–D.

                       A B

                                                 C            D

                                              FIGURE 10.2                                   (4)

 10.3      State TWO uses of square threads in the workshop environment.                    (2)
                                                                                            [18]

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Mechanical Technology: Fitting and Machining 15                                DBE/November 2024
                                           NSC Confidential

 QUESTION 11: SYSTEMS AND CONTROL (DRIVE SYSTEMS) (SPECIFIC)

 11.1      FIGURE 11.1 below shows a hydraulic press.

                           f=?N                                  F = 600 N

                                   PLUNGER
                                   aplunger = 0,018 m²                           L
                     l=?           mm                              RAM
                                                               Aram = 0,2 m²    L = 30 mm
                                                               mm
                                                  FLUID

                                                   FIGURE 11.1

          Calculate the following:

           11.1.1          Fluid pressure in the hydraulic system in Pa                            (2)

           11.1.2          Force applied on the plunger                                            (3)

           11.1.3          The displacement (l) of the plunger in mm                               (3)

 11.2      Which component is used to determine the hydraulic pressure?                            (1)

 11.3      State the purpose of a hydraulic filter.                                                (1)

 11.4      FIGURE 11.4 below shows a hydraulic valve. Answer the questions that
           follow.

                                                 FIGURE 11.4

           11.4.1          Identify the valve.                                                        (1)

           11.4.2          State TWO functions of the valve.                                          (2)

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Mechanical Technology: Fitting and Machining 16                              DBE/November 2024
                                           NSC Confidential

 11.5      The belt drive system of a compressor is shown in FIGURE 11.5 below.

                                                              NDN = 1 100 r/min
                                                               DDN = 600 mm
                              Pulley linked to
                              compressor

                                                    DDR = 220 mm
                                                    NDR = ? r/min

                         Pulley linked to motor

                                              FIGURE 11.5

          Calculate the following:

           11.5.1      The rotational frequency of the drive pulley in r/s                           (4)

           11.5.2      The torque on the driven pulley if the power transmitted is
                       236,65 kW                                                                     (3)

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Mechanical Technology: Fitting and Machining 17                                DBE/November 2024
                                           NSC Confidential

 11.6      FIGURE 11.6 below shows a gear drive system connected to an electric
           motor.

                     NA = 980 r/min
                     TA = 45

                                                                           ND = ? r/min
                                                     TC = 20
                                                                           TD = 42
                                                                            Output shaft
                 Electric motor

                                                T B = 24

                                               FIGURE 11.6

           Calculate the following:

           11.6.1        Rotation frequency of the output shaft in r/s if the electric motor
                         rotates at 980 r/min                                                      (4)

           11.6.2        Gear ratio                                                                (3)

           11.6.3        The direction in which the shaft of the electric motor will rotate if
                         the output shaft rotates clockwise                                        (1)
                                                                                                   [28]

                                                                                     TOTAL:        200

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Mechanical Technology: Fitting and Machining  1                           DBE/November 2024
                                             NSC Confidential

                    FORMULA SHEET FOR MECHANICAL TECHNOLOGY:
                              FITTING AND MACHINING

1.       BELT DRIVES

1.1      Belt speed = πDN
                         60

1.2      Belt speed = π D  t  N             (t = belt thickness)
                              60

1.3      Belt mass = Area × Length × Density         (A = thickness × width)

                         Diameter of driven pulley
1.4      Speed ratio =
                         Diameter of driver pulley

1.5      Belt length (flat) = [(D + d) × 1,57] + (2 × centre distance)

                            π D  d     D  d2
1.6      Open-belt length =                        2c
                                2            4c

                               π D  d  D  d 
                                                          2

1.7      Crossed-belt length =                                2c
                                   2         4c

1.8      Power (P) =
                         T1  T2  π D N
                                   60
          Where:
                T1 = force in the tight side
                T2 = force in the slack side
                T1 – T2 = effective tensile force (Te)

                                                     T1
1.9      Ratio between tight side and slack side =
                                                     T2

                                  T1
1.10      Width =
                       Permissible tensile force

1.11     NDR × DDR = NDN × DDN

1.12     Torque = Force × Radius

                         2π NT
1.13     Power (P) =
                           60

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Mechanical Technology: Fitting and Machining   2                                         DBE/November 2024
                                           NSC Confidential

2.     STRESS AND STRAIN

       Ashaft = π d
                         2
2.1
                     4

       Apipe = π D  d 
                   2   2
2.2
                             4

                                    Maximum stress/Break stress
2.3     Safety factor =
                                        Safe working stress

                                                                    F
2.4    Stress = Force                                 OR     σ
                     Area                                           A

                         Change in length                           ΔL
2.5     Strain =
                          Original length             OR     ε
                                                                    oL

                                     Stress                             σ
2.6    Young's modulus =                              OR     E
                                     Strain                             ε

3.     HYDRAULICS

3.1    Pressure = Force                               OR     P
                                                                    F
                             Area                                   A

3.2    Volume = Area × Stroke length (l or s)

3.3    Work done = Force × Distance

3.4    PA = PB

       FA  F
3.5        B
       AA  AB

4.     GEAR DRIVES

                                 2π NT
4.1    Power (P) =
                                   60

                                  Product of teeth on driven gear                            Ninput
4.2    Gear Ratio =                                                     OR   Speed ratio =
                                  Product of teeth on driver gear                            Noutput

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Mechanical Technology: Fitting and Machining   3                                DBE/November 2024
                                           NSC Confidential

         Ninput    Product of teeth on driven gear
4.3              =
         Noutput   Product of teeth on driver gear

4.4    NA × TA = NB × TB

4.5    Torque = Force × Radius

4.6    Torque transmitted = Gear ratio × Input torque
                     Pitch-circle diameter                            PCD
4.7    Module =                                         OR     m=
                        Number of teeth                                T

                                   Circular pitch × Number of teeth
4.8      Pitch-circle diameter =
                                                   π
                                      OR

                              PCD = CPT
                                     

4.9    Outside diameter (OD) = PCD + 2(m)

4.10   Addendum = Module                     OR               a=m

4.11   Dedendum (b) = 1,157 × m              OR               Dedendum (b) = 1,25 × m

4.12   Cutting depth (h) = 2,157 × m         OR               Cutting depth (h) = 2,25 × m

4.13   Clearance (c) = 0,157 × m             OR               Clearance (c) = 0,25 × m

4.14   Circular pitch (CP) = m × π

4.15   Working depth (WD) = 2 × m            OR               Working depth (WD) = 2 × a

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Mechanical Technology: Fitting and Machining   4                                       DBE/November 2024
                                           NSC Confidential

5.        KEYWAYS

5.1       Width (W) = D
                            4

5.2       Thickness (T) = D
                                 6

5.3       Length (L) = 1,5 × D
          Where:
                 D = Diameter of shaft

5.4       Standard taper for taper key: 1 in 100 or 1 : 100

6.        CINCINNATI DIVIDING HEAD TABLE FOR MILLING MACHINE

                                                      Hole circles
      Side 1       24           25      28      30      34       37      38     39    41   42       43
      Side 2       46           47      49      51      53       54      57     58    59   62       66
                                                     Change gears
      Gears    24 × 2           28      32      40      44       48      56     64    72   86      100

6.1       Indexing = 40              (n = number of divisions)
                        n

               A  n 40
                                                                      A  n 
          Dr                                                     Dr              40
6.2                                          OR
          Dn    A     1                                          Dn              A

          Where:
                A = chosen number of divisions
                n = real number of divisions

7.        DOVETAILS
          Where:
                 R = Radius of precision roller
                 y = Distance from top edge of dovetail in relation to bottom corner of dovetail
                 x = Distance from middle of precision roller to bottom corner of dovetail
                 θ = Dovetail included angle (normally 60°)
                 h = Height of dovetail
                 w = Minimum width of dovetail
                 W = Maximum width of dovetail
                 m = Distance between rollers
                 M = Distance over rollers

Copyright reserved                                                                         Please turn over

### Page 22

Mechanical Technology: Fitting and Machining   5                                  DBE/November 2024
                                           NSC Confidential

8.     TAPERS

             θ D-d
8.1    tan    =           (l = Taper length)
             2 2l

                                 L D - d 
8.2    Tail stock set - over =                (L = Distance between centres)
                                    2l

9.     SCREW THREADS

9.1    Mean diameter = Outside diameter – (½ × Pitch)             OR           Dm = OD ‒ P
                                                                                         2
9.2    Effective diameter (Deff) = Pitch diameter (Dp) = Mean diameter (Dm)

9.3    Lead = Pitch × Number of starts

9.4    Height of screw thread = 0,866 × Pitch (P)

9.5    Depth of screw thread = 0,613 × Pitch (P)

                                  Lead
9.6    Helix angle: Tan θ =
                                 π  Dm

9.7    Leading angle = 90° ‒ (Helix angle + Clearance angle)

9.8    Following angle = 90° + (Helix angle ‒ Clearance angle)

9.9    DP = DN – (0,866 × P)

Copyright reserved                                                                    Please turn over

### Page 23

Mechanical Technology: Fitting and Machining  6            DBE/November 2024
                                          NSC Confidential

10.    PYTHAGORAS' THEOREM AND TRIGONOMETRY

                              r
          y

                                       𝜽
                          x
                  y
10.1    Sin θ 
                  r

                  x
10.2   Cos θ 
                  r

                  y
10.3   Tan θ 
                  x

10.4    r 2  x2  y2

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