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Deep-Dive Design Cases

Four fully worked fixture designs with step-by-step engineering calculations: cutting forces, clamping forces and complete error budgets. Follow the numbers through every case.

iHow Each Case Is Organised

Part and operation — what is being machined and why a fixture is needed.
Required tolerance — the drawing requirement the fixture must guarantee.
Locating scheme — datums, locators and the positioning analysis.
Clamping scheme — clamp type, position and the clamping-force calculation.
Error budget — every error source summed by root-sum-square against the tolerance.

*Notes on the Numbers

Formulas use typical handbook data: k_c is the specific cutting force, C_M and C_P are empirical drilling constants, μ is the friction coefficient and K is the clamping safety factor.

The error budget is summed as a root-sum-square (RSS): the square root of the sum of the squared individual errors, a statistically realistic way to combine independent sources.

Values illustrate the method. Always verify cutting forces, clamp capacity, friction and tool clearance for your own material, tooling and machine.

1Case 1 — Drill Jig for a Bearing Cap

Drill two Ø12H8 dowel holes in a grey cast iron bearing cap (HBS 190). Hole position within Ø0.10 mm, batch 5000 parts per year.

Required tolerance

Hole size Ø12H8 (+0.027 / 0).
Hole position within Ø0.10 mm for the two-hole pattern.

Locating scheme

Primary: three flat pads on the machined base flange (datum A, 3 points).
Secondary: two short pins against the split-line face (datum B, 2 points).
Tertiary: one pin against the end face (datum C, 1 point) — a full 3-2-1 scheme.

Clamping scheme

Two strap clamps press the part onto the base pads, beside the holes to be drilled.
Clamp force is directed toward the locators, never over unsupported areas.

Calculation 1 — cutting torque and thrust

Drilling cast iron with a Ø12 mm twist drill, feed s = 0.25 mm/rev.

Torque M = 10 · C_M · D² · s^0.8 = 10 · 0.021 · 12² · 0.25^0.8 ≈ 10 N·m

Thrust P = 10 · C_P · D · s^0.8 = 10 · 42.7 · 12 · 0.25^0.8 ≈ 1690 N

Calculation 2 — required clamping force

The thrust tries to lift the part; the torque tries to rotate it about the drill axis. Friction on the base pads at radius r ≈ 40 mm, μ = 0.2, safety factor K = 2.5.

Total clamp Q = K · M / (μ · r) = 2.5 · 10 000 / (0.2 · 40) ≈ 3100 N

Per clamp Q = 3100 / 2 ≈ 1.6 kN

An M10 screw strap clamp delivers 4–6 kN, so the design has a comfortable margin. Position the clamps so they do not cover the holes being drilled.

Error budget (position Ø0.10 mm)

Error source	mm
Locating error (datum + bushing fit)	0.020
Bushing runout and wear	0.020
Fixture machining error (bushing positions)	0.030
Clamping deformation	0.010
Drill deflection and tool wear	0.020
Root-sum-square total	0.047
Allowable (half of Ø0.10)	0.050

Result: RSS error 0.047 mm < 0.05 mm allowance. The 3-2-1 + bushing layout passed the 500-piece first-article run.

2Case 2 — Precision Boring Fixture for a Gearbox Housing

Finish-bore a Ø80H7 hole in a grey cast iron gearbox housing to size tolerance 0.03 mm and position Ø0.05 mm. Batch 500 per year, cycle target 4 min.

Required tolerance

Bore size Ø80H7 (+0.030 / 0).
Bore position within Ø0.05 mm of datums A, B, C.
Roundness within 0.01 mm.

Locating scheme

Primary: machined base flange on three pads (datum A).
Secondary: one side face against two fixed stops (datum B).
Tertiary: end face against one stop (datum C).

Clamping scheme

Four hydraulic swing clamps on the top flange, 8 kN each, pressing toward the base pads.
Clamps sit outside the spindle swing circle; a pressure switch confirms clamping before the cycle starts.

Calculation 1 — boring cutting forces

Boring pass: depth of cut t = 1.5 mm, feed f = 0.15 mm/rev, specific cutting force k_c ≈ 2100 N/mm² for cast iron.

Tangential F_t = k_c · t · f = 2100 · 1.5 · 0.15 ≈ 470 N

Axial F_x ≈ 0.4 · F_t ≈ 190 N, toward the fixture wall

Calculation 2 — clamping force against axial thrust

The axial force tries to push the housing off the stops. Four clamps, friction μ = 0.15, safety factor K = 2.5.

Per clamp Q = K · F_x / (n · μ) = 2.5 · 190 / (4 · 0.15) ≈ 790 N

Each clamp provides 8 kN — over ten times the requirement — because the large force is needed to hold the housing rigid for the 0.03 mm size tolerance.

Error budget (size and position)

Error source	mm
Spindle + boring bar runout	0.008
Bushing-to-bore alignment	0.010
Locator wear (pads)	0.005
Clamping deformation of the wall	0.006
Thermal growth during the cycle	0.008
Root-sum-square total	0.017
Allowable (size tolerance 0.03)	0.030
Allowable (position 0.05)	0.050

Result: RSS 0.017 mm is about half the 0.03 mm size tolerance, leaving margin for tool wear. First-article parts measured 0.008 mm roundness and 0.012 mm position.

3Case 3 — V-Block Milling Fixture for a Shaft Keyway

Mill an 8 mm × 4 mm keyway along a Ø40 h8 steel shaft. Keyway position relative to the shaft axis within 0.05 mm, batch 3000 per year.

Required tolerance

Keyway width 8 mm, depth 4 mm.
Keyway axis position relative to the shaft axis within 0.05 mm.

Locating scheme

Shaft diameter located in two 90° V-blocks — the axis position is set by the V geometry.
End face against one stop controls the axial position of the keyway.

Clamping scheme

Two screw strap clamps press the shaft into the V-blocks.
Clamp force direction points directly into the V opening.

Calculation 1 — positioning error of the V-block

For a shaft of diameter D in a V-block of included angle α, the axis height error equals the diameter variation divided by 2·sin(α/2).

Axis error Δ = δD / (2 · sin(α/2)) = 0.039 / (2 · sin 45°) = 0.028 mm

The Ø40 h8 shaft tolerance is 0.039 mm. At 90°, the V reduces the axis error to 0.028 mm — inside the 0.05 mm budget. A 60° V would give 0.039 mm and lose the margin.

Calculation 2 — milling force and clamping force

Slot mill: a_e = 8 mm, a_p = 4 mm, feed per tooth f_z = 0.08 mm, z = 3 teeth, k_c ≈ 2000 N/mm², cutter Ø63 mm.

Cutting force F_c = k_c · a_p · f_z · z · √(a_e/D) = 2000 · 4 · 0.08 · 3 · 0.36 ≈ 700 N

Total clamp Q = K · F_c / (2 · μ · sin 45°) = 2.5 · 700 / (2 · 0.2 · 0.707) ≈ 6200 N

Per clamp Q = 6200 / 2 ≈ 3.1 kN

Two M10 screw clamps at about 4 kN each provide the needed 6.2 kN with margin.

Error budget (keyway position 0.05 mm)

Error source	mm
V-block axis error (from Δ above)	0.028
V-block manufacturing error	0.010
Keyway runout vs shaft axis (machine)	0.020
Clamping distortion of the shaft	0.012
Tool deflection in the slot	0.020
Root-sum-square total	0.043
Allowable	0.050

Result: RSS 0.043 mm < 0.05 mm. The 90° V-block scheme keeps every keyway within tolerance across the full shaft diameter spread.

4Case 4 — Functional Gage for a Ø30H7 Bore

Design a go/no-go functional gage to check a Ø30H7 bore: size 30.000 – 30.021 mm with position tolerance Ø0.05 at MMC. Volume 10 000 parts per year.

Required tolerance

Bore size Ø30H7 (30.000 – 30.021 mm).
Position within Ø0.05 at maximum material condition.

Locating scheme

Gage pin locates in the bore at its virtual condition (MMC minus the position tolerance).
Gage base registers on the part datums A, B, C.

Clamping scheme

No clamping — the part is loaded by hand; only its own weight acts on it, avoiding distortion.
A small leaf-spring hold-down keeps the part against the datum face during measurement.

Calculation 1 — virtual size of the go pin

The go pin must pass through the bore at its worst-case virtual size: the MMC of the bore minus the position tolerance.

Go pin D_go = 30.000 − 0.050 = Ø29.950 mm

Calculation 2 — gage tolerance split (rule of 1/10)

The 0.05 mm position tolerance is split between the gage manufacturing tolerance and its wear allowance.

Manufacturing = 0.10 · 0.05 = 0.005 mm

Wear allowance = 0.10 · 0.05 = 0.005 mm

Go pin new / worn Ø29.945 mm, worn limit Ø29.950 mm

Error budget (gage repeatability)

Error source	mm
Gage pin manufacturing size	0.0015
Datum register alignment	0.0015
Indicator repeatability	0.0010
Operator / seating variation	0.0020
Root-sum-square total	0.0031
Allowable (gage tolerance 0.005)	0.0050

Result: RSS 0.0031 mm is well under the 0.005 mm gage tolerance. The functional gage replaces four separate measurements and repeats within 0.003 mm.

5Case 5 — Broaching Fixture for a Hub Keyway

Broach an 8 mm × 4 mm keyway through a Ø25 H7 hub bore. Keyway position relative to the bore axis within 0.03 mm, batch 4000 parts per year.

Required tolerance

Keyway width 8 mm, depth 4 mm (internal keyway broach).
Keyway axis position relative to the bore axis within 0.03 mm.

Locating scheme

The Ø25 H7 bore is located on a hardened pilot plug (datum A); the pilot also guides the broach through the part.
The bottom face seats on the fixture base (datum B), so the pull force is reacted by the fixture body, not the clamp.

Clamping scheme

A hydraulic clamp presses the part onto the base during loading and broach pull-out.
The broaching force pushes the part into the base — a positive stop — so the clamp only resists the small retraction force.

Calculation 1 — broaching force

Internal keyway broach: width b = 8 mm, chip lift c = 0.04 mm per tooth, specific cutting force p = 3000 N/mm², z = 4 teeth in contact (30 mm part, 8 mm tooth pitch).

Broach force F = p · b · c · z = 3000 · 8 · 0.04 · 4 ≈ 3840 N

Calculation 2 — required clamping force

The pull force is taken by the pilot and the base. During pull-out the retraction friction is about 0.1·F ≈ 380 N; friction μ = 0.15, safety factor K = 2.5.

Clamp force Q = K · F_ret / μ = 2.5 · 380 / 0.15 ≈ 6300 N

One hydraulic clamp rated 10 kN covers the 6.3 kN requirement with margin. Position it so it does not obstruct the broach path.

Error budget (keyway position 0.03 mm)

Error source	mm
Pilot plug runout vs bore	0.008
Bore-to-pilot fit clearance	0.012
Pilot guide wear	0.010
Base flatness / seating	0.006
Broach deflection + puller alignment	0.015
Root-sum-square total	0.024
Allowable	0.030

Result: RSS 0.024 mm < 0.03 mm. The pilot-located broaching fixture keeps the keyway within tolerance across the full bore-size spread.

6Case 6 — Cylindrical Grinding Fixture between Centers

Cylindrical-grind a Ø40 h6 journal on a hardened steel shaft to 0.01 mm runout to centers and 0.004 mm roundness. Batch 2000 parts per year.

Required tolerance

Journal size Ø40 h6 (−0.016 / 0).
Runout to the center axis (datum A) within 0.01 mm; roundness within 0.004 mm.

Locating scheme

Part mounted between dead centers — the axis between the center points is datum A.
The fixed headstock center locates the part axially; center holes are ground to a 60° cone.

Clamping scheme

A spring tailstock center applies a light axial force to seat the part against the fixed center.
A driving dog transmits rotation — no radial clamping, so the journal is not distorted.

Calculation 1 — grinding forces

Finish OD plunge grind: depth 0.02 mm, wheel Ø300 mm at 2000 m/min. Typical forces: radial F_n ≈ 160 N into the wheel, tangential F_t ≈ 60 N.

Radial F_n ≈ 160 N

Tangential F_t ≈ 60 N

Calculation 2 — required center force

The radial force acts at the journal, distance a = 60 mm from the fixed center; the spring center resists it at the far end, length b = 120 mm. Safety factor K = 2.5.

Center force Q = K · F_n · a / b = 2.5 · 160 · 0.5 ≈ 200 N

A spring center provides 300–500 N, so the part stays seated under the 200 N demand — the fixture simply keeps the axis stable while the wheel does the work.

Error budget (runout 0.01 mm)

Error source	mm
Center-hole roundness / 60° cone	0.004
Center tip wear / misalignment	0.004
Workhead + wheelhead runout	0.003
Thermal growth of the shaft	0.004
Wheel dressing / grinding pressure	0.003
Root-sum-square total	0.008
Allowable	0.010

Result: RSS 0.008 mm < 0.01 mm. Between-centers grinding repeats within tolerance across the batch, with the driver transmitting rotation without radial clamping.

7Case 7 — Gear Hobbing Fixture with Expanding Arbor

Hob a 45-tooth spur gear (module 2) on a steel blank. Pitch-circle runout to the bore within 0.03 mm, adjacent pitch error within 0.02 mm. Batch 5000 parts per year.

Required tolerance

Pitch-circle runout to the bore axis within 0.03 mm.
Adjacent pitch error within 0.02 mm (hobbing quality 7–8).

Locating scheme

Blank bore Ø30 H7 located on an expanding arbor (datum A = bore axis); the blank face seats on a ground base plate (datum B).
The expanding sleeve grips the bore over its full length without damaging the ground surface.

Clamping scheme

A hydraulic drawbar pulls the arbor to expand the sleeve and seats the blank on the base plate.
The friction grip at the bore resists the hob's tangential force, so the blank cannot rotate on the arbor.

Calculation 1 — hobbing forces

Module 2 hob, blank Ø94 mm, feed 1.5 mm/rev, full tooth depth 4.5 mm. Typical loads: tangential F_t ≈ 1500 N, radial F_r ≈ 2000 N.

Tangential F_t ≈ 1500 N

Radial F_r ≈ 2000 N

Calculation 2 — arbor grip force

The friction grip at the bore must hold the tangential force: friction μ = 0.2 at the bore, safety factor K = 2.5.

Grip force Q = K · F_t / μ = 2.5 · 1500 / 0.2 ≈ 19 kN

An expanding arbor rated 30 kN gives margin. A positive drive (key or dog in the blank face) would remove the friction demand entirely.

Error budget (runout 0.03 mm)

Error source	mm
Arbor + expanding sleeve runout	0.010
Blank bore fit on the sleeve	0.012
Base plate face runout	0.008
Machine spindle runout	0.010
Hob runout + thermal growth	0.010
Root-sum-square total	0.023
Allowable	0.030

Result: RSS 0.023 mm < 0.03 mm. The expanding arbor keeps pitch-circle runout within tolerance across the batch.

These seven cases cover the common fixture families — drilling, boring, milling, inspection, broaching, grinding and gear cutting. In every one the same method works: set the tolerance, prove the locators, size the clamps from the forces, then sum the errors against the budget.