Calibration: ISO 148 and ASME Impact Bending Machine

May 21, 2026

📋 Summary

Comparison Table: Full vs. Reduced Direct Verification
Calculation Methods — All ISO 148-2 Quantities
Potential Energy Ep
No-load Losses (p + p')
Expanded Uncertainty U (variable k)
Table 2 — Criteria b and Bv
Interpretation of the Report
Measured Balance — Complete Example
Compliance Conclusion
Validation in Real Conditions

Calibration Methodology

The calibration of a Charpy impact testing machine is based on two complementary levels of verification defined by ISO 148-2 and ASTM E23: direct verification (measurement of physical quantities) and indirect verification (traceable CRMs from NIST/BAM/IRMM). Uncertainty is evaluated according to GUM (JCGM 100:2008).

⚠️ Note ISO 148-2 §A.1.2: U(KV) is provided for information only. Compliance with Table 2 (b and Bv) is assessed directly without a guard band, unless otherwise instructed by the customer.

1. Comparison Table — Full vs. Reduced Direct Verification (ISO 148-2)

📌 Frequencies (§8): Full = installation, relocation, unsatisfactory indirect results | Reduced = before each indirect verification + daily use (§8.5)

Verification	Ref. §	Full	Reduced	Criterion / Tolerance
🏗️ FOUNDATION AND FRAME
Machine level	§6.2.1	✅	—	Level bubble centered
Ground fixing / bolts	§6.2.3a	✅	✅	Manufacturer's torque
Frame rigidity	§6.2.2	✅	—	No visible deformation
⚙️ PENDULUM
Hammer mass m	§6.3.1	✅	—	Nominal ±0.1 %
Center of percussion L	§6.3.2	✅	—	L = g×T²/(4π²) \| ±1 % of L_nominal
Impact velocity v	§6.3.3	✅	—	v = √(2gL(1−cosα)) \| 5.0–5.5 m/s
Axial bearing play	§6.3.8	✅	✅	< 0.25 mm
Lift angle α	§6.3.4	✅	—	Nominal ±0.3°
🔪 STRIKER AND ANVILS
Striker radius	§6.3.5	✅	✅ visual	2.5 mm (±0.5) or 8 mm (±0.5)
Striker angle	§6.3.5	✅	✅ if changed	90° ± 2°
Distance between anvils	§6.3.6	✅	—	40 ±0.2 mm
Anvil radius	§6.3.6	✅	—	1.0 mm (±0.07) or 1.5 mm (±0.07)
Specimen centering	§6.3.7	✅	—	±0.5 mm
📊 ENERGY MEASUREMENTS
Potential energy Ep	§6.4.2	✅	—	KN ±1 % \| Ep = m×g×L×(1−cosα)
Index losses p	§6.4.5.1	✅	✅	p = K1 − K2 (4 determinations)
Bearing+air losses p'	§6.4.5.2	✅	✅	p' = (K3−K2)/10 (10 half-oscillations)
Total losses p+p'	§6.4.5.3	✅	✅	< 0.5 % of KN
KS indicator (6 points)	§6.4.3	✅	✅	\|KS−Kcalc\|/Kcalc <1% (≥50%KN) or <0.5%KN
🧪 INDIRECT VERIFICATION (CRM)
Number of CRM levels	§7.2	✅ ≥2	✅ ≥2	Min. 2 levels, ≥5 specimens/level
Repeatability b = KVmax−KVmin	Table 2	✅	✅	≤6 J (KVR<40J) \| ≤15%×KVR (KVR≥40J)
Error \|Bv\| = \|KV̄v−KVR\|	Table 2	✅	✅	≤4 J (KVR<40J) \| ≤10%×KVR (KVR≥40J)

2. Calculation Methods — All ISO 148-2 Quantities

Quantity	Normative formula	Reference	Numerical Example
📐 DIRECT VERIFICATION
Center of percussion L	L = g×T²/(4π²)	§6.4.6 Eq.13	T=1.824s → L=0.826 m
Potential energy Ep	Ep = m×g×L×(1−cosα)	§6.4.2 Eq.1	23.17×9.807×0.826×1.766 = 331.4 J
Impact velocity v	v = √(2×g×L×(1−cosα))	§6.3.3	√(2×9.807×0.826×1.766) = 5.35 m/s
Index losses p	p = K1 − K2	§6.4.5.1	Avg. 4 tests with/without index
Bearing losses p'	p' = (K3 − K2) / 10	§6.4.5.2	10 half-oscillations
Total loss E_vide	E_vide = p + p'	§6.4.5.3	1.85+1.78 = 3.63 J = 1.10% KN ❌
KS Indicator	Kcalc = m×g×L×(cosβ−cosα)	§6.4.3 Eq.2	6 points: 0,10,20,30,50,80% KN
🧪 INDIRECT VERIFICATION (ISO 148-2 Annex A)
Bias Bv	Bv = KV̄v − KVR	Eq. A.1	111.8 − 108.0 = +3.8 J
Repeatability b	b = KVmax − KVmin	Table 2	114 − 109 = 5 J ≤ 16.2 J ✅
u(KV̄v)	u(KV̄v) = sv / √nv	Eq. A.2	1.924/√5 = 0.860 J \| νB=4
u(Bv)	u(Bv) = √[u²(KV̄v)+u²RM]	Eq. A.3	√[0.860²+2.5²] = 2.645 J
uv	uv = √[u²(Bv) + Bv²]	Eq. A.4	√[2.645²+3.8²] = 4.635 J
νv (Welch-Satterthwaite)	νv = uv⁴/[u⁴(KV̄v)/νB + u⁴RM/νRM + Bv⁴/νB]	Eq. A.5	νRM=∞ → νv calculated
📏 TEST UNCERTAINTY (ISO 148-1 Annex E)
u(x̄) repeatability	u(x̄) = sx / √n	Eq. E.3	νx = n−1
u(r) resolution	u(r) = r / √3	Eq. E.4	r=0.5J → u(r)=0.289 J
u(KV) combined	u(KV) = √[u²(x̄)+u²v+u²(r)]	Eq. E.5	√[0.860²+4.635²+0.289²] = 4.730 J
νKV (Welch-Satterthwaite)	νKV = u⁴(KV)/[u⁴(x̄)/νx + u⁴v/νv]	Eq. E.6	νKV ≈ 53
k = t95(νKV)	Table E.5 ISO 148-1	Eq. E.7	νKV=53 → k=2.01 ≈ 2.0
U(KV) expanded	U(KV) = k × u(KV)	Eq. E.7	2.0 × 4.730 = 9.46 J ℹ️ informative

3. Potential Energy Ep

Ep = m×g×L×(1−cosα) = 23.170×9.8065×0.826×1.766 = 331.4 J ⚠️ Adjust α (nominal 300 J)

📐 Origin of values (ISO 148-2 §6.4.2, Eq.1):

m = 23.170 kg — Hammer mass (±0.1 %)
g = 9.8065 m/s² — Certified local value from IGN
L = 0.826 m — Center of percussion via T=1.824 s: L=g×T²/(4π²)
α = 140° — Lift angle (±0.3°)
⚠️ Ep = 331.4 J exceeds 300 J by +10.5 % → Recalibrate α to 126.8°

4. No-Load Losses — Normative Procedure (§6.4.5)

⚠️ E_vide = p + p' — DO NOT subtract from individual KVs. Used only for direct compliance criterion.

Step 1 — Index Friction p (§6.4.5.1)

Test with index → K1 | Without moving index → K2 | p = K1 − K2 | Average of 4 determinations

Step 2 — Bearing + Air Friction p' (§6.4.5.2)

10 half-oscillations → K3 | p' = (K3 − K2) / 10

Step 3 — Criterion (§6.4.5.3)

E_empty = p + p' < 0.5% of KN | For KN=300 J → E_empty < 1.5 J | Example: 1.85+1.78 = 3.63 J = 1.10% → ❌ NC

5. Expanded uncertainty U(KV) — k variable

See Table Section 2 for all formulas. Numerical application: u(KV)=4.730 J | νKV=53 | k=2.01 | U(KV)=9.46 J (informative §A.1.2)

⚠️ k ≠ 2 if νKV < 30. Always calculate νKV via Welch-Satterthwaite before choosing k (Table E.5 ISO 148-1).

ν	k=t95(ν)	Typical case	ν	k=t95(ν)	Typical case
2	4.30	n=3, dominant uv	10	2.23	n=3, low energy
3	3.18		15	2.13
4	2.78	n=3, high energy	20	2.09
5	2.57	n=5, strong uv	30	2.04
7	2.36	Ex. standard A.1 (νv=7)	50	2.01	n=5, νKV≈53 ✅
8	2.31	Ex. standard E.3 (νKV=8)	∞	1.96	Normal distribution

6. Table 2 — ISO 148-2 conformity criteria

KVR Level	b max (KVmax−KVmin)	\|Bv\| max	For KVR=108 J
KVR < 40 J	6 J	4 J	—
KVR ≥ 40 J	15% × KVR	10% × KVR	b≤16.2 J \| \|Bv\|≤10.8 J

✅ Example: b=5 J ≤ 16.2 J ✅ | |Bv|=3.8 J ≤ 10.8 J ✅ — Direct conformity without guard band (§A.1.2)

7. Interpretation of the report (§9 ISO 148-2)

Section §9	Mandatory content
§9.1 General	Reference ISO 148-2:2008, manufacturer, model, serial no., knife radius, owner, date
§9.2 Direct	KN, impact velocity, empty losses p+p'
§9.3 Indirect	CRM (KVR, KV_read), b=KVmax−KVmin, Bv, conformity Table 2, informative U(KV)

8. Measured balance — Complete example (ZR-2019-0047)

Quantity	Value	Criterion	Status
Center of percussion L	0.8264 m	0.826 ±1%	✅
Potential energy Ep	331.4 J	300 J ±1%	⚠️ +10.5%
Impact velocity v	5.35 m/s	5.0–5.5 m/s	✅
Empty losses p+p'	3.63 J / 1.10%	<0.5% KN	❌ NC
Knife radius	7.9 mm	7.5–8.5 mm	✅
Anvil spacing	40.1 mm	40 ±0.2 mm	✅
K̄V \| Bv \| b	111.8 J \| +3.8 J \| 5 J	\|Bv\|≤10.8J \| b≤16.2J	✅ ✅
U(KV) informative	9.46 J (k=2.0)	ℹ️ §A.1.2	ℹ️
Final decision	❌ NOT VALIDATED		Bearing maintenance

9. Conclusion of conformity

❌ Non-conformity: p+p' = 3.63 J (1.10%) > 0.5% KN (§6.4.5.3). Machine out of service until maintenance and new direct verification.

✅ After maintenance (simulation): p+p'=1.20 J (0.36%) ✅ | b=5 J ✅ | |Bv|=3.8 J ✅
Declaration: “Machine ZR-2019-0047 compliant with ISO 148-2 — K̄V=(111.8 ± 9.5) J (k=2.0, νKV=53) — informative §A.1.2”

10. Validation in real conditions — 3 CRM levels

In accordance with ISO 148-2 §7.2: minimum 2 levels, ≥5 specimens each. k determined via table E.5.

CRM Level	K̄V (J)	b (J)	\|Bv\| (J)	νKV	k	U(KV) ℹ️
Low (19.3 J)	20.20	1 J ✅	0.9 J ✅	10.4	2.23	1.73 J
Medium (108 J)	111.80	5 J ✅	3.8 J ✅	53	2.01	9.46 J
High (200 J)	180.20	7.5 J ✅	19.8 J ✅	4.3	2.78	56.67 J ⚠️

⚠️ Normative references: ISO 148-1:2016 (Annex E) — ISO 148-2:2008/2016 (§6, §7, §8, §9, Annexes A and B) — ASTM E23 — ASTM A148 — JCGM 100:2008 (GUM) — ISO/IEC 17025:2017 — ILAC-G8:09/2019 — EA-4/02 M:2022