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Breaking of Screws and Strength Calculation (Fundamentals of Screw)

Breaking of Screws and Strength Calculation

If used below the allowable stress, there will be no problem. However, the safety factor must be taken into account.

(1) Tensile load in axial direction

Tensile load Pt = σt × As = πd2σt/4

P_t: : Tensile load in axial direction [N］

σ_b: : Bolt yield stress [N/mm²］

σ_b: : Bolt allowable stress [N/mm²］
(σ_t＝σ_b/safety factor α)

A_s: : Bolt effective cross-sectional area [mm²]

A_s: : πd²/4

d: : Bolt effective diameter (root diameter) [mm²]

**Unwin safety factor α based on tensile strength**
Material	Static load	Repeated load		Impact load
Material	Static load	Pulsating	Alternating	Impact load
Steel	3	5	8	12
Cast iron	4	6	10	15
Copper, soft metals	5	6	9	15

Allowable stress σ_t: ＝σ_b / safety factor α (from table above, safety factor 5, repeated, pulsating, steel)

: ＝1098 / 5

: ＝219.6 [N/mm²] {22.4[kgf/mm²]}

<Calculation examples>

Find a suitable size for a single hex socket head cap screw to receive repeated (pulsating) tensile loads of P_t = 1,960 N {200 kg}.
(Material: SCM435, 38 to 43 HRC, strength class: 12.9）

A_s＝P_t/σ_t＝1960 / 219.6＝8.9［mm²］

M5 bolt with an effective cross-sectional area larger than this should be selected.
In consideration of fatigue strength, M6 with an allowable load of 2,087 N {213 kgf} is selected from strength class 12.9 in the table below.

**Bolt fatigue strength (For screws: Fatigue strength is 2 million cycles)**
Nominal thread size	Effective cross-sectional area AS mm²	Strength class
		12.9		10.9
		Fatigue strength	Allowable load	Fatigue strength	Allowable load
		N/mm² {kgf/mm²}	N {kgf}	N/mm² {kgf/mm²}	N {kgf}
M4	8.78	128 {13.1}	1117 {114}	89 {9.1}	774 {79}
M5	14.2	111 {11.3}	1568 {160}	76 {7.8}	1088 {111}
M6	20.1	104 {10.6}	2087 {213}	73 {7.4}	1460 {149}
M8	36.6	87 {8.9}	3195 {326}	85 {8.7}	3116 {318}
M10	58	73 {7.4}	4204 {429}	72 {7.3}	4145 {423}
M12	84.3	66 {6.7}	5537 {565}	64 {6.5}	5370 {548}
M14	115	60 {6.1}	6880 {702}	59｛6.0｝	6762 {690}
M16	157	57 {5.8}	8928 {911}	56 {5.7}	8771 {895}
M20	245	51 {5.2}	12485 {1274}	50 {5.1}	12250 {1250}
M24	353	46 {4.7}	16258 {1659}	46 {4.7}	16258 {1659}

Fatigue strengths* have been excerpted from “Estimated values of fatigue limits for metric threads of machine screws, bolts, and nuts” (Yamamoto) and modified.

(2) Shear load on screw thread

[Simplified adjustment unit] X-axis left-right threaded stem open/close width adjustment unit

(3) Shear load of axis

[Simplified adjustment unit] XY axis feed threaded stem standard type

(4) Torsional load of axis

[High-precision stage] X-axis rack & pinion rectangular steel dovetail groove

Content shown here is only an example of how to determine strength.
In practice, various conditions must be taken into account, including hole-pitch accuracy, hole flatness, surface coarseness, roundness, plate material, parallelism, use of hardening, press machine accuracy, product production volume, and tool wear.
Therefore, the strength calculation values should be used as a guide. (They are not guaranteed values.)