Technical Data  Drive chain  Chain selection

Selection Formulae

Symbols and units used in formulae

Code Description SI Unit {Gravity unit }
αb Load deceleration m/s2 m/s2
αs Load acceleration m/s2 m/s2
C Center distance in pitches - -
C′ Center distance between shafts m m
d Pitch circle diameter of the reducer output shaft sprocket mm mm
d1 Pitch circle diameter of the small sprocket mm mm
d2 Pitch circle diameter of the large sprocket mm mm
D Outer diameter of the drum mm mm
Fb Chain tension during deceleration kN kgf
F'b Design chain tension during deceleration kN kgf
FC Chain tension of shuttle drive kN kgf
F'C Design chain tension of shuttle drive kN kgf
Fℓ Chain tension from torque on load side (actual load) kN kgf
F'ℓ Design chain tension from torque on load side (actual load) kN kgf
Fm Chain tension from prime mover rated output kN kgf
F'm Design chain tension from prime mover rated output kN kgf
Fms Chain tension from starting torque of prime mover kN kgf
F'ms Design chain tension from starting torque of prime mover kN kgf
Fmb Chain tension from braking torque of prime mover kN kgf
F'mb Design chain tension from braking torque of prime mover kN kgf
FS Chain tension when accelerating kN kgf
F'S Design chain tension when accelerating kN kgf
FW Chain tension from load (actual load) kN kgf
F'W Design chain tension from load (actual load) kN kgf
f1 Coefficient of friction between roller and rail (with lubrication 0.14 No lube 0.21) - -
G Standard acceleration from gravity G = 9.80665m/S2 - -
i Speed ratio (example) if ratio is 1/30 then i = 30 - -
Iℓ{GD2ℓ} Converted moment of inertia of the loaded prime mover shaft kg･m2 kgf･m2
Im{GD2m} Moment of inertia of the prime mover shaft kg･m2 kgf･m2
K Shock factor - -
Kn RPM - -
Ks Service factor - -
Ku Imbalance load factor - -
Kv Pin gear speed factor - -
Kz Number of teeth factor - -
L Chain length (No. of links ) - -
m Unit mass of chain {Weight } kg/m kgf/m
M{W} Mass of load {Weight } kg kgf
n RPM of the small sprocket r/min rpm
n1 RPM of driver shaft r/min rpm
n2 RPM of driven shaft (RPM of driven shaft ) r/min rpm
P Chain pitch mm mm
R Inertia ratio - -
S Attachment height for RS attachment chain (distance from the drum surface to the chain pitch center ) mm mm
tb Deceleration time s s
tS Acceleration time s s
Tb Motor braking torque %(kN･m) %(kgf･m)
Tmax Maximum (stalling) torque of motor %(kN･m) %(kgf･m)
TS Starting torque of motor %(kN･m) %(kgf･m)
Tℓ Load torque kN･m kgf･m
Tm Working torque kN･m kgf･m
Tn Rated torque of the prime mover kN･m kgf･m
V Chain speed m/min m/min
Vℓ Load speed m/min m/min
Z Number of teeth of large sprocket - -
Z′ Number of teeth of small sprocket - -
ω Angular velocity of the prime mover shaft rad/min rad/min
ωb Angular deceleration of the prime mover shaft rad/s2 rad/s2
ωS Angular acceleration of the prime mover shaft rad/s2 rad/s2

Formulae

  • 1. Perform all selections using a transmission efficiency, including the chain, of η = 1.
  • 2. Use the values calculated in items 13 and 14 of this table for the tension and kW ratings used for selection.
Item SI Unit {Gravity unit }

1. Chain length (No. of links )：L
Winding drive

Ordinary transmission between two shafts

  • (1)When the number of teeth and distance between shafts has been decided for both sprockets:

    L = Z + Z' 2 + 2C + Z - Z' 6.28 2 C

  • (2)When the number of links of chain and the number of teeth has been decided:
    C = 1 8   2L - Z - Z' + (2L - Z - Z')2 - 8 9.86 (Z - Z')2
    Even if the fractional part of the value found for L (below that of the decimal point) is small, round it up to the nearest integer and add a link.
    An offset link must be used when an odd number of links exist. However, if possible, change the number of teeth on the sprocket or the distance between shafts so that an even number of links may be used.

Pin gear drive

When using a chain with attachment around a drum

L = 180° tan-1 P D + 2S

  • P：Chain pitch
  • D：Outer diameter of the drum
  • S：Height of attachment
Pin gear drive
  • * Round L up to an even number of links.
  • * When attaching the chain attachment around the drum, insert shims at equal intervals for adjustment.

2. Chain speed ：V

V = P × Z' × n 1000 (m/min)

3. Chain tension from rated output (kW) and rated RPM of motor: Fm ：Fm

Fm = 60 × kW V (kN)

Fm = 6120 × kW V (kgf)

4. Moment of inertia where the prime mover shaft converts the moment of inertia of the load I (GD2) ：Iℓ(GD2ℓ)

Iℓ = M × V 2πn1 2 (kg・m2)

GD2ℓ = W × V πn1 2 (kgf・m2)

5. Rated torque of the prime mover ：Tn

Tn = 9.55 × kW n1 (kN・m)

Tn = 974 × kW n1 (kgf・m)

6. Working torque ：Tm

Tm = Ts(%) + Tmax(%) 2 × 100 × Tn (kN・m)
or
Tm = Ts(kN・m) + Tmax(kN・m) 2 (kN・m)

Tm = Ts(%) + Tmax(%) 2 × 100 × Tn (kgf・m)
or
Tm = Ts(kgf・m) + Tmax(kgf・m) 2 (kgf・m)

7. Chain tension from starting torque ：Fms

Fms = Ts(%) × i {d/(2 × 1000)} × 100 × Tn × 1(kN)
or
Fms = Ts(kN・m) × i d/(2 × 1000) × 1(kN)

Fms = Ts(%) × i {d/(2 × 1000)} × 100 × Tn × 1(kgf)
or
Fms = Ts(kgf・m) × i d/(2 × 1000) × 1(kgf)

Chain tension from braking torque ：Fms

Fmb = Tb(%) × i {d/(2 × 1000)} × 100 × Tn × 1.2*(kN)
or
Fmb = Tb(kN・m) × i d/(2 × 1000) × 1.2*(kN)

※ : Constants

Fmb = Tb(%) × i {d/(2 × 1000)} × 100 × Tn × 1.2*(kgf)
or
Fmb = Tb(kgf・m) × i d/(2 × 1000) × 1.2*(kgf)

※ : Constants

8. Acceleration time ：ts
If acceleration time is already known, use that.

ts = (Im + Iℓ) × n1 9550 × (Tm - Tℓ) (s)

ts = (GD2m + GD2ℓ) × n1 375 × (Tm - Tℓ) (s)

9. Deceleration time ：tb
If deceleration time is already known, use that.

±：When there is a negative load, such as a hanging load, use -Tℓ.

tb = (Im + Iℓ) × n1 9550 × (Tb ± Tℓ) (s)

tb = (GD2m + GD2ℓ) × n1 375 × (Tb ± Tℓ) (s)

10. Acceleration

  • Linear motion ：αs
  • Rotational motion ：ωs

Assuming linear acceleration.

In other situations, calculate using maximum acceleration.

Linear motion (Load acceleration ) αs = Vℓ ts × 60

Rotational motion (Angular velocity of the prime mover shaft ) ω = 2π × n1

Rotational motion (Angular acceleration of the prime mover shaft ) ωs = ω ts × 60

11. Deceleration

  • Linear motion ：αb
  • Rotational motion ：ωb

Assuming linear acceleration.

In other situations, calculate using maximum deceleration.

Linear motion (Load deceleration ) αb = Vℓ tb × 60

Rotational motion (Angular velocity of the prime mover shaft ) ω = 2π × n1

Rotational motion (Angular deceleration of the prime mover shaft ) ωb = ω tb × 60

12. Chain tension when accelerating ：Fs

Linear motion Fs = M × αs 1000 + Fw

Rotational motion Fs = Iℓ × ωs × i 1000 × d 2 × 1000 + Fw

Linear motion Fs = M × αs G + Fw

Rotational motion Fs = GD2ℓ/4 × ωs × i d 2 × 1000 × G + Fw

Chain tension during deceleration ：Fb

Linear motion Fb = M × αb 1000 + Fw

Rotational motion Fb = Iℓ × ωb × i 1000 × d 2 × 1000 + Fw

Linear motion Fb = M × αb G + Fw

Rotational motion Fb = GD2ℓ/4 × ωb × i d 2 × 1000 × G + Fw

13. Design kW(for general selection )

 Design kW = Rated kW of motor kW × Ks (kW)

14. Design chain tension

Design chain tension from motor ：F'm

 F'm = Fm × Ks × Kn × Kz (kN) {kgf}

Design chain tension from starting torque ：F'ms

 F'ms = Fms × K × Kn × Kz (kN) {kgf}

Design chain tension from stalling torque ：F'mb

 F'mb = Fmb × K × Kn × Kz (kN) {kgf}

Design chain tension of shuttle drive ：F'c

 F'c = Fc × Ks × Kn × Kz (kN) {kgf}

Design chain tension when accelerating ：F's

 F's = Fs × Kn × Kz (kN) {kgf}

Design chain tension during deceleration ：F'b

 F'b = Fb × Kn × Kz (kN) {kgf}

Design chain tension from load ：F'w

F'w = M × Ks × Kn × Kz × G 1000 (kN)

F′w = W (Or Fw ) × Ks × Kn × Kz(kgf)

If the mass M (weight W) is not known, use the rated torque Tn of the motor to calculate the shaft torque T = Tn x i kN·m {kgf·m}, and use F = 2T/d in place of W.

15. Inertia ratio ：R

R = Iℓ Im

R = GD2ℓ GD2m

16. Conversion of the flywheel effect (GD2) to moment of inertia(I)

1kg・m2...(I) 4kgf・m2...(GD2)

All chain tensions in the above formulae are the tensions when one strand of chain is used.

When using two or more strands of chain, calculate the chain tension for one strand and multiply it by the imbalance load factor Ku (Table 4) for the number of strands used.

×
(Drag to move. )

Imbalance load factor Ku

When using two or four chains for lifting or shuttle traction drive, the chain load will not be uniform.

This must be accounted for by multiplying the following imbalance load coefficient Ku to adjust the left-and-right load imbalance.

(ex. ) For four lifting strands, the imbalance load factor for one strand

Ku = 0.6 × 0.6 = 0.36

Table 4 Imbalance load factor Ks
two 0.6
four 0.36
Back to top