technical data Synchronous Belts and Belt Sprockets Selection

Selection based on torque/Selection example

Items required for selection

The items required for selection are as follows. Please define the conditions for each.

  • ・Motor output torque N・m, output shaft rotation speed r/min, shaft diameter
  • - Type of driven machine, rotation speed r/min, shaft diameter
  • ・Center distance
  • - Daily usage time and startup frequency
  • ・Speed ratio
  • - Whether or not an idler is used
  • ・Other conditions

Determining the design torque

The design torque is calculated using the following formula:

Pt = Pm × (Ko + Ki + Ks) × Ka × Ke※

*When using Ultra PX Belt HA specification (oil/water resistant) in an environment where it may be exposed to oil or water, or when using PX Belt water resistant specification in an environment where it may be exposed to water, multiply the operating atmosphere coefficient (Ke) by 1.2.

Determining belt size and pulley tooth count

  • (1) Use the provisional selection table to provisionally select a belt size based on the design torque and small pulley rotation speed.
  • (2) Please provisionally select the belt width and the number of teeth of the pinion pulley from the standard transmission torque table in the Product Info. When doing so, please note the following:
    • - Select a number of teeth for the pinion pulley other than the colored portion of the standard transmission torque.
    • - Select a small pulley so that its pitch diameter is greater than the belt width.
    • - Make sure that the usable range of the small pulley shaft hole satisfies the diameter of the shaft being used.
  • (3) Determine the number of teeth on the large pulley based on the number of teeth on the small pulley and the speed ratio. Also, check the shaft bore diameter to be used.

Selection of belt length and center distance

  • (1) Calculate the approximate length of the belt (L') and select the belt with the closest length to this value from the belt length list.

    L'= 2C + 1.57 (Dp + dp) + (Dp - dp)2 4C

    • L': Approximate belt length mm
    • C: Center distance mm
    • Dp: Large pulley pitch circle diameter mm
    • dp: Pitch circle diameter of small pulley mm
  • (2) Calculate the center distance (C) from the selected belt length (L).

    C = B + B2 - 2(Dp - dp)2 4

    B = L - 1.57(Dp + dp)

    • L: Belt length mm

Correction by number of meshing teeth

It is not recommended to use a pulley with less than six meshing teeth, but if you must use one, please make adjustments based on the number of meshing teeth.

After determining the number of teeth in mesh, determine the meshing correction factor using Table 6.

Also, design the meshing angle so that the drive pulley is 120° or more and the driven pulley is 90° or more.

Zm = N × Φ 360°

Φ = 180° - 57°(Dp - dp) C

  • Zm: Number of meshing teeth on pinion
  • N: Number of teeth on pinion pulley
  • Φ: Belt winding angle around the small pulley (degrees)
  • Dp: Large pulley pitch circle diameter mm
  • dp: Pitch circle diameter of small pulley mm
  • C: Center distance mm

Checking the belt width

Check that the belt width satisfies the design torque.

Pt ≦ Pr × Kw × Km × KL

Kw ≧ Pt Pr × Km × KL

sizing example (selection based on torque)

Items required for selection

The items required for selection are as follows:

item Content
Motor output shaft torque, rotation speed, shaft diameter Rated torque 18.6N・m (100%), 1500 r/min, 32mm
Type of driven machine, rotation speed, shaft diameter Intermittent drive conveyor, 300 r/min, 30 mm
Center distance 250mm～350mm
Daily usage time and startup frequency 8 hours/day, 5 times/day
speed ratio 1：1
Whether or not an idler is used None
Other terms Servo motor reducer 1/5, pulley outer diameter Φ100 or less

Determining the design torque

Determine the design torque by finding each correction factor that suits the operating conditions.

  • Load correction factor (Ko) ..... 1.5
  • Correction factor when using idler (Ki) ..... 0
  • Acceleration correction factor (Ks) ..... 0
  • Start-stop frequency correction factor (Ka) ..... 1.2
  • Design torque Pt = Pm × (Ko + Ki + Ks) × Ka × Ke * = 18.6 × (1.5 + 0 + 0) × 1.2 = 33.48
    The design torque from the servo motor reducer 1/5 is 5 x 33.48 = 167.4 N m.

Determining belt size and pulley tooth count

  • (1) Temporarily select a belt size from the temporary selection table. In this case, UP8M-HC is temporarily selected based on the design torque (167.4 N m) and drive pulley rotation speed (300 r/min = 1500/5).
  • (2) Select the belt width and number of pulley teeth from the standard transmission torque table, taking into consideration the speed ratio, shaft diameters of the prime mover and driven machine, and other conditions.
    In this example, we will select UP8M-HC (belt width 40 mm) with 36 pulley teeth (dp = 91.67 mm, flange outer diameter Φ97 mm). Refer to the dimensions of each pulley.

Determining belt length and center distance

  • (1) Calculate the approximate length of the belt (L').

    L' = 2C + 1.57(Dp + dp) + (dp - dp )2 4C = 2 × 300 + 1.57(91.67 + 91.67) + (91.67 + 91.67)2 4 × 300 = 887.84mm

    The belt that comes closest to this approximate length is 880UP8M (110 teeth) from the list of types and dimensions.

  • (2) Calculate the center distance (C) at this time.

    B = L - 1.57(Dp + dp) = 880 - 1.57(91.67 + 91.67) = 592.15

    C = B + B2 - 2(Dp - dp)2 4 = 592.15 + 592.152 - 2(91.67 - 91.67)2 4 = 296.07mm

Correction by number of meshing teeth

Determine the number of belt teeth that mesh with the pinion pulley and determine the meshing correction coefficient.

Φ = 180° - 57°(Dp - dp) C = 180° - 57°(91.67 - 91.67) 296.07 = 180°

Zm = N × Φ 360° = 36 × 180 360° = 18 teeth

Therefore, from the meshing correction coefficient table, Km = 1.0.

Determining the belt width

The belt width that satisfies the design torque is finally determined.

Kw ≧ Pt Pr × Km × KL = 167.4 68.5 × 1.0 × 0.9 = 2.72

Therefore, the belt that satisfies the width coefficient is UP8M40-HC (belt width 40mm).

Selection results

  • Belt: BG880UP8M40-HC
  • Small pulley: PT36P8M40AF or BF
  • Large pulley: PT36P8M40AF or BF
  • Center distance: 296.07mm

After deciding on the pulley model number, you can select the pulley fastening method.

Please also refer to the calculation formula used for belt selection.