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Calculation

Calculation of belt width

Precise design to tooth shear strength
For the calculation of the belt width the actual torque characteristic of the drive motor - from drive or brake - is to be used. At first the maximum motor torque according to formula (2) is to be converted to the respective circumferencial force FU. From the calculated circumferencial force the minimum width of the timing belt, according to formula (1), can be

calculated.

The result of the calculated belt width (b in cm) is the required belt width for transmit the circumferencial force FU via the meshing teeth from the pulley to the belt (or reverse). The calculated belt width is to be rounded-up to the next larger standard belt width.

Check the tensile load

Check the tensile loads for the calculated belt width, which become effective due to the pre-tension force FV according to formula (7) and the overlapping circumferencial force FU according to formula (8). The max. permitted tensile loads according to formula (9) must not be exceeded.
If necessary, select the next larger belt width.

Safety factors

Special additional safety factors are not necessary for the BRECO® polyurethane timing belt. When, however, in addition to the maximum circumferencial force FU are to be expected unevennesses, variations or impact shocks, which are not yet cosidered in the design, any additional safety factors can be added to the belt width.

Accuracy of the rotational to linear translation of movement

The BRECO® polyurethane timing belt transmits rotational movements into the corresponding linear motions via the pulley of the drive station. The procedure can be repeated as often as required and is a continous operation with BRECO® polyurethane timing belts. Deviation from the linear line can occur due to different forces and tolerances. The following is a description of causes and measures to be taken.

1. Precision of repeatability
The term repeatability of a linear drive implies the capability of regaining a position once accessed under the same conditions. In linear systems, repeatabilities of notably less than +/- 0.1 mm per metre of path travelled can be achieved with BRECO®-AT timing belts. Prerequisite for a consistent repeatability is the retaining of the minimum pre-tension force according to the equation (7).

2. Positioning precision
The term positioning precision of a linear drive is the capability to convert the turning angle of the pulley into the attendant setpoint linear path via the timing belt. The achievable actual linear path depends on the active forces and of the tolerances of all assembly groups involved in the sequence of movement.
Measures: Individual measures according to the following points 3 - 8 are to be applied, depending on the dominating values.

Stiffness / force-extension behaviour
If varying forces act on the linear unit, a correspondingly different elongation becomes effective. The corresponding “specific elasticities” are indicated in the Technical Data for steel cord tension members.
Measures: Plan a wider timing belt to keep the elongation small. The positioning deviation resulting from the elongation behaviour can be calculated with the equations (12) and (13). Ensure a dimensionally stable surrounding design.

4. Inverse fault
When a linear position is moved to from a different direction, an inverse fault could occur in relation to the desired position. In other words: If the forces acting on the linear unit inverse, an inverse fault could occur.
Measures: Design linear guides and the entire system such that low friction occurs. Design the pulley of the drive pulley assembly with a narrower tooth gap or with a "0" tooth gap. Normal requirements with regard to the positioning precision are reached with the standard tooth gap. For the use of special tooth gaps, please ask for our technical support.

5. Length tolerance, pitch deviation
A length tolerance in the timing belt leads to a pitch deviation. In this case, all pitches remain identical in relation to each other. Once installed, amongst others, a length tolerance/pitch deviation depends on the pre-tension applied. The length tolerance/pitch deviation is available in pre-defined ranges, due to the production method.
Measures: Use BRECO® polyurethane timing belts in the minus tolerance range, and pre-tension to the setpoint dimension once installed. Ask for our specialist support.

6. Pitch faults
The term pitch faults defines irregularities of neighbouring pitches. Pitch faults have no cumulative effect within one belt section.
Meaures: Design the pulley of the drive pulley assembly as large as possible. The larger the number of teeth meshing in the pulley, the more efficient pitch errors are suppressed.

7. Eccentricity fault, centre offset
The eccentricity fault and/or centre offset of at least one pulley or tension roller involved can lead to an irregular movement in the linear system. This type of fault should be assumed when sinusoidal movements occur in the linear movement sequence.
Measures: Check the concentric precision and the centre offset. Reduce the tolerance range, if necessary.

8. Ambient temperature, elongation under heat
The linear elongation under heat of the BRECO® polyurethane timing belt with steel cord tension members shows the same values as the linear elongation under heat of a surrounding steel structure. No change of the pre-tension force is then to be expected. In the case of a surrounding aluminium structure and a rise of the ambient temperature, a slight increase of the pre-tension can be expected. The attendant linear path changes with the linear elongation behaviour under heat of the surrounding structure.
Measures: The influence of elongation under heat in the belt and also in the surrounding structure are minor. Temperature influences only need to be taken into account in exceptional cases.

User information

Part of the offered formulae contain simplified assumptions.
e.g. calculation of the positioning deviation according to equations (12) and (13): The elongation behaviour of the tension member is also taken into account in the area of the pulley angle of wrap. However, the elasticity of the belt tooth has been neglected. e.g. the vibration behaviour according to equation (14):
Only the vibrating mass m of the linear slide mL is taken into account. The vibrating mass of the timing belt, the pulleys as well as the retroaction of the elasticity to the surrounding structure have not been taken into consideration.

For this reason, we point out that corresponding deviations have to be expected, depending on the drive geometry selected.