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Timing Belt System Selection


This section documents the rigorous industrial-style selection process used to define the timing-belt transmission. The geometric and packaging constraints established here directly governed the final layout, motor mounting, and structural profile of the base.

V-Model Traceability: This page sizes the S8M timing-belt transmission to deliver RM-4 (Yaw angular velocity ≥ 150°/s). The tooth-skip mitigation strategy provides the design basis for subsystem acceptance criterion ROT-AC-1 (Transmission & support integrity — zero tooth-skip under shock load and reversal).

Motor Specifications

The drive calculations and hardware selection were based on motor parameters from a standard 400 W ZD-series unit with a 5GU25KB gearbox. This motor was chosen as it is a readily available school inventory item that provides substantial low-speed torque.

Parameter Specification
Model755BLD 400-24GU, 5GU, 25KB
Rated Power400 W (24 V)
Rated Speed3000 RPM (before gear reduction)
Gearhead5GU25KB with a 1:25 Gear Ratio
Output Shaft Speed120 RPM (after gear reduction)
Output Torque32 Nm (Allowance Torque: 20.0 Nm)

Torque Analysis Requirements

The rotating base is subject to three primary torque components: belt resistance/deformation, steady conformal rotation against friction, and holding/stall torque. The drive system must generate sufficient startup torque to reliably overcome:

Estimates place the maximum stall rotation torque at approximately ~102 Nm. The motor's 30 Nm allowance torque multiplied by the timing belt's transmission ratio ensures these operational demands are comfortably met.

Belt vs Gear Drive Rationale

A timing belt was explicitly chosen over a direct gear drive because it provides several mechanical advantages in a punch-receiving environment:

Tooth Profile Selection

Before standardising on the S8M series, different tooth profiles were evaluated:

Step 1: Required Speed Ratio

The original yaw-speed target was approximately 25 RPM. Using the 120 RPM output from the motor gearbox, the ideal required kinematic ratio was calculated as:

i = nin / nout = 120 / 25 = 4.8 i = Zlarge / Zsmall ≈ 4.8

This established a target reduction of 4.8:1 for the belt stage.

Step 2: Design Power

The belt must be sized not just for the motor's nominal power, but for the design power (Pd) using an overload service factor (Ks) of 2.2 to account for start/stop transients and the impulsive nature of punch resistance:

Pd = Pt × Ks = 400 W × 2.2 = 880 W = 0.88 kW

Step 3: Belt Series Selection

Candidate series from standard Misumi selection guides (H, S8M, P8M600, MTS8M, UP8M, EV5GT) were evaluated. The S8M series was selected because its 8 mm pitch provides excellent high-torque transmission capabilities while remaining flexible enough for the required wrap angles in our spatial envelope.

Step 4: Pulley Selection & Final Ratio

Based on the allowable minimum number of teeth at 120 RPM for the S8M series to prevent extreme bending stress on the belt, a 20-tooth small pulley was selected. For the large pulley, physical packaging constraints inside the 110 mm inner ring dimension of the slewing bearing mandated a 70-tooth pulley to match the slewing-bearing inner-ring geometry and allow screw-through fastening into the threaded mounting holes.

Small Pulley (20T) Pitch Diameter: dp = (8 × 20) / π = 50.93 mm Large Pulley (70T) Pitch Diameter: Dp = (8 × 70) / π = 178.25 mm Final Speed Ratio: 1:3.5 (Revised from 4.8:1 due to spatial constraints)

Step 5: Belt Length & Centre Distance

With an approximate initial desired centre distance (C') estimated at 286.18 mm (which incorporates a 30 mm assembly allowance), the theoretical belt length (Lp') was computed:

Lp' = 2C' + [π(Dp + dp) / 2] + [(Dp - dp)2 / 4C'] Lp' = 2(286.18) + [π(178.25 + 50.93) / 2] + [(178.25 - 50.93)2 / 4(286.18)] Lp' ≈ 946.5 mm

To align with standard off-the-shelf belt sizes, a standard belt length of 952 mm was selected from the catalogue. The final corrected centre distance (C) was then established based on this belt:

b = 2Lp - π(Dp + dp) = 2(952) - π(178.25 + 50.93) = 1184.0 C = [b + √(b2 - 8(Dp - dp)2)] / 8 = 289.0 mm

This final 289.0 mm dimension strictly dictated the mounting hole placement for the motor on the welded base.

Step 6: Belt Width

The required belt width (Bw) is calculated using the design power (Pd), reference transmission capacity (Po = 1.176 kW), engagement correction coefficient (Km = 1), and reference belt width (Wp = 60 mm).

Bw = [ Pd / (Po × Km) ] × Wp Bw = [ 0.88 / (1.176 × 1) ] × 60 = 44.89 mm → Final selected hardware belt width: 32 mm

The 32 mm width ensures that the belt can handle impulse loads without shearing teeth, but it also forced the base height profile to accommodate this clearance requirement.

Final Transmission Specifications

Parameter Selected Value
Belt SeriesS8M
Pitch8 mm
Belt Width32 mm
Small Pulley Teeth20
Large Pulley Teeth70 (fits inner ring mounting holes)
Speed Ratio1:3.5
Approx. Belt Length~952 mm
Centre Distance289.0 mm
Small Pulley RPM120 RPM
Output RPM34.3 RPM (205.7°/s)
Worst Case ScenarioStraight strike at 45° angle point

Tooth Skip Under Shock Mitigation

A critical risk in belt-driven systems is "tooth skip." If a user delivers a hard strike while the base is actively accelerating, maintaining low-velocity positioning, or reversing, the impulse can cause the belt to jump teeth if not properly constrained. To mitigate this risk without requiring excessive static belt tension (which could cause binding and instability), the design incorporates:

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