You selected the right AGMA Class gearbox . You calculated the belt tension perfectly. But the moment you hit "Start," the belt snaps or the gearbox makes a terrifying clunk. The culprit is likely your Starting Method . In conveyor systems, the starting torque profile matters more than steady-state power. Note: We previously discussed VFDs as Energy Savers for pumps and fans. For conveyors, however, the goal is not lowering your electric bill—it is preventing your gearbox from exploding. Table of Contents 1. The Physics of Shock Loads 2. Why Soft Starters Stall Conveyors 3. The VFD Torque Advantage 4. Comparison: Cost vs. Protection 5. Final Verdict Advertisement 1. The Physics of Shock Loads When an AC induction motor starts Direct-On-Line (DOL), it draws 600% to 800% of its rated current (Inrush Current). More importantly, it produces a sudden spike known as Locked-Rotor Torqu...
In the post [Polynomial Cam Function (Part 3)], we explored the characteristics of the 5th-degree profile. Now, we put it to work.
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We will revisit the same die-press example from [Timing Diagram (Part 4)]. Originally, without overlap, the acceleration was a massive 4.154 m/s2. Using a Cycloid profile with overlap, we reduced it to 0.804 m/s2.
This time, we will use a Fifth-Degree (3-4-5) Polynomial combined with a Linear Cam Function. While the peak acceleration reduction might be similar to the Cycloid, the real advantage here is control—specifically, the ability to blend different motion segments seamlessly without stopping.
The Motion Strategy
Our constraints remain the same: Total displacement is 50 mm, and the die must dwell inside the hole for 30 mm.
Unit Conversion Note:
The equations we derived calculate velocity in mm/rad. To convert to real-world time domain:
• Velocity (mm/s) = Velocity (mm/rad) × Ï‰ (rad/s)
• Acceleration (mm/s2) = Acceleration (mm/rad2) × Ï‰2
The equations we derived calculate velocity in mm/rad. To convert to real-world time domain:
• Velocity (mm/s) = Velocity (mm/rad) × Ï‰ (rad/s)
• Acceleration (mm/s2) = Acceleration (mm/rad2) × Ï‰2
The Displacement Profile
Figure 1: The displacement profile divided into Linear (A-B) and Polynomial (B-C) sectors to optimize flow.
We have divided the motion into specific sectors to optimize the flow. Notice how we use a Linear segment (A-B) to handle the approach, connected to Polynomial segments for the heavy lifting.
| Sector | Function | Start Angle (°) | End Angle (°) | Start Height (mm) | End Height (mm) |
|---|---|---|---|---|---|
| A-B | Linear | 62 | 77 | 1.43 | 0.43 |
| B-C | Fifth-Degree | 77 | 206 | 0.43 | 50.00 |
| C-D | Dwell | 206 | 306 | 50.00 | 50.00 |
| D-A | Fifth-Degree | 306 | 62 | 50.00 | 1.43 |
Figure 2: The physical cam profile generated from the calculated displacement values.
Velocity Matching: The Secret to Smoothness
Figure 3: Velocity graph showing perfect continuity. The linear slope matches the polynomial start velocity exactly.
This is where the polynomial shines. To connect the Linear segment (A-B) to the Polynomial segment (B-C) without a shock, the velocities must match perfectly.
Calculating the Slope:
Slope (Velocity) = (0.43 - 1.43) / (77 - 62) = -0.0667 mm/deg
We input this value (-0.0667) as the Start Velocity (v0) for our polynomial calculation in sector B-C. This ensures a perfectly continuous transition with zero jerk spike.
Acceleration Analysis
Figure 4: Acceleration graph. We confirm there are no vertical spikes (Infinite Jerk) at the transition points.
Using motion simulation in Excel, we can visualize the result. We verify that there are no infinite spikes (Jerk) at the connecting points.
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Figure 5: Using Excel to calculate and verify the kinematic values before cutting metal.
Modern Application: Electronic Camming (E-Cam)
Today, physical cams are being replaced by Electronic Camming (E-Cam) profiles inside servo drives. However, the math remains identical.
Figure 6: Simulation of the die-press mechanism driven by the optimized polynomial profile.
By programming these 5th-degree polynomials into your servo controller, you can achieve smoother motion, higher speeds, and longer machine life—all without changing a single mechanical part.
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