In automation design, the choice between a Stepper Motor and a Servo Motor is often decided by budget. But looking at the price tag alone is a mistake that leads to machine failure. Steppers are excellent for holding loads stationary (high holding torque). Servos are kings of high-speed motion. If you choose a stepper for a high-speed application, it will lose torque and "miss steps." If you choose a servo for a simple low-speed application, you have wasted $500. This guide explains the physics behind the choice. Table of Contents 1. Open Loop vs. Closed Loop (The Risk) 2. The Torque Curve: Speed Kills Steppers 3. Inertia Mismatch 4. Selection Summary Advertisement 1. Open Loop vs. Closed Loop (The Risk) The biggest difference is not the motor itself, but how it is controlled. Figure 1: Steppers run "blind" (Open Loop). Servos use an encoder to verify position (Closed Loop). ...
In the previous post [Timing Diagram (Part 1 - No Overlap Movement)], we determined that without overlap, our die must travel 50mm within a tight cam angle of just 55 degrees.
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Now, we must ask: What is the physical cost of this rapid movement?
To answer this, we calculate the Maximum Acceleration. In Machine Dynamics, acceleration is directly proportional to Force (F = m × a). High acceleration means high inertial forces, which lead to severe wear, vibration, and the need for expensive oversized servo motors.
Step 1: The Time Calculation
First, we need to convert our "Cam Angle" into actual "Time" in seconds.
Let:
N = Machine Speed (pieces per hour)
Bm = Indexing Angle (degrees)
Cycle time (sec) = 3600 / N
Indexing time tm = (Bm / 360) × Cycle time
Indexing time tm = (Bm / 360) × (3600 / N)
tm (sec) = (10 × Bm) / N
Step 2: Cycloid Cam Profile Equations
The die moves using a Cycloid Cam Profile, which is the industry standard for high-speed indexing because it has finite jerk.
Displacement Equation (h):
h = hm × [ t/tm - 1/(2Ï€) × sin(2Ï€ × t/tm) ]
Where:
hm = Maximum displacement (meters)
tm = Indexing time (seconds)
Ï€ = 3.14159...
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To find acceleration, we differentiate displacement twice.
Velocity (v = dh/dt):
v = (hm/tm) × [ 1 - cos(2Ï€ × t/tm) ]
Acceleration (a = dv/dt):
a = (2Ï€ × hm / tm2) × sin(2Ï€ × t/tm)
Step 3: The Maximum Acceleration Formula
The maximum acceleration (amplitude) occurs when the sine function equals 1. Therefore, the peak acceleration is:
amax = (2 × Ï€ × hm) / tm2
The Engineering Insight:
Notice that acceleration is inversely proportional to the square of the time (tm2). Since time is proportional to the cam angle (Bm), we arrive at a critical rule for Cam Design:
If you double the indexing angle, the maximum acceleration reduces by a factor of FOUR!
Notice that acceleration is inversely proportional to the square of the time (tm2). Since time is proportional to the cam angle (Bm), we arrive at a critical rule for Cam Design:
If you double the indexing angle, the maximum acceleration reduces by a factor of FOUR!
Step 4: Real-World Calculation (No Overlap)
Let's calculate the forces for our current "No Overlap" design from Part 1.
Parameters:
Machine Speed (N) = 2000 pcs/h
Cam Angle (Bm) = 55 deg (Very tight!)
Stroke (hm) = 50 mm = 0.05 m
1. Calculate Time (tm):
tm = (10 × 55) / 2000 = 0.275 seconds
2. Calculate Max Acceleration (amax):
amax = (2 × 3.1416 × 0.05) / 0.2752
amax = 4.154 m/s2
This is nearly 0.5 G of constant acceleration force, repeated 2,000 times an hour. This will likely cause premature wear on the cam followers and linkages.
In the Next Post (Part 3), we will apply the "Overlap" technique to increase the indexing angle and see how dramatically this acceleration number drops.
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