If you’re setting up a punching operation with pneumatic or hydraulic presses, the servo feeds are relatively simple, because you have full control over the presses and when they’re fired. Mechanical presses running in continuous require a balance of timing and accelerations. If your timing is off, you could break tooling or miss your target. If your accelerations are off, the feed rolls could slip and induce a variance or even leave marks on the part.

Timing is directly impacted by production rate and press angle. The higher the rate, the faster the press has to run. The faster the press runs, the more acceleration you need to make servo moves. Ultimately, production rate is capped by the capability of the press motor/drive and the maximum acceleration rate of the servo motor.

The most efficient way to dial in a particular production line is to setup the servo to handle the most extreme production rate and minimize setup changes for less-demanding applications. The demands of production – balancing speed, quality, wear, and cost – might require a unique set of parameters for every job a line might run. This post will walk through the math of using press speed and part/punch distance to calculate the speeds and accelerations required from the servo.

## Example Setup

Let’s use an example press that is capable of 300 spm, and we must produce a part with multiple punch hits of varying lengths. Only the longest move is a concern, and in this case it’s a 5.5″ move. Our servo motor driving the feed rolls is capable of a maximum acceleration of 575 ips^{2}.

When we load the die into the press and inch the tooling into place, we see that the press angle is 50º. This is the total angle of the press rotation that the tooling is in contact with the material. In this case the punch enters the steel at 155º and exits when the press is at 205º. I always recommend a safety margin of 5º (2.5º on either side). So the entry angle is 152.5º and the exit angle is 207.5º.

We have all the critical values we need in order to calculate the values we need in order to quote reliable numbers for the production run. The variables are:

- Maximum Press Speed: 300 spm
- Longest Move: 5.5″
- Maximum Acceleration: 575 ips
^{2} - Press Angle: 55º

There are several approaches we could take to see if the press and servo system can punch this part at maximum speed, but I’m going to walk through the exercise to find the theoretical longest part/punch we could make at maximum press speed using the maximum acceleration available to the motor. Most manufacturers would not want to design for this, because it would shorten the life of the system due to the wear from such a high duty cycle, but it’s helpful to know your upper limits.

Feed roll slip should also be a major concern using such a high acceleration, especially if the tolerances on the part are very tight. Having the rolls treated (bead blasted, knurling, etc) might help, but this is outside the scope of this discussion. A second, material encoder can help with tolerance problems related to slip, but not if we’re planning to run the setup at maximum values. If you’re already running at the theoretical maximum, slip will immediately create problems as you are locked into the timing of the stroke while the press is running, and any spin-out of the rolls on the material means you’ve already lost some of the time you needed to complete the move before the tooling contacts the material again.

### Calculating Theoretical Maximum Output

I usually approach this by running the formula for a triangular motion profile. This is where the servo spends half the move accelerating and half decelerating. If the shortest distance between to points is a straight line, then the shortest time between two points is a triangular move.

Since time and distance in this application are directly proportional, we can solve for the maximum distance the servo can achieve based on the time it’s allowed to move between press operations. Before we can do that, we must first figure out how much time the servo will have during the move angle of the press’ rotation.

Total Stroke Time (t_{S}) = 1 m / spm

t_{S }= 60 s / 300 spm

t_{S} = 0.2 s

If the Pressing Angle (Θ_{P}) is 55º, then the remaining angle is the Move Angle (Θ_{M}) – the degrees of rotation of the press where the servo is safe to move the material before the tooling comes back into contact with the material.

θ_{M} = 360º – θ_{P}

θ_{M} = 360º – 55º

θ_{M} = 305º

The Move Angle is a percentage of one full rotation of the press, therefore the Time to Move (t_{M}) is equal to the same percentage of the Total Stroke Time.

θ_{M}% = 305º / 360º

θ_{M}% = 84.722%

t_{M} = θ_{M}% x t_{S}

t_{M} = 84.722% x 0.2 s

t_{M} = 0.1694 s

This means the servo has 0.1694 s to move the material into position once the tooling clears it before the tooling comes back into contact with it on the next cycle. With this information and the Maximum Motor Acceleration from the servo, we can calculate the longest move the servo can possibly accomplish at Maximum Press Speed.

There are two formulas you can use to calculate triangular motion profiles – one to find the maximum velocity the system must achieve at the top of the triangle, and another to find the maximum acceleration needed in order to achieve that velocity. For this example, we only need to concern ourselves with the acceleration formula. We will need to rearrange the variables to find the distance.

**Acceleration Required to Achieve Maximum Velocity During a Triangular Move**

a = acceleration required to achieve maximum velocity (575 ips^{2})

d = distance to be covered during the move

t_{M} = time available to move the distance (0.1694 s)

a = 4d / t_{M}^{2}

575 ips^{2 }= 4d / (0.1694 s)^{2}

575 ips^{2 }x (0.1694 s)^{2 }= 4d

575 ips^{2 }x (0.1694 s)^{2 }/ 4 = d

4.127″ = d

We can see that the longest move we can possibly make at 300 spm with our current servo motor is 4.127″. Now we know what our limits are on this setup. We cannot run our theoretical customer’s product with a 5.5″ move at Maximum Press Speed with the servo feeder that we have. If this is to be a regular production run with high volumes, we probably wouldn’t want to run the system at maximum anyway due to increased wear issues. Most systems are sized to run at 80% of their maximum duty cycle, so we’ll re-run our numbers with that in mind to find out what the output of our process should be.

80% of our Maximum Motor Acceleration (575 ips^{2}) is 460 ips^{2}. Since we’re now focused on the achieving the customer’s part, we’ll use the longest punch distance for that part (5.5″) to find the shortest time in which we can make that move. That time will dictate the speed of the press. To begin, we’ll go back to the formula to calculate acceleration for a triangular move, but this time we’ll rearrange the equation to find the Move Time (t_{M}).

a = acceleration required to achieve maximum velocity (460 ips^{2})

d = distance to be covered during the move (5.5″)

t_{M} = time available to move the distance

a = 4d / t_{M}^{2}

460 ips^{2 }= 4(5.5″) / t_{M}^{2}

t_{M}^{2} x 460 ips^{2 }= 4(5.5″)

t_{M}^{2} = 4(5.5″) / 460 ips^{2}

t_{M} = √4(5.5″) / 460 ips^{2}

t_{M} = 0.2186 s

Instead of rounding the result for t_{M},I truncated it because we’re trying to get the servo to the finish line before the press in the real world. We want to end up on the right side of that calculation instead of fighting it if the tooling is 100 μs earlier than the servo. I realize that it shouldn’t be, since we already built some safety margin into the Pressing Angle, but I’d rather make the servo work a tiny bit harder than take a chance at snapping a punch or deforming a hole. Mechanical presses can have variances in their speed, too.

Now that we’ve calculated a Move Time, we must find the new Total Stroke Time, which will include the time to complete the Pressing Angle. Since the angles are fixed regardless of press speed, we can simply reuse the percentages we calculated earlier. We know t_{M} is 84.722% of t_{S}.

t_{S} = t_{M} / 84.722%

t_{S} = 0.2186 s / 84.722%

t_{S} = 0.258 s

Now we go back to the very first formula we used to convert press speed to time per stroke, and rearrange it to find the speed of the press in strokes per minute.

t_{S }= 60 s / Press Speed

0.258 s = 60 s / Press Speed

Press Speed x 0.258 s = 60 s

Press Speed = 60 s / 0.258 s

Press Speed = 232 spm