# Help with linear solenoid calculations (engine valve actuators)

In summary: ...stopped halfway between the open and closed positions....stopped in the middle of the stroke....stopped in the middle of the valve face....stopped in the middle of the cylinder....stopped at the top of the piston....stopped at the bottom of the piston....stopped at the bottom of the cylinder....stopped at the top of the flywheel....stopped at the top of the flywheel....stopped at the bottom of the coil....stocked at the bottom of the coil....loaded at the top of the coil....
TL;DR Summary
Calculating linear solenoid parameters
Hello, thanks in advance, I do many many things, jack of all trades but master of none. Would some one be willing to help me with some formulas and calcs for making my own linear solenoid? I can give the final specs I'm after then I could use advice on materials and other variables.

I'd like to make a linear solenoid that uses 12vdc and is capable of pushing 300lbs with a 1/2" stroke. It would be momentarily energized consistently 14 times a second and would be in a 200 degree environment, what type of material would be most efficient for the plunger, frame and sleeve? Also what gauge wire and how many turns? If anyone knows of something in these parameters that already exists and doesn't cost an arm and a leg. I've got a mill and a lathe and can make may things I just want this to be reliable and well built. Thanks I look forward to learning more in this area, I know electrical theory as I was an electrician for 6 years so I'm not completely in the dark. Thanks again.

I do not have complete experience in designing and making linear solenoid. I only learned some power electronics from undergraduate courses at university, but I am a little interested in this topic.

I believe that if you understand the basic principles of electromagnetics, you can try to design your own spreadsheet to help you calculate the relationship between related parameters. For example, you can define the input parameters as the input electric power to the coil, stroke length and the required plunger force, and then let the spreadsheet calculate the required number of coil turns, shaft diameter, etc.

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I'm fighting a brain tumor unfortunately so some days I have bits and pieces I can't remember, I know more turns of wire would give me more force, I can't remember how the size of the wire affects it. I can't think of the correct terminology to search for a formula right now either.

Welcome to PhysicsForums.
uses 12vdc and is capable of pushing 300lbs with a 1/2" stroke. It would be momentarily energized consistently 14 times a second and would be in a 200 degree environment
An electrical solenoid does not sound like a good match for this application so far. Can you say more about the application? Is that 200C or 200F? Is the application/stroke continuous? Like, could you start with a heavy flywheel rotating and generate these linear back-and-forth motions from it?

200F, yes that's what I'm trying to eliminate is a camshaft in a engine and operate the valves with a linear solenoid and depending on whether I could use the valve stem as a core or I could still use the rocker arm as a force multiplier and put the solenoid under it I should be able to reduce the force needed from the solenoid by approximately 1/3rd but then I'm adding more moving parts in turn which is more friction, more wear and another possibility of a breaking point. Both ways have their advantages and disadvantages so I'm not sure which one is better.

Ah got it. Is 300 pounds a typical force for ICE valve springs? How big of an engine is this?

Since the technology exists already, have you looked at existing electric valve actuators? That might be a good place to start, to see how they are built and used...

https://en.wikipedia.org/wiki/Camless_piston_engine

https://www.greencarcongress.com/2019/08/20190820-empa.html

Yes I've seen all this but I'm working with a 1283 ci 6 cylinder the valve face is around 2" and the stem is like 1/2" diameter because the increased stroke and bore the compression ratio is at its max any more would pre-detonate the fuel before the spark plugs does. I had to eliminate the cam for the crankshaft to clear the cam. All the commercial ones are for way smaller motors and plus they are like 500 a piece which I can't afford, all the machine work I've done myself because I can't even come close to affording to paying someone to do it, plus I've done it many times before but have always stopped stroke addition because the obstruction of the camshaft. Thanks for helping me tackle this. I appreciate it.

Wow, that's a big engine. I'm still not convinced that electrical valve actuation is the best way to go, so since this thread is currently in the EE forum, I'll page a couple mechanical folks to get their thoughts... @Ranger Mike @jrmichler

Start by making some assumptions to do some ball park calculations:

Assume the valve stem is 0.5" diameter and 6" long.
Assume the valve face is 2" diameter and 0.3" thick.
Assume that the moving mass of stuff attached to the valve is equal to the mass of the valve.
Assume the valve is the density of steel.
Then the total moving mass is 1.2 lbs.

Assume that valve travel from closed to fully open is 0.5".
Assume engine is designed to run 1500 RPM.
Assume that the valves need to open or close in 90 degrees of engine shaft rotation.
Then the valves need to move 0.5" in 10 msec.

Assume a simple triangular velocity motion profile as shown in the sketch:

It moves 0.5" in 10 msec by accelerating for 5 msec and decelerating for 5 msec.
The acceleration is a = 2*d/t^2 = 2 * 0.25 / 0.005^2 = 20,000 in/sec^2.
The force to move the valve is 20,000 / 386 * 1.2 lbs = 62 lbs.

Assume that the cylinder pressure is 100 PSI at the instant of exhaust valve opening.
The force to open the exhaust valve is 3.14 in^2 * 100 PSI = 314 lbs.
Total force required is 62 + 314 = 376 lbs.
Add a safety factor, design for 500 lbs force.
Assume a peak magnetic field strength of 1.5 Tesla.
That's about 130 lbs pull per square inch of pole area.
You need pole area 500 / 130 = 4 square inches.

Now assume a concept design, such as:
This design has two electromagnets. One pulls the valve open and decelerates the valve when closing. The other pulls the valve closed and decelerates the valve when opening. Not shown is a position feedback device so the controller knows the valve position.

Now you need to design the electromagnets for 1.5 Tesla through a 0.5" physical gap. The magnetic air gap is 1.0" because the field goes from the electromagnet, through the air, through the valve actuator, then back through the air to the electromagnet.

To give an idea of what the electromagnet will look like, I once designed an electromagnet that pulled 1600 lbs force through a 1/8" air gap, and turned on and off 55 times per second. The duty cycle was approximately on for 9 msec, then off for 9 msec. Peak current was 50 amps, and it needed about 170 volts to meet the di/dt requirements. The drawings in US Patent #6,389,941 of this electromagnet are only approximately to scale, but you can get an idea of the magnet size from the drawing. The knife cylinders are 10" apart on center, and the electromagnet stack was about 4" thick. The laminations were 0.014" thick steel of a special magnetic alloy.

At this point, take a break, and search electromagnetic valve actuator engine. Notice how much effort is going into ways to reduce the electrical energy needed to actuate valves. Then decide if you really want to do this.

berkeman
In an ordinary cam driven valve train, the whole train is carefully "wound up" and then "released" in each cycle. This is likely to require considerable control logic to avoid fatiguing the valves to failure.

my two cents - yes a solenoid could open a valve on an ICE. 200 psi spring rating is typical. The biggest problem with the current cam / valve design is heat. Much goes into cooling the valve train via engine oil.
Next big thing i see isthe solenoid is either open or closed. So far a successful square lobe camshaft has not come on the market. Bump stick grinders have labored for decades to provide optimum camshaft profiles.
When a solenoid opening profile and closing profile gets close to current mechanical camshaft design you will have an ultimate preformance enhancement. A programmable camshaft with variable timing.

Air has mass. A cam will ramp up lift gradually ( per degree crankshaft rotation) until max lift. It holds this lift as long as that application dictates performance at a particular RPM.
That is why we use3 angel valve seats to smooth flow the combustion chamber. We angle cut the cylinder head to make a straighter shot from intake port to combustion chamber. We flow bench the intake and exhaust ports for max flow or volume as the application requires. A Daytona 500 cylinder head can not work on a engine used in tractor pulls.

Some engine builders have a mechanical means to change rocker arm ration via engine oil and vary the valve lift. This is going in the right direction.
But air has mass and you can not just go max lift and expect good results. If this was the case, we would run square cam lobes.

my opinion.

berkeman
Thanks again for all the input so I definitely understand what everyone is saying so then is seems like cutting the cam up in 3 pieces and machining a bearing block for it to sit on so the lobe is directly under the rocker arm and possibly running it with a dc motor with a speed controller would be a better route, because ethe motor has 3 separate blocks and heads and valve covers. So it started out 830 some cid I got it to 1283 right now but if I can move the cam out of the way I can gain another 1-2" of stroke and I'm boring it another .5" so it would gain me another 100 cubes minimum.

Do you guys think that would be a better route or have any other options? I'd have to use a crankshaft position sensor to control speed of each motor.

I'd have to use a crankshaft position sensor to control speed of each motor.
Worse.

It's not speed you need to synchronize, it is position.
You will need a position sensor on each cam to keep them in synchronization with the crankshaft.

That's true, speed and position, as the rpms increase so will the speed of the motor.

possibly running it with a dc motor with a speed controller
There is a big problem with that approach. An IC engine camshaft is an oscillating torque load. There is a positive torque while the valve is opening, which changes to a negative torque while the valve is closing. It does this once per cam revolution in a four cylinder engine (or one bank of a V-8).

The motor driven cam slows down during valve opening and speeds up during valve closing. The oscillating camshaft torque is a disturbance torque into the system. The motor / cam / controller system response is typically second order. The result is a system response where the cam changes timing with changes in engine speed.

I had a very similar problem with an industrial machine that had a cam driven component. The cam speed and disturbance torque were roughly equal to that of an IC engine running 1500 RPM. We wanted to servo drive it in order to get variable cam timing. Our cam timing accuracy specification was +/- 1 degree from the programmed timing, which is similar to the cam timing accuracy specification of an IC engine. We had the best servo motor and drive, it was properly sized and applied, and the company's best EE tuning the drive. The best setup still had +/- 10 degrees cam timing error, and that error changed with speed. I looked at adding a flywheel, but the minimum size flywheel needed would have been too large to fit in the machine.

A DC motor with speed controller would not work well enough to get the engine to run at all. This application needs accurate position control over a speed range while subject to a high disturbance torque input. Position control is far more complex than speed control. This link is about installing a servo motor of the type that would be used in this application: https://literature.rockwellautomation.com/idc/groups/literature/documents/in/mp-in001_-en-p.pdf. And this link is about tuning the drive: https://literature.rockwellautomation.com/idc/groups/literature/documents/at/motion-at005_-en-p.pdf. The drive is the electronic black box that runs the servomotor.

berkeman

## 1. What is a linear solenoid?

A linear solenoid is an electromechanical device that converts electrical energy into linear motion. It consists of a coil of wire wrapped around a metal core, and when an electrical current is passed through the coil, it creates a magnetic field that pushes or pulls the core in a linear direction.

## 2. How are linear solenoids used in engine valve actuators?

Linear solenoids are commonly used in engine valve actuators to control the opening and closing of the engine valves. When an electrical current is applied, the solenoid's plunger moves, which in turn opens or closes the valve. This allows for precise control of the engine's air and fuel intake, improving performance and efficiency.

## 3. What factors should be considered when calculating the size of a linear solenoid for an engine valve actuator?

When calculating the size of a linear solenoid for an engine valve actuator, factors such as the required force, stroke length, and operating voltage must be taken into account. The size and number of turns of the coil, as well as the type and strength of the core material, also play a role in determining the solenoid's size and performance.

## 4. Are there any standard formulas for calculating linear solenoid parameters?

Yes, there are standard formulas that can be used to calculate the parameters of a linear solenoid, such as the force and inductance. These formulas take into account the solenoid's physical dimensions, number of turns, and operating conditions. However, it is important to note that these formulas are only approximations and may vary depending on the specific design and materials used.

## 5. What are some common challenges in designing and using linear solenoids for engine valve actuators?

One common challenge in designing and using linear solenoids for engine valve actuators is achieving the desired force and stroke length while keeping the size and weight of the solenoid within the constraints of the engine. Other challenges include minimizing power consumption, reducing heat generation, and ensuring reliability and durability in harsh operating conditions.

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