Automotive Steering Force, Determining the Lever Arm

[chevique]

TL;DR Summary

I have completed a motion study using SolidWorks to calculate the force required to steer tires in a certain amount of time. I am crunching numbers to determine the mechanical advantage provided by a steering linkage to demonstrate to my supervisor that the motion study makes sense.

It appears that I am unable to attach any images here, so I'll do my best to paint a picture for you.

I completed a motion study using SolidWorks to calculate the force required to steer tires in a certain amount of time. I am confident in the motion study, but I need to complete a separate calculation to instill confidence in the motion for my manager.

I have completed a lot of work, and the one thing I keep getting hung up on is how to calculate the mechanical advantage. Simple, right? But the design, from what I've seen, is not typical. I have good reason to believe there is a mechanical advantage because the calculated kingpin torque far exceeds what the motion study simulated. The calculated kingpin torque was calculated using the length of the "effective radius arm." The effective radius arm is defined as the distance between the center of the kingpin axis and the line formed between one point and its mirror point on the circumference of rotation parallel to the kingpin axis.

I have a double-ended cylinder attached to a steering linkage on either side. The linkage converts the linear motion of the steering cylinder to the rotational motion of the tire assembly, which rotates about its kingpin axis. However, the linkage does not directly connect to the kingpin - this is the design oddity I alluded to. Instead, the linkage is attached to another pin - call it the prince pin - on the tire assembly that is offset by a fixed radius. It is this pin that rotates itself and the tire assembly about the kingpin.

Now, I am wondering if I have to separate the idea of the lever arm from the that of the effective radius arm. The length of the effective radius arm correlates very well with the simulated changes in force, but it doesn't suffice to explain the torque. One thing that does seem to make the numbers appear reasonable is if I identify the lever arm as being the distance from the kingpin axis to the point where the cylinder attaches to the linkage. Though this makes the numbers seem nice, I am doubtful. The way I see it the, the force applied to the cylinder's pin is transferred over to the prince pin. It is through the prince pin that the force acts on the tire assembly; hence why I'm hesitant to separate the notion of the lever arm from the effective radius arm.

Or could the distance between the prince pin and the cylinder pin be the lever arm? If so, would that make the prince pin a fulcrum and the distance from it to the kingpin the load arm?

Anyway, a lot of information. I hope that I was clear enough. A point in the right direction will be greatly appreciated.

Thank you so much for taking the time to read this!

 

[Lnewqban]

Welcome!

Are you familiar with this mechanism?:

https://en.m.wikipedia.org/wiki/Ackermann_steering_geometry

 

[Baluncore]

Welcome to PF.

It appears that I am unable to attach any images here, ...

There is a button on the lower left of the edit window, that allows you to attach files or images. Alternatively, you can post a link to an existing diagram on the web.

The problem you pose is an interesting one, but without a diagram, I am only guessing. It seems you have reduced the problem to a simple linkage analysis. The use of a trigonometric model may fail due to obscured sign changes, while a vector solution may succeed. We need that diagram.

The steering in a vehicle is designed to operate while moving forwards along the road. A model that does not couple the two front wheels through the tire contact patches on the road, and through the steering geometry, will not give a true result.

 

[Ranger Mike]

When researching todays automobile steering one must consider many factors. The amount of effort used to turn the steering wheel is one input. If you desire a faster steering " time" you can change the rack and pinion steering ratio quite easily. Let us say you have a passenger car that will turn 90 degrees left when the steering wheel is tuned 90 degrees. You can change out the ration so it will turn 90 degrees in 45 degrees of the wheel. With todays power steering where we have electronic linear motors the effort by the driver would be the same. Same physical input. Let us explore what happens when a car is cornering.


To change a tires direction there must be outside force applied to rotate the tire about its contact patch. Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force. Note the repeated use of the verb remains. We can think of this law as preserving the status quo of motion. The steering linkage input will be this external force.



The front tires will not turn the same as they will follow two different radius paths. This is due to built in Ackermann. The inside wheel turns more than the outside wheel, ensuring that all four tires trace out a circle with a common center point, preventing tire scrubbing and improving handling Ackermann effect.


It will take different amount of forces on each tire due to more down force being applied on each tire. The body roll of the car will add down force on the outside tire and lift up the inside tire. This is due to momentum. Momentum is the product of an object's mass and velocity. This means that momentum is directly proportional to both mass and velocity. The larger the mass of the object, the more momentum it has. Similarly, for velocity, objects that are moving faster also have more momentum.


The inside tire will actually lift up the car and the outside tire will go to a droop condition due to steering Caster.



A lot of times a quick steering car can really cause trouble so designers intentionally make the steering neutral to avoid front ire overload, loss of traction and creating a dangerous situation.

 

[Baluncore]

The effective radius arm is defined as the distance between the center of the kingpin axis and the line formed between one point and its mirror point on the circumference of rotation parallel to the kingpin axis.

The radius arm length, is the distance between the kingpin axis of rotation, and the linear axis, along which the force is being applied. The distance must be measured along a radius line, that is perpendicular, to both the kingpin axis and the line of force application. Obviously, the radius arm length will vary, depending on the steering offset from straight ahead.

Forklift trucks have rear steering, and often use an extra pin and link, to reach and recover from, high steering angles.

The bucket on an excavator is operated through an extra link, that allows greater than 180° of bucket curl, from one hydraulic cylinder.

 

[chevique]

TL;DR Summary: I have completed a motion study using SolidWorks to calculate the force required to steer tires in a certain amount of time. I am crunching numbers to determine the mechanical advantage provided by a steering linkage to demonstrate to my supervisor that the motion study makes sense.

It appears that I am unable to attach any images here, so I'll do my best to paint a picture for you.

I completed a motion study using SolidWorks to calculate the force required to steer tires in a certain amount of time. I am confident in the motion study, but I need to complete a separate calculation to instill confidence in the motion for my manager.

I have completed a lot of work, and the one thing I keep getting hung up on is how to calculate the mechanical advantage. Simple, right? But the design, from what I've seen, is not typical. I have good reason to believe there is a mechanical advantage because the calculated kingpin torque far exceeds what the motion study simulated. The calculated kingpin torque was calculated using the length of the "effective radius arm." The effective radius arm is defined as the distance between the center of the kingpin axis and the line formed between one point and its mirror point on the circumference of rotation parallel to the kingpin axis.

I have a double-ended cylinder attached to a steering linkage on either side. The linkage converts the linear motion of the steering cylinder to the rotational motion of the tire assembly, which rotates about its kingpin axis. However, the linkage does not directly connect to the kingpin - this is the design oddity I alluded to. Instead, the linkage is attached to another pin - call it the prince pin - on the tire assembly that is offset by a fixed radius. It is this pin that rotates itself and the tire assembly about the kingpin.

Now, I am wondering if I have to separate the idea of the lever arm from the that of the effective radius arm. The length of the effective radius arm correlates very well with the simulated changes in force, but it doesn't suffice to explain the torque. One thing that does seem to make the numbers appear reasonable is if I identify the lever arm as being the distance from the kingpin axis to the point where the cylinder attaches to the linkage. Though this makes the numbers seem nice, I am doubtful. The way I see it the, the force applied to the cylinder's pin is transferred over to the prince pin. It is through the prince pin that the force acts on the tire assembly; hence why I'm hesitant to separate the notion of the lever arm from the effective radius arm.

Or could the distance between the prince pin and the cylinder pin be the lever arm? If so, would that make the prince pin a fulcrum and the distance from it to the kingpin the load arm?

Anyway, a lot of information. I hope that I was clear enough. A point in the right direction will be greatly appreciated.

Thank you so much for taking the time to read this!

Okay, I am able to attach the image. As an additional note, in this image, only one end of the cylinder is shown, but on the other end it is attached similarly to the other tire assembly.

 

[chevique]

Welcome!

Are you familiar with this mechanism?:

https://en.m.wikipedia.org/wiki/Ackermann_steering_geometry

It appears that the linkage attaches directly to the kingpin. Not so in my geometry. I attached a picture in the replies.

 

[chevique]

Welcome to PF.

There is a button on the lower left of the edit window, that allows you to attach files or images. Alternatively, you can post a link to an existing diagram on the web.

The problem you pose is an interesting one, but without a diagram, I am only guessing. It seems you have reduced the problem to a simple linkage analysis. The use of a trigonometric model may fail due to obscured sign changes, while a vector solution may succeed. We need that diagram.

The steering in a vehicle is designed to operate while moving forwards along the road. A model that does not couple the two front wheels through the tire contact patches on the road, and through the steering geometry, will not give a true result.

I uploaded the picture in one of the replies.

 

[Lnewqban]

It appears that the linkage attaches directly to the kingpin. Not so in my geometry. I attached a picture in the replies.

That oblique line may represent the position at which both wheels are parallel; therefore, Ackerman is there.
The represented piston rotates that left wheel a lesser angle when pushing than when pulling.

 

[jack action]

Can you show us your Free Body Diagrams for the linkages? It should answer your questions.