# Why is longitidunal force of tyre calculated negative in SIMULINK?

With the help of the Vehicle Dynamics Blockset of SIMULINK, it is easy to obtain longitidunal force (tractive force) of tyre by some of inputs. You can see one of examples below. In this simulation, Fz is sinusoidal (like Double Lane Change), vehicle speed is ramp and Axle Torque is constant.

What is the meaning of negative Fx? Is it possible?

Thanks,

• Could you update the question with what are the required parameters for the block you used ? Could you provide a link to the documentation page? – NMech Feb 13 at 12:53
• in.mathworks.com/help/vdynblks/ref/longitudinalwheel.html – voo Feb 13 at 13:41
• Hi, you can download my slx. file: gofile.io/d/JPIuj1. Parameters can be found in this file. – voo Feb 13 at 13:52

## 1 Answer

In the help page you can see a line mentioning how Rolling Resistance is calculated...

Block uses the method in SAE Stepwise Coastdown Methodology for Measuring Tire Rolling Resistance.
The rolling resistance is a function of tire pressure, normal force, and velocity. Specifically,


$$M_y=Re\left\{a+b \|V_x\|+c V_x^2\right\}\{F_z^\beta p_i^a\} \tanh(4 V_x)$$

Notice the term $$F_z^\beta$$

While the other terms remain more or less the same (pressure should increase), in the plot you have $$F_z$$ increases, and therefore rolling resistance increases. As a result, there is an additional negative force, while the increase in $$F_z$$ occurs.

• Rolling resistance can be ignored in this toolbox and there is no calculation about this resistance in my simulation. When i increase the torque, Fx becomes completely positive. I think negative Fx is because of the longitidunal slip ratio. Some of the values of ratio make the force negative. I have found some of articles about DLC simulation and seen that Fx was calculated negative in some of the time intervals. – voo Feb 13 at 15:14
• From the layout of your post, I thought that scope 4 was $Fz$, and scope 3 was $F_x$. Because, it would take me a looong time to download and install a trial academic version of MATLAB and run your model (and I don't want to do that to be honest), could you update your original post to name what each scope describes? Also please give some indication of the DLC maneuver (how hard are you swerving, the velocity etc). – NMech Feb 13 at 15:22
• I have updated the graphs. In DLC, Fz changes according to steering angle. I didn't define steering angle in here, only wanted to imitate DLC maneuver. In here, Fz is sinus like DLC. I cannot understand how the traction force becomes negative in this kind of accelerating conditions. – voo Feb 13 at 15:36
• Angular velocity, rad/s. Also Torque: Nm, Fz: N, Vx: m/s and Fx: N – voo Feb 13 at 15:39
• I was running similar models about 2-3 years ago. It's very easy one little parameter to set you off, and yield very unrealistic results. Seeing a negative force, is not prohibitive though, in real life you would expect to see a rolling resistance. – NMech Feb 13 at 16:01