Vehicle speed from engine speed Calculation

 Vehicle speed from engine speed Calculation 

Here we will calculate the speed of the wheel drive from the drive is coming from the Engine. 

so the given values are:-

where:

• ω_e [rad/s] – rotational speed of the engine
• ω_g [rad/s] – rotational speed of the gearbox output shaft speed
• ω_d [rad/s] – rotational speed of the differential crown wheel
• ω_wr [rad/s] – rotational speed of the right wheel
• ω_wl [rad/s] – rotational speed of the left wheel
• v_wl [m/s] – linear speed of the left wheel
• v_wr [m/s] – linear speed of the right wheel
• i_x [-] – gear ratio of the engaged gear
• i₀ [-] – gear ratio of the differential
• r_w [m] – static radius of the wheel

To have a simple calculation, we are going to assume that the vehicle is moving in a straight line, and also that both wheels have the same radius. This means that:

So some equation will be made :-

ωwr=ωwl=ωw---------------(1)

vwr=vwl=vw=vv------------(2)

ωc=ωe---------------------------(3)(  the clutch speed ω_c [rad/s] is equal with the engine speed ω_e [rad/s].)

ωg=ωcix------------------------(4) (wheel torque calculation )

 

The rotational speed of the differential crown wheel is also reduced, being equal gearbox output shaft speed divided by the differential gear ratio:

ωd=ωgi0------------------------(5)

 

ωwr=ωwl=ωd----------------(6) The left and right wheel speeds are equal with the differential speed:

ωw=ωeix⋅i0-------------------(7)( the formula for wheel speed function of engine speed:)

ωe=Ne⋅π30--------------(8) (the conversion from rpm to rad/s )

Nw=ωw⋅30π-------------(9)( wheel speed N_w in [rpm], from [rad/s], )

vw=ωw⋅rw-----------------------(10) (linear speed is a calculated function of rotational speed and radius) 

 

Combining equations (7), (8) and (10), gives the expression of the vehicle and wheel speed function of engine speed and gearbox and differential gear ratios:

vv [m/s]=vw [m/s]=Ne⋅π⋅rw30⋅ix⋅i0----------------(11)

If we want to have the speed in [kph], the formula becomes:

 

Vv [kph]=Vw [kph]=3.6⋅Ne⋅π⋅rw30⋅ix⋅i0-------------------(12)

example:-

Example 1. Calculate vehicle speed in [kph] for a vehicle with the following parameters:

engine speed, Ne = 2400 rpm
gearbox (1st) gear ratio, ix = 4.150
final drive ratio, i0 = 4.160
tire size marking 225/55R17

Step 1. Calculate the (free static) wheel radius from the tire size marking. The method for calculating the wheel radius is described in the article How to calculate wheel radius. The calculated wheel radius is r_w = 0.33965 m.

Step 2. Calculate the wheel torque using equation (12).

Vv=3.6⋅2400⋅π⋅0.3396530⋅4.150⋅4.160=17.96 kph

Independent variable is = 

• engine speed, N_e 
• gearbox (1^st) gear ratio, i_x 
• final drive ratio, i₀ 
• tire size marking (225/55R17)

dependent variable is = 

• vehicle speed in [kph]

source -https://x-engineer.org/