When tuning rolls, you need to pay attention to the balance of weight transfer.

Continuing from the last time, we will continue with the theme of roles.§ 15So, I gave a lecture on the basic mechanism of rolls.In the calculation of the roll angle, it may have been much smaller than the image you have.From the driver's point of view, the distance between the head and the roll center is large, so even at a small angle, the movement of the field of vision becomes large, giving a feeling of anxiety.
By the way, the roll moment that affects the magnitude of the roll angle is the force that presses the road surface through the suspension when viewed from the tire side.It increases on the outer ring side and decreases on the inner ring side, but the change in the original tire load due to the weight of the vehicle is called weight transfer.Weight transfer changes the CP (cornering power) performance of the tire and affects the steering characteristics as previously learned.And the greater the weight transfer, the greater the effect.
Therefore, this time, let's consider the main points of tuning the roll rigidity, starting from the relationship between roll and weight transfer.It may be a little detour, but I hope you will do your best to get along.


■ Principle of weight transfer: Left and right two-wheeled vehicles that do not roll
First of all, in order to let you know the principle, let's consider the weight transfer of left and right two-wheeled vehicles such as rear cars that do not roll (that is, without suspension).The driving condition is a steady circular constant speed turning state where no forward / backward acceleration occurs.
Weight transfer begins when centrifugal force pushes the center of gravity.The center of gravity pushed to the side acts as a frictional force on the tire contact patch, so the load moves from the inner ring to the outer ring and counters the centrifugal force.Centrifugal force is applied to the vehicle body using the distance (center of gravity height) from the "center of gravity to the ground surface" as a lever, and the force is received at the distance (half of the tread) from the "ground surface just below the center of gravity to the tire contact patch".

Let's compare this to the upright state of a human being.The human "center of gravity" is said to be near the sacrum in the pelvis.The height is about 56% of the height of an adult male when measured from the floor (sole). The "tread" is the distance between your feet.When a force is applied from the side of the pelvis, the force of the foot on the side that is naturally pushed is released, and the "load transfer" is to step on the foot on the opposite side.You can imagine that the load transfer is smaller when you open your legs and lower your pelvis.

Once you understand the principle so far, you can see how to know the magnitude of weight transfer.Weight transfer due to centrifugal force is caused by the relationship between the center of gravity, the surface of the earth, and the L-shaped lever that connects the tires, working on the left and right as shown in the figure. The power relationship of the L-shaped lever is the principle of leverage itself, so it can be expressed by a simple mathematical formula.

・ Weight transfer amount of one wheel (N) x tread (m) x 1/1 = lateral acceleration (G) x body weight (N) x center of gravity height (m) x 2/1

This load transfer increases and decreases on the left and right two wheels, and as a result, the load transfer amount (load difference) is as follows.

・ Weight transfer amount (N) = lateral acceleration (G) x vehicle weight (N) x center of gravity height (m) ÷ tread (m)÷ 1/2 × 2(ring)

here(1/2)と(× 2)If you organize, you will get such a beautiful formula.

Now, let's calculate the weight transfer amount using a concrete example.
・ Conditions: Lateral acceleration: 0.5G Body weight: 5000N (approx. 510kg) Center of gravity height: 0.5m Tread: 1.5m

・ Weight transfer amount (N) = 0.5G x 5000N x 0.5m ÷ 1.5m ≒ 833.3N

In other words, it was found that there is a difference of 833.3N (about 85kg, 16% of the vehicle weight) between the load of the inner ring and the outer ring.
This is the principle of weight transfer.

■ Principle of weight transfer: Rolling left and right two-wheeled vehicles

Next, I will attach a suspension to this car and roll it.Think about what makes it different from a non-rolling car.The rolling car has a roll center between the height of the center of gravity and the surface of the earth as shown in the figure on the right.Above the roll center is a rotational motion due to the roll moment, and below it is a rigid body that does not roll, so it is a moment due to the L-shaped lever (it is troublesome, so we will call it the L-shaped moment hereafter).In other words, all you have to do is calculate them separately and add them together..

Now, let's first consider the load transfer due to the roll moment.When a roll moment is applied, the spring on the inner ring side of the suspension that opposes it expands and the outer ring side contracts.

The total amount of force corresponding to the amount of expansion and contraction is the amount of load transfer.The calculation is a bit tedious, but first, faithfully to the basics, first find the roll angle and then multiply it by the roll stiffness.Since the roll angle was calculated in §15, the basic specifications are the same and the following conditions are added so that it is easy to compare with the non-rolling car in the previous section by describing only the calculation formula.
* Additional conditions: Roll center height: 0.2m Roll rigidity: 20000N ・ m / rad　







・ Calculation: 0.5G x 5000N x (0.5m-0.2m) ÷ 20000N ・ m / rad = 0.0375rad (2.141deg)

Now that you know the roll angle, you can find the force applied to the spring by multiplying it by the roll rigidity, and divide it by the tread in the same way as the L-shaped moment to find the amount of load transfer.


・ Calculation: 0.0375rad × 20000N ・ m / rad ÷ 1.5m ＝ 500.0N

Next, consider the load transfer due to the L-shaped moment.
Here, the relationship between the roll center height, the ground surface, and the tread can be considered in terms of the L-shaped moment.By the way, the roll center is the geometric fulcrum of the suspension, and its position is moved by the roll.However, when calculating the L-shaped moment, the ground clearance (roll center height) is used instead of the position of the roll center.



・ Calculation: 0.5G x 5000N x 0.2m ÷ 1.5m ≒ 333.3N



Therefore, the total weight transfer amount, which is the sum of the roll moment and the L-shaped moment, is the same as that of the "non-rolling vehicle".In other words, the amount of load transfer in the simple calculation is not related to the presence or absence of rolls.

But that is a natural result.As some of you may have already noticed, the troublesome formulas on the way can actually be calculated more easily just by making a detour. In a two-wheeled vehicle, the roll rigidity that determines the roll angle and the roll rigidity that calculates the amount of load transfer are the same, so if the roll angle of ① is substituted into the calculation formula of ② above, the term of roll rigidity disappears.

・ Weight transfer amount due to roll moment (N) = Centrifugal force (N) × {Center of gravity height (m) -Roll center height (m)} ÷ Tread (m)

Furthermore, the formula (XNUMX) is also simplified as follows, and finally the roll center section disappears.

・ Total load transfer = ② ＋ ③ = Centrifugal force (N) × {Center of gravity height (m) -Roll center height (m)} ÷ Tread (m) + Centrifugal force (N) × Roll center height (m) ÷ Tread (m) )



・ Calculation: 0.5G x 5000N x 0.5m ÷ 1.5m ≒ 833.3N

This is not the case with a normal four-wheeled vehicle with different front and rear roll rigidity, but in the case of two wheels, the roll angle, roll rigidity, and roll center height are irrelevant.In other words, the simple calculation of a two-wheeled vehicle has the same formula as a non-rolling vehicle.Weight transfer is determined only by the basic package of "body weight", "center of gravity height" and "tread".

But what about the exact calculations detailed in §15?The result will change.The reason, which I mentioned in the previous lecture, is the center of gravity.Roll moment due to gravityIs added.
In the simple calculation, it is omitted because the degree of influence is small, but strictly speaking, because the vehicle body tilts due to the roll, the positional relationship between the center of gravity and the roll center shifts, and gravity that tries to pull the center of gravity downward is added. ..In other words, by calculating the roll angle exactly, there is a difference from the simple calculation.
Now, I will rewrite the exact calculation formula of the roll angle dealt with in §15.From the roll rigidityBody weight (N) x {Center of gravity height (m) -Roll center height (m)}Notice that is being pulled.

・ Calculation: 2500 N × 0.3 m ÷ (20000 N ･ m / rad-5000 N × 0.3 m) ≒ 0.0405 rad (2.323deg)

・ Weight transfer amount due to roll moment (N) = 0.0405rad × 20000N ・ m / rad ÷ 1.5m = 540.0N ・ ・ ・ ①

・ Load transfer by L-shaped moment (N): 2500N × 0.20m ÷ 1.5m ≒ 333.3N ・ ・ ・ ②

Therefore, (① ＋ ②) = 873.3N, and the amount of load transfer is 4.8% (40N) larger than the simple calculation.This 40N is the roll moment due to gravity, and the more you roll, the larger the load transfer.
Therefore, strictly speaking, a car that does not roll (less) has less load transfer and is more advantageous in terms of maneuverability.It's a little detailed, but this is also one of the merits of increasing the roll rigidity.As a basic knowledge of tuning, if you remember the general reasoning, you may be able to brag about it somewhere.§ 12As explained in, the weight transfer affects the CP performance of the tire, and the larger it is, the lower the total CP of the inner and outer wheels tends to be. With four wheels, if there is a difference before and after that, the steering characteristics of understeer (US) and oversteer (OS) will change.
■§ 13Then, since it was not a direct theme, I calculated the SA of each wheel by simple calculation, but in reality, this degree of error was included.

■ Principle of weight transfer: Rolling four-wheeled vehicle
Next, in order to see the effect on the steering characteristics in detail, let us consider the relationship between roll and weight transfer in a four-wheeled vehicle.

In the calculation procedure, the wheelbase is not related to the weight transfer by the roll, so (2) assume a four-wheeled vehicle with the wheelbase as short as possible (almost the image of a left and right two-wheeled vehicle), and (XNUMX) the load of the virtual two-wheeled vehicle. Calculate the amount of movement by the calculation method of the two-wheeled vehicle, and ③ distribute the result to the front and rear wheels.The specific calculation formula is shown below.

 

However, it may be difficult to understand by explaining only mathematical formulas, so the process of thinking is introduced below.
The purpose of the calculation is to know the general tendency, so we will proceed with a simple simple calculation.

① When two same two-wheeled vehicles are connected
First, we start by calculating the roll angle in order to know the amount of load transfer due to the roll moment.
The specifications of this virtual two-wheeled vehicle double the "vehicle weight" and "roll rigidity", so you only need to add two wheels (in red) to each.
In the calculation formula, the numerator and denominator "x2 wheels" are arranged, and in the end, it becomes the same as the original two-wheeled vehicle.Also, since the calculation formula is long and complicated, the "distance from the center of gravity to the roll center height (roll axis just below the center of gravity)", which is the lever of the roll moment, is set to "hs (m)".


・ Calculation of roll angle

・ Calculation = 0.5G x 5000N x2 wheels× 0.3m ÷ 20000 (N ・ m / rad) ×2 wheels= 0.0375rad (2.148deg)

・ Calculation of load transfer amount
Again, the basic idea is the same as the original two-wheeled vehicle.All you have to do is consider the value obtained by adding the roll rigidity of the front and rear wheels as one wheel, calculate the total load transfer amount corresponding to the roll angle, and distribute by the roll rigidity ratio of the front and rear wheels.In fact, here as well, the "roll rigidity (deficit) of the entire vehicle body" is organized, and the same calculation as the original two-wheeled vehicle can be performed.

・ Calculation of front wheels = 0.0375 ÷ 1.5m ×40000N ･ m / rad× 20000N ・ m / rad ÷40000N ･ m / rad= 500N ... ①
* In the case of this car, the front and rear are the same value.

Next, consider the load transfer for the L-shaped moment.
Here, only the "weight", "roll center height", and "tread" of the front and rear wheels are related, so it is okay to calculate the front and rear separately.



・ Calculation of front wheels = 0.5G x 5000N x 0.2m ÷ 1.5m = 333.3N ・ ・ ②
* In the case of this car, the front and rear are the same value.

Combining two-wheeled vehicles with the same specifications in this way produces the same results as the original two-wheeled vehicle.Since the amount of load transfer is the same for both front and rear wheels, the amount of change in CP is also the same.Therefore, it was found that it does not affect the steering characteristics.
Then, what kind of effect will it have on the steering characteristics if two-wheeled vehicles with different specifications are connected?Let's compare it with the above example car that combines two-wheeled vehicles with the same specifications.From here, notice the difference in the amount of load transfer between the front and rear wheels.


(120) When the front wheel load is 1.2% (80 times) and the rear wheel load is 0.8% (XNUMX times)　* Specifications other than vehicle weight are the same.* Click to open the enlarged image.

The point here is that the weight of the car body does not change, and the front and rear weight distribution is "front wheel: rear wheel = 60:40".

<Amount of load transfer due to roll moment>
・ Calculation of roll angle
The roll angle is the same as the example car because the weight of the car body does not change.

・ Calculation of load transfer amount
The amount of load transfer is the same as the example car because the roll angle and the front and rear roll rigidity are the same.


<Amount of load transfer due to L-shaped moment>
Since the front wheel load is 1.2 times, the load transfer amount is also 1.2 times.Since the rear wheel load is 0.8 times, the load transfer amount is also 0.8 times.

		Front wheel (front and rear%)	Rear wheel (front and rear%)	Total (example car%)
Body weight (N)		6000 (60%)	4000 (40%)	10000 (100%)
Weight transfer amount	Roll moment (N)	500.0 (50%)	500.0 (50%)	1000.0 (100%)
	L-shaped moment (N)	400.0 (67%)	266.6 (33%)	666.6 (100%)
	Total (N)	900.0 (57%)	766.6 (43%)	1666.6 (100%)

・ Consideration of calculation results
Since the basic package is the same as the example car, the total weight transfer does not change, but if the front and rear weight distribution changes, it will be affected by the L-shaped moment.In the case of this car, the amount of load transfer is "front wheel> rear wheel", so the amount of CP change is also "front wheel> rear wheel", so it tends to be US.

③ When only the roll rigidity of the rear wheels is tripled.* Specifications other than roll rigidity are the same.　

The point is that when the roll rigidity of the rear wheels is tripled, the front-rear ratio of the roll rigidity becomes "front wheel: rear wheel = 1: 3", and the roll rigidity of the entire vehicle body is doubled.

<Amount of load transfer due to roll moment>
・ Calculation of roll angle
The roll rigidity of the entire vehicle is doubled, and the roll angle is reduced by half accordingly.


・ Calculation of load transfer amount
By reducing the roll angle by half, the amount of load transfer on the front wheels is also halved.Even if the roll angle of the rear wheel is 1/2, the roll rigidity is 1 times, so the load transfer amount is 2 times at "1/2 x 1".





<Amount of load transfer due to L-shaped moment>
-Since it is the same as the example vehicle except for the roll rigidity, the amount of load transfer does not change.

		Front wheel (front and rear%)	Rear wheel (front and rear%)	Total (example car%)
Roll rigidity (N ・ m / rad)		20000 (25%)	60000 (75%)	80000 (200%)
Weight transfer amount	Roll moment (N)	250.0 (25%)	750.0 (75%)	1000.0 (100%)
	L-shaped moment (N)	333.3 (50%)	333.3 (50%)	666.6 (100%)
	Total (N)	583.3 (35%)	1083.3 (65%)	1666.6 (100%)

・ Consideration of calculation results
Since the basic package is the same as the example car, the total weight transfer does not change, but it was found again that the roll rigidity affects the front-rear distribution of the load transfer by the roll moment.In the case of this car, the amount of load transfer tends to be OS because the amount of change in the rear wheel CP is large in "front wheel <rear wheel".


④ When the roll center height of the rear wheels is increased by 1.5 times.* Specifications other than the roll center height are the same.

The point here is that the roll center heights before and after are different, so the roll axis connecting them tilts and hs (m) changes. Since hs (m) is the distance from the center of gravity to the roll axis lowered vertically, if the position of the center of gravity is known, it can be calculated by that ratio.

In the case of this car, the weight distribution between the front and rear is 50:50, so the center of gravity is in the center of the wheelbase.Therefore, hs (m) is also the center of the front and rear roll center heights, the front wheel roll center height is 0.2m (0.3m to the center of gravity height), and the rear wheels are 0.3m (0.2m to the center of gravity), so hs (m). ) Is the average value of 0.25m (5/6 compared to the example vehicle).

<Load transfer by roll moment>
・ Calculation of roll angle
Since hs (m), which is the lever of centrifugal force, is 5/6 of the distance of the example vehicle, the roll angle is also reduced to 5/6.



・ Calculation of load transfer amount
Since the roll angle is 5/6, the amount of load transfer is also 5/6.Since the front and rear roll rigidity is the same, the front and rear distribution of the load transfer amount is also the same.

<Amount of load transfer due to L-shaped moment>
Here, only the rear wheels with higher roll center heights are affected.
The amount of load transfer is proportional to the height of the roll center.

		Front wheel (front and rear%)	Rear wheel (front and rear%)	Total (example car%)
Roll center height (m)		0.2	0.3	-
Weight transfer amount	Roll moment (N)	416.6 (50%)	416.6 (50%)	833.3 (83%)
	L-shaped moment (N)	333.3 (40%)	500.0 (60%)	833.3 (125%)
	Total (N)	749.8 (45%)	916.5 (55%)	1666.6 (100%)

・ Consideration of calculation results
Since the basic package is the same as the example car, the total weight transfer does not change, but changing the roll center height affects both the roll moment and the L-shaped moment.Weight transfer due to roll moment is reduced by shortening hs (m) from 0.3m to 0.25m. The height of the roll center directly affects the L-shaped moment.In this case, the total load transfer amount is "front wheel <rear wheel", and the amount of change in the rear wheel CP is larger than that of the front wheel, so it tends to be OS.

Up to this point, I thought about the extreme settings to understand the basic tendency, but since the basic package (body weight, center of gravity height, tread) is common, the total amount of load transfer does not change, only the front and rear distribution. Notice that is changing.Next, let's verify the actual tuning effect.

■ Verification of realistic tuning effect
Vehicles handled in §15Tune to and verify the effect.The running conditions are the same as in the previous example, the tuning contents are the following three ways, and the load transfer amount for each is calculated.Here, not only the effect of lowering the height of the center of gravity due to lowdown, but also the total amount of load transfer changes as a result of rigorous calculation considering the roll moment due to gravity in reality.Also, pay attention to the change in the distribution before and after that.

Tuning parts	Main Specifications
Large diameter stabilizer	Spring constant change rate: 140% for front wheels / 200% for rear wheels
Low down spring	Spring constant change rate: 140% for front wheels / 120% for rear wheels ・ Vehicle height: -20mm

　■ Case study and confirmation of results (weight transfer)

Weight transfer amount	Front wheel (N)	Rear wheel (N)	Total		Roll angle (Deg) Standard ratio
			N	Standard ratio
① Large diameter stabilizer only
Load transfer by roll moment	598.8	445.1	1043.9	98.7%	1.81 (99.1%)
Load transfer by L-shaped moment	146.6	306.0	452.6	100.0%
Total (before and after%)	745.4 (49.8%)	751.1 (50.2%)	1496.5	99.1%
② Lowdown spring only
Load transfer by roll moment	595.6	456.5	1052.2	99.5%	1.85 (95.0%)
Load transfer by L-shaped moment	111.5	270.9	382.55	85.1%
Total (before and after%)	707.2 (49.2%)	727.5 (50.8%)	1434.7	95.0%
③ Large diameter stabilizer + low down spring
Load transfer by roll moment	599.5	443.1	1042.6	98.6%	1.57 (94.4%)
Load transfer by L-shaped moment	111.5	270.9	382.5	84.5%
Total (before and after%)	711.0 (49.8%)	714.1 (50.2%)	1425.1	94.4%
(Reference) Standard car
Load transfer by roll moment	595.0	462.0	1057.0	-	2.19
Load transfer by L-shaped moment	146.6	306.0	452.6	-
Total (before and after%)	741.6 (49.1%)	768.0 (50.9%)	1509.6	-

Although there are differences depending on the case, it was found that the roll angle and the amount of load transfer decreased, the front-rear balance of the load approached 50:50, and the steering characteristics also tended to be good in Kansei engineering.

■ Tuning of steering characteristics by weight transfer
As mentioned above, you can understand that the tuning of the steering characteristic can be adjusted by the amount of load transfer before and after.For example, a car with strong understeer can reduce understeer by increasing the roll rigidity of the rear wheels and shifting the load transfer distribution from the front wheels to the rear wheels.Oversteer cars, on the other hand, increase the roll rigidity of the front wheels to reduce oversteer.
Since the amount of load transfer varies greatly depending on the height of the roll center, it is possible to tune the steering characteristics by changing the layout of the front and rear suspensions.However, tuning that simply reduces hs will eventually narrow the tuning range of the steering characteristics, and the characteristics of the front and rear wheel weight distribution, which is the characteristic of the car, will appear as it is.

If the roll rigidity ratio of the front and rear is changed in order to improve the poor steering characteristics caused by weight distribution, a larger roll moment will be required, and as a result, the car will have a low potential for dynamic sensitivity overall. increase.Furthermore, in order to transmit that moment, the torsional rigidity between the front and rear wheels of the body must be increased, which requires a large weight increase.
Considering this, you can see the importance of carefully tuning rolls based on proper calculations.Of course, it is also necessary to choose a base car with good characteristics.At the time of the basic design of the car, it was made with the consistent idea of ​​(XNUMX) improving the weight distribution, (XNUMX) lowering the height of the center of gravity, and (XNUMX) setting a roll center where the roll moment arm (hs) becomes smaller. A car (just a roadster packaging!) Is ideal.When tuning a mass-produced car, it is essential to have moderation that reflects the driver's tastes on top of the basics.

In this lecture, you may think that you were particular about the minute numbers again, but I think that the fact that the slight difference in seasonings is the decisive factor for the taste is similar to the world of food.Humans are creatures with such delicate sensibilities.
However, there are still issues to be considered regarding the dynamic sensitivity of roles.This time, we dealt with the case where the roll angle does not change due to steady circular turning, but in actual cornering, the roll angle changes with the change of G, so the influence of the rate of change such as the angular velocity and angular acceleration comes out.Next time, I will give a lecture on the transient characteristics of this roll, that is, "the taste of the roll", so please look forward to it.