The taste of the roll is determined by how the "angular velocity" rises ... its calculation and sensitivity evaluation.

We will continue to work on the theme of roles.The purpose of the lectures so far has been to promote understanding of the basic mechanism, so in order to proceed as simply as possible, the concept of the time axis has been omitted. I think that you have already fully understood the basic principle as a result of "the roll angle stabilizes when the roll moment and roll rigidity are balanced."
But if you look at the actual role process, it's pretty complicated.Momentary / instantaneous roll angular acceleration (rad / sec) even if the final roll angle is the same²) And the angular velocity (rad / sec) are not always the same.The driver feels relieved if he rolls slowly and gently, and it is not difficult to imagine that he feels uneasy if he is glaring and sudden.Therefore, not only the absolute value of the roll angle, but also its "transient characteristics", "roll progress", and "how the roll speed changes until it finally reaches XNUMX", so to speak, "the taste of the roll". It is necessary to prepare an evaluation axis for the dynamic sensibility.
Therefore, in this lecture, we will verify the roll progress mechanism over time and the actual tuning effect by calculation and graph as much as possible.Since the roll speed is related to many factors and changes continuously, I generally do not do this calculation, but as usual, to answer the basic question "Why does it happen?" I will talk about it in a rather rough simplification, so I would like you to take it as a principle theory and use it for your own intellectual tuning.I think there are some esoteric parts, but please ignore the small numbers and do your best so that you can draw an image of the overall "power relationship".


■ Why does the roll speed change?
Let's first look at the mechanism that determines the roll speed.Roll is generated when the roll moment caused by the lateral acceleration (G) rotates the vehicle body around the roll center (as a result, the vehicle body rotates on its axis).On the other hand, the suspension catches the rotating car body like a stretchable rod and suppresses the roll.Therefore, the roll speed increases as the roll moment increases, and decreases as the suspension force that opposes it increases.This is the principle.
But before that, in fact, there is another factor that determines the roll speed.It is the property that what is stationary remains stationary, the so-called inertia.In a simple straight motion, "force (N) required to move = mass (kg) x acceleration (m / sec)"²) ”, So the larger the mass, the harder it is to move, and it tries to maintain that state.The same applies to roll (rotational motion), and "difficulty in rotation" is determined by the mass distribution with respect to the center of gravity of the vehicle body, and the farther the heavy object is from the center of gravity, the more difficult it is to rotate.The concept is called the moment of inertia, and its calculation formula is as follows.The same idea can be basically obtained, only the mass of the straight motion is changed to the moment of inertia. (For details on the moment of inertia, seeSee §9please. )

・ Roll moment (Nm) = moment of inertia (kgm)²) × Angular acceleration (rad / sec²）
(The unit of moment of inertia has little meaning. Think of it as a coefficient.)

Therefore, the process of determining the roll speed can be summarized as follows. (XNUMX) When a roll moment is applied, (XNUMX) angular acceleration is generated according to the moment of inertia inherent in the vehicle.And the angular acceleration produces ④ roll speed (angular velocity) according to the passage of time.However, through the process, ⑤ suspension opposes and suppresses the car body that is about to roll, so ⑥ the roll speed at each moment changes depending on the force relationship.

Here, I simply called the suspension for the time being, but the springs and dampers that make up the suspension have different mechanisms to counter the roll.In addition, the actual role process is progressing in parallel with such complicated elements intertwined, but in the following, a boldly simplified model to understand the effects of each. I will try to calculate the roll speed easily by setting.

* Click to open the enlarged image.

The model used here is a left and right two-wheeled vehicle that ignores the wheelbase as before.In addition, it is assumed that the driving conditions are such that a lateral acceleration of 0.5G is suddenly applied at a certain point, ignoring the steering speed and the yaw angle caused by it.Otherwise, the uncertainties of how to drive will be introduced and it will be out of control.

■ Roll speed in floating state without suspension
First, this is a completely unlikely case in reality, but let's calculate in a floating state without suspension (springs & dampers).

The calculation method first calculates the angular acceleration from the roll moment.After calculating the angular acceleration, multiply it over time to derive the angular velocity at that time.If the angular velocity can be calculated, the roll angle can be understood from the relationship with the passage of time, so the entire roll can be seen.

・ Calculation of angular acceleration (The following calculation is obtained by modifying the formula in the previous section and including the specifications and driving conditions of the model vehicle.)

・ Angular acceleration = roll moment ÷ moment of inertia = 750Nm ÷ 175kgm²≒ 4.29rad / sec²

At a small roll angle, the roll moment is constant, and since it is assumed that there is no suspension to suppress it, the angular acceleration does not change and is always constant.

・ Calculation of angular velocity
Next, the angular velocity is calculated from the angular acceleration.The angular velocity increases by 4.29 rad / sec per second.
For example, after 0.2 seconds, you can simply calculate as follows.

・ Calculation of angular velocity after 0.2 seconds = 4.29 rad / sec²× 0.2sec ≒ 0.86rad / sec

・ Calculation of roll angle
The change in roll angle can be calculated from the relationship between "acceleration and elapsed time" because it is accelerating at the same angular acceleration from the stationary state.The calculation is to calculate the angular velocity after acceleration from 0 rad / sec and divide by 2 to obtain the average angular velocity.Multiply that average angular velocity by the elapsed time again to get the roll angle up to that point.As an example, let's calculate again after 0.2 seconds.

・ Roll angle = angular acceleration (rad / sec²) × Elapsed time (sec) ÷ 2 × Elapsed time (sec)
・ Roll angle (after 0.2 seconds) = 4.29 rad / sec x 0.2 sec²÷ 2 ≒ 0.09rad ≒ 4.91deg

The table below summarizes the results of the stepwise calculation from 0 to 0.35 seconds later.As you can see from each formula, the angular velocity increases in proportion to time, and the roll angle increases in proportion to the square of time.

Item	unit	Elapsed time (sec)
		0.0	0.05	0.10	0.15	0.20	0.25	0.30	0.35
Roll moment	Nm	750.0	750.0	750.0	750.0	750.0	750.0	750.0	750.0
Angular acceleration	rad / sec2	4.29	4.29	4.29	4.29	4.29	4.29	4.29	4.29
Angular velocity	rad / sec	0.00	0.21	0.43	0.64	0.86	1.07	1.29	1.50
Roll angle	rad	0.00	0.01	0.02	0.05	0.09	0.13	0.19	0.26
	you	0.00	0.31	1.23	2.76	4.91	7.67	11.05	15.04

* Click to open the enlarged image.

In this case, you can understand that the angular acceleration is determined by the roll moment and the moment of inertia, and the angular velocity and roll angle are determined accordingly.In other words, the magnitude of the moment of inertia, which is a characteristic unique to the vehicle body, determines everything, so the characteristics of the base vehicle are important.

■ Roll speed with only the damper attached
Next, let's purely examine the effect of the damper on the roll speed.The specifications shown on the right are the ones with only the damper attached to the floating car.The damper is actually more complicated because the damping force changes depending on the piston speed and interacts with the angular velocity each time, but here, to see only the effect of the damping force, the damping force (total expansion and contraction) is determined by the piston speed. Let's assume that you have installed a damper that does not change (set to 600N) and calculate its effect.
First is the calculation of the drag moment of the damper (hereinafter referred to as the drag).During the roll, the inner ring side of the damper expands, the outer ring side contracts, and the damping force of both wheels generates drag to counter the roll.The drag force as the moment is the product of the total damping force, which is the sum of the damping force on the extension side and the compression side, with half of the tread as the lever.

・ Damper drag (Nm) = tread (m) ÷ 2 × (extension side damping force + contraction side damping force)
Drag (Nm) = 1.5m ÷ 2 x 600N = 450Nm

The drag force (450Nm) of the damper is attenuated to 750Nm with the image of suppressing the roll moment (300Nm).In other words, it worked to weaken the roll moment to 300 Nm (assumed to be the effective roll moment).

・ Effective roll moment (Nm) = Roll moment (Nm) -Damper drag (Nm) ≒ 750Nm-450Nm ≒ 300Nm

From here onward, the calculation method is the same, except that the roll moment is simply changed to the effective roll moment.The calculation formulas are listed just in case.

・ Angular acceleration (rad / sec²) = Effective roll moment (Nm) ÷ moment of inertia (kgm)²）
・ Angular velocity (rad / sec) = angular acceleration (rad / sec)²) × Time elapsed (sec)
・ Roll angle (rad) = angular acceleration (rad / sec)²) × Elapsed time (sec)²÷ 2

Let's see how it changes over time.In the graph, the specifications for raising the floating state and damping force to 120% in the previous section are also shown so that the effects of the difference in damping force can be easily compared.

Item	unit	Elapsed time (sec)
		0.0	0.05	0.10	0.15	0.20	0.25	0.30	0.35
Roll moment	Nm	750.0	750.0	750.0	750.0	750.0	750.0	750.0	750.0
Damper damping force	N	600.0	600.0	600.0	600.0	600.0	600.0	600.0	600.0
Damper drag	Nm	450.0	450.0	450.0	450.0	450.0	450.0	450.0	450.0
Effective roll moment	Nm	300.0	300.0	300.0	300.0	300.0	300.0	300.0	300.0
Angular acceleration	rad / sec2	1.71	1.71	1.71	1.71	1.71	1.71	1.71	1.71
Angular velocity	rad / sec	0.00	0.09	0.17	0.26	0.34	0.43	0.51	0.60
Roll angle	rad	0.00	0.00	0.01	0.02	0.03	0.05	0.08	0.11
	you	0.00	0.12	0.49	1.11	1.96	3.07	4.42	6.02

* Click to open the enlarged image.

From the calculation result, the damper drag suppresses the roll moment (750Nm), so the effective roll moment is 300Nm, which is 40% of the floating state by simple comparison.Along with this, the angular acceleration and angular velocity are suppressed, and the degree of progress of the roll angle changes at 40%.
If the damping force is further increased to 120% (720N), the effective roll moment will be 28% in the floating state, and the angular acceleration, angular velocity, and degree of progress of the roll angle will also be 28%, so the tendency will be gentle.
In other words, the damping force of the damper absorbs and weakens the roll moment that is the input to the vehicle body, and as a result, it suppresses the generation of angular acceleration, so it has the effect of lowering the angular velocity, and the higher the damping force, the stronger the tendency. ..Therefore, one of the conclusions to the theme of this lecture is "The key to determining the roll speed is the setting of the damping force of the damper."However, as a function of the suspension as a whole, the damper generates drag only when the angular velocity occurs (when the roll progresses), and the maximum roll angle cannot be determined, so there is a problem that it rolls to the point where there is a physical limit. I have.

■ Roll speed with only the spring attached
Next, let's examine the effect of the spring on the roll speed.Remove the damper in the previous section and install only the spring as shown in the figure on the right.

Both dampers and springs have the same ultimate purpose of suppressing roll, but the process is different.
The damper suppresses the progress of the roll by attenuating the roll moment, while the spring expands and contracts according to the roll moment to accumulate the force against the roll.As a result, the accumulated roll moment becomes a reaction force moment (hereinafter referred to as reaction force) with respect to the vehicle body and tries to bounce the roll (reduces the angular acceleration).In other words, imagine that the effect is different, such as a damper that is effective in reducing the input (reduction of the effective roll moment) and a spring that is effective in reducing the output (reduction of the effective angular acceleration).

The calculation of the reaction force is basically the same because it only squares the "half of the tread" in the formula for calculating the damper drag. The reason for squaring is that the reaction force of the spring increases with the amount of expansion and contraction (roll angle x half of the tread), and it is multiplied by the lever of the "lever" (half of the tread) again. ((§ 15It is the same as multiplying the roll rigidity explained in the above by the roll angle. )
Now, let's actually calculate.For example, the reaction force of the spring when the roll angle is 1.0 deg (0.017 rad) is calculated as follows.Originally, the unit of the reaction force of the spring is Nm, but here, in order to clarify the role of the spring, the spring reaction force (Nm) is the moment of inertia (175kgm).²) Divided by the angular acceleration in the deceleration direction (rad / sec)²) To proceed with the calculation.

・ Spring reaction force (Nm) = tread (m)²÷ 2 × spring constant (N) × roll angle (rad)
Reaction force (Nm) = 1.5m²÷ 2 × 15000N × 0.017rad (1.0deg) ≒ 286.8Nm
Reaction force (rad / sec²) = 286.8Nm ÷ 175kgm²≒ 1.63rad / sec²

From the calculation results, the reaction force of the spring at a roll angle of 1.0 deg is 1.63 rad / sec.²It was found that the angular acceleration in the deceleration direction of is generated.The final angular acceleration (effective angular acceleration) can be obtained by subtracting this reaction force from the angular acceleration calculated from the effective roll moment and moment of inertia.

・ Effective angular acceleration when the roll angle is 1.0 deg = angular acceleration (rad / sec)²) -Reaction force (rad / sec²）
= 4.29rad / sec²-1.63 rad / sec² ≒ 2.66 (rad / sec²)

If the effective angular acceleration can be calculated in this way, the angular velocity at that time can be derived from the relationship between the acceleration and the passage of time.When actually calculated, as shown below, the reaction force of the spring is -0.17 rad / sec at a roll angle of 2.55 deg and about 4.29 sec from the start of the roll.²Reached and angular acceleration (4.29rad / sec²) Is canceled out, the acceleration becomes 0, and the roll angle becomes stable.The graph also shows the case where the spring constant is set to 120%.please refer.

Speaking in detail, if you have knowledge of science, you may have already noticed that the formula for calculating the angular velocity from the reaction force of the spring is a function that depends only on the roll angle, so it should be calculated from the elapsed time. You can not.Therefore, knowing that an error will occur in the absolute value, in order to know the image-like tendency, I tried to find an approximate value by accumulating the changes in the minimum time stepwise.It is, so to speak, "power work" using Excel spreadsheets.Just in case, the outline of the calculation is shown below.
Up to the previous section, the angular acceleration (equal acceleration) was always constant, so the angular velocity and roll angle that accompanied it also changed regularly.However, in this case, the effective angular acceleration is constantly changing, so it is not possible to describe it in a coarse table every 5 / 100sec as shown below.The actual calculation is done every 0.01 sec.
For example, in the case of the column at 0.10 sec (blue-filled part) in the table, strictly speaking, there is a time axis from "0.10000 ... 1" to "0.10999 ... 9", and during that time, the acceleration is added while changing. I am.

The calculation in the table is calculated with the acceleration fixed during this minimum time axis.Therefore, the angular velocity is 0.10000 rad / sec before acceleration is applied (forcibly expressed at 1 ... 0.37 sec), and about 0.01 seconds after that, it becomes 0.40 rad / sec (0.10999 ... at 9 sec). , The roll angle changes with it, and so on.

Item	unit	Elapsed time (sec)
		0.0	0.05	0.10		0.15	0.16	0.17	0.18 ~ 0.35
				Before the lapse	After the lapse
Roll moment	Nm	750.0	750.0	750.0		750.0	750.0	750.0	750.0
Damper drag	Nm	0	0	0		0	0	0	0
Effective roll moment	Nm	750.0	750.0	750.0		750.0	750.0	750.0	750.0
Angular acceleration	rad / sec2	4.29	4.29	4.29		4.29	4.29	4.29	4.29
Spring reaction force	rad / sec2	0	0.33	1.59	1.93	3.52	4.29	4.29	4.29
Effective angular acceleration	rad / sec2	4.29	3.96	2.70		0.76	0.0	-45.0	0.0
Angular velocity	rad / sec	0	0.21	0.37	0.40	0.45	0.45	0.0	0.00
Roll angle	rad	0.00	0.21	0.02	0.02	0.04	0.04	0.04	0.04
	you	0.00	0.01	1.15	1.15	2.35	2.55	2.55	2.55

* Click to open the enlarged image.

In the graph above that summarizes the results, you can imagine the process by which the reaction force of the spring determines the maximum roll angle.However, in this simple calculation, if the spring constant is increased, the degree of progress of angular acceleration and angular velocity tends to decrease, but in reality (it is far from this principle theory, so I will not go into the details. ), Please note that increasing the spring constant will rather increase the roll speed, partly due to the influence of another factor such as the natural frequency of the roll.
Also, in the graph, the angular acceleration and angular velocity change rapidly at the moment when the maximum roll angle is reached (around 0.17 sec), which indicates that there remains a problem in suppressing the roll by the spring alone. ..Since the source of the reaction force is the absorbed roll moment, it cannot exceed it, so even if the increase in angular velocity is suppressed, it cannot be a force to decelerate, and the angular velocity becomes maximum when the maximum roll angle is reached. ..
The force relationship between acceleration and reaction force is balanced and the effective acceleration becomes 0, and although it must be stable there, a dynamic angular velocity remains ... For this angular velocity that remains without deceleration, a spring The image is that he really resisted ... but the explanation of how it converges extends to another difficult problem of "spring vibration", so I will omit the details and cover this weakness. It is the damper.

By the simulation so far, you can understand the characteristics of the car body, the drag force of the damper, and the division of roles of the reaction force of the spring. Simulate.

■ Roll seasoning by setting the damper
The main thing is the relationship between the spring and the damper.Even if increasing the damping force of the damper slows down the roll speed, in common sense, it means "hardening the damper", so it is not a problem if the ride quality and other factors are adversely affected.
Then, what kind of damping force should be set to give what kind of seasoning ... The index is "critical damping force".As you can see, the damping force increases in proportion to the piston speed.Detail isSee §10From the conclusion, it should be said that it is the "allowable limit when increasing the damper damping force", and it can be calculated for each piston speed according to the spring weight of the car and the spring constant of the spring. I can do it.Therefore, by setting the percentage of the actual damping force to the critical damping force (damping ratio) according to the piston speed, the desired ride quality can be obtained.
The graph above shows the case where the damping ratio is fixed at 40% (blue line) and 90% (red line) over the entire range with respect to the critical damping force, and 0.1% → 90 by the time of piston speed = 40 m / sec. It is a damping force characteristic graph when it is gradually lowered to% (green line).By the way, the damping ratio of 100% is the critical damping force, and 0% is the same as when only the spring where the damper is not functioning is installed.
Next, let's simulate how the roll progresses in these three patterns of damping force settings.The vehicle is the left and right two-wheeled vehicle used in the previous section, and the calculation method is the same, so only the results and graphs are shown.By the way, the time axis is expanded to 2.0 sec so that the process up to the maximum roll angle can be easily imagined.By that amount, the table is in 0.2 sec increments, and the mesh is even coarser, but in reality it is calculated every 0.01 sec.

<Comparison of angular acceleration>
Except for the moment when the roll starts (theoretical value in which the damper is not moving yet even though the roll moment is generated), the angular acceleration decreases depending on the damping ratio.
It can be read that the higher the damping ratio, the more effective the initial (~ 0.20sec) damping, and the more the angular acceleration is suppressed.

 

unit (Rad / sec2）	Elapsed time (sec)
	0.00	0.20	0.40	0.60	0.80	1.00	1.20	1.40	1.60	1.80	2.00
40%	4.29	-0.28	-0.13	-0.08	-0.06	-0.05	0.00	-0.00	0.00	0.01	-0.00
90%	4.29	-0.08	-0.06	-0.04	-0.04	-0.03	-0.02	-0.03	-0.01	-0.01	-0.00
90% → 40%	4.29	-0.19	-0.06	-0.00	-0.02	-0.06	-0.02	0.01	-0.01	-0.01	-0.01

<Comparison of angular velocity>
For the angular velocity, the difference between the rising curve up to 0.10 sec and the deceleration method after that can be read depending on the damping ratio.It can be seen that the higher the damping ratio, the more the increase in the angular velocity at the beginning of the roll is suppressed.In addition, it can be read that the angular velocity that had been rising when only the spring was used has converged.

 

 

unit (Rad / sec)	Elapsed time (sec)
	0.00	0.20	0.40	0.60	0.80	1.00	1.20	1.40	1.60	1.80	2.00
40%	0.00	0.09	0.04	0.02	0.01	0.01	0.00	0.00	0.00	0.00	0.00
90%	0.00	0.05	0.04	0.03	0.02	0.02	0.01	0.01	0.01	0.00	0.00
90% → 40%	0.00	0.06	0.04	0.02	0.02	0.01	0.01	0.01	0.00	0.00	0.00

<Comparison of roll angles>
Since the angular acceleration and angular velocity change depending on the damping ratio, the way the roll advances will ultimately differ.From the start of the roll, at 0.1 sec (initial roll), the "damping ratio 40%" is 90% and the "78% → 90%" is 40% ​​for the roll angle of "damping ratio 84%". I'm staying.

 

 

unit (Deg)	Elapsed time (sec)
	0.00	0.20	0.40	0.60	0.80	1.00	1.20	1.40	1.60	1.80	2.00
40%	0.00	1.12	1.83	2.18	2.36	2.45	2.50	2.53	2.54	2.54	2.55
90%	0.00	0.61	1.18	1.52	1.78	2.05	2.21	2.29	2.40	2.50	2.55
90% → 40%	0.00	0.83	1.38	1.76	2.00	2.19	2.29	2.40	2.47	2.53	2.55

From the above simulation, we were able to see the difference due to the damping ratio characteristics.The graph below is a damping ratio / damping force characteristic diagram that was used as an index when I developed the AutoExe height-adjustable suspension.You can see that the damping force in the low speed range is raised (the damping ratio is high).The damping ratio is set high at the initial stage of the roll (~ 0.1m / sec), the damping force is generated quickly, and the riding center area / protrusion area and the rough road area after that are lowered to suppress the damping force. This is the result of thinking that it would be a preferable characteristic.

Settings such as the one with a fixed damping ratio of 90% can moderate the angular velocity in the initial roll range, but the ride will be too hard after the riding center area.On the other hand, if you fix it at 40%, you will not be able to suppress the angular velocity sufficiently in the initial roll range, and you will feel uneasy because the roll characteristics will suddenly become glaring.
This time, for a simple comparison, we calculated and compared the total damping force, but in reality, we will further refine the ride quality by distributing the total damping force to the expansion side and the contraction side.The roll characteristics are set by increasing the ratio of the extension side while keeping the contraction side that causes the feeling of pushing up modest.
Even in the development of mass-produced vehicles, the seasoning of the damper is determined by considering the damping ratio to be set according to the concept and application of the vehicle.Once the damping ratio is determined, we will make a prototype damper that is engineered from the specifications, but since it is human sensitivity that determines the final "seasoning", there is no digital answer that solves mathematical equations.It is important how humans feel.

■ Verification of actual tuning effect
Finally, as an example of the actual tuning effect, we will add AutoExe tuning parts to the NC Roadster and verify the effect.The driving conditions are the same as in the previous section, and the roll center is fixed and the calculation is performed without considering the influence of the roll moment due to the change in vehicle height and gravity.Since we only reflect the setting values ​​in the above formulas, we will only describe the results.The scale of the table differs from 0.2 sec.

Tuning content	Damper specifications Upper: Damping force (N) Lower: Damping ratio (%)			Spring specifications
	Piston speed (m / sec)			Spring constant (N / mm)	Standard ratio
	0.05	0.1	0.3
standard car	549.0 (54%)	647.9 (32%)	1132.8 (18%)	44.4	-
① Damper (standard)  ＋ Low down spring (Spring constant up)	549.0 (54%)	647.9 (32%)	1132.8 (18%)	56.8	128%
② Sports damper (increased damping force)  + Spring (standard)	619.5 (60%)	974.1 (48%)	1923.5 (31%)	44.4	100%
③ Sports damper (increased damping force)  ＋ Low down spring (Spring constant up)	619.5 (53%)	974.1 (42%)	1923.5 (28%)	56.8	128%
④ Vehicle height adjustable suspension	579.2 (47%)	787.3 (32%)	1416.3 (19%)	64.8	146%

* Damping force and spring constant are calculated by converting to the wheel position.

Tuning content	Elapsed time (sec)
	0.00	0.05	0.10	0.15	0.20	0.50	1.00	1.50
Angular acceleration (rad / sec2）
standard car	4.55	1.18	-0.00	-0.70	-0.90	-0.04	-0.02	0.00
① Damper (standard)  ＋ Low down spring (Spring constant up)	4.55	1.13	-1.13	-0.98	-0.90	-0.06	-0.02	0.00
	Standard ratio	96%	-	140%	100%	134%	69%	14%
② Sports damper (increased damping force)  + Spring (standard)	4.55	0.61	-0.25	-0.42	-0.34	-0.04	0.01	-0.02
	Standard ratio	52%	-	60%	38%	91%	-41%	-477%
③ Sports damper (increased damping force)  ＋ Low down spring (Spring constant up)	4.55	0.55	-0.34	-0.47	-0.23	-0.04	-0.02	0.00
	Standard ratio	47%	-	68%	26%	85%	88%	16%
④ Vehicle height adjustable suspension	4.55	0.88	-0.30	-0.78	-0.41	-0.05	-0.01	-0.00
	Standard ratio	75%	-	111%	46%	117%	48%	-22%
Angular velocity (rad / sec)
standard car	0.00	0.12	0.14	0.12	0.07	0.02	0.00	0.00
① Damper (standard)  ＋ Low down spring (Spring constant up)	0.00	0.12	0.13	0.10	0.06	0.01	0.00	0.00
	Standard ratio	99%	96%	89%	76%	69%	75%	95%
② Sports damper (increased damping force)  + Spring (standard)	0.00	0.10	0.10	0.08	0.06	0.02	0.00	0.00
	Standard ratio	86%	72%	70%	82%	141%	210%	0%
③ Sports damper (increased damping force)  ＋ Low down spring (Spring constant up)	0.00	0.10	0.10	0.07	0.05	0.02	0.00	0.00
	Standard ratio	85%	69%	63%	74%	109%	117%	50%
④ Vehicle height adjustable suspension	0.00	0.11	0.11	0.08	0.05	0.01	0.00	0.00
	Standard ratio	93%	82%	71%	66%	72%	62%	22%
Roll angle (deg)
standard car	0.00	0.21	0.59	0.97	1.24	1.78	1.99	2.01
① Damper (standard)  ＋ Low down spring (Spring constant up)	0.00	0.21	0.58	0.93	1.16	1.58	1.72	1.73
	Standard ratio	100%	98%	96%	93%	89%	86%	86%
② Sports damper (increased damping force)  + Spring (standard)	0.00	0.20	0.49	0.75	0.95	1.61	1.95	2.01
	Standard ratio	92%	83%	78%	77%	91%	98%	100%
③ Sports damper (increased damping force)  ＋ Low down spring (Spring constant up)	0.00	0.20	0.49	0.73	0.91	1.46	1.69	1.73
	Standard ratio	92%	82%	75%	73%	82%	85%	86%
④ Vehicle height adjustable suspension	0.00	0.21	0.54	0.82	1.01	1.43	1.57	1.58
	Standard ratio	96%	91%	85%	81%	81%	79%	79%

* Click to open the enlarged image.

In each case, it can be read that the angular velocity in the initial roll range is slowed down by tuning.In terms of sensitivity, it can be said that the roll characteristics at the moment of steering have become more gentle.Also, I think we could confirm that the roll tendency does not change even if the same damper is used and the combination of springs is changed.
The conclusion of which combination is best ... is, of course, a matter of choice based on the driver's sensibility.In short, I think it is important to clarify the purpose and identify the tuning parts to achieve it based on proper knowledge.

■ With dynamic sensitivityRelevance
It has been said that the initial roll (piston speed 0.1 m / sec or less) is important for setting the damping force.In this area, the damping force is difficult to rise, and the friction of the guide part of the damper shaft, gas, and oil seal part has an effect.In the past, there was a response that could be said to be a painstaking measure to improve the characteristics at the beginning of the roll by increasing the friction of the seal part.However, if the friction is large, the movement of the damper shaft will be suppressed and it will not be smooth, which will lead to a deterioration in ride quality.
A good damper is a damper that has a strong damping force even in a small area.For that purpose, it is advantageous to eliminate the adjustment valve and make the structure as simple as possible.The more complicated it is, the more the damper oil escapes from the clearance between the parts, and the damping force in the minute area becomes harder to rise.In recent years, mass-produced dampers have improved the quality of their components, and their performance has improved beyond comparison with the past.In other words, it depends on the tuner that sets whether to use or kill good materials.There may not be many opportunities to set the damping force at the individual level, but I think that you can choose and enjoy the damper that suits you by deepening your knowledge.

I have been giving lectures on the theme of rolls three times in the past.The actual roll angle is about 2.0 ° for sports cars, so if the tread is 1.5m, the wheel stroke is about 2.6cm.Various factors influence each other in a complex manner on this minute movement to determine the process, and human sensibilities have the ability to be delicately perceived.
Roll is said to be an exercise that is easy for everyone to feel and has the greatest impact on human sensibilities.With its own semicircular canals, it senses the angular velocity and acceleration transmitted from the car and transmits it to the brain as an electrical signal.At that time, the preferred roll is recognized as "pleasant", and conversely, if there is a deviation from the expected value, it is felt as "unpleasant" and induces motion sickness.Making such changes in behavior a favorable characteristic for the driver leads to the development of a car with excellent dynamic sensitivity.