#### 2.1. Tire Uniformity Definition

A tire is an annular elastic body made of various materials such as rubber, steel cord, and polyester. Its quality, size, and rigidity are uneven during the structural design and production process. Tire uniformity testing means that the tire is inspected for uneven size, mass, and force under certain conditions of pressure, load, and speed [

4]. Tire uniformity measurement involves the rotation of the tire by applying a load on a rotating drum that is in contact with the tire. Force sensors mounted beside the tire shaft measures the fluctuation of forces and moments in the circumferential direction. The unevenness of the tire mainly includes uneven mass, uneven size, and uneven rigidity [

5].

Figure 1 shows a schematic of the unevenness of a tire.

When a vehicle is running, uneven mass will result in dynamic and static imbalances, causing the tires to generate undulating forces and moments when rotating. The magnitudes of the forces are related to mass imbalance, shape imbalance, and stiffness imbalance. Unbalanced forces in the plane of rotation produce radial, tangential, and lateral excitation forces. Uneven and asymmetrical mass distribution about the rotating shaft causes a coupling imbalance, which produces a rotational moment on the wheel, which is expressed as a returning moment and a turning moment of the frequency change when the wheel rotates [

6]. For uneven tire mass, a weight can be added to the rim to reduce the impact on vehicle performance.

A tire is an elastomer that can be characterized by a radial spring in the circumferential direction, and unevenness in stiffness may occur in the circumferential direction, mainly manifested as fluctuations in circumferential direction force, taper effect force, and angle effect force [

7]. Uneven size will cause radial runout and lateral runout, and the tire will be polygonal in the process of rolling, instead of circular. It can affect the vibration or sway of the vehicle when riding.

#### 2.2. Definition of Tire Uniformity Parameters

(1) The radial force (RF) is the force perpendicular to the spindle of the high-speed uniformity test machine, indicating the amount of load applied to the tire.

(2) The lateral force (LF) is the force parallel to the spindle of the high-speed uniformity test machine, reflecting the vehicle’s handling performance.

(3) Tangential force (TF) is the driving force of tire and high-speed uniformity testing machine, reflecting the driving performance of the vehicle.

(4) Radial force fluctuation (RFV) refers to the fluctuation of radial force during one or more cycles of positive or negative rotation of a tire under a certain load, pressure, and speed, showing the upper and lower runout of the tire.

(5) Lateral force fluctuation (LFV) refers to the fluctuation of the inner side of the tire during one or more cycles of positive or negative rotation of the tire under a certain load, pressure, and speed, which is manifested as the left and right deviation of the car.

(6) Tangential force fluctuation (TFV) refers to the fluctuation of the driving direction of the tire during one or more cycles of positive or negative rotation under a certain load, pressure, and speed.

(7) Radial force 1st-10th harmonic (H1RFV-H10RFV) The relationship between the radial force of the tire and the angle of rotation of the tire obtained by the force fluctuation test is a resonance curve. The tire rotates forward or reverses one or more cycles. Force fluctuations can be decomposed into 1st to 10th harmonics by Fourier transform, where the primary component of the original waveform is called the fundamental or first harmonic.

(8) Lateral force 1st-10th harmonic (H1LFV-H10LFV) The relationship between the tire lateral force and the tire rotation angle obtained by the force fluctuation test is a resonance curve, and the tire is rotated forward or reversed one or more cycles. Force fluctuations can be decomposed into 1st to 10th harmonics by Fourier transform, where the primary component of the original waveform is called the fundamental or first harmonic.

(9) Tangential force 1st–10th harmonic (H1TFV-H10TFV) The relationship between the tangential force of the tire and the angle of rotation of the tire obtained by the force fluctuation test is a resonance curve. The tire is rotated forward or reversed for one or more cycles. Force fluctuations can be decomposed into 1st to 10th harmonics by Fourier transform, where the primary component of the original waveform is called the fundamental or first harmonic.

(10) Lateral force offset (LSFT) is the average value of the force integral on the inside of one or more cycles of forward or reverse rotation, reflecting the quality of the lateral uniformity of the tire.

(11) The taper effect (CON) does not change the lateral force offset of the sign due to the change in the direction of rotation of the tire, reflecting the force on the shoulders of the tire.

(12) The angular effect (PLY) changes the lateral force offset of the sign as the direction of rotation of the tire changes, reflecting the structural design of the belt.

(13) Torque fluctuation (SATV) is the fluctuation of the restoring torque to restore the steering wheel to the straight driving position relative to the reference value.

(14) Flip torque fluctuation (OTTV) is the fluctuation of the rolling moment in the tire straight line direction from the reference value.

Figure 2 shows the partial uniformity parameter.