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Abstract: In order to solve the problem of low light efficiency and high cost of L ED motorcycle signal, a new method based on mathematical model of L ED light intensity distribution is proposed. Based on the mathematical model of the light intensity distribution of the curved L ED array, the design is applied to the light distribution design of L ED motorcycle signal light. The Tra2cepro optical simulation software was used to simulate the L ED motorcycle brake light designed by this method. The results show that the mathematical model of the light intensity distribution of the curved L ED array is correct and can meet the requirements of the national motorcycle light distribution standard. The light distribution design of the L ED motorcycle signal light is realized.

**0 Preface**

At present, the universal motorcycle brake light source is still dominated by incandescent lamps, and the red light distribution lens realizes the light distribution requirement. The disadvantage is that the incandescent lamp is easy to damage, the power consumption is large, the life is short, the reliability is poor, and the road traffic is given. Bring security risks and so on. LEDs (light-emitting diodes) have the advantages of small size, long life and low energy consumption, which are gradually applied to the light source of motor vehicles. At present, there are three main design schemes for the general L ED motorcycle signal light: the first one is to directly arrange multiple piranha type L ED in a flat shape and sealed in the lampshade. The disadvantage is that a considerable part of the light is in the national standard. Outside the range required by the light distribution screen, the light energy is wasted; the second is to use a plurality of ball cap type L ED to be arranged in a planar shape and sealed in the lamp cover, and the light distribution lens is used for light distribution, and the disadvantage is that a part of the light passes through The light lens is refracted, scattered and absorbed, resulting in a relatively low light efficiency of the lamp; the third is to arrange a plurality of piranha type L ED into a plane, and the light is combined by a parabolic concentrator and a light distribution lens. The disadvantage is that the concentrator design cost is high, and the light loss of the light distribution lens is large. The LED motorcycle signal designed by the three light distribution design schemes has low light efficiency, large loss of light energy and high design cost.

If we can theoretically establish a mathematical model of the L ED intensity distribution, study the light intensity distribution of a L ED array and eliminate the need for concentrators and light beams to meet national standards, thus providing design for L ED motorcycle signal lights. A new fast and practical method with important theoretical and practical guiding significance.

**1 Mathematical model of the intensity distribution of a curved LED array**

**1. 1 Mathematical model of single LED intensity distribution**

First, a distribution model of the individual L ED light intensity is established, as shown in Figure 1. Wherein, the center of the detected spherical surface is (0,0,0), the radius is r, Î± represents the horizontal direction angle of the L ED light source; Î² represents the vertical direction angle of the L ED light source; Î¸ represents the single L ED light OM and the optical axis OL Angle Ï† represents the angle between the L ED optical axis OL and its projection on the xy plane; Î³ represents the angle between the L ED optical axis OL and the y plane projection and the Y axis.

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