- Email: [email protected]
Study on segmented reflector lamp design based on error analysis
Journal of Materials Processing Technology 129 (2002) 529–533
Study on segmented reflector lamp design based on error analysis H. Liu*, J.L. Yuan College of Mechanical and Electronical Engineering, Zhejiang University of Technology, Hangzhou 310014, PR China
Abstract This paper discusses the basic principle and design method for car lamp light distribution, introduces an important development: high efficient and flexible car lamp with reflecting light distribution—the segmented reflector (multi-patch) car lamp, and advances a design method for a segmented reflector based on error analysis. It establishes an error-analyzing model for a segmented reflector according to the analysis of error in the production process of the segmented reflector. Based on this error-analyzing model and by the use of analyzing software developed for segmented reflector light distribution, it reasonably considers reflector errors in manufacturing, such as reflector surface spray-painting and the plating of aluminum. Thus it can provide the shapes of reflector patches for a segmented reflector, and direct the plan of the production process efficiently. The method advanced in this paper has been applied successfully to develop segmented reflector lamps for several types of cars and has been used to a great extent in the factory. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Car lamp design; Light distribution; Segmented surface reflector
1. Introduction An important symbol of the fast development of China’s economy is the increasing demand for cars. Car sales have increased during recent years, with sales in family cars. The car lamp is an important and necessary safety item, as well as being ornamental, as it is the eyes of the car. In China, as more highways are put to use and a continuous demand is made on the car’s properties, the requirements of car lamps are becoming increasingly more stringent. The current fashion in the car lamp’s in the word is the segmented reflector lamp. One standard distinguishing feature of the deluxe car from the common car is whether or not a segmented reflector lamp is used. The traditional lamp, in which the shape of the reflector is a paraboloid the light distribution is accomplished by a reflector and a lens. The reflectors only plays the role of reflecting light, and the lens has the role of light distribution. This method is so-called refractive light distribution. Now the domestic headlamp basically uses this form. Its disadvantages are the low use of light energy, and lack of space for the lamp exterior, because the lens must be nearly perpendicular to the horizontal for the purpose of light distribution, which cannot satisfy or fit the demand of car exterior design. The segmented reflector *
Corresponding author. Tel.: þ86-571-88320341; fax: þ86-571-88320130. E-mail address: [email protected] (H. Liu).
lamp achieves light distribution through a reflector, and the lens takes the role of protecting the lamp, which is called reflecting light distribution. The reflecting and light distribution functions are integrated, i.e. the reflector assumes the task of reflecting and distributing, and the original distributing lens is only a protective shell. Thus for the same dimensions and the same bulb, the high beam intensity is 1.8 times that of the paraboloid reflector. This solves the problem of dazzling light, and at the same time it can illuminate the road in front of the car, i.e. the low beam has clear light and a shaded cut-off line and achieves a good effect in preventing the dizziness of the eyes, whilst the high beam intensity reaches ideal numerical values. This segmented reflector lamp changes the three-in-one traditional car lamp into a two-in-one car lamp. It has the advantage of good light distribution, high light efficiency (especially for the high beam), ease in adjusting the light beam, relatively low cost of manufacturing, and increased strength of the lamp (resistance to impact). What is more, the lamp exterior is not limited by light distribution; and the gradient angle of lens can be large, which forcefully supports the design of the car exterior. This not only satisfies the increasing demand for gas kinetics in car design, but also of good looks for the lamp exterior and fitting the car modeling, which accelerates the development of car modeling. The technique of a segmented reflector lamp gives the car lamp the composite function of both lighting and decorating. The trend of car lamp development is the phasing out of the
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 6 2 7 - 1
530
H. Liu, J.L. Yuan / Journal of Materials Processing Technology 129 (2002) 529–533
traditional paraboloidal lamp and the wide use of the segmented reflector lamp with good properties of light distribution and high use of light energy. More and more deluxe car’s use this kind of lamp. It is necessary to study the design method of this lamp to promote its application further in Chinese industry.
2. Basic theory There are serious stipulations for the light distribution of the headlamp in the Chinese standard for cars, which demand a very precise light intensity distribution of the headlamp besides, drivers must turn on dipped headlights to change the light intensity and light flux distribution when cars meet, i.e. the light of the car must illuminate the front road and traffic signal marks, and must not give an uncomfortable dazzling light on the oncoming driver [1]. This is the usual so-called change between ‘‘high beam’’ and ‘‘low beam’’. Low beam is the shortened light form that not only prevents dazzling a driver but illuminates the road immediately ahead, whilst high beam is the parallel light that illuminates the road for some distance ahead. The standard used in China is the same as that in Europe; it is a headlamp system which has an asymmetrical low beam with clear light and a shaded cut-off line. The light distribution area of the headlamp is asymmetrical. The center is a high intensity ray area to illuminate the two sides of the road ahead. The ray transpires in a horizontal line so that the driver can tell the width of the road. At the same time, the light intensity is very low in the direction of the oncoming driver in order to reduce the possibility of dazzling light. Parallel light is a demand in the high beam, and in appointed areas, the light intensity must fit the national standard. To satisfy the above demands, the traditional headlamp is composed of three parts: the lamp-housing, the reflector and the lens. Because the material used for the reflector is steel, the geometrical shape is designed as a paraboloid for the sake of calculating the light distribution and for easy shaping. For the high beam, it is easy to secure an approximately parallel light as long as if the filament for the high beam is in focus, and the light produced by the main filament is reflected as straight lines parallel to the optical axis of the reflector with only slight dispersion. But for the low beam, it is insufficient to depend only on the reflector. According to the national standard, the low beam is a light shape that has an asymmetrical clear light and a shaded cutoff line. The demand of the light shape of the low beam is that on a light distribution screen which is away from the headlamp by 25 m (which is plumb to the light of the headlights), the angle of the bias line is 158: the area above the cut-off line is dangerous and may produce dazzling light. The light of this area consists of two parts, dipped headlights producing one, with the other being light reflected from the road, so the highest light intensity is limited. Contrarily, the
area under the cut-off line provides the light intensity to illuminate the road; so that the minimal value of light intensity should be specified. In order to avoid great contrast, the light intensity of the area near the car should not be too high. The cut-off line extends along with the bias line to ensure that the dipped headlights can illuminate the righthand side of the road [2]. The light which reaches the road consists of two portions. One is direct light emitted by the filament of the dipped headlights, but as the intensity of this light is high, it is necessary to add a light mask ahead of the filament for turning back direct light. The other is reflected light from the reflector. For the sake of the requirement of dipped headlights, the reflected light must fall in the light shape. Traditional light distribution, the surface of lens is modified: it is made up of numerous small faces. According to optical theory, the light ray is reflected by the reflector and changes its direction. Then the light ray reaches the lens, and changes its direction again, i.e. if the faces on the light distribution lens are rational, the image of light ray will tally with light shape, and the light intensity can also reach the corresponding value. Thus, in traditional light distribution, the main work is to select the optimal face to obtain the optimal light shape. In light distribution design, errors mainly caused by optical calculation should be taken into account. In the optical calculating lamp-house model, it is very important that existing errors be compared with the real filament and it fittings. Multiplying the result by 80% compensates for these errors for traditional light distribution. Applications show that this method is satisfactory. For light distribution with a segmented reflector, it is insufficient to do so because errors exist in the surface of the reflector as well as in the model of the filament. The segmented reflector not only plays the role of reflecting the light, but also refracting light to form the light shape. Any difference between the calculated reflector and the manufactured reflector will influence the light shape. How to consider this kind of error is the problem to be solved.
3. Light distribution with a segmented reflector With the fast development of the thru-way, the dynamics question arising in running is considered, and at the same time, the requirement’s of the car shape are many. The clipper-built shape is the main-stream trend of the car’s shape. As one feature cannot be ignored, demands on the shape of the headlamp have increased. The method of traditional light distribution cannot satisfy the demand. This becomes a factor restricting the development of the shape of the car. In traditional light distribution, the lens is a light distributing lens, and the primary objective is light distribution, so that the shape of the car lamp is simple, such as rectangular or circular, the lens must plumb the level (light shape) orientation, and the permitted transformation angle of bias is very small. Thus it cannot meet the streamline
H. Liu, J.L. Yuan / Journal of Materials Processing Technology 129 (2002) 529–533
requirement. To improve this situation, some light distribution methods have come into being, and the segmented reflector becomes the optimal method. Segmented reflector light distribution is not the same as the traditional method: the lens is a safeguard of the lamp body and not just a light distribution lens, and so the transformation of the angle of bias is not restrained any longer. The shape of lens can be designed into whatever is used to meet the need of the exterior of a car. In this method, the light distribution lens is a reflector, and the surface of reflector is not a simple paraboloid. Generally, it is a complicated free surface to realize the required optical characteristics. The basic theory of segmented reflector light distribution is: the complicated reflecting surface consists of many inerratic faces according to a certain rule. The inerratic faces reflect the light emitted by the filament of the low beam; and refract and sum to form the light shape of the low beam of the headlamp. The lens is only a safeguard for the lamp body. Because the lens is designed to be transparent and of small refraction, the segmented faces of the reflector can approximately ascertain the light shape of the low beam and the light intensity. In the process of light distribution, the real source of dipped headlights is extended, not point sized, and tends to spread out the beam slightly and blur’s the edges of the illumination pattern. The light emitted by any point of the filament irradiates any point, according to optical theory and the ray tracing way, so that the reflection direction can be made certain, and the reflecting light ray direction reaching the light distribution masks through the lens. The projection point is the image of the light ray. The next step is to analyze every point on the filament and every patch on the surface of reflector; all images will form the light shape of dipped headlights [3,4]. To illustrate the light distribution algorithm for a segmented reflector, plane-reflecting elements are used to describe each segmented patch. The light image for one patch reflecting on a screen in 25 m distant is the sum of the images of plane-reflecting elements. The following are the equations for calculating the image of a reflecting element in the case where the data of the size and position of the reflecting element and the lamp-housing are known. The relationship among the injecting ray I, the reflecting and the normal vector ray R n is shown in Fig. 1. From point LðX1 ; Y1 ; Z1 Þ to point MðXm ; Ym ; Zm Þ the injecting ray I can be expressed as
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The unit vector of I is I 0 ¼ fIx ; Iy ; Iz g I ðxm xi Þi þ ðym yi Þj þ ðzm zi Þk ¼ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jIj ðxm xi Þ2 þ ðym yi Þ2 þ ðzm zi Þ2 According to the equations about a vector quantitative product and a vector product: 0 0 n0 I ¼ n0 R
(1)
0 0 n0 I ¼ n0 R
(2) 0
Assume that the unit vectors of n0 and R are n0 ¼ fnx ; ny ; nz g;
0 ¼ fRx ; Ry ; Rz g R
Solving Eqs. (1) and (2) 2 2n2x þ 1 6 ðRx ; Ry ; Rz ÞT ¼ 4 2ny nx 2nz nx
2nx ny 2n2y þ 1 2nz ny
2nx nz
2ny nz 7 5 2n2z þ 1
ðIx ; Iy ; Iz ÞT
(3)
can be Thus for a given plane-reflecting element (known n) R obtained from (3) when I is known. Therefore the light distribution shape of the headlamp can be calculated. For the particularity of the light shape, the light distribution shape on the light distribution screen can be divided into several areas. According to optical knowledge, a reflector can be divided into several corresponding areas (every area including umpty inerratic patches). In the ideal light shape, most of the light is distributed horizontally, and less vertically. The light intensity is digressive from the center to the two sides. Horizontally, the reflector converges the light and spread out the light, and vertically, the reflector converges the light. Thus the light can be decomposed into a horizontal component and a vertical component. Based on the analysis of the light character, horizontally, reflecting units can be taken as of free surface character, and vertically, reflecting units can be free surface and paraboloidal. In [1], the reflector is divided into 15 patches, and every patch is an elliptically spherical paraboloid or hyperboloidal paraboloid. Fig. 2 shows one example by CAE technology analysis.
I ¼ ðxm xi Þi þ ðym yi Þj þ ðzm zi Þk ¼ fxm xi ; ym yi ; zm zi g
Fig. 1. Relationship among I, n and R.
3
Fig. 2. Surface sketch map for segmented reflector.
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4. Segmented reflector design According to anterior section discussion and light distribution calculation expressions, one can find the reflector that meets the requirements of light distribution, but to emphasize, the reflector by calculation is ideal: it does not consider the later manufacture tache effect. Through mould manufacture, injection figuration, spray-paint and aluminum processing, the reflector obtained may not be in accordance with the reflector by light distribution calculation. Differences exists between the calculated reflector and the manufactured reflector. Owing to its light reflecting character, a small diversification of the reflector will reduce a large diversification of the light distribution shape on light distribution screen at 25 m distance, so the light distribution quality cannot be ensured. To ensure that the reflector by light distribution calculation is in accordance with that from the reflector from practical manufacture, the error effect of the surface shape must be reasonably considered, namely the error effect of the manufacture tache. The error influence on the reflector light distribution model is the error of the position of the bulb filament, the error of lampshade manufacture, and the error of reflector manufacture. Traditional refraction light distribution (namely the revolving paraboloid reflector car lamp) adopted a simplified calculation, namely discount of the analysis result (the point light intensity on the light distribution screen) by 80%. For the reflecting light distribution of the segmented reflector, because the reflector completes reflecting and light distribution, its analysis result (light intensity and light shape) cannot be simply dealt with discounting. Here one error sensitivity analysis method is given. This method reasonably considers that the error of the reflector by manufacture affects the light distribution and sensitivity. The error of the reflector mainly lies in mould machining, surface spray-painting and aluminum asymmetry. One can uniformly describe those errors by a mathematical model as follows. Suppose one of the reflector segments is Zi ¼ Zi ðx; yÞ;
x; y 2 Oi
cess. For the example of reflector spray-paint, when the base paint does not solidify, it is easy for it to flow to produce an asymmetrical thickness. Thus the choice of the base paint and the placement of the drying reflector after spray-painting, should be considered when setting down the process. Utilizing the original surface’s excursion and then calculating the light distribution, can provide the light distribution for error sensitivity and maximum permissible value. The thickness scope of spray-paints and aluminum has a reference value if every segment is calculated in this way.
5. Applying a CAE technique The light distribution of the segmented reflector discussed in Section 2 shows only in theory the superiority of reflected light distribution, and because the light distribution is for each segment, the amount of computing is increasingly greater. With the application of CAE, it is possible to realize the segmented reflector. The research adopts the finite element method in structural analysis. A segment is divided into some reflecting elements and then each reflecting element is analyzed by the ray tracing way. Thus the position of the segment for a reflected surface is obtained. The model is called an optical numeric analysis model, and it has the advantage of being suitable for multi-segments and ideal precision, and can be easily realized by a program. In light distribution by a segmented reflector, the light’s shape after light distribution is the total of filament image that is produced by the filament after reflection. Since a streamlined vehicle requires a headlamp with good optical quality, the design could be carried out point-by-point for the reflector surface (reflector element) of the headlamp. Each small reflected element on the reflector surface needs to be optimized; thus the light shape is produced. Then analyzing the shape for the low beam, the reflected light should be below the cut-off line and the greatest intensity of light shape is close by the turning point. In order to make the light shape
(4)
The effect of manufacturing error can be shown as the splice of one error surface di ðx; yÞ and the original surface Zi ðx; yÞ, namely Zi ¼ Zi ðx; yÞ ¼ Zi ðx; yÞ þ di ðx; yÞ
(5)
The shape of the error surface is complicated. It relates to the manufacturing process. In spite of the particular shape difficulty expressed, the splice result is equal to the excursion of original surface Zi ðx; yÞ–Z orientation and the turn around X- and Y-axis. Thus the error surface influence on the light distribution and light intensity, is not necessarily worked out by Eq. (5) and calculation, as one can directly utilize the original surface’s shift and turn for calculation. Studying the shape and effect of light distribution sensitivity can guide one in setting down the manufacture pro-
Fig. 3. Flow chart for light distribution.
H. Liu, J.L. Yuan / Journal of Materials Processing Technology 129 (2002) 529–533
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the cut-off line, the dispersion area and maximum light intensity, the surface shape of the reflecting areas are adjusted. Every reflecting element is analyzed to obtain the anticipated light shape, and create one modified segmented reflector exterior. Fig. 3 shows the basic flow chart of light distribution, whilst Fig. 4 shows the working sketch map of the light distribution CAE software, and Fig. 5 gives an example. Fig. 4. Sketch map for CAE analysis.
6. Conclusions Segmented reflector, also called patch surface reflector, is a free surface reflector, meaning that the reflector consists of umpty surface segment, where the surface segments shape can be random. In light distribution, because every segment’s shape and position is modifiable, the optical intensity and position of the shape on the light distribution screen, which is obtained by the light given off by the lamp-housing reflecting through patches, can be obtained by optical numerical computing. This provides the required optical shape of the reflecting light distribution. In a real application, the reflector design must consider the influence of manufacturing error. The light distribution CAE software according to the method of this paper has been applied successfully in company.
Fig. 5. An example for CAE analysis.
distribute uniformly, the reflecting element should be as small as possible. The basic modus of making use of an optics CAD system is constructing the reflector basic model, according to factual circumstances, creating a paraboloid first (or other forms), there after creating the paraboloid, creating a reflecting area on it and mesh gridding, so that this reflecting exterior is meshed by hundreds of reflecting elements. Under the condition of giving ideal light shape parameters such as
References [1] Standard of PR China, GB4599-94, Photometric Characteristics of Headlamps for Motor Vehicles, China Standard Press, Beijing, 1995 (in Chinese). [2] Y.H. Mo, Guangxi Mech. 2 (1999) 21–23 (in Chinese). [3] J. Zhou, J.Y. Zhang, T.M. Zhou, L. Zhou, Lamp Light. 3 (23) (1999) 1–5 (in Chinese). [4] Q.L. Tu, J. Zhongqing Ind. Manage. College 11 (1999) 17–20 (in Chinese).
Study on segmented reflector lamp design based on error analysis H. Liu*, J.L. Yuan College of Mechanical and Electronical Engineering, Zhejiang University of Technology, Hangzhou 310014, PR China
Abstract This paper discusses the basic principle and design method for car lamp light distribution, introduces an important development: high efficient and flexible car lamp with reflecting light distribution—the segmented reflector (multi-patch) car lamp, and advances a design method for a segmented reflector based on error analysis. It establishes an error-analyzing model for a segmented reflector according to the analysis of error in the production process of the segmented reflector. Based on this error-analyzing model and by the use of analyzing software developed for segmented reflector light distribution, it reasonably considers reflector errors in manufacturing, such as reflector surface spray-painting and the plating of aluminum. Thus it can provide the shapes of reflector patches for a segmented reflector, and direct the plan of the production process efficiently. The method advanced in this paper has been applied successfully to develop segmented reflector lamps for several types of cars and has been used to a great extent in the factory. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Car lamp design; Light distribution; Segmented surface reflector
1. Introduction An important symbol of the fast development of China’s economy is the increasing demand for cars. Car sales have increased during recent years, with sales in family cars. The car lamp is an important and necessary safety item, as well as being ornamental, as it is the eyes of the car. In China, as more highways are put to use and a continuous demand is made on the car’s properties, the requirements of car lamps are becoming increasingly more stringent. The current fashion in the car lamp’s in the word is the segmented reflector lamp. One standard distinguishing feature of the deluxe car from the common car is whether or not a segmented reflector lamp is used. The traditional lamp, in which the shape of the reflector is a paraboloid the light distribution is accomplished by a reflector and a lens. The reflectors only plays the role of reflecting light, and the lens has the role of light distribution. This method is so-called refractive light distribution. Now the domestic headlamp basically uses this form. Its disadvantages are the low use of light energy, and lack of space for the lamp exterior, because the lens must be nearly perpendicular to the horizontal for the purpose of light distribution, which cannot satisfy or fit the demand of car exterior design. The segmented reflector *
Corresponding author. Tel.: þ86-571-88320341; fax: þ86-571-88320130. E-mail address: [email protected] (H. Liu).
lamp achieves light distribution through a reflector, and the lens takes the role of protecting the lamp, which is called reflecting light distribution. The reflecting and light distribution functions are integrated, i.e. the reflector assumes the task of reflecting and distributing, and the original distributing lens is only a protective shell. Thus for the same dimensions and the same bulb, the high beam intensity is 1.8 times that of the paraboloid reflector. This solves the problem of dazzling light, and at the same time it can illuminate the road in front of the car, i.e. the low beam has clear light and a shaded cut-off line and achieves a good effect in preventing the dizziness of the eyes, whilst the high beam intensity reaches ideal numerical values. This segmented reflector lamp changes the three-in-one traditional car lamp into a two-in-one car lamp. It has the advantage of good light distribution, high light efficiency (especially for the high beam), ease in adjusting the light beam, relatively low cost of manufacturing, and increased strength of the lamp (resistance to impact). What is more, the lamp exterior is not limited by light distribution; and the gradient angle of lens can be large, which forcefully supports the design of the car exterior. This not only satisfies the increasing demand for gas kinetics in car design, but also of good looks for the lamp exterior and fitting the car modeling, which accelerates the development of car modeling. The technique of a segmented reflector lamp gives the car lamp the composite function of both lighting and decorating. The trend of car lamp development is the phasing out of the
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 6 2 7 - 1
530
H. Liu, J.L. Yuan / Journal of Materials Processing Technology 129 (2002) 529–533
traditional paraboloidal lamp and the wide use of the segmented reflector lamp with good properties of light distribution and high use of light energy. More and more deluxe car’s use this kind of lamp. It is necessary to study the design method of this lamp to promote its application further in Chinese industry.
2. Basic theory There are serious stipulations for the light distribution of the headlamp in the Chinese standard for cars, which demand a very precise light intensity distribution of the headlamp besides, drivers must turn on dipped headlights to change the light intensity and light flux distribution when cars meet, i.e. the light of the car must illuminate the front road and traffic signal marks, and must not give an uncomfortable dazzling light on the oncoming driver [1]. This is the usual so-called change between ‘‘high beam’’ and ‘‘low beam’’. Low beam is the shortened light form that not only prevents dazzling a driver but illuminates the road immediately ahead, whilst high beam is the parallel light that illuminates the road for some distance ahead. The standard used in China is the same as that in Europe; it is a headlamp system which has an asymmetrical low beam with clear light and a shaded cut-off line. The light distribution area of the headlamp is asymmetrical. The center is a high intensity ray area to illuminate the two sides of the road ahead. The ray transpires in a horizontal line so that the driver can tell the width of the road. At the same time, the light intensity is very low in the direction of the oncoming driver in order to reduce the possibility of dazzling light. Parallel light is a demand in the high beam, and in appointed areas, the light intensity must fit the national standard. To satisfy the above demands, the traditional headlamp is composed of three parts: the lamp-housing, the reflector and the lens. Because the material used for the reflector is steel, the geometrical shape is designed as a paraboloid for the sake of calculating the light distribution and for easy shaping. For the high beam, it is easy to secure an approximately parallel light as long as if the filament for the high beam is in focus, and the light produced by the main filament is reflected as straight lines parallel to the optical axis of the reflector with only slight dispersion. But for the low beam, it is insufficient to depend only on the reflector. According to the national standard, the low beam is a light shape that has an asymmetrical clear light and a shaded cutoff line. The demand of the light shape of the low beam is that on a light distribution screen which is away from the headlamp by 25 m (which is plumb to the light of the headlights), the angle of the bias line is 158: the area above the cut-off line is dangerous and may produce dazzling light. The light of this area consists of two parts, dipped headlights producing one, with the other being light reflected from the road, so the highest light intensity is limited. Contrarily, the
area under the cut-off line provides the light intensity to illuminate the road; so that the minimal value of light intensity should be specified. In order to avoid great contrast, the light intensity of the area near the car should not be too high. The cut-off line extends along with the bias line to ensure that the dipped headlights can illuminate the righthand side of the road [2]. The light which reaches the road consists of two portions. One is direct light emitted by the filament of the dipped headlights, but as the intensity of this light is high, it is necessary to add a light mask ahead of the filament for turning back direct light. The other is reflected light from the reflector. For the sake of the requirement of dipped headlights, the reflected light must fall in the light shape. Traditional light distribution, the surface of lens is modified: it is made up of numerous small faces. According to optical theory, the light ray is reflected by the reflector and changes its direction. Then the light ray reaches the lens, and changes its direction again, i.e. if the faces on the light distribution lens are rational, the image of light ray will tally with light shape, and the light intensity can also reach the corresponding value. Thus, in traditional light distribution, the main work is to select the optimal face to obtain the optimal light shape. In light distribution design, errors mainly caused by optical calculation should be taken into account. In the optical calculating lamp-house model, it is very important that existing errors be compared with the real filament and it fittings. Multiplying the result by 80% compensates for these errors for traditional light distribution. Applications show that this method is satisfactory. For light distribution with a segmented reflector, it is insufficient to do so because errors exist in the surface of the reflector as well as in the model of the filament. The segmented reflector not only plays the role of reflecting the light, but also refracting light to form the light shape. Any difference between the calculated reflector and the manufactured reflector will influence the light shape. How to consider this kind of error is the problem to be solved.
3. Light distribution with a segmented reflector With the fast development of the thru-way, the dynamics question arising in running is considered, and at the same time, the requirement’s of the car shape are many. The clipper-built shape is the main-stream trend of the car’s shape. As one feature cannot be ignored, demands on the shape of the headlamp have increased. The method of traditional light distribution cannot satisfy the demand. This becomes a factor restricting the development of the shape of the car. In traditional light distribution, the lens is a light distributing lens, and the primary objective is light distribution, so that the shape of the car lamp is simple, such as rectangular or circular, the lens must plumb the level (light shape) orientation, and the permitted transformation angle of bias is very small. Thus it cannot meet the streamline
H. Liu, J.L. Yuan / Journal of Materials Processing Technology 129 (2002) 529–533
requirement. To improve this situation, some light distribution methods have come into being, and the segmented reflector becomes the optimal method. Segmented reflector light distribution is not the same as the traditional method: the lens is a safeguard of the lamp body and not just a light distribution lens, and so the transformation of the angle of bias is not restrained any longer. The shape of lens can be designed into whatever is used to meet the need of the exterior of a car. In this method, the light distribution lens is a reflector, and the surface of reflector is not a simple paraboloid. Generally, it is a complicated free surface to realize the required optical characteristics. The basic theory of segmented reflector light distribution is: the complicated reflecting surface consists of many inerratic faces according to a certain rule. The inerratic faces reflect the light emitted by the filament of the low beam; and refract and sum to form the light shape of the low beam of the headlamp. The lens is only a safeguard for the lamp body. Because the lens is designed to be transparent and of small refraction, the segmented faces of the reflector can approximately ascertain the light shape of the low beam and the light intensity. In the process of light distribution, the real source of dipped headlights is extended, not point sized, and tends to spread out the beam slightly and blur’s the edges of the illumination pattern. The light emitted by any point of the filament irradiates any point, according to optical theory and the ray tracing way, so that the reflection direction can be made certain, and the reflecting light ray direction reaching the light distribution masks through the lens. The projection point is the image of the light ray. The next step is to analyze every point on the filament and every patch on the surface of reflector; all images will form the light shape of dipped headlights [3,4]. To illustrate the light distribution algorithm for a segmented reflector, plane-reflecting elements are used to describe each segmented patch. The light image for one patch reflecting on a screen in 25 m distant is the sum of the images of plane-reflecting elements. The following are the equations for calculating the image of a reflecting element in the case where the data of the size and position of the reflecting element and the lamp-housing are known. The relationship among the injecting ray I, the reflecting and the normal vector ray R n is shown in Fig. 1. From point LðX1 ; Y1 ; Z1 Þ to point MðXm ; Ym ; Zm Þ the injecting ray I can be expressed as
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The unit vector of I is I 0 ¼ fIx ; Iy ; Iz g I ðxm xi Þi þ ðym yi Þj þ ðzm zi Þk ¼ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jIj ðxm xi Þ2 þ ðym yi Þ2 þ ðzm zi Þ2 According to the equations about a vector quantitative product and a vector product: 0 0 n0 I ¼ n0 R
(1)
0 0 n0 I ¼ n0 R
(2) 0
Assume that the unit vectors of n0 and R are n0 ¼ fnx ; ny ; nz g;
0 ¼ fRx ; Ry ; Rz g R
Solving Eqs. (1) and (2) 2 2n2x þ 1 6 ðRx ; Ry ; Rz ÞT ¼ 4 2ny nx 2nz nx
2nx ny 2n2y þ 1 2nz ny
2nx nz
2ny nz 7 5 2n2z þ 1
ðIx ; Iy ; Iz ÞT
(3)
can be Thus for a given plane-reflecting element (known n) R obtained from (3) when I is known. Therefore the light distribution shape of the headlamp can be calculated. For the particularity of the light shape, the light distribution shape on the light distribution screen can be divided into several areas. According to optical knowledge, a reflector can be divided into several corresponding areas (every area including umpty inerratic patches). In the ideal light shape, most of the light is distributed horizontally, and less vertically. The light intensity is digressive from the center to the two sides. Horizontally, the reflector converges the light and spread out the light, and vertically, the reflector converges the light. Thus the light can be decomposed into a horizontal component and a vertical component. Based on the analysis of the light character, horizontally, reflecting units can be taken as of free surface character, and vertically, reflecting units can be free surface and paraboloidal. In [1], the reflector is divided into 15 patches, and every patch is an elliptically spherical paraboloid or hyperboloidal paraboloid. Fig. 2 shows one example by CAE technology analysis.
I ¼ ðxm xi Þi þ ðym yi Þj þ ðzm zi Þk ¼ fxm xi ; ym yi ; zm zi g
Fig. 1. Relationship among I, n and R.
3
Fig. 2. Surface sketch map for segmented reflector.
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4. Segmented reflector design According to anterior section discussion and light distribution calculation expressions, one can find the reflector that meets the requirements of light distribution, but to emphasize, the reflector by calculation is ideal: it does not consider the later manufacture tache effect. Through mould manufacture, injection figuration, spray-paint and aluminum processing, the reflector obtained may not be in accordance with the reflector by light distribution calculation. Differences exists between the calculated reflector and the manufactured reflector. Owing to its light reflecting character, a small diversification of the reflector will reduce a large diversification of the light distribution shape on light distribution screen at 25 m distance, so the light distribution quality cannot be ensured. To ensure that the reflector by light distribution calculation is in accordance with that from the reflector from practical manufacture, the error effect of the surface shape must be reasonably considered, namely the error effect of the manufacture tache. The error influence on the reflector light distribution model is the error of the position of the bulb filament, the error of lampshade manufacture, and the error of reflector manufacture. Traditional refraction light distribution (namely the revolving paraboloid reflector car lamp) adopted a simplified calculation, namely discount of the analysis result (the point light intensity on the light distribution screen) by 80%. For the reflecting light distribution of the segmented reflector, because the reflector completes reflecting and light distribution, its analysis result (light intensity and light shape) cannot be simply dealt with discounting. Here one error sensitivity analysis method is given. This method reasonably considers that the error of the reflector by manufacture affects the light distribution and sensitivity. The error of the reflector mainly lies in mould machining, surface spray-painting and aluminum asymmetry. One can uniformly describe those errors by a mathematical model as follows. Suppose one of the reflector segments is Zi ¼ Zi ðx; yÞ;
x; y 2 Oi
cess. For the example of reflector spray-paint, when the base paint does not solidify, it is easy for it to flow to produce an asymmetrical thickness. Thus the choice of the base paint and the placement of the drying reflector after spray-painting, should be considered when setting down the process. Utilizing the original surface’s excursion and then calculating the light distribution, can provide the light distribution for error sensitivity and maximum permissible value. The thickness scope of spray-paints and aluminum has a reference value if every segment is calculated in this way.
5. Applying a CAE technique The light distribution of the segmented reflector discussed in Section 2 shows only in theory the superiority of reflected light distribution, and because the light distribution is for each segment, the amount of computing is increasingly greater. With the application of CAE, it is possible to realize the segmented reflector. The research adopts the finite element method in structural analysis. A segment is divided into some reflecting elements and then each reflecting element is analyzed by the ray tracing way. Thus the position of the segment for a reflected surface is obtained. The model is called an optical numeric analysis model, and it has the advantage of being suitable for multi-segments and ideal precision, and can be easily realized by a program. In light distribution by a segmented reflector, the light’s shape after light distribution is the total of filament image that is produced by the filament after reflection. Since a streamlined vehicle requires a headlamp with good optical quality, the design could be carried out point-by-point for the reflector surface (reflector element) of the headlamp. Each small reflected element on the reflector surface needs to be optimized; thus the light shape is produced. Then analyzing the shape for the low beam, the reflected light should be below the cut-off line and the greatest intensity of light shape is close by the turning point. In order to make the light shape
(4)
The effect of manufacturing error can be shown as the splice of one error surface di ðx; yÞ and the original surface Zi ðx; yÞ, namely Zi ¼ Zi ðx; yÞ ¼ Zi ðx; yÞ þ di ðx; yÞ
(5)
The shape of the error surface is complicated. It relates to the manufacturing process. In spite of the particular shape difficulty expressed, the splice result is equal to the excursion of original surface Zi ðx; yÞ–Z orientation and the turn around X- and Y-axis. Thus the error surface influence on the light distribution and light intensity, is not necessarily worked out by Eq. (5) and calculation, as one can directly utilize the original surface’s shift and turn for calculation. Studying the shape and effect of light distribution sensitivity can guide one in setting down the manufacture pro-
Fig. 3. Flow chart for light distribution.
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the cut-off line, the dispersion area and maximum light intensity, the surface shape of the reflecting areas are adjusted. Every reflecting element is analyzed to obtain the anticipated light shape, and create one modified segmented reflector exterior. Fig. 3 shows the basic flow chart of light distribution, whilst Fig. 4 shows the working sketch map of the light distribution CAE software, and Fig. 5 gives an example. Fig. 4. Sketch map for CAE analysis.
6. Conclusions Segmented reflector, also called patch surface reflector, is a free surface reflector, meaning that the reflector consists of umpty surface segment, where the surface segments shape can be random. In light distribution, because every segment’s shape and position is modifiable, the optical intensity and position of the shape on the light distribution screen, which is obtained by the light given off by the lamp-housing reflecting through patches, can be obtained by optical numerical computing. This provides the required optical shape of the reflecting light distribution. In a real application, the reflector design must consider the influence of manufacturing error. The light distribution CAE software according to the method of this paper has been applied successfully in company.
Fig. 5. An example for CAE analysis.
distribute uniformly, the reflecting element should be as small as possible. The basic modus of making use of an optics CAD system is constructing the reflector basic model, according to factual circumstances, creating a paraboloid first (or other forms), there after creating the paraboloid, creating a reflecting area on it and mesh gridding, so that this reflecting exterior is meshed by hundreds of reflecting elements. Under the condition of giving ideal light shape parameters such as
References [1] Standard of PR China, GB4599-94, Photometric Characteristics of Headlamps for Motor Vehicles, China Standard Press, Beijing, 1995 (in Chinese). [2] Y.H. Mo, Guangxi Mech. 2 (1999) 21–23 (in Chinese). [3] J. Zhou, J.Y. Zhang, T.M. Zhou, L. Zhou, Lamp Light. 3 (23) (1999) 1–5 (in Chinese). [4] Q.L. Tu, J. Zhongqing Ind. Manage. College 11 (1999) 17–20 (in Chinese).