Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 UDK - UDC 678.056:678.7 Izvirni znanstveni članek - Original scientific paper (1.01) Ocena tlaka v kalupu za stroškovni model obstojnosti stroja za batno brizganje Cavity-Pressure Estimation for a Piston-Moulding Life-Cycle Cost Model Charl L. Goussard - Anton H. Basson (Stellenbosch University, South Africa) Pričujoči prispevek predstavlja in vrednoti postopek za hitro oceno tlakov v kalupu med batnim brizganjem termoplastičnih materialov. Postopek uvaja analitične rešitve v manjšem številu nadzornih prostornin. Rezultat je delno analitičen model, namenjen uporabi med optimizacijo konstrukcije strojev za batno brizganje, kar vodi do optimizacije stroškov v celotnem krogu obstojnosti izdelka. Model je prav tako mogoče prilagoditi primerom brizganja. S tem namenom so pojasnjene tudi nekatere prednosti in pomanjkljivosti batnega brizganja v primerjavi z injekcijskim. Glavna prednost delno analitičnega modela je hitrost, s katero je določena razmeroma točna ocena tlaka brizganja v kalup. Tak pristop pride še posebej v poštev, kadar bi bile numerične simulacije preobsežne in časovno potratne, na primer v primerih optimizacij s širokim razponom neodvisnih spremenljivk. Prav tako so obravnavani različni analitični tokovni modeli, ki jih je moč najti v literaturi, ter njihova možnost uporabe v področju injekcijskega brizganja. Sledi obravnava izpeljanega delno analitičnega modela z njegovimi pripadajočimi poenostavitvami. Njegovi rezultati so primerjani z numeričnimi rešitvami na treh primerih. Ti primeri so pokazali, da je model dovolj natančen za zasnovo konstrukcije naprave in za raziskave stroškovnih usmeritev obstojnosti naprave. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: brizganje polimerov, batno brizganje, tlaki v kalupu, optimiranje stroškov) In this paper we propose and evaluate an approach for quickly estimating the cavity pressures during the piston moulding of thermoplastics. The approach applies analytical solutions in a small number oj control volumes. The resulting semi-analytical model is intended for use when optimising the design oj piston moulding machines, leading to a life-cycle cost optimisation. The model is also applicable to similar injection-moulding cases. Some advantages and disadvantages of piston moulding, compared to injection moulding, are discussed. The main contribution of the semi-analytical model is the speed with which a reasonably accurate estimate of the cavity injection pressure is calculated. This approach is useful in cases when numerical simulations would be too cumbersome and time consuming, e.g., in optimisation studies where the independent variables could vary over a wide range. Different analytical flow models found in the literature and their applicability to injection moulding are discussed. This is followed by a discussion oj the derived semi-analytical model, with its underlying simplifications. The results from the semi-analytical model are compared to numerical solutions for three case studies. These case studies show that the model is sufficiently accurate for machine-layout design purposes and for investigating life-cycle cost trends. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: injection moulding, piston moulding, cavity pressure, cost modelling) 0 INTRODUCTION Lomolding is a piston moulding process designed to make similar parts to injection moulding. Its main operational sequence (illustrated in Fig. 1) starts by measuring off in the metering cylinder the exact amount of molten thermoplastic required for a part, transferring the melt to the moulding cylinder and then pushing the melt into the moulding cavity with the moulding piston. During solidification, the moulding piston holds the cavity under pressure and the piston face forms part of the cavity wall. The area where the melt enters the cavity is much larger than the typical sprue of injection moulding, which is anticipated to bring advantages, 491 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 such as the ability to mould long fibres, lower material shear rates, and lower clamping-force requirements. A life-cycle cost model is being developed to optimise the designs of the lomolding machine and to investigate the range of products suitable for the profitable application of lomolding. This model is aimed at the part of the life-cycle cost of a lomolded product that is related to the processing (as opposed to that contributed by the material used, the distribution, disposal, etc). The processing’s contribution to the life-cycle cost is largely determined by the design of the lomolding machine and the processing parameters. Typical issues that must be addressed, considering the life-cycle cost and the quality of a part, are the optimum ratio of the moulding-piston area to the part projected area, the choice between electric and hydraulic actuators, and the choice between a single piston and multiple piston arrays. The effect of design and process choices on the energy consumption must also be assessed. These machine-design and processing parameters are strongly driven by the injection pressure needed to fill a mould cavity, as well as the clamping force needed to resist the cavity pressures to avoid material flashing. To investigate the processing’s contribution to the life-cycle costs and to optimise the design for minimum cost, a method is therefore needed to quickly obtain the injection pressure and clamp force needed to produce a certain part for a range of operating parameters (i.e., cycle time, melt and mould temperatures, and material properties). As little as metering cylinder possible user intervention should be required in the early design phases to facilitate the automation of the optimisation process, but the dominant physical aspects, such as the effect of fill rate, solidification rate against the mould walls during mould filling, and the non-Newtonian character of the flow, must be accounted for. In practice, numerical simulation programs (Cadmould, Mouldflow, etc.) are used to analyse the behaviour of the molten material before expensive moulds are manufactured. These programs require a large amount of user interaction (creating a mesh, setting large numbers of process and material parameters, cumbersome postprocessing, etc.) to accurately simulate a specific part and are therefore not suitable for the cost modelling required to explore the overall machinedesign decisions and optimisation. Numerical methods can, however, be used to obtain more accurate pressure predictions once the solution region is narrowed down with the use of other methods. This approach can be used when similar trends are predicted by the approximate and the more accurate methods. Analytical solutions for non-Newtonian flow with solidification in simple geometries have been reported, e.g., the flow between parallel plates, the flow in round tubes and disc flow geometries (outlined in Section 3). Since the analytical solutions are only applicable to a limited range of geometries, they cannot be applied as such in the cost model. The approach described in the present paper is to subdivide the cavity into a small number of simple, large control volumes and to use the melt from plasticiser moulding piston cavity Fig. 1. The lomolding process 492 Goussard C. L. - Basson A. H. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 analytical solutions to approximate the flow in each control volume. The key factors in the success of the approach are formulating an equivalent flow pattern in each control volume and selecting the appropriate analytical solution for that control volume, such that the prediction of the solidification rate gives the correct overall results. Once the effective flow areas (h*) are known, the pressure profiles can be calculated fairly easily. The work presented in this paper was driven by the development of lomolding. However, most of the results are equally applicable to injection moulding. The paper’s main contribution is an approach to reasonably accurately estimate the cavity pressures during mould filling, which is fast and simple enough to use for optimisation studies. 1 LITERATURE REVIEW Researchers have shown an interest in theoretical and experimental studies involving fluid flow with solidification in circular tubes and on the walls of parallel-plate channels. The effect of this solidification layer on laminar flow heat transfer has been reported ([1] to [3]). Zerkle and Sunderland [1] and Lee and Zerkle [4] studied the steady solidification of fluid flow for Newtonian fluids with constant physical properties and no viscous heating. They cast the energy equation into a form which is similar to one that describes the classical Graetz problem. The solution is found by the method of the separation of variables and it takes the form of an infinite sum of eigenvalues. Janeschitz-Kriegl [5] and Dietz et al. [6] proposed methods to calculate the thickness of the frozen layer that is formed on the cold cavity walls during the injection-moulding process. Janeschitz-Kriegl [5] used a steady-state heat-transfer coefficient, and the viscous heat generated was estimated from the average melt velocity and the pressure gradient under isothermal conditions. Dietz et al. [6] estimated the thickness of the frozen solid layer by applying the solution for an infinite solid slab. Janeschitz-Kriegl [7] showed in a later paper that a more detailed study with the aid of coupled motion and energy equations will not improve the accuracy of the solid-layer thickness estimation. Effects such as the glass transition or the crystallization kinetics at extreme rates of cooling and shearing have a strong influence on these results. Richardson et al. [8] described the benefits of decomposing moulding networks into basic geometries and solving an analytical flow problem for each segment. This scheme aided mould-maker decisions regarding hot-runner, sprue and mould design. Richardson [9] extended the solution of Zerkle and Sunderland [1] and Lee and Zerkle [4] to non-Newtonian fluids with viscous heating. Again, the energy equation is transformed and the temperature and the frozen-layer thickness are expanded in a power series. The thickness of the frozen layer is then computed by substituting the first three terms of the power series into the energy equation. This solution is well suited for material flows with high Graetz (Gz) numbers, i.e., in the thermal-entrance region. The Graetz number is the ratio between the heat convection in the flow direction and the heat conduction in the direction perpendicular to the flow. In the work presented here, the solutions for flow between parallel plates were used. These solutions and how they are adapted to compute flows in discs, for instance, are described in more detail in Section 2. Richardson also published three papers on flows with freezing of variable-viscosity fluids. The first [10] described developing flows with very high heat generation due to viscous dissipation that is large enough to cause significant variations in viscosity. However, the difference between the polymer temperature at the inlet to a specific part of the mould network and the melting temperature of the polymer is assumed not to cause significant variations in polymer viscosity. The second paper [11] described developing flows with very low heat generation due to viscous dissipation. Furthermore, the difference between the temperature of the polymer at the entry to a specific part of the mould network and the melting temperature of the polymer is assumed to be sufficiently large so as to cause significant variations in polymer viscosity. Polymer flows in pipes, between discs and between parallel plates were considered. These results compare reasonably well with the results obtained from Richardson’s [9] previous paper, as long as the flow Graetz number is sufficiently large. However, combining the closed-form solutions for the three different geometry types, as will be required for the work presented in this paper, is not feasible. In the third paper, Richardson [12] discussed solutions for cases where the polymer flow is fully developed. Ocena tlaka v kalupu za batno brizganje - Cavity-Pressure Estimation for Piston Moulding 493 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 The first models proposed by Richardson [10] did not produce good results for typical lomolding flows when compared to numerical simulation results. It could be argued that the variations in the shear rate are overshadowed by the large difference between the polymer inlet temperature and the polymer melt temperature (± 70°C) and therefore the second paper [11] produces more acceptable results. The third paper’s flow solutions are not applicable to lomolding as the flows considered in the work presented here are generally undeveloped with regard to the temperature field. All of the above papers consider polymer injection at a constant flow rate. This constant-flow-rate phase comprises approximately the first 90% of the polymer-injection stage and is followed by polymer injection at a constant pressure. Richardson published three more case studies involving cavity filling at a constant pressure: freezing off at polymer injection gates [13], freezing off in round and flat cavities [4] and freezing off in disc cavities [15]. As cavity filling occurs at a more or less constant polymer flow rate for such a large part of the injection stage, the focus in the work presented here was placed on filling at a constant flow rate. Hill [16] proposed solutions to find the equilibrium height of the solidified polymer layer, where the polymer temperature increases due to viscous dissipation in equilibrium with the temperature drop due to heat conduction to the cold cavity wall. However, attention was restricted to the Newtonian case, for which numerical solutions are provided as well. Neither the equilibrium nor the Newtonian-flow assumptions are reasonable for the work presented here. Today, far more complex cavities and flow geometries can be analyzed with numerical methods. Analytical models are often used to test numerical algorithms for simple case studies. Yang et al. [17] compared the results for the steady solidification of non-Newtonian fluids flowing in round tubes. Gao et al. [18] studied the effect of variable injection speed during injection-mould filling. They also tested their numerical algorithms against simple analytical solution case studies. The scarcity of more recent papers reporting analytical solutions is probably due to the complexity of the physics involved, limiting analytical solutions to a very few simple geometries. In recent years, however, considerable effort has been invested in developing numerical simulations, mostly using finite-element modelling, that can handle the complex geometries commonly encountered when processing plastics. 2 SEMI-ANALYTICAL MODEL This section describes Richardson’s [9] analytical model briefly as well as the adaptation of the model to flows in channels of varying width. All the equations in this section come from [9]. Fig. 2 shows a schematic of the polymer flow between parallel plates. The flow is symmetrical with respect to the centreline and therefore only half of the cavity is shown. The half-height of the cavity is given by h, and the distance between the centreline and the solidified layer, by h. The solution is split into two regions, a thermal-entry region and a melt-front region. The melt-front region comprises most of the total flow length in typical cases. The pressure drop (AP) over the entire flow length is given by Equation 1: AP=//*J ((m + 2)Q~ 0{2wh*m+2 ) dx (1). The half-height of the polymer melt region (h*) is found by introducing: 0 = 1- h* h (2). For the thermal-entrance region, 8 is given by: S = 6<9*r(4/3) 1 6(m + 2)Gz + 0 and for the melt-front region, by: 8 = 4w E f - e\ Gz -2 ~\ Gz3 (3) (4), where: e ks(Tm kL(T,-Tm) r(4/3)= 0.893 x L = — L X , f L a=(sf/2K)05 (5) (6) (7) (8) (9) m e 494 Goussard C. L. - Basson A. H. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 \ frozen polymer molten Ay polymer AfA h* melt\ fronti y_ h _A thermal entrance region melt front region kL /(rL Fig. 2. Polymer flow in a channel kS /(rS (10). The Stefan number (Sf) is the ratio of the heat required to raise the polymer temperature from the cavity wall temperature to the polymer melting point, and the heat required to melt the polymer solid. Once the half-height of the polymer-melt region is found for a control volume, the pressure drop can be calculated. These equations were derived for cases where the flow-channel width remains constant and the flow front enters the cavity evenly over the whole channel width. Consider a typical moulding case: a rectangular cavity with constant thickness is filled through a sprue in the centre of the cavity. Fig. 3 shows a quarter of such a cavity. Clearly, the longest flow path is given by the diagonal line D running from the injection point to one corner. This longest flow path is divided into a number of control volumes. To calculate h* for a specific control volume at a certain time, it is necessary to know the flow-front position along D, the start point of the control volume with respect to D, the length of this control volume along D and the average width of the control volume. l/2 To place a particular control volume at an equivalent x-position in the analytic model, assumptions have to be made about the upstream and downstream conditions: • The upstream flow-path length in the semi-analytical model is taken to be the same as the true (geometric) length. • The upstream and downstream flow-path width is taken to be equal to the average width of the control volume under consideration. • Once the melt front has passed through the control volume, its position is calculated using the above flow-channel width (even though this will, in general, not coincide with the true flow-front position). Case studies, as shown here, have confirmed that the approximated upstream geometry gives reasonable results, even though any upstream variation in flow area will influence the time that the flow front takes to reach a control volume. The approximated downstream geometry can deviate from the true geometry without affecting the solidified layer thickness in the control volume under consideration since, for these cases where the flow rate is constant, the only upstream effect is in the pressure gradient. injection point R F1 F2 longest symmetry line Fig. 3. Schematic of the polymer flow front in a rectangular cavity (quarter segment shown) x Ocena tlaka v kalupu za batno brizganje - Cavity-Pressure Estimation for Piston Moulding 495 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 The pressure drop and the height of the solid layer from the side of the cavity to the longest symmetry are calculated for this control volume in a line. Note that these flow control volumes fall away straightforward manner, as described above. It is when working with a square cavity (see Fig. 4). necessary, in order to solve Equation 1 correctly, to From position F2 onwards the control-volume width check if a control volume is positioned entirely in is calculated as four times the length of a line the thermal-entrance region, entirely in the melt- perpendicular to D, extending from side to side. front region or contains both. Fig. 5 shows that the assumptions made for Therefore, it is necessary to calculate the the equivalent widths of the control volumes equivalent width, volume and start position along approximate the true flow case numerically D for each control volume. From Fig. 3 it is clear calculated by Cadmould. that the flow front will be circular until the nearest It now remains to calculate the position of side of the rectangle (b/2) is met. Therefore, the the melt-flow front as closely as possible to the true radius of the largest circular flow front is given by flow phenomenon. As is clear from Fig. 3, the Equation 11 : hatched area is the only area not accounted for in b the control volumes. To preserve the filling time, R = - (11). the volume associated with the hatched area is added to all the control volumes on a per-volume Up to this point, the equivalent control- basis, except for the round control volumes. Once volume width is given by Equation 12: this correction has been applied, it is easy to calculate the position of the flow front. wi = 27iRi (12). The semi-analytical model is validated in the next section using different case studies. From F1 to F2 (Fig. 3, note F2 is where the longest symmetry line meets the edge of the cavity) 3 CASE STUDIES the equivalent flow widths are set equal to four times (note Fig. 3 shows a quarter of the cavity) The semi-analytical model was implemented the length of a line perpendicular to D, extending in software by the authors. This section shows some l/2 D/ \.\b/2 R Fig. 4. Schematic of the polymer flow front in a square cavity Fig. 5. Flow lines for a rectangular cavity filled in the centre as calculated with Cadmould 496 Goussard C. L. - Basson A. H. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 results to verify the semi-analytical model. The most restrictive requirement of the analysis presented above is that the flow Graetz number must be sufficiently high, which is explored later in this section. The results of the semi-analytical model are compared with those of Cadmould. Although it would have been preferable to compare the results directly with experimental data, Cadmould is a widely accepted simulation tool in industry and therefore its results have considerable credibility. Furthermore, numerical simulations can give details that are extremely difficult to measure, such as the thickness of the solidified layer. Two polymer materials suited for lomolding were selected for the case studies, i.e., Novolen 1100 N (a homogeneous polypropolene) and Celstran PP GF30 (a polypropolene with 30% glass-fibre component). The material properties for these materials given by Cadmould [19] and Osswald and Menges [20] were used and are summarised in Table 1. Cadmould [19] provides a Carreau viscosity model for these two materials. The unit shear-rate viscosity (µ*) and the viscosity shear-rate coefficient (m) are found by fitting a power-law model to the Carreau model. The power-law viscosity model is given in Equation 13: m = m ?u ?y (13). The figures in this section showing the results use the following abbreviations: AM for the semi-analytical model result; CM for the Cadmould numerical result; Cel for the Celstran material; and Nov for the Novolen material. The first case study is the filling of a 500-mm-diameter disc, 3 mm thick, with the injection occurring along the circumference of an 80-mm- diameter piston into the cavity. Therefore, the flow-path length is shown in Fig. 6 as 210 mm. The disc is filled in one second at a constant flow rate. Fig. 6 shows that the growth of the solid layer along the flow path (a radial line) is underestimated, relative to Cadmould, for both materials. The pressure drop along the flow path relates well to the results obtained with Cadmould (Fig. 7). The lowest calculated Graetz number was 209 for the Celstran material and 230 for Novolen. The second case study involves a square cavity with a length and breadth of 200 mm and a thickness of 2 mm. The injection point is in the centre and the longest flow path D is equal to 100^2 mm. The cavity is filled in 0.5 seconds. As can be seen from Fig. 8, the semi-analytical model overestimates the growth of the solid layer in this case, especially near the end of the flow path. This leads to higher predicted pressure drops for both materials, as is clear from Fig. 9. The lowest calculated Graetz number was 134 for the Celstran material and 143 for Novolen. Note the sudden rise near the end due to the narrowing flow area. The last case study is that of a rectangular cavity, 300 mm x 200 mm, with a thickness of 3 mm. The longest flow path D is equal to 180.28 mm. The cavity is filled in one second. Fig. 10 shows that the height of the solid layer is reasonably well predicted for both materials. As a result of this, Fig. 11 shows good agreement for the pressure drop across the rectangular cavity. The lowest calculated Graetz number was 191 for the Celstran material and 209 for Novolen. In some situations a cavity will be filled in a time that will minimize the pressure drop experienced during filling. However, if this filling time is too long, a larger injection-pressure-capacity machine may be used, since this will save costs Table 1. Material properties Property Novolen 1100 N Celstran PP GF30 Unit Unit shear-rate viscosity (m*) 5655 6958 N.s/m2 Viscosity shear-rate exponent (m) 2.63 3.31 Melt inlet temperature (Ti) 220 260 °C Polymer melting temperature (Tm) 154 170 °C Cavity-wall temperature (Tw) 40 55 °C Polymer-melt thermal conductivity (kL) 0.236 0.150 W/mK Polymer-melt density (rL) 910 994 kg/m3 Polymer thermal diffusivity (a) 0.1043 0.0685 10-6 m2/s Ocena tlaka v kalupu za batno brizganje - Cavity-Pressure Estimation for Piston Moulding 497 -1 m Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 0.7 0.6 -0.5 -0.4 0.3 0.2 0.1 i 0 -—Cel CM — Cel AM -----Nov CM ^^ Nov AM 0 50 100 150 200 250 Radius [mm] Fig. 6. Growth of the solid layer in a disc cavity Fig. 8. Growth of the solid layer in a square cavity Fig. 10. Growth of the solid layer in a rectangular cavity during the machine’s lifetime as the part cycle time will be reduced. The fill rate directly influences the Graetz number, but the analytical model is only applicable to “large” Graetz numbers. It is therefore worth investigating what the influence is of the Graetz number on the accuracy of the semi-analytical model and what acceptable numerical values for the Graetz number would be. 200 150 100 < 50 0 Cel CM Cel AM Nov CM Nov AM 0 0.25 0.5 0.75 Time [sec] Fig. 7. Pressure drop occurring in a disc cavity 250 - 200 150 % 100 50 0 Cel CM Cel AM Nov CM Nov AM 0 0.6 0.2 0.4 Time [sec] Fig. 9. Pressure drop occurring in a square cavity Fig. 11. Pressure drop occurring in a rectangular cavity Figures 12 to 15 show the influence of the Graetz number on the results obtained with the semi-analytical model for the same case studies used above. It is compared to numerical results obtained from Cadmould [19]. The Graetz numbers reported in the figures are the smallest calculated at the end of the filling stage under a constant flow rate. The objective was to find the filling time for 498 Goussard C. L. - Basson A. H. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 Fig. 12. Pressure drop for different filling times in a disc cavity for Celstran material which the pressure drop across the cavity would be a minimum. These pressure drops are then compared to those found using the analytical model. It is also checked to see if this local minimum occurs at more or less the same filling time for both the analytical and numerical results. Figures 12 and 13 show that for the disc cavity the pressure-drop results differ significantly for the two models when the Graetz number drops below 100. The analytical model estimates the lowest pressure drop around a 2-seconds filling time. However, Cadmould estimates these minima at around 4 seconds for both materials. At 2 seconds the error for the semi-analytical model is 6% in the case of the Novolen material and less in the case of Celstran. At 4 seconds this error grows to 59% in the worst case, which is again for the Novolen material. At this point the Graetz number is 37, well below 100. In the case of the square cavity shown in Figures 14 and 15, the analytical model predicts l< 500 400 300 200 100 0 500 Cel CM 400 Cel AM 300 Gz 200 100 0 0 2 4 6 8 10 Time [sec] 700 600 -500 400 i 300 200 -100 0 600 Nov CM 4 500 Nov AM t 400 300 t 200 100 0 700 0 2 4 6 8 10 Time [sec] 12 Fig. 13. Pressure drop for different filling times in a disc cavity for Novolen material the smallest pressure drop at around a filling time of 1 second for both materials. This compares well to the filling times found by Cadmould, especially in the case of the Novolen material. The minimum pressure drop varies very little across a filling time of 1 to 10 seconds in the case of the Celstran material. The error of the semi-analytical model is at most 33% for the Novolen case at a filling time of 1 second. At this point the Graetz number is equal to 57. In the case of the rectangular cavity (Figures 16 and 17), both models predict a minimum pressure drop at around a 2-seconds cavity-fill time. In the case of the Novolen material it is noted that the analytical model calculates a slightly smaller filling time. The semi-analytical model’s error is 49%, at most, for the Novolen case at a filling time of 2 seconds. At this point the Graetz number is equal to 83. It is clear from these results that the semi-analytical model is reasonably well suited to finding 600 500 400 300 K 200 -100 0 600 500 400 300 200 100 0 0 12 34 56 Time [sec] Fig. 14. Pressure drop for different filling times in a square cavity for Celstran material Fig. 15. Pressure drop for different filling times in a square cavity for Novolen material Ocena tlaka v kalupu za batno brizganje - Cavity-Pressure Estimation for Piston Moulding 499 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)7-8, 491-502 300 250 - 200 150 h !