{"id":78486,"date":"2022-07-19T17:44:28","date_gmt":"2022-07-19T15:44:28","guid":{"rendered":"https:\/\/ivmtech.it\/?page_id=78486"},"modified":"2022-10-25T17:50:11","modified_gmt":"2022-10-25T15:50:11","slug":"distribuzione-della-forza-peso","status":"publish","type":"page","link":"https:\/\/ivmtech.it\/en\/pillole-tecniche\/distribuzione-della-forza-peso\/","title":{"rendered":"Wheel load distribution"},"content":{"rendered":"<p>[vc_row][vc_column][vc_text_separator title=&#8221;The importance of measuring the distribution of vertical forces per wheel in static conditions for maintenance&#8221; color=&#8221;custom&#8221; border_width=&#8221;2&#8243; accent_color=&#8221;#ffd200&#8243; el_class=&#8221;sticky&#8221;][vc_empty_space height=&#8221;20px&#8221;][vc_column_text css_animation=&#8221;left-to-right&#8221;]<span style=\"font-weight: 400;\">For any type of vehicle, a correct load distribution exerted by its contact points on the ground is one of the fundamental requirements for optimal static and dynamic behaviour.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In the case of a railway vehicle, an even load distribution is essential for safety and running quality.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let&#8217;s consider the bogie scheme below:<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-78547 size-full\" src=\"https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img.png\" alt=\"\" width=\"1124\" height=\"402\" srcset=\"https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img.png 1124w, https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img-300x107.png 300w, https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img-768x275.png 768w, https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img-500x179.png 500w, https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/pillola-1-img-800x286.png 800w\" sizes=\"(max-width: 1124px) 100vw, 1124px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">The main influence factors on the load distribution are essentially three:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Stiffness of the primary suspension at each wheel<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Coplanarity of the contact points with the track<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Eccentricity of the load<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">The ideal condition for a bogie is:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">primary suspension springs in perfect condition and with the same stiffnesses;<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">perfect coplanarity of the 4 contact points with the track;<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">load on the geometric centre of gravity (without eccentricity).<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">When a single factor deviates from the ideal condition, it affects the load distribution. In particular, if there is an alteration of the <\/span><i><span style=\"font-weight: 400;\">springs of the primary suspension that leads to different stiffnesses<\/span><\/i><span style=\"font-weight: 400;\">, the load distribution exerted by the wheels will be different and the load on the two diagonals of the bogie will <\/span><b>always<\/b><span style=\"font-weight: 400;\"> be unbalanced. If \u2018\u2019Fi\u2019\u2019 are the forces exerted by each wheel, it results in (F1 + F4) \u2260 (F2 + F3).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Similarly, if there is no coplanarity of contact points due to twisted tracks or bogie frame deformation, the diagonals will <\/span><b>also<\/b><span style=\"font-weight: 400;\"> be unbalanced.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The non-coplanarity of the contact points also<\/span> <span style=\"font-weight: 400;\">occurs when the four wheels are not evenly worn. During the measurement of the wheel load distribution, this latter condition is often more difficult to verify than twisted tracks or twisted bogies, also due to wheel accessibility.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Unlike the other two cases, the presence of eccentric load does not affect the difference between the two diagonals if the other two ideal conditions are verified, ensuring (F1 + F4) = (F2 + F3). On the other hand, a load that is not perfectly centred in the geometric centre of gravity involves different vertical loads:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F1 \u2260 F2 \u2260 F3 \u2260 F4.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">To easier understand the behaviour of a railway bogie, an analytic model was created in order to interact, change parameters and verify how these variations affect the wheel loads.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Below you can find a link to access a platform called Bogie Playground:\u00a0\u00a0<\/span><\/p>\n<p><span style=\"color: #ffcc00;\"><strong><a style=\"color: #ffcc00;\" href=\"https:\/\/powerve-156508.web.app\/login\">BogiePlayground (powerve-156508.web.app)<\/a><\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">Why is correct load distribution important?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For wheeled vehicles, in particular for railway vehicles, the load distribution mainly affects two phenomena:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Acceleration \/ braking phase<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Running safety on twisted tracks<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">As regards the first phenomena, specifically the <\/span><b>braking phase<\/b><span style=\"font-weight: 400;\">: when a braking torque is applied to a railway axle, the system of forces acting on the single wheel can be represented as follows:<\/span><\/p>\n<p><img loading=\"lazy\" class=\"wp-image-78494 size-full alignleft\" src=\"https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/foto-2-pillola-1.png\" alt=\"\" width=\"454\" height=\"223\" srcset=\"https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/foto-2-pillola-1.png 454w, https:\/\/ivmtech.it\/wp-content\/uploads\/2022\/07\/foto-2-pillola-1-300x147.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">where:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">P<sub>eff<\/sub> = vertical load on the wheel<\/span><span style=\"font-weight: 400;\">;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Q = radial force exerted by the braking element;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">f \u2019 = friction coefficient;\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">f<sub>ad<\/sub> = wheel-rail adhesion coefficient;<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">On the contact surface, between the braking element and the wheel, a friction force opposite to the sliding force between the two elements arise, which is:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<sub>a <\/sub><\/span> <span style=\"font-weight: 400;\">=<\/span> <span style=\"font-weight: 400;\">Q*f<\/span><b>\u2019<\/b><\/p>\n<p><span style=\"font-weight: 400;\">This frictional force generates a torque of opposite direction to that of the motion and of a magnitude equal to the product F<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">*r, with \u201cr\u201d radius of the wheel.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">To remain in a macro-adhesion regime, the adhesion force to the wheel-rail interface should remain greater, or at least identical, to the force exerted by the braking element, i.e.:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">F<sub>a <\/sub>\u2264 f<sub>ad<\/sub><\/span><span style=\"font-weight: 400;\">*P<sub>eff<\/sub><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, an uneven distribution of the load, which results in a variation of P<\/span><span style=\"font-weight: 400;\">eff<\/span><span style=\"font-weight: 400;\"> of the single wheel, for the same braking force acting on the entire wheelset, can lead to a slip of one of the two wheels. This circumstance would result in an unwanted yaw effect on the bogie.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We have briefly seen how an uneven wheel load distribution would affect the braking phase of a railway vehicle. The same can be said for the acceleration phase.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let&#8217;s now see how an imbalance of vertical forces affects the <\/span><b>running safety when running on twisted tracks<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In general, running safety is guaranteed when the wheel-rail interaction forces remain within certain limits that prevent vehicle derailment or permanent deformation of the track.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Specifically, a railway vehicle is in a risky condition when the wheel flange comes into contact with the rail. In this case it is necessary to consider the Y \/ Q ratio between the transverse force exerted by the wheel on the rail (Y) and the vertical load of the wheel (Q).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In fact, due to the force Y and the friction coefficient at the contact point, the wheel tends to change the axis around which it rotates. The new axis will be orthogonal to the contact surface and will pass through the contact point between the flange and the rail. In this new condition the wheel tends to lift but it is the weight force Q to oppose. So, any cause that may involve a decrease in the vertical wheel load can cause an increase in the Y \/ Q ratio and therefore an increase in the risk of derailment.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">One of the most significant track defects that can pose a safety hazard is the twist.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The definition of the twist (g defined in thousandths) is the variation along the rail axis of the vertical slope and is expressed as the ratio between this vertical difference h over a longitudinal reference distance d (usually wheelbase or bogie centre distance):<\/span><\/p>\n<p><span style=\"font-weight: 400;\">g (\u2030) = h\/d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The twist represents the most common cause of derailment since, in general, its presence alters the wheel load distribution, leading to load imbalance.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Once a certain critical value has been exceeded, the vehicle wheel first tends to decrease part of its weight, then to rise, triggering the overlap of the flange on the top of the rail, finally the derailment of the rolling stock.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A correct, and therefore balanced, distribution of the vertical forces per wheel of a vehicle means that it is more capable of adapting to track irregularities.<\/span>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_text_separator title=&#8221;The importance of measuring the distribution of vertical forces per wheel in static conditions for maintenance&#8221; color=&#8221;custom&#8221; border_width=&#8221;2&#8243; accent_color=&#8221;#ffd200&#8243; [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":78476,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v15.9 - 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