BACKGROUND

[001] Carriages are used in a variety of functions to support, carry or transport equipment or material. Image forming apparatuses, such as two or three dimensional (2D or 3D) printers, sometimes include such carriages that are to be moved over or across a print bed to enable components included In the carriages to perform various operations during formation of an object, e.g. a 3D object The carriages may be independently movable over the print bod and are to move along an axis or shaft,

[002] Shafts are sometimes fitted with housings which may employ linear guides, such as bearings or sliders, In contact with the shaft to reduce stresses between the shaft and the housing,

[003] In some image forming apparatuses, such as 3D printers, carriages are fitted with guides employing housings with multiple contact guiding elements to linearly guide the shafts when the image forming apparatus Is in function,

BRIEF DESCRIPTION

[004] Some non-limitng examples of the present disclosure are described in the following with reference to the appended drawings, in which:

[005] Fig. 1 schematically illustrates a linear guide with a preloading spring, according to an example. [006] Fig, 2 schematically illustrates a linear guide with & thermal

compensation block, according to an example.

[007] Fig. 3 schematically illustrates a linear guide with a thermal

compensation block, according to another example,

[008] Fig, 4 schematically illustrates a linear guide with sliders and a thermal compensation block,, according to another example.

[009] Fig. S schematically illustrates an image forming apparatus with a carriage, according to an example.

DETAILED DESCRIPTION

[010] Fig, 1 schematically Illustrates a multl-beahng housing for a shaft with a preloading spring, according to an example. Multi-bearing housing 100 comprises a housing 105. The support plate 105 may be made of a first material, e.g. aluminium, and may be of a shape, e.g. U-shaped, defining an opening 110 for receiving a shaft 112, The support plate 105 may host multiple contact guiding elements, e.g. multiple bearings 115A, 11 SB, 1.15C rotatable around a pin 120A, 1208, 120C, respectively. The pins may be hosted In openings of the housing and may be affixed to the housing 105, Each bearing may have an inner ring rotaiably coupled to the respective pin and an outer ring. The size, of the bearings and the location o? the pins may be selected and designed so that the outer ring to be In contact with a shaft 112, when a shaft 1 12 is introduced in the opening In a direction perpendicular to the plane defined by the housing 105, Thus, each outer ring of the bearings may contact the shaft at different points, respectively, In the example of Fig. 1 , pin 120Ά and pin 120B are substantially parallel to the axis of symmetry x-x' of the U-shaped opening so that the diameters of the outer rings of the bearings 115A, 1 1 SB to form a straight line y-y' with the centre of the shaft, when the shaft Is Introduced in the opening. In other examples one or more of the bearings may be inclined with respect to the y-y' axis. The outer rings of bearings 120A, 120B may contact the shaft at points corresponding to intersections of a horizontal diametric line of a cross section of the shaft. When the shaft is introduced in the opening, the bearing 120A, the shaft 112 and the bearing 120B. may be arranged in a straight line to form a "bearing-shaft-bearing" system. The third pin 120C may be substantially coaxial to the axis of symmetry x-x' of the U- shaped opening. Thus the respective outer ring of bearing 12SC may contact the shaft at a point located 90 degrees clockwise and anticlockwise from the points in contact with bearings 12SA and 1258, respectively.

[0011] The various pieces of the multi-bearing housing 100. namely the housing 10S* the pins 120A, 120B, 120C and the bearings 115A, 115B, 115C. as well as the shaft 1 12 Introduced in the opening., may be made of different materials. Each material may have a different thermal coefficient When in use, the various pieces may heat up and expand unequally, each piece expanding according to its expansion coefficient (the expansion being a factor of its thermal coefficient and of its length). Thus contact between the shaft and one of the hearings of the "bearing-shaft-bearing" system may be lost. This may cause instability to the carriage and loss of accuracy. Some linear guides may use a preload mechanism,, such as a spring107 attached to the housing 105 The spring 107 may be in contact and push one of the pins, e.g. pin 120A, to generate a preloading force F in order to keep all the bearings in touch with the shaft during different temperatures as thermal coefficients of all the materials may not be the same and the materials may unequally expand.

[0012] Such a preloading force F may be applied constantly and may thus increase the Hertzian contact stresses, i.e. the stresses between the bearings and the shaft, and the Von Misses stresses, i.e. stresses used to predict yielding of materials under complex, loading from the results of uniaxial tensile tests. By using spring 107, the preload force may be up to +100% of the force required with a system without preload. The linear guide 100 with preload may limit the acceleration of the carriage because the contact forces may reach the yield stress of the shaft 112 or of the bearing 1 15A. [0013] Fig, 2 schematically illustrates a linear guide for a shaft, according to an example. Linear guide 200 comprises a housing 205- The housing 205 may define an opening 210 for receiving a shaft 212, The housing 205 may host three contact guiding elements, e.g. bearings 215A, 2158 and 21 SC. Bearings 215A, 21 SB and 21 SC may be rotatahie around pins 220A, 220 B and 220C, respectively. The pins 220A, 220 _. 8 and 220C may be hosted in openings of the housing 20:5 and may he affixed to the housing 205, Instead of _. a. preload spring mechanism, the linear guide 200 may be provided with a thermal compensation block 230, The thermal compensation block 230 may be affixed to the support plate 205 and may be in contact with one or more of the pins parallel to the-x-x' .axis, e.g. with pin 220A. Placement of the thermal compensation block 230 on the support plate 205 may be performed by using e.g. a loose fining technique. In the example of Fig, 2 the: thermal compensation block 230 is placed at an outer side of the pin 220A with respect to the shaft 212.

[0014] The thermal compensation block 230 may be distributed in two parts 230A and 230B along the pin on both sides of the respective bearing, one block part per side of the bearing, On one side of the bearing, the thermal compensation block 230A, 2308 may comprise a first portion 235A, 235B, respectively In contact with the pin. The first portion 23SA, 235B may be made of a material e.g. steel, with a tensile strength higher than the tensile strength of the pin, to reduce stress on the pin. The thermal compensation block 230Ά, 230B may comprise a second portion 24GA, 2408, respectively in contact with the first portion 2.3SA, 2358, respectively. The second portion 235A, 2358 may be made by a material, e.g. zinc, with a thermal or expansion coefficient different than the thermal or expansion coefficient of the first portion 's material. However, other materials with- a thermal or expansion coefficient different than the thermal expansion coefficient of the first portion's material may be used,

[0013] During a heating event, the total elongation of the plate portion between the outer side of pin i 20A and the outer side of block 230 may be calculated as: [0016]

[0017] hi Eq, 1 t is the temperature, C _h is the thermal coefficient of the housing. wherein 4t

is the diameter of the pin, d ₂ is the radius of a. bearing, d ₃ is the diameter of the shaft and d ₄ is the width of the first portion of the plate.

[0018] During the same event, the total elongation of the respective portion of parts on the plate fie, the pins, the bearings, the shaft and the block) may be calculated as:

[0013]

[0020] Accordingly, is the thermal coefficient of the bearing, C _sh the thermal coefficient of the shaft, C _1p the thermal coefficient of the first portion of the block and C _2p the thermal coefficient of the second portion of the block.

[0021] Assuming TE ₁ = TE ₂ then may be calculated as

[0022]

[0023] Thus the size fie, the distance between proximal side and distal side of the second portion) of the second portion of the thermal compensation block may be calculated by knowing the various diameters and/or distances and thermal coefficients. The linear guide is thus modified in order to substitute the preloading spring, with a material that thermally compensates the dilatations between the housing and the system "bearing-shaft-bearing", Thus the bearings may maintain contact with the shaft during the thermal event.

[0024] Fig, 3 schematically illustrates a linear guide for a shaft, according to another example. The linear guide 300 may comprise a housing 305 with muitiple bearings 315A-315E distributed radially around the notional centre of the cross-section of the shaft 312 and rotafionally coupled with respective pins 320A-320E, respectively. In the example of Fig. 3, the linear guide comprises contact guiding elements in the form; of bearing and pin pairs. Furthermore, five such pairs are shown. In other examples the linear guide may comprise a different number of muitiple contact guiding elements that rnay be either identical (e.g. pairs of bearings and pins or sliders) or different (for example a combination of bearing and pin pairs with sliders). The linear guide may comprise a first thermal compensation block 330, in contact with pin 320A, The thermal compensation block 330 may be distributed in two parts 330A, 3308 along the outer side of the pin 320A and on both sides of the bearing 31 SA and may be made of a material with an expansion coefficient different (e.g.. higher) than the expansion coefficient of at least the pin 320A. The linear guide 300 may further comprise a second thermal compensation block 335 in contact with pin 32GB. The thermal compensation block 335 may be similarly distributed in two parts 335A. 3358 along the outer side of the pin 3208 and on both sides of the bearing 315B and may be made of a material similar or identical to the material of thermal compensation block. 330. The linear guide 300 may further comprise a third thermal compensation block 340 in contact with pin 320D. The thermal compensation block 340 may be similarly distributed in two parts 340A, 3408 along the outer side of the pin 320D and on both sides of the bearing 315P and may also be made of a material similar or identical to the material of either thermal compensation block 330 or thermal compensation block 335. During a thermal event, e.g. during acceleration of the carriage along the shaft, the thermal compensation blocks 330, 335 and 340 may compensate dilatations between the housing 305 and the respective bearing and pin pairs. Thus the bearings may maintain contact with the shaft during the thermal event. [9925] Fig, 4 schematically illustrates a linear guide with sliders and a thermal compensation block, according to another example, linear guide 400 comprises a housing 405. The housing 40S may define an opening 410 for receiving a shaft 41.2» The housing 406 may host three contact guiding elements, e.g. sliders 41SA, 41 SB and 41 SC. Each slider may have a rectangular shape with a proximal side facing the opening 410, The linear guide 400 may be provided with a thermal compensation block 43C. The thermal compensation block 430 may be affixed to the support plate 405 and may be in contact with a distal side of the one or more of the sliders, in the example of Fig. 4 the thermal compensation block 430 is illustrated in contact with the distal side of slider 4 I SA,

[0013] The thermal compensation block 430 may comprise a first portion 430A in contact with the pin. The first portion 430A may he made of a materia), e.g. steel, with a tensile strength higher than the tensile strength of the housing 405. The thermal compensation block 430 may comprise a second portion 430B in contact with the first portion 430A, respectively. The second portion 4306 may be mads of a material, e.g. zinc, with a thermal or expansion coefficient different than the thermal or expansion coefficient of the first portion's material. However, other materials with a thermal or expansion coefficient different than the thermal expansion coefficient of the first portion ^' s material may be used. When the shaft is introduced in the opening, the slider 415A, the shaft 412 and the slider 41 SB may he arranged in a straight line to form a "slider-shaft-siider" system. Similar calculations may thus he performed, as the ones performed for calculating the st¾e of thermal compensation block in the example of Fig. 2, to calculate the size of thermal compensation block 430 or the size {i.e. the distance between proximal side and distal side) of the second portion 4308 of thermal compensation block 430. During a thermal event, e.g. during acceleration of the carriage along the shaft, the thermal compensation block 430 may compensate dilatations between the housing and the "slider-shaft-slider" system. Thus the sliders may maintain contact with the shaft during. the thermal event. [0027] Pig. 5 schematically illustrates an image forming apparatus ^, with a carriage, according to an example,.. The Image forming apparatus 500 may comprise carriage 550. Carriage 550 may be moveable along shaft 512. A linearguide 605 may comprise multiple contact guiding elements 515 to guide the carriage along the shaft. The linear guide SOS may have a main opening to host the shaft 512 and multiple contact guiding elements, e.g. hearings 515, In contact with the shaft. Each bearing may he rofatably associated with, a pin 520. The pin 520 may be located on the linear guide 505 In a direction perpendicular to the shaft direction. The pin 520 may be in contact with a thermal compensation block 530, The thermal compensation block may be made of a material with a thermal coefficient different than the thermal coefficient of the linear guide,

[0028] All of the features disclosed in this specification (Including any accompanying claims, abstract and drawings), and/or all of the operations of any method or process so disclosed, may be combined In any combination, except combinations where at least some of such features and/or operations are mutually exclusive.

£0028} Each feature disclosed In this specification (Including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose; unless expressly stated otherwise,

[0O3OJ Although a number of particular Implementations and examples have been disclosed herein, further variants and modifications of the disclosed devices and methods are possible. For example, not all the features disclosed herein are included in all the implementations, and implementations comprising other combinations of the features described are also possible. As such, representative examples of the present disclosure have utility over a wide range of applications, and the above discussion is not intended and should not be construed to be limiting, but is offered as an illustrative discussion of aspects of the disclosure. What has been described and illustrated herein is an example of the disclosure along with some of its variations. The terms, descriptions and figures used herein are set forth by way of illustration only and are not meant as limitations. Many variations are possible within the spirit end scope of the disclosure, which is intended to be defined by the following claims - and their equivalents - in which all terms are meanl in their broadest reasonable sense unless otherwise indicated.